ABSTRACT BOOK - maltepe.edu.tr · We also thank Belma T. Ak»sit who voluntarily agreed to be...

INTERNATIONAL CONFERENCE OF

MATHEMATICAL SCIENCES

04-10 AUGUST 2009

ISTANBUL, TURKEY

Supported by

MALTEPE UNIVERSITY

ABSTRACT BOOK

1. FOREWORD

On behalf of the Organizing Committee, we are very pleased to welcome you to the International Conferenceof Mathematical Sciences, ICMS, Istanbul, 2009 to be held in Istanbul (Turkey) from 4th to 10th August, 2009.

We hope that, ICMS 2009 will be one of the most beneficial scientific events, bringing together mathematiciansfrom all over the world, and demonstrating the vital role that mathematics play in any field of science.

Welcome to our conference, Maltepe University, Istanbul!

Kemal KoymenChairman of the Organizing Committee

Huseyin CakallıVice-Chairman of the Organizing Committee

i

International Conference of Mathematical Sciences, 04-10 August 2009, Maltepe University, Istanbul, Turkey

2. COMMITTEES

INTERNATIONAL SCIENTIFIC COMMITTEE

A.D. Turkoglu (Turkey) A. Fawaz (USA)

A. Tiryaki (Turkey) Alexander Abanin (Russia)

A. Malek (Iran) Amalia Pielorz (Poland)

B. Rhoades (USA) B. Zeren (Turkey)

Boyan Dimitrov (USA) Dejan Ilic (Serbia)

Dogan Comez (USA) Dra Laura S. Aragone (Argentina)

E. Fokoue (USA) E. Alexov (USA)

E. Guzel (Turkey) E. Malkowsky (Serbia)

E. Savas (Turkey) Ersan Akyıldız (Turkey)

Ewa Stronska (Poland) F. M Danan (Syria)

F. Akman (USA) F. Dik (USA)

G. Anastassiou (USA) G. Thuo (USA)

G. Vanden Berghe (Belgium) H. A. El-Metwally (Egypt)

H. Bereketoglu (Turkey) H. Elsalloukh (USA)

H. Nour Eldin (Denmark) H. Pendharkar (USA)

H. Coskun (USA) H. Cakallı (Turkey)

H. Miller (Sarajevo) Haydar Es (Turkey)

H. Hilmi Hacısalihoglu (Turkey) Hongde Hu (USA)

Huseyin Kocak (USA) I.G. Avramidi (USA)

I. Canak (Turkey) I. Kombe (USA)

Ivan Jeliazkov (USA) J. Abadie (France)

J. Diblik (Czech Republic) J. Fischer (USA)

J. Gao (USA) J.K. Kim (Korea)

J. M. Cushing (USA) J.Z. Farkas (UK)

Javier F. Rosenblueth (Mxico) Jiling Cao (New Zealand)

K Wang (China) K. Fahem (Algeria)

K. I. Noor (Pakistan) K. Khan (USA)

K.L. Man (Ireland) Kemal Koymen (Turkey)

Ke Wu (U.S.A.) L. Hadji (USA)

Liana Kovaleva (Russia) Ljubisa Kocinac (Serbia)

M. Cekirge (Turkey) M.M.M. Jaradat (Qatar)

M.R. Karim (USA) M.S.R. Chowdhury (Pakistan)

M. Yousef (USA) M. Buntinas (USA)

ii


M. Dik (USA) M.F. Shaughnessy (USA)

M. Matejdes (Slovakia) Mark Burgin (USA)

Miroslav Zeleny (CZ) Mohamed M.A.El-Sheikh (Egypt)

N. Billor (USA) N. Dogan (Turkey)

N. Aydin (USA) O. Domanska (Ukraine)

O. Dosly (Check Republic) O. Akman (USA)

O. Gursoy (Turkey) O. Mucuk (Turkey)

O. Akın (Turkey) Oner Cakar (Turkey)

Pratulananda Das (India) Pablo Amster (Argentina)

R. Diaz (Colombia) R.J. Swift (USA)

R. Sharma (USA) R. Wu (USA)

R. Patterson (USA) S. Bityukov (Russia)

S. Sun (USA) S. Elaydi (USA)

Sajid Hussain (Canada) T. Tanrıverdi (Turkey)

Vera W. De Spınadel (Argentina) W.H. Ruckle (USA)

Xiaoping Shen (USA) Y. Lio (USA)

Y. Cohen (Israel) Yi Mu (Australia)

Zbigniew Piotrowski (USA)

ORGANIZING COMMITTEE

K. Koymen (Rector of Maltepe University, Turkey) H. Cakallı (Maltepe University, Turkey)

O. Gursoy (Maltepe University, Turkey) A. Demirel (Maltepe University, Turkey)

I. Taylan (Maltepe University, Turkey) M. Dik (Rockford College, USA)

MANAGING COMMITTEE

Kemal Koymen (Chairman) Huseyin Cakallı (Vice-Chairman)

Ozkan Deger Ibrahim Canak

Yılmaz Erdem Umit Totur

Can Guler Allaberen Ashyralyev

Ali Rıza Baloglu Mehmet Unal

Fatih Gunaydın Aysem Calıskur

iii


3. SESSIONS

The lectures in the following parallel sessions are to be held before and after keynote speakers lectures:

1. Qualitative Theory of Differential Equations, (Oscillation, Boundedness and Stability), AydınTiryaki (Izmir University, Turkey) and Mehmet Unal, (Bahcesehir University, Turkey)

2. Algebra, Bedriye Melek Zeren and Temha Erkoc, (Istanbul University, Turkey)

3. Geometry, Bayram Sahin, (Inonu University, Turkey)

4. Industrial Mathematics & Statistics, Yuhlong Lio , (University of South Dakota, USA)

5. Design Theory, Hadi Kharaghani, (University of Lethbridge, Canada)

6. Numerical Functional Analysis, Allaberen Ashyralyev, (Fatih University, Turkey)

7. Summability, Ekrem Savas, (Istanbul Commerce University, Turkey)

8. The Metallic Means Family, Vera W. de Spinadel, (University of Buenos Aires, Argentina)

9. Optimization, Control and Neural Networks, Alaeddin Malek, (Tarbiat Modares University, Iran)

10. Scientific Computing and Numerical Analysis, Sayed Hodjatollah Momeni-Masuleh, (TarbiatModares University, Iran)

11. Fixed Point Theory, Duran Turkoglu, (Gazi University, Turkey)

12. Topology and Abstract Analysis, Jiling Cao, (Auckland University of Technology, New Zealand)

13. DATICS Workshop, K. L. Man, (University College Cork, Ireland)

14. Mathematics Education and Popularization of Mathematics, Ahmet Sukru Ozdemir, (MarmaraUniversity, Turkey)

15. Other (none of the above but related to Mathematics), Huseyin Cakallı, (Maltepe University, Turkey)and Ayse Sonmez, (Istanbul University, Turkey)

iv


4. ACKNOWLEDGMENTS

We thank firstly William Ruckle and then all the other scientific committee members who gave suggestionon making the conference better.

We also thank Belma T. Aksit who voluntarily agreed to be involved in the conference as a local logisticorganizer two weeks before the first day of the conference and spent a lot of time to keep the conference alive.

There are many people who spent a lot of time and effort to make this conference possible. We would liketo thank especially to the following young colleagues who had contributed to the success of this conference invarious ways:

Ozkan Deger, Istanbul University, TurkeyAyse Sonmez, Istanbul University, TurkeyIbrahim Canak, Adnan Menderes University, Turkey.

To speak honestly, without Ozkan Deger this abstract book would have been only a dream.

v


5. CONTENTS

1. FOREWORD i

2. COMMITTEES ii

3. SESSIONS iv

4. ACKNOWLEDGMENTS v

5. CONTENTS 1

6. KEYNOTES 22

Optimization with Recurrent Neural Networks: Recent Advances and New Perspectives 23Alaeddin Malek

Compact and Fredholm Operators on Some Matrix Domains of Triangles 24Eberhard Malkowsky

Simulating Probability with R 25Jane Horgan

Uncertainty Qualification in Simulations 26M. Y. Hussaini

Where Algebra and Topology Meet: a Cautionary Tale 27Robin Harte

7. ABSTRACTS 28

Silver Block Intersection Graphs 29A. Ahadi, N. Besharati, E.S. Mahmoodian, M. Mortezaeefar

Spectral Properties Of Difference Operator Over The Space bvp (1 ≤ p < ∞) 30A. M. Akhmedov

Fixed Point Theory For Inward Set-Valued Maps In Hyperconvex Metric Spaces 31A. Amini-Harandi

Generalized Logistic Distribution: Bayesian Estimations 32A. Asgharzadeh, A. Fallah

About Continued Fractions Expansions of Metallic Means 33A. Redondo Buitrago

A Theoretical And Numerical Investigation Of Heteroclinic Connection In Two-DimensionalIncompressible Flow 34

A. Deliceoglu

Common Fixed Point Theorems For Maps Under a Contractive Condition of Integral Type 35A. Djoudi

An Analysis on Fourier Series Expansion 36A. Ghyasi, M. H. Rahmani Doust

1


Estimation And Prediction Of Weibull Parameters From Common Percentiles With Outliers 37A. H. Abd Ellah

Optimal Control with Fuzzy Chance Constraints 38A. Heydari, S. Ramezanzadeh

Chaotification Of Discrete Dynamical Systems 39A. Ikhlef, N. Mansouri

k-Tuple Total Domination in Graphs 40A. P. Kazemi, M.A. Henning

Fusion Frames and g-Frames in Hilbert spaces and Hilbert C∗-module 41A. Khosravi

Options and Partial Differential Equations 42A. Kor, M. Can

On Fuzzy p-Ideals and Fuzzy H-ideals in BCI-Algebras 43A. Kordi, A. Ahmadi, A. Moussavi

Global Properties Of A Class Of Models For HIV Infection Of Cd4+ T Cells And Macrophages 44A. M. Elaiw

Application of Model Predictive Control to Dynamic Economic Dispatch with Emission 45A. M. Elaiw, A. M. Shehata

Color Gamut Computation Using Neural Networks 46A. Malek, N. Hosseinipour-Mahani, S. Ezazipour

The Unite Subduced Cycle Index Table of Some Molecules 47A. Moghani, A. Zaeembashi, M.R. Sorouhesh

Color Reconstructions by the New Fuzzy Logic-Based model 48A. Moghani, A. Zaeembashi

On Bayesian Estimation For An M/G/1 Queue With Optional Second Service 49A. R. Mohammadi, M. R. Salehi-Rad, A. Abassi

On Pseudo Implicative BCK Ideals Of Pseudo-BCK Algebras 50A. Moussavi, A. Ghassemi, A. Kordi

Skew Power Series Extensions Of Principally Projective Rings 51A. Moussavi

Entropy In IVSs 52A. Pouhassani

Block Preconditioned Methods in Solution of Hyperbolic Equations 53A. Shayganmanesh, M.M. Arabshahi

Numerical Solution Of The Two Dimensional Nonlinear Volterra Integro-DifferentialEquations With Separable Kernels By The Differential Transform Method 54

A. Tari, S.Shahmorad

Numerical Solution Of Two Dimensional Linear Volterra Integral Equations Of The SecondKind By The Tau Method With An Error Estimation 55


Stability Of Homotopy Perturbation Technique For An Inverse Diffusion Problem 56A. Zakeri, Q. Jannati

2


Design and Implementation of a Secure E-learning System for the Wireless Networks 57Abbas Fadhil Mohammed Ali AL-Juboori

On Some Numerical Methods For The Neutron Transport Equation In 2-D Plane Geometry 58Abdallah Tamrabet Larpi, Abdelouahab Kadem

A Study of the Supercritical Solution of the Stationary Negative Forced KdV Equation 59Abdelaziz Hamad, Mukheta Isa

A singular Gierer-Meinhardt System Of Elliptic Equations In RN 60Abdelkrim Moussaoui, Brahim Khodja, Saadia Tas

Fault Detection in a Complex System: A New Statistical-Based Approach 61Abdelmalek Kouadri, Ahmed Chaib, Abdallah Namoune

Model Reduction of a Large Scale System Using PCA Technique 62Abdelmalek Kouadri, Mimoun Zelmat, Abdallah Namoune

Adjoint Of Sublinear Operators 63Abdelmoumene Tiaiba

Generalized Einstein’s Tensor For A Weyl Manifold And Its Applications 64Abdulkadir Ozdeger

Tests for Trend: a Simulation Study 65Abdullah Almasri

A Note On Comparison Between Laplace And Sumudu Transfoms 66Adem Kılıcman, Hassan Eltayeb, Kamel Ariffin Bin Mohd Atan

Some Properties in Nonsmooth Analysis of Perturbation Function in Vector Optimization 67Agamali Agamaliyev, Serkan Ilter

Prediction In A Trivariate Normal Distribution Via A Linear Combination Of OrderStatistics 68

Ahad Jamalizadeh, Mina Habibi

Solving Capacitated Vehicle Routing Problem with a Rank-based Ant Colony System 69Ahmad Nejoomi-Markid, Ardeshir Dolati

The Effects Of Web Supported Instruction And Use Of Instructional Materials On Students’Mathematics Anxieties, Attitudes And Achievements 70

Ahmet Arslan, Ahmet Sukru Ozdemir

The Effect Of Teaching With The Mathematics Activity Based On Purdue Model On TheAchievement Of Non-Gifted Students 71

Ahmet Sukru Ozdemir, Esra Altıntas

Developing ASAB Cryptology Technique with Irrational Numbers Perspective 72Ahmet Sukru Ozdemir, Ahmet Bilal Yaprakdal

The Effects of The Lessons Plans Prepared on The Multiple Intelligence Approach toMathematical Achievement 73

Ahmet Sukru Ozdemir, Fatmagul Durmus

An Analytical Approach To The Fractional Foam Drainage Equation 74Ahmet Yıldırım

2-Edge Connected Subgraph Problem, Complete Description 75Aider Meziane, Aoudia Lamia

3


Fuglede-Putnam Theorem For (p, k)-Quasihyponormal And Class (Y )Operators 76Aissa Nasli Bakir

A Certain Subclass Of P-Valently Analytic Functions Of Bazilevic Type 77Ajab Akbarally, Maslina Darus

A new Form to Newton-Pade Approximants 78Alexey Lukashov, Cevdet Akal

Minimizing Makespan in a Two-Machine Stochastic Flowshop 79Ali Allahverdi, H. Aydilek

Minimizing Average Job Completion Time in a Two-Stage Assembly Flowshop with SetupTimes 80

Ali Allahverdi, Fawaz S. Al-Anzi

Polytopes Of Majorization And g-Majorization 81Ali Armandnejad

Generalization of Clark’s Derivation And Subdifferential 82Ali Farajzadehd

Triangle Matrix And Infinite Linear Systems Of Differential Equations 83Ali Fares, Bruno de Malafosse

An Operational Method for Solving Non-linear Volterra Integro-Differential Equations 84Ali Khani, Sedaghat Shahmorad

The Existence Of The Optimal Control Of Systems With Quadratic Quantity Criterium 86Ali Mahmud Ateiwi, Iryna Volodymyrivna Komashynsk

Differentiation in a New Viewpoint 87Ali Parsian

On common Periodic Points Conjecture, History and Some Related Questions 88Aliasghar Alikhani-Koopaei

Optimization Of The EDM Process With Multiple Performance Characteristics Based OnThe Orthogonal Array And Grey Relational Analysis Method 89

Alireza Abdi, Mehdi Eskandarzade, Ali Naser

Group Theory on Some Chemical Nanostructures 90Alireza Gilani, Ali Moghani

Well-Posedness of Basset Difference Equations 91Allaberen Ashyralyev

A note on Fractional Schrodinger Differential And Difference Equations 92Allaberen Ashyralyev, Betul Topcu

On The Numerical Solution Of Parabolic Stochastic Differential Equation 93Allaberen Ashyralyev, Mehmet Emin San

On The Parabolic Inverse Problem With An Unknown Source Function 94Allaberen Ashyralyev, Oznur Demirdag, Abdullah S. Erdogan

Wave Approach in Dynamical Discrete-Continuous Systems 95Amalia Pielorz

Introduction to a Method For Solving a Kind of Integrals 96Amin Daneshmand Malayeri

4


Simulation in Math and Its Effects on Education 97Amin Daneshmand Malayeri

Introduction to a Sequence in Natural Numbers With Logical Properties 98Amin Daneshmand Malayeri

A new non-linear optimization of parameters in Michaelis-Menten kinetics 99Amir Heydari

The Search Method Based On Soft Computing For Linear Cryptanalysis Of Block Ciphers 100Amir Hossein A.E. Tabatabaei

A Survey on Search Methods Based on Soft Computing for Cryptanalysis of Block Ciphers101Amir Tabatabaei

2-Orthogonal Polynomials And Linear “2–Generalized” Birth And Death Processes 102Ammar Aboukhemis, Ebtissem Zerouki

A New Approach To Numerical Algorithms 103Ana Paula Lopes, Antonio Jose Pascoal

Using Moodle As A Tool For Learning And Developing Math Skills 104Ana Paula Lopes, Lurdes Babo, Jose Azevedo, Cristina Torres

Comparison Of Speeds Of Convergence In Some Families Of Summability Methods ForFunctions 105

Anna Sheletski

On Families Of Generalized Norlund Matrices As Bounded Operators On lp 106Anne Tali

Some Notes On Improvement Of Convergence By Regular Matrices 107Ants Aasma

The Almost Everywhere Convergence Of The Fourier-Laplace Series 108Anvarjon Ahmedov

A New Approach to Quantile Regression 110Arash Ardalan, H.A. Mardani-Fard

Exponential Family And Special Entropy Relation 111Arman Beitollahi

The Arithmetic Foundations Of Mathematics: Constructing New Mathematics WithNegative Numbers Beyond Infinity 112

Armen G. Bagdasaryan

Some Results on an Advanced Impulsive Differential Equation with Piecewise ConstantArgument 113

Arzu Ogun, Gizem Seyhan, Huseyin Bereketoglu

Some Forms Of The Banach-Steinhaus Theorem In The Locally Convex Cones 114Asghar Ranjbari

N-dimensional Moment Invariants Based Approach For The Analysis Of MammographyImages Using GRID 115

Azir Aliu, Margita Konpoposka

Analysis Of A System Of Multi-Term Fractional Differential Equations With PolynomialCoefficients 116

Azizollah Babakhani

5


New Dynamic Hysteresis Model By Means Of Soft Computing Approach 117B. Boudjema, M. Mordjaoui, M. Bouabaz, R. Daira

Asymptotically Central Net In Semigroup Algebras And Inner Invariant Extensions Of DiracMeasures 118

B. Mohammadzadeh

A Comparative Study On The Response Of Prismatic And Non-Prismatic Timoshenko BeamsTo Accelerating Loads 119

B. Omolofe

A Criterion Of Optimization Of A Modified Green’S Function In Two Dimensional ElasticWaves 120

B. Sahli, L. Bencheikh

Boundary Value Problem For The Linear Elasticity Equations 121Benabderrahmane Benyattou, Abita Rahmoune

Mathematical Methods for Modeling of Lightning and Thunderstorm Electrification 122Beyza C. Aslan, William Hager

Role Of Noncompatible And Discontinuous Mappings To Prove Coincidence And CommonFixed Point Theorems In Various Spaces 123

Bhavana Deshpande

Modeling And Optimization In Estimating And Budgeting Projects Using Gath And GevaFuzzy Clustering Approach 124

Bouabaz Mohamed, Belachia Mouloud, Boudjema Bouzid, Mordjaoui Mourad

On Idealized Electromagnetic Singularities in Arbitrary Nonrelativistic Motion 125Burak Polat

Stability and Optimal Control 126C.C. Remsing

Nonparametric Regression: A Brief Overview And Recent Developments 127C.J. Swanepoel

On Curvature Inheriting Symmetry In Finsler Space 128C. K. Mishra, Gautam Lodhi

Adaptive Error Estimation for Linear Functionals Approximation and Applications 129Chin-Yun Chen

Fixed Points And Fuzzy Stability Of A Quadratic-Quartic Functional Equation 130Choonkil Park

Semilinear Evolution Equations On Discrete Time 131Claudio Cuevas, Carlos Lizama

Fractional Differential Equations in term of Comparison Results and Lyapunov Stability withInitial Time Difference 132

Coskun Yakar

Inverse System in The Category Of Sostak Fuzzy Topological Spaces 133Cigdem Gunduz (Aras)

Time Optimal Control Problem Via Differential Inclusions 134D. Affane

6


Semi-analytical Solution of the First and Second Kind Abel Integral Equations UsingFractional Differential Transform Method 135

D. Nazari, S. Shahmorad

A Specific Artificial Neural Network based Model for the Identification of Pollution Sources 136Dalila Acheli, Abdelmalek Kouadri, Abdallah Namoune

Exemples Of Differential Games With Stochastic Perturbations Associated With SolutionsOf Nash Equilibrum And Open Loop Strategies 137

Daniela Ijacu

Transitive Designs Constructed From Finite Groups 138Dean Crnkovic, Vedrana Mikulic, Andrea Svob

He’s homotopy Perturbation Method For A General Riccati Equation 139Deniz Agırseven, Turgut Ozis

Introduction Of A Circular Number Line 140Dharmendra Kumar Yadav

Domination Dot-Critical On A Harary Graph 141Doost Ali Mojdeh, Somayeh Mirzamani and Roslan Hasni

Acceptance Single Sampling Plan with Fuzzy Parameter 142E. Baloui Jamkhaneh, B. Sadeghpour-Gildeh, G. Yari

Defining Sets Of Combinatorial Designs: Recent Developments 143E. Sule Yazıcı

Silver Graphs 144Ebadollah S. Mahmoodian

The Characterisation of Compact Operators on Spaces of Stongly Summable and BoundedSequences 145

Eberhard Malkowsky

On Weak Nil-Armendariz Rings 146Ebrahim Hashemi

An Extension of the Poisson-Lindley Distribution And Its Applications 147Eisa Mahmoudi

On Some New Sequence Spaces With An Index Defined By A Modulus Function 148Ekrem Savas , Hamdullah Sevli

On Double Lacunary ∆σ-Statistical Convergence Of Sequences Of Fuzzy numbers 149Ekrem Savas

The Algorithms Of The Program Control Construction For Some Classes Of The DynamicSystems 150

Elena Chalykh

Optimal Control of The Elliptic Type Differential Inclusions with Dirichlet and NeumannBoundary Conditions 151

Elimhan N. Mahmudov, Ozkan Deger

Optimal Control of Discrete and Differential Inclusions in Gradient Form 152Elimhan N. Mahmudov, Murat Unal

The New Numerical Algorithms For Solving Multiplicative Differential Equations 153Emine Mısırlı, Yusuf Gurefe

7


On New Inequalities Via Convex Functions 154Erhan Set

On Optimal Vertex Colorings Of Graphs 155Esmaeil Parsa

Linear Operator on univalent Function of Complex Order 156Essam Aqlan

Dynamics For Hyperbolic Non-Invertible Maps 157Eugen Mihailescu

Modified Atkinson Method: Forward Search Algorithm 158F.M.O. Hamed

Advanced Thermal Imaging and Measurement Techniques: Application to a Printed CircuitBoard 159

F.A. Mohammadi, F. Farrokhi, M.C.E. Yagoub

Numerical Solutions Of NBSP For Elliptic Equations 160F.S.O. Tetikoglu

An Algorithm for Robot Path Planning in Environments with Flashing Off-On Obstacles,Using Cellular Automata 161

Farid Alaghmand, Vahid Ahmadi, Nesa Najafi, H.Haji Seyyed Javadi

Multiple-Criteria Assembly Flowshop Scheduling Problem 162Fawaz S. Al-Anzi, Ali Allahverdi

On Three New Functions Which Determine The Equation Of The Ruled Surface 163Filiz Kanbay

Application of Least Square Method to Numerical Solution of Second-Order Boundary ValueProblems 164

G. B. Loghmani

Fuzzy Troubleshooting Of A Complex Desalination Dehydration Plant 165G. Zahedi, S. Saba

The Baer Criterion For Acts Over Semigroups 166Gh. Moghaddasi

The Greeks of Indonesian Call Option 167Gunardi, J.A.M. vander Weide

Determination Of Sintering Kinetics Of Mullite By Differential Dilatometry 168H. Belhouchet, M. Hamidouche, N. Bouaouadja,V. Garnier, G. Fantozzi

Singularity of The Solutions Of Some Transmission Problems In A Dihedral 169H. Benseridi, M. Dilmi

Completion of Cone Metric Spaces 170H. Cakallı, A. Sonmez

Completion of Cone Normed Spaces 171H. Cakallı, A. Sonmez

Some Topological Properties Of Cone Metric Spaces 172H. Cakallı, A. Sonmez

8


Approximating The P.D.F Of α-Stable Distribution By Using Pade And Spline Interpolation173H. Fallahgoul, S.M. Hashemiparast

Common Fixed Points of New Iterations for Two Asymptotically NonexpansiveNonself-Mappings in Banach Spaces 174

H. Kızıltunc, M. Ozdemir, S. Akbulut

Cone D-Metric Spaces With ∆-Distance And Fixed Point Theorems Of ContractiveMappings 175

H.Lakzian, E. Agheshte Moghadam

Cone Metric Spaces With w-Distance And Fixed Point Theorems Of Contractive Mappings 176H.Lakzian, F.Arabyani

Weighted Function Algebra on Weighted Flows, Compactifications of Weighted Flows,Existence and None Existence 177

H. Lakzian, R. Jahanpanah

Prediction Of Technical State Of Petrol Equipments (Thermic Motor Case) 178H. Meglouli, E.Bouali.F.Ait Hocine

Detecting And Adjusting Inconsistencies Through A Graphical And Optimal Approach inAHP 179

H. Navidi, M. Ahmadi

A summability Factor Theorem By Using An Almost Increasing Sequence 180H. Nedret Ogduk

Topological Left Almost Convergence and Extreme Points of Amenable Locally CompactSemigroups 181

H. P. Masiha

A Simultaneously Determination Of The Optimal Trajectory And Control For VibratingShell Systems By Measures 182

H.R. Sahebi, S. Ebrahimi, A. Fakharzadeh J.

Evaluating A Novel Cellular Automaton Based Energy-Conservating Solution In MobileWierless Sensor Networks 183

H. Haj Seyyed Javadi, Se. Adabi, A. Rezaee

Growth of Solutions of Linear Differential Equations With Entire Coefficients Having theSame Order and Type 184

H. Saada

Existence And Uniqueness Results Of Some Fractional BVP 185H. Seddiki, S. Mazouzi

Copulas Pareto: Characterizations and Dependence Measures 186Hakim Bekrizadeh

The Importance of Using The “Omega Calculus” in Computer Algebra 187Halil Snopce, Ilir Spahiu, Azir Aliu

An Approach for Simultaneously Determining the Optimal Trajectory and Control of aHeating System 188

Hamid Reza Sahebi, Sara Ebrahimi

An Equity-efficiency Location of a Noisy Facility in a Continuous Plane 189Hamidreza Navidi, Ruhollah Heydari, Saeed Safari Moghadam

9


Holditch-Type Theorems for The 1-Parameter Closed Motions Using Lorentzian MatrixMultiplication 190

Handan Yıldırım, Salim Yuce, Nuri Kuruoglu

Optimal Control For High Order Pdes 191Hanif Heidari, Alaeddin Malek

Counting Of The Distinct Fuzzy Subgroups Of The Dihedral Group D2pn 192Hassan Naraghi

Analyzing Near-Normal Data Using A New Class Of Skew Distributions 193Hassan Elsalloukh

Common Zeros Of Exponential Polynomials And Shapiro Conjecture 194Hassane Abbas, Ahmed Hajj-Diab

What Are Copulas? 195Heydar Ali Mardani-Fard, Arash Ardalan

Congruence Relations On Generalized Fuzzy Subsemimodules 196Hossein Hedayati

U-statistic Testing in Competing Risk Models in Two-Sample Cases 197Hossein Jabbari Khamnei, Hadise Akbari

Generalized Cauchy Problem: Caputo type 198Hossein Parsian

The Projective Quarter Symmetric Metric Connections and Reccurent Projective CurvatureTensor 199

Hulya BagdatlıYılmaz, Aynur Uysal

A Fixed Point Theorem Without Convexity 200Hulya Duru

On computing The Eigenvectors Of Structured Matrices 201Hulya Kodal Sevindir

On The Relationship Between Regression Analysis and Mathematical Programming 202I. Mufit Giresunlu, Esra Ertan

Solutions Of The Topological Structure In The Early Universe Via Conformal Motions 203I. Yılmaz, I. Turkyılmaz, C. Camcı, C. Aktas, M. Sahin, M. Battaloglu

Tauberian Theorems For (A)(C,α) Summability Method 204Ibrahim Canak, Yılmaz Erdem, Umit Totur

Some Tauberian Theorems For Borel Summability Methods 205Ibrahim Canak, Umit Totur

On Tauberian Theorems For (A, k) Summability Method 206Ibrahim Canak, Umit Totur, Mehmet Dik

Some Characteristics of Systolic Arrays 207Ilir Spahiu, Halil Snopce, Azir Aliu

Solution of the Cauchy Problem for a Degenerate Parabolic Equation 208Iryna Volodymyrivna Komashynsk

Control Adaptive for Binary Time series 209Isaac Almasi, Reza Jalilian

10


Solution of mixed B.V.P including a first order three dimensional P.D.E with nonlocal andglobal boundary conditions 210

J. Ebadpour , D. Jabbari Sabegh

Rational approximation on closed curves 211J.I.Mamedkhanov

Estimation of stochastic differential equations with applications in finance 212J.A. Shali, K. Aghajani

A Semi Numerical-Analytical Method for Solving Nonlinear Integro-Differential Equations 213Jafar Ahmadi Shali, Parviz Darania

Gardner’s Mathematical Intelligence Theory to Measure Managers Mathematical Intelligenceand Organizational Effectiveness in East Azerbaijan’s Gas Company 214

Jafar Beikzad, Mohammad Reza Noruzi

A Description Of 3-Place Functions Of Idempotent Algebras 215Jafar Pashazadeh

Bootstrap-based tests for two measures of association 216Jan W.H. Swanepoel, James S. Allison

Common fixed points of nonlinear contraction in Menger spaces 217Javid Ali, M. Imdad

Conditions for Uniqueness of Fractional Powers 218Javier Pastor

Minimization Theorems And Fixed Point Theorems For A Generalized Metric 219Jeong Sheok Ume

Hereditary orders in the quotient ring of a skew polynomial ring 220John S. Kauta

Extensional Flows With Viscous Heating 221Jonathan Wylie, Huaxiong Huang

On a size-structured two-phase population model with infinite states-at-birth 222Jozsef Z. Farkas,Peter Hinow

Solution of the system of tenth-order boundary value problems using Non-polynomial spline223K. Farajeyan

On Commutative Distributive Algebras with Division Operations 224K. Shahbazpour, M. Soltani

A condition for points and compact subsets of C(X) to be Gδ Subsets of RX 225Kelaiaia Smail

Estimate Of The Parameters Of The Stochastic Differential Equations. Balck-Scholes Model226Khaled Khaldi, Samia Medahi

Corner Detection Based On Uncalibrated Images 227Khaled Al-Shalfan

Studies on Sensitivity of Clock and Data Recovery Circuits to Power Supply Noise 228Khalil I. Mahmoud, R. Rajasekar, J. Dhurga Devi, P.V. Ramakrishna

Scatter Search for Vehicle routing 229Kheffache Rezika and Ouafi Rachid

11


Simultaneous Quadruple Series Equations Involving Generalized Bateman-K Functions 230Kuldeep Narain

On Identification of Distribution for Two Independent Markov Chains to the SubjectReliability Criterion 231

Leader Navaei

On Identification Of Distributions For Multiple Lao Hypotheses Testing 232Leader Navaei

Hypotheses Optimal Testing Via Large Deviations Techniques 233Leader Navaei

The Subdifferential of a Convex Functional on Regulated Function Space 234Luis Antonio Fernandes de Oliveira, Roseli Arbach

Computation of Expected Interference Between FSS and Imt-Advanced for Fixed and MobileUsers in Deferent Malaysian Environments 235

Lway Faisal Abdulrazak, Tharek Abd. Rahman

Kanan Fixed Point Theorem On Generalized Metric Space With Extended Kind OfContraction 236

M. Alimohammady, M. Ramzannezhad

Some Mapping Properties Of Strongly p−Summing 237M. Belaib, D. Achour

Some Results About Algebraic Properties Of Generalized Cellular Automata 238M. K. Dadsetani, H. Haj Seyyed Javadi, Sa. Adabi

Classification of Systems of Nonlinear ODEs: Multi-Species Interaction 239M.H. Rahmani Doust, M. N. Modoodi

Quasirecognition By The Prime Graph Of The Group Cn(2) 240M. Foroudi Ghasemabadi, Ali Iranmanesh

A Set Theory Based Centralized Diagnosability in Discrete Event Systemss 241M. Ghasemzadeh, M. Shirmohammadi

Two-Dimensional Mechanical Stresses in a Hollow FGM Sphere 242M. Jabbari, A.H. Mohazzab

Genetic Algorithm based on Fuzzy System for Uncapacitated P-Median Problem 243M. Jalali Varnamkhasti

On Regularized Quasi-Semigroups and the Evolution Equation 244M. Janfada

Fuzzy 2-Normed Spaces and its Fuzzy I-Topology 245M. Janfada, A. Nezhadali

On The Basis Number Of The Lexicographic Product Of Two Graphs And Some RelatedProblem 246

M.M.M. Jaradat, M.K. Al-Qeyyam

Application of Graph Theory in Stability of Nonlinear Complex Dynamic Systems 247M. Kidouche, H. Habbi

Applications of Numerical Solution Method HPM 248M. Matinfar

12


Discrete First-Order Four-Point Boundary Value Problem 249M. Mohamed, M. S. Jusoh

Serial-Parallel Access Method (SPAM) for Instruction Cache Performance Improvement 250M. Mohtashamzadeh, M. Fathy, M. Soryani

Applying the WKB Method to The Bifurcation of an Everted Spherical Shell Made of ElasticVarga Material 251

M.S. Pour, M.Vakilian

Application Of Generalized Purcell Method For Real Eigenvalue Problems 252M. Rahmani, S. H. Momeni-Masuleh

Design, Manufacture And Optimization Of Intelligent Cane For Blinds By AvrMicrocontroller 253

M. Reza, A. Malek

Monomial Irreducible sln(C)-Modules 254M. Shahryari

Multiple Confounded and Orthogonal Replicated Full Factorial BIB Designs 255M. Shamsuddin, M. Albassam

Fractional sn−k Factorial BIB Designs 256M. Shamsuddin, M. Albassam

Multi-Stage Multi-Phase BIB Designs 257M. Shamsuddin

A Fuzzy Goal Programming Approach to Multi-Objective Transportation Problems 258M. A. Yaghoobi

A model to create orthogonal Graeco Latin square experimental designs 259Mahdi Bashiri, Ehsan Korani

Distributions Of Order Statistics From A Bivariate Selection Elliptical DistributionAs Mixtures Of Univariate Selection Elliptical Distributions 260

Mahdi Salehi, Ahad Jamalizadeh

Total Ordering Cones in Rn and Optimality Condition for Set-Valued Optimization Problems261Mahide Kucuk, Mustafa Soyertem, Yalcın Kucuk

Repairable 2-Consecutive-2-Out-Of-n:F System 262Mahmoud Boushaba

Prey-Predator System And Lotka-Volterra Model 263Mahmoud Maheri, Somayyeh Gholizadeh

Fixed Point Theorems With Contractive Conditions Involving Product On Cone MetricSpaces 264

Mahpeyker Ozturk, Metin Basarır

A Simple Algorithm For Inverse General Pentadiagonal Matrix With LU Method 265Majid Erfaniyan, Seyed Masih Ayat

Identification Of All DEA Efficient Facets 266Majid Zohrehbandian

On A Class Of Divergent Sequences 267Malisa R. Zizovic, Dragan Djurcic, Ljubisa D.R. Kocinac

13


Quasi-Permutation Representations of the Borel and Maximal Parabolic Subgroups of G2(2n)268Maryam Ghorbany

P-Adic Study in Linear 2-Normed Spaces 269Mehmet Acıkgoz

The Effect Of Multiple Intelligence Approach In Project Based Learning To MathematicsLearning Achievement 270

Mesut Tabuk , Ahmet Sukru Ozdemir

A Unified Approach To Generalized Continuities 271Milan Matejdes

On Analysis Of Nonlinear Dynamic System Of Separation 272Mimoun Zelmat

A SystemC QoS Router Design With Virtual Channels Reservation In A Wormhole-SwitchedNoC 273

Mohamed Horchani

Determination of Residual Stress by Artificial Neural Network in Hsla-100 Steel Weldments274Mohammad Heidari

A survey on Mathematics’ role on Customer Relationship Management (CRM) to ImproveCustomer Satisfaction and Production Increase 275

Mohammad Reza Noruzi, Narges Sariolghalam

Generalized Bi-Quasi-Variational Inequalities for Quasi-Pseudo-Monotone Type II Operatorson Compact Sets 276

Mohammad Showkat Rahim Chowdhury

Stability Analysis of Infectious Disease with Media Coverage and Poverty 277Mohammed Al Jaffreh, Rajinder Sharma

Modelling The Interaction Between Crude Oil Price And Other Commodities Price 278Mohd Tahir Ismail, Zetty Ain Kamaruzzaman

A new System Of Implicit Variational-Like Inclusion Problems Involving (h(., .), η)-MonotoneOperators 279

Mohsen Alimohammady, Mehdi Roohi

Some Characterizations of Multi-Criteria Shortest Path in A Multi-Valued Network 280Moncef Abbas

Asymptotic Behaviour Of A Dynamic Problem Of Linear Elasticity With Tresca BoundaryConditions 281

Mourad Dilmi

Generalized Potentials In Weighted Variable Exponent Lebesgue Spaces On HomogeneousSpaces 282

Mubariz G. Hajibayov, Stefan G. Samko

Fixed Points of Mappings Satisfying a New Condition in Cone Metric Spaces 284Muhib Abuloha, Duran Turkoglu

Using the Algebra of Hypergraph for Reconstruction Phylogenetic Trees 285Mulia Astuti Msc, Dr.Irawati, Dr.Intan Muchtadi-Alamsyah,Dr.Ahmad Muchlis, Achirul Akbar S.Si dan Muliana, A. Halim MSi

Some Applications of Determinant in Undergraduate Statistics Courses 286Munir Mahmood

14


Implementation of New Algorithm for Steepest Descent Method 287Mustafa bin Mamat, Aw Siew Yee, Ismail bin Mohd

On Some Generalized Sequence Spaces Of Fuzzy Numbers Defined By A Sequence Of OrliczFunctions 288

Mustafa Kayıkcı, Selma Altundag, Metın Basarır

Fybrid Broyden Method For Unconstrained Optimization 289Mustafa Mamat, Ismail Mohd, Leong Wah June

Discretization Methods for Nonconvex Differential Inclusions 290Mustapha Yarou

On the Non-Commuting Graph Of The Simple Groups 291N. Ahanjideh, A. Iranmanesh

Mixed Problems for systems of First Order PDE 292N.A. Aliev, O.H. Asadova

Properties of γtr-Vertex Critical Graphs 293N. Jafari Rad

Variational Analysis Of A Frictionless Contact Problem For Viscoplastic Materials WithInternal State Variables 294

N. Lebri

Non-Uniqueness of Solution of Tticomis Problem for Degenerating Multidimensional MixedHyperbolic-Parabolic Equations 295

N. Orshubekov

Bayesian Methods For The Occurrence Of REM Among Apnea Patients 296N.Z. Mohd Saata, K. Ibrahim, A. A., Jemain,S.H. AlMashoor

Fully Spectral Methods for the Solution of High Order Differential Equations 297N. Vaissmoradi, A. Malek, S. H. Momeni-Masuleh

Prime Submodules Of Multiplication Modules And Cohen-Macaulay Property 298N. Zamani

Decomposition of Additive Processes 299Nadia-Mirela Stoian

Linear And Nonlinear Models Of Heredity For Blood Groups And Rhesus Factor 300Nasir Ganikhodjaev, Jamal I. Daoud, Makhsuma Usmanovaa

Equivalent of elliptic integrals 301Necat Tasdelen

Numerical Solutions Of Hyperbolic Equations With The Nonlocal Integral Condition 302Necmettin Aggez

Hilbert Transforms And Related Topics Associated With The Dunkl-Hermite Functions 303Nejib Ben Salem, Taha Samaali

Effect of a Deformable Free Surface on the Marangoni Convection in a Horizontal PorousLayer Permeated by a Fluid Layer in the Presence of Internal Heat Generation 304

Nor Fadzillah Mohd Mokhtar, Norihan Md Arifin, Roslinda Nazar, Fudziah Ismail, Ioan Pop

Generalized Flat Eeg with Depth Orientation and Regression 305Noraini Ismail, Tahir Ahmad, Arminora Idris, Siti Rahmah AwangOl

15


Generalized Characteristic Polynomials Of A Square Matrix 306Nosratollah Shajareh-Poursalavati

A Quasistatic Contact Problem With Slip Dependent Friction For Linear Elastic Materials 307Nouiri Brahim, Benabderrahmane Benyattou

New Method For Constructing Exact Solutions To Nonlinear PDEs 308Nouredine Benhamidouche, Arioua Yacine

A Tabu Search Algorithm to Find the Pareto Solutions of Dual Response Systems in QualityEngineering 309

O. Koksoy, C. H. Aladag

Numerical Approximation of Dirichlet Problem in Bounded Domains and Applications 310Oana Rachieru

A Note On The Multipoint Nonlocal Boundary Value Problems For Elliptic-ParabolicEquations 311

Okan Gercek

Spectral Properties Of One Class Of Sign-Symmetric Matrices 312Olga Y. Kushel

The Development of Mathematics Problem Solving Attitude Scale (MPSAS) 313Orhan Canakcı, Ahmet Sukru Ozdemir

Global Geometries In Space Kinematics 314Osman Gursoy, Muhsin Incesu

Local Group-Groupoids 315Osman Mucuk, H.Yesim Ay, Berrin Bagrıyanık

Quasilinearity Of The Classical Sets Of Sequences Of Fuzzy Numbers And Some RelatedResults 316

Ozer Talo, Feyzi Basar

A Note On Hyperbolic Equations With Nonlocal Boundary And Dirichlet-NeumannConditions 317

Ozgur Yıldırım

On The Asymptotic Behaviour Of The Negative Part Of the Second Order DifferentialOperator 318

Ozlem Baksi

Solving Linear Programming Using Newton Method And Goldstein Conditions 319P. Khosravi, H. Navidi, A. Malek

Recent Trends in Fixed Point Theorems and Applications 320P. P. Murthy

Application Of Stochastic Differential Equations Models For Solving Ship Roll Motion 321P. Nabati, R. Farnoosh

Torsion Graph of Modules 322P. Malakooti Rad, SH. Ghalandarzadeh, S. Shirinkam

Existence Of Fixed Point In C-Contraction 323Parvin Azhdari

16


Numerical Solutions of Nonlinear Volterra-Fredholm Integro Differential-DifferenceEquations 324

Parviz Darania, Karim Ivaz

Neural Networks in the Analysis of Nucleotide Genomic Signals 325Paul Dan Cristea

Effect Of Feedback Mechanism Over Ad Hoc Network For Audio & Video Communications327Pejman Panahi

A Graph Coloring Approach To Airline Crew Scheduling Problem 328Pınar Dundar, Hande Tuncel, Onur Kılıncceker

On The Galerkin Method For Non-Linear Evolution Equation 329Polina Vinogradova

Characterization Properties Of Some Classes Of p-valent Meromorphic Functions InvolvingCertain Convolution Structure 330

Poonam Sharma

The Initial Flow Past an Impulsively Started Oscillating Circular Cylinder 331Qasem Al-Mdallal

On Covering of Products of T - generalized State Machines 332R. Ameri, M. Sadeghi

Bayesian Test for Homogeneity Hypothesis 333R. Farnoosh, A. Hajrajabi

On Application Mathematical Procedures for Data Envelopment Analysis to ResourceAllocation Strategy of Police Organization 334

R. Poursaberi

Generalized Humbert Matrix Polynomials 335Raed S. Batahan

Contra-Gamma-Continuous Mappings in Topological Spaces 336Raja Mohammad Latif, Muhammad Razaq

Potential Flow On Two Identical Tubes 337Rajai S. Alassar

The Most Accurate Approximation For Numerical Solution Of Stochastic DifferentialEquation With Poisson White Noise By Skew-Normal Distribution 338

Ramzan Rezaeyan, Rahman Farnoosh

Spline Solution of Fourth-Order Obstacle Boundary-Value Problems 339Reza Jalilian

Existence Of Positive Solutions For A Discrete Boundary Value Problem 340Rodica Luca-Tudorache

Classification Of Exceptional Train Algebras Of Rank 3 And Type (4, 2): Step 1 341Roseli Arbach , Luis Antonio Fernandes de Oliveira

Large Probability Models Of Access Control Security System Architecture 342Roushanak Lotfikar , Bagher Arayesh

On The Fuzzy Minimal Spaces 343S. A. Mohammadzadeh, Mehdi Roohi

17


Fisher Information of a Single Qubit System 344S. Abdel-Khalek

Path Planning Algorithm for Mobile Robot Based on Multilayered Cellular Automata 345S. Behmanesh, H.S.Javadi, H.Erfani

Frictionless Contact Problem On Nonlinear Elasticity 346S. Boutechebak, N. Lebri

Experimental Approach of Flux Estimation in Real Time for Induction Motors Drives 347S. Grouni, A. Aibech, R. Ibtiouen, M. Kidouche, O. Touhami

Heat Conduction Equation At Micro And Nano Scale: Approximation Methods 348S. H. Momeni-Masuleh

Fixed Point Of Mappings In Fuzzy 2-Metric Spaces 349S. Jahedi, K. Jahedi

Armijo Rule and Strong Wolfe Line Search in Generalized Newton Method 350S. Ketabchi, M. Parandegan, H. Navidi

Hash Function Based on Chaos 351S.M. Hashemiparast, H. Fallahgoul

Different Convergences In Approximation Of Evolution Equations 352S. Piskarev

Using Fractional Factorial Design And Its Application To Study Of Effective Factors OnAmount Of Chest Drainage By Gomco Suction Pumps After Cardiac Surgery 353

S. S. Moghadam, R. Heidari, M.Ahadpour

Improving Energy Relaxation of Hopfield Network With Augmented Lagrange Multipliers 354S. Sathasivam

Weakly Continuous Modules 355S. Shirinkam, SH. Ghalandarzadeh, P. Malakooti Rad

New Algorithms Based On The Interior Point Method For Convex Quadratic Programming356S. Tahmasebzadeh, H. Navidi, A. Malek

Cech Homology Groups of Sostak Fuzzy Topological Spaces 357Sadi Bayramov, Cigdem Gunduz (Aras)

Convergence To Common Fixed Points For Asymptotically Nonexpansive Mappings By AModified Iteration Process 358

Safeer Hussain Khan, Mujahid Abbas

A Modified Nonlinear Conjugate Gradient Algorithm For Unconstrained Optimization 359Saman Babaie-Kafaki, Reza Ghanbari, Nezam Mahdavi-Amiri

Claims Validation SystemFuzzy Approach 360Sanjeev Kumar, Pooja Pathak

An Algorithm For Solving The Fractional Burgers Equations 361Selin Sarıaydın, Ahmet Yıldırım

On Generalized Paranormed Statistically Convergent Sequence Spaces Defined By OrliczFunction 362

Selma Altundag, Metin Basarir

General Weyl-Heisenberg Frames 363Shahram Banaei, Vahid Aghapouramin

18


Necessary Conditions For Singular Controls In Systems With Nonlocal Boundary Conditions364Sharifov Ya. A., Mamedova M.B.

Why Magnetic Monopoles Are Not Seen? 365Siamak Khademi

Modelling The Effect Of Vaccination Policy On Epidemics With Time Delay 366Sumit Kumar Banerjee

Algebraic Method Applied To Solving Inversion Problem Of Single Layered Rigid Pavements367T. Akhlaghi

Trapezoidal Fuzzy Data In Possibility Linear Regression Analysis 368T. Razzaghnia

The k-ε Model in Turbulence 369Tanfer Tanriverdi

Trapezoidal Approximation Based On Middle Of Maxima And Middle Of Support 370Tayebeh Hajjari

Frobenius Q-Groups and 2-Transitive Frobenius Q-Groups 371Temha Erkoc, Erhan Guzel

Order Norm Completion of Cone Metric Spaces 372Thabet Abdeljawad

Stability, Bifurcations And Non-Linear Eigenvalue Problems In Physics 373Todor L. Boyadjiev

The Properties Of Fuzzy Submodules Of A R-Module And Their Radicals 374V. Aghapouramin

Analytical Solution Of The Heat Conduction Equation In One-Dimensional SphericalCoordinates At Nanoscale 375

V. Mohammadi-Fakhar, S. H. Momeni-Masuleh

On the symmetry of Hamiltonian systems 376V.G. Gupta, P. Sharma

Solving Singular Initial Value Problems of Emden-Fowler and Lane-Emden Type 377V.G. Gupta, P. Sharma

Some Spectral Propersties Of Linear Operators In Umd Spaces And Applications 378Veli B. Shakhmurov

The Metallic Means Family (MMF) 379Vera W. de Spinadel

Rao-blackwellized Estimates for the Multivariate Bayesian Inference 380Vilda Purutcuoglu, Ernst Wit

The Guelph Expansion: A Special Mathematical Formulation for Polynomial Expansion 381Wajdi M. Ratemi, Hussein Abdullah

On The Solvability Of Abel-Poisson Integral Equation In Downward Continuation ForGravity Field Modeling 382

Y. Allahtavakoli, A. Safari

Non linear boundary value problem: Faedo-Galerkin methode of the non linear boundaryvalue problem 383

Y. Boukhatem, B. Benyattou, R. Abita

19


The Average Chebyshev Distance In A Grid 384Y. Tavakoli, H. Haj Seyyed Javadi, Sa. Adabi

Symmetry Classes Of Tensors Associated With Young Subgroups 385Y. Zamani, M. Shahryari

Necessary Conditions Of Second Order Optimality For Systems With Three-Point BoundaryConditions 386

Yagub A. Sharifov, Shamo I. Djabrailov

On D12 Modules 387Yahya Talebi, Ali Reza Moniri

FPGA Implementation of Vedic Signed Multiplier 388Yajnesh Padiyar, Mahalinga V. Mandi, Ramesh S, Dileep D

On Generalized Weak Subdifferentiability of Vector Valued Functions from Rn to Rm 390Yalcın Kucuk, Ilknur Atasever, Mahide Kucuk

A New Management Approach To Optimize The Use Of The Operating Room 391Yasmina Kerboua Ziari, Djamel Chaabane, Ahmed Benzaoui

A Note On Reidemeister Torsion And Period Matrix Of Riemann Surfaces 392Yasar Sozen

Numerical Solution Of A Non-Classical Hyperbolic-Parabolic Problem 393Yıldırım Ozdemir

Smoothing the Global Mean Based on Functional Principal Component Analysis 394Yucel Tandogdu, Ovgu Cidar

Sensitivities in Determining the Slope Parameter in Functional Regression 395Yucel Tandogdu

Kaplasky.S Construction And The Classes Of The Weak Hopf Algebra In 2,3 Dimension 396Z. Chebel, A. Makhlouf

Quadrature Formula For Semi-Bounded Solution Of Characteristic Singular IntegralEquation Of Cauchy Type 397

Z. K. Eshkuvvatov, N.M.A. Nik Long, M.Abdulkawi

Some Results On Products Of Conjugacy Classes 398Z. Mostaghim

Pairwise Semiregular Properties on Generalized Pairwise Regular-Lindelof Spaces 399Zabidin Salleh, Adem Kılıcman

Efficient Block Method For Solving Directly Third Order Ordinary Differential Equations 400Zanariah Abdul Majid Mohamed Suleiman

Three Point Block Backward Differentiation Formula For Solving Stiff Ordinary DifferentialEquations 401

Zarina Bibi Ibrahim , Mohamed Suleiman, Khairil Iskandar Othman

Processing Of Cyclic Graphs With Recursive Neural networks 402Zeinab Rezaei

A Note On The Solution Of The General Linear Matrix Differential Equations 403Zeyad Al-Zhour

20


Solving the Boundary Value Problem of the Wind Turbine Blade Equation (Calculation ofthe Mode Shape Functions) 404

Zine Labidine Mahri

Similarity Solution Of The Coagulation Equation In An Electro-Rheological ColloidalSuspension 405

Zineb Mimouni, Jonathan A.D. Wattis

On Additive Self-Dual Codes Over GF(4) And Their Applications 406Zlatko Varbanov

8. ABOUT MALTEPE UNIVERSITY, ISTANBUL AND TURKEY 407

21


6. KEYNOTES

The abstracts of the keynote lectures are given in the following.

22


Optimization with Recurrent Neural Networks:

Recent Advances and New Perspectives

Alaeddin Malek

Department of Applied Mathematics, Tarbiat Modares University,

P.O.Box14115-175, Tehran, Iran

[email protected]

Abstract

This talk will provide a condensed presentation of the main features of recurrent neural network models and general

optimization problems. It will focus on advances that have been made by our team over recent years. First of all, it will

address the linear, quadratic and nonlinear programming, monotone variational inequalities and complementarity problems.

Analysis of related network dynamics based on the methodology of artificial neural network models will be proposed. After

this, variant recurrent neural network models for corresponding optimization problems will be discussed and new algorithms

will be presented that maintain full accuracy and efficiency. The theoretical and numerical approaches are investigated. As

a direct result of this work we have founded some efficient hybrid neural network models that produce significantly better

results than the previous algorithms. The talk will conclude by discussing some of the real life applications facing this

research area.

References[1] Malek, A. Applications of Recurrent Neural Networks to Optimization Problems. Chapter 12 of the book: Recurrent Neural Networks,

Editted by Xiaolin Hu and P. Balasubramaniam, Published by In-The, Vienna, Austria (2008).

[2] Yashtini, M.; Malek, A. A discrete-time neural network for solving nonlinear convex problems with hybrid constraints. Appl. Math.Comput. 195 (2008), no. 2, 576–584.

[3] Malek, A.; Alipour, M. Numerical solution for linear and quadratic programming problems using a recurrent neural network. Appl.Math. Comput. 192 (2007), no. 1, 27–39.

[4] Yashtini, M.; Malek, A. Solving complementarity and variational inequalities problems using neural networks. Appl. Math. Comput.190 (2007), no. 1, 216–230.

[5] Ghasabi-Oskoei, H.; Malek, A.; Ahmadi, A. Novel artificial neural network with simulation aspects for solving linear and quadraticprogramming problems. Comput. Math. Appl. 53 (2007), no. 9, 1439–1454.

[6] Malek, A.; Shekari Beidokhti, R. Numerical solution for high order differential equations using a hybrid neural network—optimizationmethod. Appl. Math. Comput. 183 (2006), no. 1, 260–271.

[7] Malek, A.; Oskoei, H. G. Numerical solutions for constrained quadratic problems using high-performance neural networks. Appl.Math. Comput. 169 (2005), no. 1, 451–471.

[8] Malek, A.; Yari, A. Primal-dual solution for the linear programming problems using neural networks. Appl. Math. Comput. 167

(2005), no. 1, 198–211.

2000 Mathematics Subject Classification. 49J20, 35E99, 47F05Key words and phrases. Optimal control

23


Compact and Fredholm Operators on Some Matrix

Domains of Triangles

Eberhard Malkowsky

Department of Mathematics, University of Giessen, Arndtstrasse 2,

D-35392 Giessen, Germany

Faculty of Information Technologies, Taduesa Koscuska 63,

11000 Belgrade, Serbia

[email protected]

Abstract

We present some general results for the determination of the β–duals of triangles in FK spaces and the characterisation

of some classes of matrix transformations on them. Furthermore, we give a short introduction to the Hausdorff measure

of noncompactness which we apply to establish necessary and sufficient conditions for compact linear operators between

the matrix domains of triangles in the sets of convergent and null sequences. Finally, we give a sufficient condition for a

bounded linear operator from the matrix domain of a triangle in the space of null sequences into itself to be a Fredholm

operator.

2000 Mathematics Subject Classification. 46A45,40H05Key words and phrases. Sequence spaces, matrix transformations, Hausdorff measure of noncompactness, compact and Fredholmoperators

24


Simulating Probability with R

Jane Horgan

School of Computing Dublin City University, Dublin, Ireland

[email protected]

Abstract

We outline the role of the open-source statistical programming environment R in teaching probability. Taking advantage

of its powerful graphical and simulation facilities, we show how the mathematical approach can be augmented by one of

experimentation. R is used not only for calculation and data analysis but also to illustrate statistical concepts, to simulate

distributions, and to explore by experimentation different scenarios in decision making.

References[1] Horgan Jane M. (2008), Probability with R: An Introduction with Computer Science Applications, Wiley, Hoboken, New Jersey.

[2] Tutorials Interactive. http://www.computing.dcu.ie/ jhorgan/stats/index.htm

[3] Venables, W.N., Smith, D.M. and the R Development Core Team (2004), An Introduction to R: A Programming Environment forData Analysis and Graphics. http://www.r-project.org/

2000 Mathematics Subject Classification.Key words and phrases.

25


Uncertainty Qualification in Simulations

M. Y. Hussaini

School of Computational Science, Florida State University,

Dirac Science Library, Tallahassee, FL 32306, USA

[email protected]

Abstract

Uncertainty in simulations is due to the stochastic nature of geometric and physical parameters, the indeterminate

nature of initial/boundary conditions, and the inadequacy of physical models coupled with discretization errors. These

uncertainties can be classified into two types: parametric (aleatory) and model form (epistemic). Whereas probability

theory can deal with parametric uncertainty, some generalization of probability theory is required to deal with the model

form of uncertainty. Among the generalizations of probability theory, evidence theory is relatively well-developed. The

presentation will briefly discuss some techniques based on these theories to quantify uncertainty in the context of some

representative problems.

2000 Mathematics Subject Classification. 68T37, 76F40, 86A10Key words and phrases. Evidence theory; Parametric and epistemic uncertainties; Turbulence models; Hurricane track.

26


Where algebra and topology meet: a cautionary tale

Robin Harte

School of Mathematics Trinity College, Dublin, Ireland

[email protected]

Abstract

In a sense the Kuratowski conditions reduce topology to algebra. In another sense a simple property of Banach algebras

ushers in a curious topology for rings.

References[1] Per Ara, Gert Pedersen and Francesc Perera, A closure operation in rings, Int. Jour. Math. 12 (2001) 791-812.

[2] Dragana Cvetkovic-Ilic and Robin Harte, On the algebraic closure in rings, Proc. Amer. Math. Soc. 135 (2007) 3547-3552.


27


7. ABSTRACTS

The abstracts are ordered by the name of the first author.

This is not a proceedings, the abstracts in this book have been printed as submitted by the authors and theauthors are responsible for the correctness of their abstracts and defending their works during their presenta-tions at the conference.

Papers presented at the mathematical sessions of the conference can be published in the Istanbul UniversitesiFen Fakultesi Matematik Dergisi (University of Istanbul, Faculty of Science, Journal of Mathematics) upon arequest of author/ or coauthor after reviewing process.

Some of chosen full papers presented at the mathematical sessions of the conference which can make a volumeof a book which is both coherent and self-sufficient may be published by Cambridge Scholars Publishing afterreviewing process.

28


Silver Block Intersection Graphs

A. Ahadi1, N. Besharati 2, E.S. Mahmoodian3, M. Mortezaeefar4

1,3,4Department of Mathematical Sciences Sharif University of Technology

Tehran, I.R. Iran

2Department of Mathematics, University of Mazandaran

baboolsar, Iran, and Payame Noor University

[email protected]

Abstract

Any maximum independent set of a graph is called a diagonal of that graph. Let c be a proper (r + 1)-coloring of anr-regular graph G. A vertex x in G is said to be rainbow with respect to c if every color appears in the closed neighborhoodN [x] = N(x) ∪ x. Given a diagonal I of G, the coloring c is said to be silver with respect to I if every x ∈ I is rainbowwith respect to c. We say G is silver if it admits a silver coloring with respect to some I. In [1] the following problem isasked: Find classes of silver r-regular graphs G.

Here we study the class of block intersection graphs of Steiner triple systems, STS(v). Given a design D, a series ofblock intersection graphs Gi, or i-BIG, i = 0, ..., k; can be defined in which the vertices are the blocks of D, with twovertices adjacent if and only if the corresponding blocks intersect in exactly i points. Let D be an STS(v), G2 and G3 areempty graphs, so we consider only G0 and G1. G0 is a strongly regular graph SRG(b, b − 3r + 2, b − 6r + 13, b − 5r + 8),and G1 is an SRG(b, 3(r − 1), r + 2, 9). The aim of this talk is to characterize G0, and G1 for being silver.

We show that:

• For v = 7 and 9, G0 and G1 both are silver.

• For any STS(13) or STS(15) non of G0 or G1 are silver.

• Let D be an affine plane of order n. Then both 0-BIG(D) and 1-BIG(D) are silver.

• For each w, where 9|w, we construct a Steiner triple system D = STS(w) for which, the 1-BIG(D) is silver.

• For any v > 9, 0-BIG(STS(v)) is not silver.

• If 9 - v and an STS(v) which has v3 parallel class, then G1 = 1-BIG(STS(v)) is not silver.

• If 9 - (v − 1) and an STS(v) which contains v−13 parallel class, then G1 = 1-BIG(STS(v)) is not silver.

References[1] M. Mahdian and E. S. Mahmoodian, The roots of an IMO97 problem, Bull. Inst. Combin. Appl., 28 (2000), 48–54.

2000 Mathematics Subject Classification. 05B07, 05C15Key words and phrases. graph coloring, Steiner triple system, block intersection graphs, silver coloring

29


Spectral properties of difference operator over the space

bvp (1 ≤ p < ∞)

A. M. Akhmedov

Baku State University, Azerbaijan

[email protected]

Abstract

In this work our purpose is to find the continuous dual bv∗p of the sequence space bvp (1 ≤ p < ∞) consisting of all

sequences (xk) such that (xk − xk−1) in the sequence space lp, to find the norm of the difference operator ∆ acting on thespace bvp, and fine spectrum with respect to the Goldberg’s classification of the operator ∆ over the space bvp.

1. The space bvp has been introduced by Basar and Altay [1], where they have proved that bvp is a BK-space, andalso have studied the α-, β- and γ-duals of the space bvp.

Define the spaces d1 and dq consisting of all sequences a = (ak) normed by

‖a‖d1 = supk,n∈N

∣∣∣∣∣∣

n∑

j=k

aj

∣∣∣∣∣∣< ∞

and

‖a‖dq =

∑

k

∣∣∣∣∣∣

∞∑

j=k

aj

∣∣∣∣∣∣

q

1/q

< ∞, (1 < q < ∞).

Lemma ([2], Theorem 2.3) bv∗1 and bv∗p are isometrically isomorphic to d1 and dq ( 1p + 1

q = 1), respectively.

2. In this part the norm of the difference operator ∆ with respect to the space bvp has been found and the fine spectrumof the operator ∆ has been examined.

Lemma ([2], Theorem 3.2) ‖∆‖ = 2.Using Lemma 1 and Lemma 2 we have the next main theorem concerning to the spectrum σ(∆) and its disjoint

partitions.Theorem

1. σ(∆) = λ ∈ C : |λ− 1| ≤ 1;2. the point spectrum σp(∆) = ∅;3. the continuous spectrum σc(∆) = λ ∈ C : |λ− 1| = 1;4. the residual spectrum σr(∆) = λ ∈ C : |λ− 1| < 1.

References[1] F. Basar, B. Altay, On the space of sequences of p-bounded variation and related matrix mappings, Ukrainian Math. J. 55 (2003),

no. 1, 136–147

[2] A.M. Akhmedov, F. Basar, The fine spectra of the difference operator ∆ over the sequence space bvp, (1 ≤ p < ∞), Acta Math.Sin. (Engl. Ser.) 23 (2007), no. 10, 1757–1768


30


Fixed point theory for inward set-valued maps in

hyperconvex metric spaces

A. Amini-Harandi

Department of Mathematics, University of Shahrekord

Shahrekord, 88186-34141, Iran

[email protected]

Abstract

Let X is a compact, admissible subset of a hyperconvex metric space M . Suppose that F : X ( M is a quasi-lowersemicontinuous set-valued map with admissible values and G : X ( X is a continuous, onto and quasi convex set-valuedmap with compact, admissible values. In addition, assume that F is weakly inward with respect to G. Then, there existsan x0 ∈ X, such that

d(G(x0), F (x0)) = infx∈X

d(x, F (x0)).

As applications, we give some coincidence and fixed point results for weakly inward set-valued maps. Our results, generalize

some well-known results in literature.

2000 Mathematics Subject Classification. 47H10, 54H25Key words and phrases. Fixed point, best approximation, coincidence point, hyperconvex metric space

31


Generalized Logistic Distribution: Bayesian Estimations

A. Asgharzadeh*, A. Fallah**

*Department of Statistics, Faculty of Basic Science,

University of Mazandaran, Babolsar, Iran

[email protected]

**Department of Statistics, University of Payam Noor,

Behshahr, Iran

[email protected]

Abstract

In this paper, we consider a Bayesian approach to estimate the generalized logistic parameters. The maximum likelihood

(ML) and the Bayes estimates are derived for the two unknown parameters and some survival time parameters. The Bayes

estimates are derived with respect to conjugate prior for the shape parameter and, discrete prior for the scale parameter of

this model. Monte Carlo simulations are presented to compare the Bayes estimates and the ML estimates of the unknown

parameters and the reliability function.

2000 Mathematics Subject Classification. 62F10, 62F15.Key words and phrases.Bayesian estimation, Generalized logistic distribution, Monte Carlo simulation.

32


About Continued Fractions Expansions of Metallic

Means

A. Redondo Buitrago

Departamento de Matematicas, I.E.S. Bachiller

Sabuco, Av. Espana 9, 02002 Albacete, Spain

[email protected]

Abstract

The Metallic Mean σp,q is the positive solution of the quadratic equation x2−px−q = 0, where p and q are some positiveinteger numbers. This family of irrational numbers was introduced by V. W. de Spinadel (1997). All of its members share

common mathematical properties providing algebraic and geometric generalizations of the Golden Mean, φ =(1 +

√5)

/ 2

and the Silver Mean, θ = 1 +√

2. Really, both aforementioned constants are σ1,1and σ2,1 , the two most important of the

Metallic Means.It is well known that the simple continued fraction expansion of the Metallic Means σp,1, are periodic. We begin

obtaining new better generalized periodic expansions for this Metallic subfamily. The odd powers of the Metallic Meanshave continued fraction expansions in terms of the certain generalized Lucas numbers. Each of this power is also someMetallic Mean. We prove that the even powers of the Metallic Means, are always the solution of a quadratic equationx2 − mx + 1 = 0, where the parameter m is also defined by means of another generalized Lucas numbers, and from thisresult, directly we achieve the generalized continued fraction expansion of this even powers.

From a simple algebraic study of the solutions of the quadratic equations of the form x2 −mx + 1 = 0, we obtain somerelations among them and the continued fractions of the Metallic Means σ1,q and σp,1,. These particular results allowestablish new relations between certain general continued fractions. Indeed, we found a recurrence relation which generatesthe integer powers of σ1,q , and this relation leads to some curious expansions of 2n, n = 0, 1, 2, . . .

We also obtain several formal expansions of the square root of the Metallic Means σp,1 and we study its convergence.

Some of them involve the square roots of the complex numbers m + 2i and m − 2i. Eventually, since the square roots of

the Metallic Means σp,1 satisfy the equality(x2 + 1

) (1− x−1)

= mx /(1 + x) , we found some fractal fractions for them.

These endless fractions provide infinites sequences of rational approximations which converge to the represented square

root.

2000 Mathematics Subject Classification. 26C10, 11J70, 11A51, 40A15Key words and phrases. Generalized continued fractions, fractal fractions, Metallic Means, Golden Mean, Silver Mean.

33


A Theoretical And Numerical Investigation Of

Heteroclinic Connection In Two-Dimensional

Incompressible Flow

A. Deliceoglu

[email protected]

Abstract

Streamline patterns and their bifurcations in two-dimensional incompressible fluid near non-simple degenerate critical

points are investigated. A normal form transformation is used to simplify the differential equations of a Hamiltonian system

that describes the streamlines. Bifurcations in the flow occur when parameters take certain degenerate values. When the

degenerate configuration is perturbed slightly, an unfolding of the system is obtained. From this, a complete description

of the bifurcations up to codimension two is given. A special flow pattern is found that in flow saddles are connected with

a single heteroclinic connection near a non-simple degenerate critical point. The theory is applied to the patterns and

bifurcations found numerically in the studies of Stokes flow in a double-lid-driven rectangular cavity.

References[1] Bakker, P.G., Bifurcation in Flow patterns, Thesis, Technical University of Delft, Netherlands (1989).

[2] Brons,M and Hartnack, J.N., Streamline Topologies Near Simple Degenerate Critical Points in Two-Dimensional Flow awayfrom Boundaries, Physics of Fluids 11 (1999) 314-324.

[3] Deliceoglu, A. and Gurcan, F., Streamline topology near nonsimple degenerate critical points in two-dimensional flows withsymmetry about an axis, J. Fluid Mech. 606 , (2008) 417-431.

[4] Gurcan, F. and Deliceoglu, A., Streamline topologies near nonsimple degenerate points in two-dimensional flows with doublesymmetry away from boundaries and an application, Physics of Fluids 17 , (2005) 1-16.

[5] Gurcan, F., Flow Bifurcations in Rectangular, Lid-Driven, Cavity Flows, Thesis, University of Leeds (1997).

[6] Hartnack, J.N., Streamlines Topologies near a Fixed Wall Using Normal Forms, Acta Mech. 136, (1999) 55-75.

2000 Mathematics Subject Classification. 76D, 37N10Key words and phrases. Incompressible Viscous Fluids, Dynamical systems in fluid mechanics

34


Common Fixed point Theorems For Maps Under a

Contractive Condition of Integral Type

A. Djoudi

Laboratoire de Mathmatiques Appliques, Universit de Annaba

Facult des Sciences, Dpartement de Mathmatiques

P.O. Box 12, 23000 Annaba. ALGERIA

[email protected]

Abstract

Two common fixed point theorems for mapping of complete metric space under a general contractive inequality of

integral type and satisfying minimal commutativity conditions are proved. These results extend and improve several

previous results particularly Theorem 4 of Rhoades [3], Theorem 4 of Sessa [4] and results of [1-2].

References

[1] A. Djoudi and A. Aliouche, Common fixed point theorems of Gregus type for weakly compatible mapping satisfying contractive

conditions of integral type, J. Math. Anal. Appl. 329 (2007) 31-45.

[2] A. Djoudi and L. Nisse, Gregus type fixed points for weakly compatible maps, Bull. Belg. Math. Soc. 10 (2003) 369-378.

[3] B. E. Rhoades, Two fixed point theorems for mappings satisfying a general contractive condition of integral type, Int. J. Math.

Math. Sci. 63 (2003), 4007-4013.

[4] S. Sessa, On a weak commutativity condition of mappings in fixed point considerations, Publ. Inst. Math. Beogard 32 (46)

(1982), 149-153.

2000 Mathematics Subject Classification. 47H10Key words and phrases. weakly compatible maps, common fixed point, contractive condition of integral type.

35


An Analysis on Fourier Series Expansion

A. Ghyasi, M. H. Rahmani Doust

Department of Mathematics, Faculty of Basic Sciences

University of Ilam, Ilam, 69315-516, Iran

[email protected], [email protected]

Abstract

The present paper is involved with the analyze of Fourier coefficients with help of extension of Gauss partial sum for

Fourier series. The Fourier series are specific and standard series of periodic functions which are discussed in varies area of

applied mathematics. The discussed functions have period Q in which they are piecewise continuously and uniform on said

period. By study on extension of the Fourier series sum on periodic functions, we are able to extend Gauss partial sum.

References[1] A. Ghyasi, Distributed Value Arithmetical Function, Moscow, 2007.

[2] A. Ghyasi, V. N. Chybarikov, Formula Summing Mordell, Journal Vistnik Math-Mec No.1, 2005.

[3] E. K. Zhambo, V. N. Chybarukov , Distributed Arithmetical Function, Moscow No. 2, 2001.

[4] G. U. Arkhupov, V. A. Sadovich and V. N. Chybarirov, Math. Analysis Text Book, Moscow, 2003.

[5] N. Piskonov , Differential and Integral Calculus, Moscow, 1974.

[6] Vinograd , Method Trigonometric Sum, Moscow, 1976.

[7] Vinogral , Number Theory, Moscow, 1981.

[8] Vinograd, Sur La Distribution Des Residues at Des Puissances , Journal Physical Math. No. 1, 1918.

2000 Mathematics Subject Classification. 4A58, 11A25, 42A16, 42A20, 42C15Key words and phrases. Expansion, Fourier coefficients, Gauss Partial Sum, Piecewise Continuously.

36


Estimation And Prediction Of Weibull Parameters

From Common Percentiles With Outliers

A. H. Abd Ellah

Department of Mathematics, Faculty of Science,

Sohag University 82524, Egypt

[email protected]

Abstract

In this paper, estimation of Weibull distribution shape and scale parameters is accomplished through use of symmetri-

cally located percentiles from a sample. The process requires algebraic solution of two equations derived from the cumulative

distribution function. Bayesian prediction limits for the future observations from two parameters Weibull distribution are

obtained in the presence of outliers of type and with random sample size. Numerical examples are used to illustrate the

procedure.

References[1] Abd Ellah, A.H. (2009) Bayesian Prediction of Weibull Distribution Based on fixed and random sample size, Republic of Azerbaijan,

Baku, 14-15 January.

[2] Abd Ellah, A.H. (2008) Comparison of estimates using record statistics from Lomax model : Bayesian and non-Bayesian ap-proaches J. Statist. Res. Iran, 3, 91-109.

[3] Abd Ellah, A.H. and Sultan, K. S (2005) Exact Bayesian prediction of Exponential lifetime based on fixed and random sample sizes,QTQM Journal , vol 2,no. 2,pp 161-175.

[4] Abd Ellah, A.H. (2004) Exact prediction Intervals for Exponential lifetime with Outliers, PSU, 7-8 April.

[5] Abd Ellah, A.H. (2003) Bayesian one sample prediction bounds for Lomax distribution, Indian J. Pure Appl. Math., 43(1), 101-109.

2000 Mathematics Subject Classification. 62E16, 62F18Key words and phrases. Parameter estimation, Two sample; Order statistics; random sample size; predictive distribution; Weibullmodel; probability coverage; average width.

37


Optimal Control with Fuzzy Chance Constraints

A. Heydari1, S. Ramezanzadeh2

1 Payame Noor University, Department of Mathematics, Tehran, Iran

a [email protected]

2 Police University, Department of Mathematics, Tehran, Iran

ramezanzadeh [email protected]

Abstract

In this paper, one of the models of optimal control problem with chance constraints is introduced, in which the parame-

ters of constraints are fuzzy, random, or fuzzy random variables. To defuzzify the constraints, we consider possibility levels

for them. The chance constraints are converted to crisp (neither fuzzy nor stochastic) constraints by chance-constrained

programming approach. The classic optimal control problem with crisp constraints is solved by Pontryagin Minimum

Principal and Khun-Taker conditions. The model is illustrated by two numerical examples.

References[1] D. Chakraborty, Redefining chance-constrained programming in fuzzy environment, FSS, 125 (2002) 327-333.

[2] A. Charns, W. Cooper, Chance constrained programming, Management Science 6 (1959) 73-79.

[3] D. Dubois, H. Prade, Ranking fuzzy numbers in the setting of possibility theory, Information sciences 30 (1983) 183-224.

[4] H. Kuakernaak, Fuzzy random variables, definitions and theorems, Information Sciences, 15 (1978) 1-29.

[5] B. Liu, Fuzzy random chance-constrained programming, IEEE Transactions on Fuzzy Systems, 9 (5) (2001) 713-720.

[6] B. Liu, Fuzzy random dependent-chance programming, IEEE Transactions on Fuzzy Systems 9 (5) (2001) 721-726.

[7] M. K. Maiti, M. Maiti, Fuzzy inventory model with two warehouses under possibility constraints, Fuzzy Sets and Systems, 157 (2006)52-73.

[8] K. Maity, M. Maiti, Possibility and necessity constraints and their defuzzification- a multi-item production- inventory scenario viaoptimal control theory, European Journal of Operational Research 177 (2007) 882-896.

[9] L. S. Pontryagin, et al., the Mathematical Theory of Optimal Process, International Science, New York, 1962.

[10] S. Ramezanzadeh, M. Memriani, S. Saati, Data envelopment analysis with fuzzy random inputs and outputs: a chance-constrainedprogramming approach, Iranian Journal of Fuzzy Systems, Vol. 2, No. 2 (2005) 21-31.

2000 Mathematics Subject Classification.Key words and phrases. Fuzzy random variable, Chance-constrained programming, Possibility level, optimal control

38


Chaotification Of Discrete Dynamical Systems

A. Ikhlef, N. Mansouri

Laboratoire d’Automatique et de Robotique

Departement d’electronique, Faculte des Sciences de l’Ingenieur

Universite Mentouri Route de Ain-El-Bey.,

25000. Constantine, Algerie


Abstract

Chaos has been extensively studied within the scientific, engineering and mathematical communities as an interestingcomplex dynamic phenomenon. Recently, the traditional trend of understanding and analyzing chaos has evolved to a newphase of investigation: controlling and creating chaos. More specifically, when chaos is useful, it is generate intentionally.However, when chaos is harmful, it is controlled. Indeed, several studies have showed that chaos can be useful or has greatpotential in many disciplines such as in high-performance circuit design for telecommunication, collapse prevention of powersystems or biomedical engineering applications to the human brain and heart. Therefore, creating chaos becomes a keyissue in such applications where chaos is important and useful [1, 2].

In a sequence of papers, the problem of chaotification of discrete systems is addressed [3, 4, 5, 6]. In a recent papera closed expression was provided for the controller, in terms of the system state vector and a set of specified Lyapunovexponents.

According to the stability theorems, a dynamical system is stable if and only if all its Lyapunov exponents are lower

or equal to zero. If at least one is positive, the system becomes completely unstable. For this, practically all methods of

chaotification are based on the change of sign of the Lyapunov exponent .

References[1] M. E. Brandt and G. Chen, Bifurcation control of two nonlinear models of cardiac activity, IEEE. Trans Circuits Syst. I. 44 (1997)

1031-1034.

[2] M. P. Kennedy, G. Kolumban and G. Kis, Chaotic modulation for robust digital communications over multipath channels, Int. J.Bifurcation and Chaos. 10 (2000) 695-718.

[3] G. Chen and D. Lai, Making a dynamical system chaotic: Feedback control of Lyapunov exponents for discrete-time dynamicalsystems, IEEE trans. Circuits syst. I, 44 3 (1997) 250-253.

[4] D. Lai and G. Chen, Making a discrete dynamical system chaotic: Theoretical results and numerical simulations, Int. J. Bifurcationand Chaos. 13 (2003) 3437-3442 .

[5] S. Codreanu, desynchronization and chaotification of nonlinear dynamical systems, Chaos, Soluton and Fractals. 12 (2002) 839-843.

[6] X. Wu, J. Lu, H. Lu and S. Wong,suppression and generation of chaos for a three-dimensional autonomous system using parametricperturbations, Chaos, Soluton and Fractals. (2007) 811-819.

[7] G. Chen and D. Lai, Feedback anti control of discrete chaos, Chaos, Int. J. Bifurcation and Chaos. 8 (1998) 1585-1590.

2000 Mathematics Subject Classification.37D45, 65P20Key words and phrases. Chaotification, discrete system, Lyapunov exponent

39


k-Tuple Total Domination in Graphs

A. P. Kazemi1, M.A. Henning2

1 University of Mohaghegh Ardabili, Department of Mathematics,

Ardabil, Iran

[email protected]

2 University of KwaZulu-Natal, School of Mathematical Sciences,

Pietermaritzburg Campus, South Africa

[email protected]

Abstract

A set S of vertices in a graph G is a k-tuple total dominating set of G if every vertex of G is adjacent to least k vertices

in S. The minimum cardinality of a k-tuple total dominating set of G is the k-tuple total domination number of G. For a

graph to have a k-tuple total dominating set, its minimum degree is at least k. When k = 1, a k-tuple total domination

number is the well-studied total domination number. When k = 2, a k-tuple total dominating set is called a double total

dominating set and the k-tuple total domination number is called the double total domination number. We determine the

k-tuple total domination number for complete multipartite graphs. Upper bounds on the k-tuple total domination number

of general graphs are presented.

References[1] Archdeacon D., J. Ellis-Monaghan, D. Fischer, D. Froncek, P. C. B. Lam, S. Seager, B. Wei, and R. Yuster, Some remarks on

domination. J. Graph Theory 46 (2004), 207–210.

[2] Chvatal V. and C. McDiarmid, Small transversals in hypergraphs. Combinatorica 12 (1992), 19–26.

[3] E. J. Cockayne and A. G. Thomason, An upper bound for the k-tuple domination number, manuscript (2007).

[4] J. Harant and M. A. Henning, On double domination in graphs, Discussiones Mathematicae Graph Theory 25 (2005), 29–34.

[5] J. Harant and M. A. Henning, A realization algorithm for double domination in graphs. Utilitas Mathematica 76 (2008), 11-24.

[6] F. Harary and T. W. Haynes, Double domination in graphs. Ars Combin. 55 (2000), 201–213.

[7] T. W. Haynes, S. T. Hedetniemi, and P. J. Slater (eds). Fundamentals of Domination in Graphs, Marcel Dekker, Inc. New York,1998.

[8] T. W. Haynes, S. T. Hedetniemi, and P. J. Slater (eds). Domination in Graphs: Advanced Topics, Marcel Dekker, Inc. New York,1998.

[9] C. S. Liao and G. J. Chang, Algorithmic aspects of k-tuple domination in graphs. Taiwanese J. Math. 6 (2002), 415–420.

[10] C. S. Liao and G. J. Chang, k-Tuple domination in graphs. Information Processing Letters. 87 (2003), 45–50.

2000 Mathematics Subject Classification. 05C69Key words and phrases. total domination, k-tuple total domination

40


Fusion Frames and g-Frames in Hilbert Spaces and

Hilbert C∗-Module

A. Khosravi

Faculty of Mathematical Sciences and Computer,

Tarbiat Moallem University, 599 Taleghani Ave., Tehran, 15618, Iran

khosravi [email protected]

Abstract

Fusion frames and g-frames were recently introduced as generalizations of frames. In this note we study their properties

in Hilbert spaces and Hilbert C∗-modules and we generalize some of the known results in frame theory to fusion frames and

g-frames. We study the behavior of these generalized frames under mall perturbations. We also show that tensor product

of fusion frames (g-frames) is a fusion frame (g-frame) and tensor product of resolution of identity is a resolution of identity

in Hilbert spaces and Hilbert C∗-modules.

References[1] P. G. Casazza, G. Kutyniok, S. Li, Fusion frames and distributrd processing, Preprint.

[2] A. Khosravi, B. Khosravi, Frames and bases in tensor product of Hilbrt spaces and Hilbert C∗-modules, Proc. Indian Acad. Sci.Math. Ser., 117 (1), 2007, 1-12.

[3] A. Khosravi, B. Khosravi, Fusion frames and g-frames in Hilbert C∗-modules, Int. J. Wavelet, Multiresolution and Inform. Process.,6 (3), 2008, 433-446.

[4] A. Khosravi, K. Musazadeh, Fusion frames and g-frames, J. Math. Anal. Appl., 342, (2008), 1068-1083.

2000 Mathematics Subject Classification.41A58, 42C15, 46L99, 47A05Key words and phrases.Frame, fusion frame, g-frame, Hilbert C∗-module, duality, perturbation.

41


Options and Partial Differential Equations

A. Kor1, M. Can2

1 Faculty of Economics and Business Administration,

International University of Sarajevo, Paromliska 66, Sarajevo, BiH.

[email protected]

2 International University of Sarajevo, Faculty of Engineering

and Natural Sciences, Paromlinska 66, 71000 Sarajevo, BiH.

[email protected]

Abstract

The aim of this paper is to show how partial differential equations appear in financial models and to present briefly

analytical and numerical methods used for effective computations of prices and hedging of options. In his thesis defended

in 1900 in the Sorbonne, Louis Bachelier proposed a probabilistic modeling of the time evolution of the price of a share. In

terms of what he calls the ’radiation of probability’, he was able to relate the distribution of probability to the heat equation,

which describes the evolution of temperature in a given media. In the first section, the reasoning of Louis Bachelier is used

to bring out a relationship between the heat equation and a modeling of the evolution of share prices. In the second section,

the equations satisfied by options prices are introduced. In the third section certain class of solutions to the Black, Scholes

and Merton Equation are introduced.

2000 Mathematics Subject Classification. 91B26, 91B28Key words and phrases. options, partial differential equations, diffusion, Merton Equation

42


On Fuzzy p-ideals and fuzzy H-ideals in BCI-algebras

A. Kordi1, A. Ahmadi2, A. Moussavi3

1,2Mathematics and Informatics Research Group, ACECR

Tarbiat Modares University

P.O.Box: 14115-343, Tehran, Iran


3Department Of Mathematics, Tarbiat Modares University


[email protected]

Abstract

The concept of fuzzy subset and various operations on it were first introduced by Zadeh. Since then, fuzzy subsets have

been applied to diverse field. The study of fuzzy subsets and their application to mathematical contexts has reached to

what is now commonly called fuzzy mathematics. Fuzzy algebra is an important branch of fuzzy mathematics. The study

of fuzzy algebraic structures was started with the introduction of the concept of fuzzy sub-groups in 1971 by Rosenfeld.

Since then these ideas have been applied to other algebraic structures such as semigroups, rings, ideals, modules and vector

spaces. In 1999, Ougen defined fuzzy subsets in BCK-algebras and investigated some properties . In 1993, Y.B. Jun applied

it in BCI-algebras. We study and give some characterizations of Fuzzy p-ideals and fuzzy H-ideals in BCI-algebras. Several

interesting properties of these concepts is studied.

References[1] Y.B. Jun, A note on nil ideals in BCI-algebras, Math. Japonica, 38 (6) (1993), 1017-1021.

[2] Y.B. Jun and J. Meng, Fuzzy p-ideals in BCI-algebras, Math. Japonica, 40 (2) (1994), 271-282.

[3] Y. Huang, On positive and weakly positive implicative BCI-algebras, Southeast Asian Bulletin of Mathematics, 26 (2002), 575-582.

[4] A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl.35 (1971) 512-517.

2000 Mathematics Subject Classification. 06F35, 03G25.Key words and phrases. pseudo-BCK algebras, positive implicative pseudo-BCK ideals

43


Global properties of a class of models for HIV infection

of CD4+ T cells and macrophages

A. M. Elaiw


Al-Azhar University Assiut Egypt

a m [email protected]

Abstract

In this paper, we study the global properties of a class of human immunodeficiency virus (HIV) models. The basic

model is a 5−dimensional nonlinear ODEs that describes the interaction of the HIV with two target cells, CD4+ T cells and

macrophages. HIV model with exposed state and model with nonlinear incidence rate are also analyzed. Lyapunov functions

are constructed to establish the global asymptotic stability of the uninfected and infected steady states. We have proven

that if the basic reproduction number R0 is less than unity, then the uninfected steady state is globally asymptotically

stable. If R0 > 1 (or if the infected steady state exists), then the infected steady state is globally asymptotically stable. In

a control system framework, we have shown that the HIV model incorporating the effect of Highly Active AntiRetroviral

Therapy (HAART) is globally asymptotically controllable to the uninfected steady state.

2000 Mathematics Subject Classification.34D23, 34D20, 92D30, 93B05Key words and phrases.Global stability, Direct Lyapunov method, HIV/AIDS, Controllability.

44


Application of Model Predictive Control to Dynamic

Economic Dispatch with Emission

A. M. Elaiw1, A. M. Shehata2

1 Department of Mathematics, Faculty of Science,


a m [email protected]

2 Department of Mathematics, Faculty of Science,


ah [email protected]

Abstract

The emission of gaseous pollutants including SO2, NOx, CO and CO2 from fossil-fueled electric power generating

plants affects the human health directly or indirectly. Therefore, the controlling of pollution in power plants has received

considerable attention in recent years. The amount of emission can be reduced by formulating dynamic economic emission

dispatch (DEED) problem which is a multi-objective optimization problem, where both fuel cost and emission are simulta-

neously minimized. The emission can also be controller by formulating an emission constrained dynamic economic dispatch

(EDED) problem where the fuel cost is minimized while treating the emission as constraints. In [1] a model predictive con-

trol (MPC) approach is proposed to the dynamic economic dispatch (DED) problem. It is proven that, the MPC approach

provides solutions converging to the optimal solution of an extended version of the DED problem and the MPC algorithm

is also robust under certain disturbances and uncertainties. In this paper we applied the MPC approach proposed in [1]

to DEED and EDED problems. Two examples are presented consisting of five and ten units, to show the convergence and

robustness of the MPC solutions.

References[1] X. Xia, J. Zhang amd A. M. Elaiw, A Model Predictive Control Approach to Dynamic Economic Dispatch Problem, submitted to

IEEE Transaction on power systems. .

2000 Mathematics Subject Classification. 93C95Key words and phrases. Dynamic economic dispatch, Dynamic economic emission dispatch, Multi-objective optimization, Modelpredictive control

45


Color Gamut Computation Using Neural Networks

A. Malek*, N. Hosseinipour-Mahani** and S. Ezazipour***

*Department of Applied Mathematics, Tarbiat Modares University,

P.O. Box 14115-175, Tehran, Iran

email:[email protected]

**Department of Applied Mathematics, Tarbiat Modares University,



***Department of Applied Mathematics, Tarbiat Modares University,



Abstract

The ability to exactly reproduce all the colors presented in an original image is the chief purpose in color reproduction.The various display devices have different achievable ranges (gamuts) of colors, it is frequently the case that some colorscannot be made to match the original color exactly. A color gamut is a set of all colors of a given image or device. For animage, the color gamut is the set of all colors that are contained in it. For devices, such as monitors or printers, the colorgamut is the set of all colors that any given device can display. Different devices usually have different gamuts, i.e. variousclasses of devices can display different sets of colors. In questions of displaying an image one usually has to consider that amonitor displays more colors than a printer. Thus in moving an image from a monitor to a printer, we need an intermediatemapping that makes it possible. The color gamut of the source device is mapped onto the color gamut of the target deviceby the intermediate transformation that is called gamut mapping. In this process, those colors that cannot be representedin the target altered to colors that can be represented. The gamut mapping is, thus, a fundamental one in any transfer ofcolor images from input to output devices. A color can be seen as a point in a three dimensional color space. Thus a gamutis just a finite subset of R3 and a gamut mapping is a transformation between two subsets of R3.

We use different color space like RGB, CMYK and Lab to describe colors in an image. The three dimensional surfaceof the color gamut is called gamut boundary. The gamut boundary information is using for implementing color gamutmapping; therefore, it plays an important role for color gamut mappings.

In this research our focus is on image gamuts of digital images. We discuss the implication of gamut and introduce

a mathematical method for describing and visualizing color gamuts. We apply a novel neural network model to solve

the associated optimization problem with an image gamut, that described first by Joachin Giesen et al. (2006). The

optimal solution of the corresponding constrained optimization problems gives the coefficients of a function that is used for

drawing the gamut boundary. Two work examples are demonstrated to show the feasibility and efficiency of this approach.

Numerical results are given.

2000 Mathematics Subject Classification.46N10, 62M45, 90C30Key words and phrases.Color gamut; Gamut mapping; Optimization problems; Neural networks.

46


The Unite Subduced Cycle Index Table of Some

Molecules

A. Moghani, A. Zaeembashi, M.R. Sorouhesh

Department of Color Physics, Institute for Colorants Paints and

Coating (ICPC), Tehran, Iran.

[email protected]

Department of Mathematics, Shahid Rajaee University, Tehran, Iran.

Department of Mathematics, Islamic Azad university,

Tehran South branch, Tehran, Iran.

Abstract

Recently, the full non-rigid (f-NRG) groups of some molecules have been showed via new structures as direct product,

semidirect product and wreath product. A subduced representation denoted by G(/Gi

) ↓ Gj as a subgroup of the coset

representation G(/Gi

)that contains only the elements associated with the elements of Gj A unit subduced cycle index

(USCI) is defined:

Z(G

(/Gi

) ↓ Gj , sd

)=

∏g∈Ω s

d(v)g

where sd(v)g

= |Gi|/|g−1Gig ∩ Gj | and Ω a transversal for the double coset decom-

positions concerning Gi and Gj for i, j = 1, 2, · · · , |Ω| . In this paper the USCI tables of some full non-rigid groups like

p−Xylene 1, 3, 5-trimethylbenzene and 1, 3, 5-triamino-2, 4, 6-trinitrobenzene are computed.

References[1] S. Fujita, MATCH Commun. Math. Comput. Chem. 55, 237-270, 2006.

[2] S. Fujita, Diagrammatical Approach to Molecular Symmetry and Enumeration of Stereoisomers, MCM, Kragujevac, 2007.

[3] A. Moghani, J. Serb. Chem. Soc. 73, 189-195, 2008.

[4] M.R Darafsheh, A.Moghani, S. Naghdi Sedeh, Acta Chim. Slov. 55, 602607, 2008.

[5] M.R Darafsheh, A.Moghani, S. Naghdi Sedeh, Acta Chim. Slov. 55, 602607, 2008.

[6] M. R. Darafsheh, A. Moghani, J. Serb. Chem. Soc. 74, 45-52, 2009

[7] M.R Darafsheh, A. Moghani, M. Karami, A. Zaeembashi and S. Naghdi, Int. J. Chem. Model 2009 (In press)

[8] M.R Darafsheh, A. Moghani, Bull. Chem. Soc. Jpn. 81, 979-982, 2008.

[9] A. Moghani, S. Naghdi Sedeh, to appear in J. Symmetry.

2000 Mathematics Subject Classification.Key words and phrases. Wreath product, Permutation group, Full non-rigid group, USCI table, p-Xylene, hexamethylethane

47


Color Reconstructions by the new Fuzzy Logic-based

model

A. Moghani, A. Zaeembashi

Department of Color Physics, Institute for Colorants Paints

and Coating (ICPC), Tehran, Iran.

[email protected]

Department of Mathematics, Shahid Rajaee University, Tehran, Iran

Abstract

Many color vision systems require a first step of classifying pixels in a given image into a discrete set of color classes.

Fuzzy sets are defined on the Hue, Saturation and Value components of the HSV color space and provide color descriptors

to follow the human intuition of color classification according to Statistical predictions. In this paper we describe pixel

color segmentation which are human perception based and useful in reconstruction too. Then, by introducing a statistical

model for a psychological experiment in color naming we will estimate our results.

References[1] A. Moghani. A Fuzzy logic-based Model in Image Processing, IMID/IDMC/ASIA DISPLAY ’08 DIGEST, pp. 943-946, 2008.

[2] M.R. Darafsheh, A. Moghani. Some Fuzzy Sets for Fuzzy Color Categorization, Italian J. Pure and Appl. Math. (In press)

[3] A. Moghani, P. Nasiri. Computational Fuzzy Color Naming, Proc. ISFS08 , pp. 184-188, 2008.

2000 Mathematics Subject Classification.Key words and phrases. Color segmentation, Fuzzy logic, Reconstruction, HSV and Lab color spaces.

48


On Bayesian estimation for an M/G/1 queue with

optional second service

A. R. Mohammadi1, M. R. Salehi-Rad2, A. Abassi3

1,2,3Department of statistics, Allameh Tabataba‘i University, Tehran, Iran

1r [email protected], [email protected], 3asieh [email protected]

Abstract

In this article, we exploit the Bayesian inference and prediction for an M/G/1 queueing system with optional second

reservice. In this model, a service unit attends customers arriving following a Poisson process and demanding service

according to a general distribution and some of customers need to reservice with probability ”p” after taking the service.

First, we approximate the service and reservice time densities with a class of Erlang mixture distributions. Then, given

observations of the system, we propose a Bayesian procedure based on birth-death MCMC method to estimate some

performance measures. Finally, we have applied the theories in practice by providing a numerical example based on the

data which have been obtained from a hospital.

2000 Mathematics Subject Classification. 62F15, 60K25Key words and phrases. M/G/1 queue, Optional service, Erlang mixture, Birth-death MCMC

49


On Pseudo Implicative BCK Ideals Of Pseudo-BCK

Algebras

A. Moussavi, A. Ghassemi and A. Kordi

Department Of Mathematics, Tarbiat Modares University

P. O. Box: 14115-170, Tehran, Iran

[email protected]

Mathematics and Informatics Research Group, ACECR,

Tarbiat Modares University,P.O.Box: 14115-343, Tehran, Iran

as [email protected]

Mathematics and Informatics Research Group, ACECR,

Tarbiat Modares University,P.O.Box: 14115-343, Tehran, Iran

[email protected]

Abstract

W.A. Dudek and Y.B. Jun gave a characterization of pseudo-BCK algebras, and provided conditions for a pseudo-BCK

algebra to be ∧-semilattice ordered (resp. ∩-semilattice ordered). Y.B. Jun, M. Kondo and K.H. Kim, introduced the

notion of positive implicative pseudo-ideals in a pseudo-BCK algebra, and then they investigated some of their properties.

In this paper the notion of pseudo-BCK ideals of a pseudo-BCK algebra is introduced and some related properties are

investigated. We investigate the relations between this pseudo ideals and several pseudo-BCK ideals. We give some

characterization theorems of pseudo-BCK ideals in pseudo- BCK algebras.

References[1] W.A. Dudek, Y.B. Jun, On pseudo-BCI algebras, (submitted).

[2] Y. B. Jun, Characterizations of pseudo-BCK algebras, Scientiae Mathematicae Japonicae Online 7(2002), 225-230.

[3] Y.B. Jun, M. Kondo and K.H. Kim, Pseudo-ideals of pseudo-BCK algebras, Scientiae Mathematicae Japonicae 58(2003), 93-97.

[4] Y.L. Liu, S.Y. Liu and Y. Xu, Pseudo-BCK algebras and PD-posets, Soft Comput. 11(2007), 91-101.

2000 Mathematics Subject Classification. 06F35, 03G25Key words and phrases. pseudo-BCK algebras, positive implicative pseudo-BCK ideals

50


Skew Power Series Extensions Of Principally Projective

Rings

Ahmad Moussavi

Department of Mathematics, Islamic Azad University,

South Tehran Branch, Tehran, Iran

[email protected]

Abstract

Let R be a ring and α be an α-compatible automorphism of R. If R is skew Armendariz, then R[[x; α]] is right principally

projective if and only if R is right principally projective and any countable subset of Sr(R) has a generalized countable

join.

References[1] J.A. Fraser, W.K. Nicholson, Reduced PP-rings. Math. Japonica 34(5) (1989) 715-725.

[2] E. Hashemi, A. Moussavi and A.R. Nasr-Isfahani, Skew power series extensions of principally quasi-Baer rings, Stud. Scie. Math.Hungar. 45 (4) (2008), 469-481.

[3] F.K. Huang, A note on extensions of principally quasi-Baer rings, taiwan. j. Math. 45 (4) (2008), 469-481.

[4] I. Kaplansky, Rings of Operators, Benjamin, New York, 1965.

2000 Mathematics Subject Classification. 16S36, 16W60, 16W10Key words and phrases. Baer ring; right p.p.-ring; α-compatible ring; Armendariz ring; skew power series ring.

51


Entropy In IVSs

A. Pouhassani

Islamic Azad University, Parand Branch. Iran

[email protected]

Abstract

In this paper the concept of IVS (Indexed Variable System) will be introduced and the entropy of a local topology will

be exhibited .Also some properties will be turned out.

References[1] Fraenkel, A. A; Bar-Hillel, Y. and Levy, A. Foundation of Set Theory , Elsevier Science Pub.B.V. , Netherlands , 1984.

[2] Moslemy Koupaey, M. H. and Pouhassani, A. Indexed Identity and Fuzzy Set Theory , Proceeding of the 6th Iranian Conference onFuzzy Systems and 1st Islamic World Conference on Fuzzy Systems (Farsi Version) , 2006 , 297.

[3] Pouhassani, A. Some Discrete Propositions in IVSs. Proceeding of WASET, V 37, Jan 2009; pp: 781-783.

[4] Walters, P. An Introduction to Ergodic Theory , Springer-Verlag , New York , 1982.

2000 Mathematics Subject Classification. 74H99Key words and phrases. indexed Identity relation, IVS, local Topology, topological Entropy.

52


Block Preconditioned Methods in Solution of

Hyperbolic Equations

A. Shayganmanesh 1, M.M. Arabshahi2

1 Department of Applied Mathematics, Faculty of Mathematics, University of Science and

Technology, Narmak, Tehran 16844, Iran

2 Department of Applied Mathematics, Faculty of Mathematics, University of Science and

Technology, Narmak, Tehran 16844, Iran

Abstract

In this article, we compare suitable preconditioners for solving linear systems arising from the class of fourth-order

approximations employed for solving hyperbolic partial differential equations, u uf(x, t, u, u, u)ttxxxta + b =subject to

appropriate initial and boundary conditions, where a and b are constants. Numerical results show that the proposed

preconditioned methods produces an accurate and oscillation free solution.

2000 Mathematics Subject Classification. 65M10, 35K40, 65M06Key words and phrases. Fourth-order approximation, Hyperbolic equation,Krylov subspace methods, Preconditioner.

53


Numerical Solution Of The Two Dimensional Nonlinear

Volterra Integro-Differential Equations With Separable

Kernels By The Differential Transform Method

A. Tari, S. Shahmorad

Department of Mathematics, Shahed University, Tehran - Iran.

[email protected]

Faculty of Mathematical science, University of Tabriz, Tabriz - Iran.

[email protected]

Abstract

In this paper, we will develop the two dimensional differential transform method (DTM) for solving a class of the

two dimensional linear and nonlinear Volterra integro-differential equations of the second kind. To this end we give some

preliminary results of the differential transform and describe the method of this paper. We also give some examples to

demonstrate accuracy of the presented method.

References[1] J. K. Zhou, Differential Transform and its Application for Electric Cicuits, Huazhong University Press, Wuhan, China, 1986.

[2] A. Arikoglu, I. Ozkol, Solution of boundary value prablem for integro- differential equations by using differential transform method,Appl. Math. Comput. 168 (2005) 1145-1158.

[3] F. Ayaz, Application of differential transform method to differential-algebraic equations, Appl. Math. Comput. 152 (2004) 649-657.

[4] F. Ayaz, Solutions of the system of differential equations by differential transform method, Appl. Math. Comput. 147 (2004) 547-567.

[5] F. Ayaz, On the two-dimensional differential transform method, Appl. Math. Comput 143 (2003) 361-374.

[6] C. K. Chen, Solving partial differential equations by two dimensional differential transform,Appl. Math. Comput. 106 (1999) 171-179.

[7] H. Guoqiang, W. Jiong, Extrapolartion of nystrom solution for two dimensional nonlinear Fredholm integral equations, J. of Comput.Appl. Math. 134 (2001) 259-268.

[8] H. Guoqiang, W. Ruifang, Richardson extrapolartion of iterated discrate Galerkin solution for two dimensional nonlinear Fredholmintegral equations, J. of Comput. Appl. Math. 139 (2002) 49-63.

[9] M. J. Jang, C. K. Chen, Y. C. Liu, Two-dimensional differential transform for partial differential equations, Appl. Math. Comput.121 (2001) 261-270.

[10] Z. M. Odibat, Differential transform method for solving Volterra integral equations with separable kernels, Math. Comput. Model.,48 (2008) 1144-1149.

[11] A. Tari, M. Y. Rahimi, S. Shahmorad, F. Talati, Solving a class of two dimensional linear and nonlinear Volterra integral equationsby the differential transform method, J. of Comput. Appl. Math, 228 (2009) 70-76.

[12] A. Tari, S. Shahmorad, A computational method for solving two dimensional linear Fredholm integral equations of the second kind,ANZIAN J., 49 (2008) 543-549.

2000 Mathematics Subject Classification. 65R20Key words and phrases. Two dimensional Volterra integro-differential equations, Differential transform.

54


Numerical Solution Of Two Dimensional Linear

Volterra Integral Equations Of The Second Kind By

The Tau Method With An Error Estimation


Department of Mathematics, Shahed University, Tehran - Iran.

[email protected]

Faculty of Mathematical science, University of Tabriz, Tabriz - Iran.

[email protected]

Abstract

In this paper, a general form of numerical approximate solution of two dimensional linear Volterra integral equationsof the second kind, which here in later TDLVIE, is discussed. It is formulated for using the operational Tau method withstandard base to convert the integral part of given integral equation, to its matrix representation.A brief introduction of developments of the Tau method is given in section 1, existence and uniqueness of solution ofTDLVIE is discussed in section 2, converting TDLVIE to a system of linear algebraic equations has been done in section 3and in section 4 some numerical examples are given to demonstrate efficiency and accuracy of the presented method.

References[1] H. Hochstadt, Integral Equations, John Wiley and Sons, New York,1989.

[2] C. G. Canuto, A. M. Qurteroni, M. Y. Hussaini, T. A. Zang, Spectral methods in fluid dynamics, Springer, 1988.

[3] E. L. Ortiz, The Tau method, SIAM J. Numer. Anal. (1969) 480-492.

[4] E. L. Ortiz and L. Samara, an operational approach to the Tau method for the numerical solution of nonlinear differential equations,Computing 27 (1981) 15-25.

[5] M. Hosseini Aliabadi, E. L. Ortiz, Numerical solution of feedback control systems equations, Appl. Math. Lett. 1(1) (1988) 3-6.

[6] M. Hosseini Aliabadi, E. L. Ortiz, Numerical treatment of moving and free boundary value problems with the Tau metho, Comput.Math. Appl. 35(8), (1999), 197-210.

[7] K. M. Liu, C. K. Pan, The automatic solution system of ordinary differential equations by the Tau method, Comput. Math. Appl.38 (1999) 197-210.

[8] M. Hosseini Aliabadi, The Buchstab’s function and the operational Tau method, Korean J. Comput. Appl. Math. 7(3) (2000) 673-683.

[9] M. Hosseini Aliabadi, The application of the operational Tau method on some stiff system of ODEs, Int. J. Appl. Math. 2(9) (2000)1027-1036.

[10] M. Hosseini Aliabadi, Solving ODE BVPs using the perturbation term of the Tau method over semi-infinite intervals, Far East J.Appl. Math. 4(3) (2000) 295-303.

[11] E. L. Ortiz and L. Samara, Numerical solution of partial differential equations with variable coefficient with an operational approachto the Tau method, Comput. Math. Appl. 10(1) (1984) 5-13.

[12] K. M. Liu and E. L. Ortiz, Numerical solution of ordinary and partial functional-differential eigenvalue problems with the Taumethod, Computing(wien) 41, 205-217,(1989).

[13] E. L. Ortiz and K. S. Pun, Numerical solution of nonlinear partial differential equations with the Tau method, J. Comput. and Appl.Math., 12/13, 511-516 (1985).

[14] M.Hosseini Aliabdi, S.Shahmorad, A matrix formulation of the Tau method for Fredholm and Volterra linear integro-differentialdifferential equations, The Korean jornal of Comput. and Appl. Math. Vol.9(2002), No.2, pp.497-507.

[15] S.M.Hosseini, S.Shahmorad, Tau numerical solution of Fredholm integro-differential equations with arbitrary polynomial bases, Appl.Math. Modeling, 27(2003) 145-154.

[16] S. M. Hosseini, S.Shahmorad, Numerical piecewise approximation of Fredholm integro-differential equations by the Tau method,Appl. Math. Modeling, 29 (2005) 1005-1021.

[17] J. pour-Mahmoud, M. Y. Rahimi and S. Shahmorad, Numerical solution of the system of Fredholm integro-differentail equations bythe Tau method, Appl. Math. Comput. 168(2005) 465-478.

[18] J. pour-Mahmoud, M. Y. Rahimi and S. Shahmorad, Numerical solution of Volterra integro-differentail equations by the Tau method

with the Chebyshef and Legendre bases, Appl. Math. Comput. 170(2005) 314-338.

2000 Mathematics Subject Classification.Key words and phrases. Two dimensional linear Volterra integral equations, Operational Tau method.

55


Stability Of Homotopy Perturbation Technique For An

Inverse Diffusion Problem

A. Zakeri, Q. Jannati

Department of Mathematics, K. N. Toosi University of Technology


[email protected]

Abstract

The Present research aims to offer a solution to one-dimensional inverse problem using the Homotopy perturbation

method (HPM). In the Problem, the values of function are known in one boundary; However, the partial differential

equations may be converted into a system of nonlinear ordinary differential equations by means of finite difference method

and discretizing the time variable. Therefore, an approximate solution can be found at discrete times if HPM is applied. It

will be demonstrated that such HPM application present 3 advantages of rapidity, accuracy and stability.

References[1] Beck. J. V., Blackwell. B., and St. Clair. Ch. J., Inverse heat conduction, ill-posed problems, John Willey and Sons, Inc, 1985.

[2] Shidfar. A. and Zakeri. A., A two-dimensional inverse heat conduction problem for estimating heat source, International Journal ofApplied Mathematics and Mathematical Science, 10(2005).1633-1641.

[3] He. J. H., Homotopy perturbation method for solving boundary value problems, Phys. lett. A. 35(2006)87-88.

2000 Mathematics Subject Classification. 74G15: 74G10: 74G75: 35R30Key words and phrases. Homotopy perturbation,Diffusion equation, Approximate solution, Inverse problem

56


Design and Implementation of a Secure E-learning

System for the Wireless Networks

Abbas Fadhil Mohammed Ali AL-Juboori

Department of Computer Science College of Science Kerbala University

[email protected]

Abstract

When the World Wide Web was launched in 1991, there was a surge of interest in the possibilities of electronic learning(or e-learning). The use of the Web as an educational medium was hailed as a harbinger of profound changes for communities,organizations and markets. By now, well over a decade later, one might expect that the concept of e-learning would bewell defined and clearly differentiated from other forms of learning. Yet there is still a lack of consensus about what e-learning represents. For all the publicity it has received in recent years, e-learning remains something of an enigma, andits boundaries are far from clear. E-learning intersects numerous. In this new industry, key concepts and understandingsare still emerging. Any study of the effectiveness and efficiency of e-learning therefore has to engage with multiple issues,including the role of e-learning in knowledge and learning, its contribution to competent performance, its relationship toorganizational transformation and strategies for embedding e-learning into other forms of electronic interaction.

E-learning refers to the use of information and communications technology (ICT) to enhance and/or support learningin tertiary education. But this covers a wide range of systems, from students using e-mail and accessing course work on linewhile following a course on campus to programmer offered entirely online. E-learning can be divided into several differenttypes. In all cases, a campus based institution is offering the courses, but using e-learning tied to the Internet or otheronline network to a different extent. Web-supplemented courses focus on classroom-based teaching but include elementssuch as putting a course outline and lecture notes on line, use of e-mail and links to online resources. Web-dependentcourses require students to use the Internet for key elements of the programmed such as online discussions, assessment, oronline project/ collaborative work, but without significant reduction in classroom time.

In this paper ,the proposed system was presented and it divided into two parts . First one is the designer ( Administrator) part who can control on all options of the system in managing and updating all information included in the data base ofthe system .The second is the user part who can navigate in all environments of the system to give the required knowledge.Very important subject was selected to include it in the secure e-learning system which is (wireless networks) because itis very important topic in the computer world . The capabilities of the system are (add , delete, update, search) for database of the system . The security was supported in the system by using the password technique. The system was designedby using Apache server , PHP, HTML, Web Page Maker , and MYSQL for data base .

References[1] Brennan, Funke & Anderson, ”What is e-learning” , article , 1997.

[2] Wikipedia ,” E-learning” , 2007.

[3] Richard w. Riley ,”Policy Brief” , 2005.

[4] Thomas J.Falkowski,Vice ,”The Foundation President of an Effective e-Learning Strategy Performance and Results” ,2004.

[5] Joe Pulichino, ”The e-learning guide (future direction in e-learning)”, Book, 2006.

[6] P. Tripathi and S. Mukerji, ”Networked Learning Environment for Students with Learning Management System (LMS)”, Paper ,INTED Conference, 2008.

[7] J. Chorro Gasco , ”Learning Evaluation with Probabilistic Nets”, University of Valencia , Paper , 2008.

[8] Alexandros Paramythis and Susanne Loidl-Reisinger, ”Adaptive Learning Environments and e-Learning. Standards”, Johannes Ke-pler University, Linz, Austria, 2007.

[9] Graham Attwell (ed.), ”Evaluating E-learning. A Guide to the. Evaluation of E-learning.”, Evaluate Europe Handbook Series Volume2, 2006.

[10] J. Casey, ”Intellectual Property Rights (IPR) in. Networked e-Learning”, A Beginners Guide for Content Developers. 2008.

2000 Mathematics Subject Classification.Key words and phrases. e-leaning, wireless, networks, secure

57


On Some Numerical Methods For The Neutron

Transport Equation In 2-D Plane Geometry

Abdallah Tamrabet Larpi*, Abdelouahab Kadem**

*University of Batna, Algeria

[email protected]

**Mathematics Department University of Setif, Algeria

[email protected]

Abstract

This paper presents an iterative method based on a self adjoint and m.accretive splitting for the numerical treatment

of the steady state neutron transport equation in 2-D plane Geometry. Theoretical results show the convergence of the

method. The convergence of the method is numerically illustrated and compare with the standard source iteration method

on a sample problem.

2000 Mathematics Subject Classification. 65T60, 65N30, 65N22.Key words and phrases.Neutron Transport equation, plane geometry, self adjoint operator, operator splitting, m-accretive operator,iterative methods.

58


A Study of the Supercritical Solution of the Stationary

Negative Forced KdV Equation

Abdelaziz Hamad*, Mukheta Isa**

* [email protected]

** [email protected]

Abstract

In this paper we consider stationary Forced KdV equation with negative Forcing term. The supercritical solitary wave

solutions of the stationary Forced KdV equation are obtained. In order to obtain the solutions the domain of the problem

has been divided in to three parts; the left, the middle and the right parts. The solution on the left and the right parts

are obtained by an analytical method. The solution on the middle part is expressed in the terms of Weierstarss elliptic

function. We have designed computer programs using Mathematica to produce the solutions. The complete solution was

found by matching the solutions of all the three parts. We have found out that there are four different solutions according

to the values of the phase shift. All solutions are positive.

2000 Mathematics Subject Classification.Key words and phrases.Stationary Forced KdV Equation; Supercritical solution.

59


A singular Gierer-Meinhardt system of elliptic

equations in RN

Abdelkrim Moussaoui1, Brahim Khodja2, Saadia Tas3

1 Department of Mathematics, A. Mira Bejaia University, 06000 Bejaia, Algeria

[email protected]

2 Department of Mathematics, Badji Mokhtar Annaba University, 23000 Annaba, Algeria

[email protected]

3 Department of Mathematics, A. Mira Bejaia University, 06000 Bejaia, Algeria

tas [email protected]

Abstract

In this talk, we study the existence and uniqueness of solution of the singular Gierer-Meinhardt system

−∆u + α (x) u = h1 (x) 1vq

−∆v + β (x) v = h2 (x) ur

vs

u (x) , v (x) −→ 0 as |x| −→ ∞

u, v > 0

in RN (N ≥ 3), where α, β, h1, h2 are given, not necessarily continuous functions, s ∈]0, 1[ and q, r > 0 such that r− s ≤ 1.

We establish the existence of the solution using Schauder’s fixed point theorem.

References[1] C. O Alves, J. V. Goncales and L. A. Maia, Singular nonlinear elliptic equations in RN , Abstract and Applied Analysis 03 (1998),

411-423.

[2] Y. S. Choi and P. J. McKenna, A singular Gierer-Meinhardt system of elliptic equations, Ann. Inst. H. Poincare, Anal. NonLineaire 17 (2000), 503-522.

[3] Y. S. Choi and P. J. McKenna, A singular Gierer-Meinhardt system of elliptic equations: the classical case, Nonlinear Anal. 55(2003), 521-541.

[4] M. Del Pino, M. Kowalczyk and X. Chen, The Gierer-Meinhardt system: the breaking of homoclinics and multi-bump ground states,Commun. Contemp. Math. 3 (2001), 419-439.

[5] M. Del Pino, M. Kowalczyk and J. Wei, Multi-bump ground states of the Gierer-Meinhardt system in R2, Ann. Inst. H. Poincare,Anal. Non Lineaire 20 (2003), 53-85.

2000 Mathematics Subject Classification. 35J55, 35J65Key words and phrases. Gierer-Meinhardt, Elliptic system, Singular, Schauder fixed point.

60


Fault Detection in a Complex System: A New

Statistical-based Approach

Abdelmalek Kouadri, Ahmed Chaib, Abdallah Namoune

Applied Control Laboratory, University of Boumerdes-Algeria

a [email protected]

Automatic Department Chimical and oil faculty University

of M’hamed Bouguerra, Algeria

chaib [email protected]

Abstract

Fault detection in stochastic dynamical systems is usually done by the generation of residuals directly reflecting the

magnitude of the faults. This faults’ indicator is used to evaluate deviations created from normal operating conditions and

measurements of the system. This test is almost always very difficult to implement in the multi-faults case. In this paper,

we propose a new detection index based on descriptive statistics. In general, statistical data can be described as a list of

subjects and their associated data. We have chosen the statistical method, namely a measure of statistical variability, which

shows how the data differs. In physical systems, variability may result only from random measurement errors: instrument

measurements are often not perfectly precise. One way is to assume that the quantity being measured is constant and

that the variation between measurements is caused by observational errors. The coefficient of variation (CV) is a good

measurement of the dispersion degree of a given data randomness. It is defined as the ratio of the standard deviation to the

mean. Therefore, to assess the detection in the multi-faults case, it is preferrable to use the CV as a fault detection index.

To estimate the average CV’s for each signal and its confidential intervals (CI), we have carried out a number of numerical

simulation experiments on a Three Tank System DTS-200. The CV and CI are calculated from twenty independent runs,

in the same operating conditions, where a single run consists of 10240 samples for each signal.


61


Model Reduction of a Large Scale System Using PCA

Technique

Abdelmalek Kouadri, Mimoun Zelmat, Abdallah Namoune

Applied Control Laboratory, University of Boumerdes-Algeria

a [email protected]

Laboratory of Applied Automation, University of Boumerds, Algeria

[email protected]

Abstract

Most of the model reduction techniques proposed in the literature are based on the use of multivariate statistical

techniques. The linear Principal Component Analysis (PCA) is one of the most known methods in data analysis. It looks

for one subspace of a smaller dimension than the initial space and projects the studied data into this space with a minimum

loss of information. Therefore, the obtained result is a representation of data with a reduction of dimension. To reduce

calculations, in the case where the correlation matrix is large, the neural network of the PCA has been proposed. In general,

neural network approaches in PCA distinguish themselves through two criteria of optimised training that are equivalent:

variances maximization of data projection and quadratic error minimization of estimated data. Most approaches which use

networks of multi-layer perceptron for obtaining the non-linear PCA model (NLPCA) encounter problems of optimization

often non-linear such as the headache of convergence and initialization of this network type. For this reason, while combining

the main curves and the Radial Basis Function Neural Networks, we propose an approach for the NLPCA with two networks

of three cascading layers. The problem of training presents a linear regression in relation with the output layer weights.

The algorithm which determines the number of nonlinear components to be retained in the NLPCA model is based on the

accumulate variance.


62


Adjoint Of Sublinear Operators

Abdelmoumene Tiaiba

Dept. of Mathematics, M’sila University,

Box: 166 Ichbilia, 28105 M’sila, Algeria

[email protected]

Abstract

Let SB(X, Y ) be the set of the bounded sublinear operators from a Banach space X into a complete Banach lattice Y .

In the present paper, we will introduce the concept of adjoint sublinear operator and we show that is olso sublinear opertor

and if T is pounded then the adjoint is ponded and Some properties as the linear case.We end this work by an application

of this type of operators on Grothendieck theorem .

2000 Mathematics Subject Classification.46B42, 46B40, 47B460, 47B65Key words and phrases.Banach lattice, factorization, Kothe space, q-convex operator, sublinear operator.

63


Generalized Einstein’s tensor for a Weyl manifold and

its applications

Abdulkadir Ozdeger

Kadir Has University, Faculty of Arts and Sciences,

Kadir Has Campus, 34083, Cibali-Istanbul, Turkey

[email protected]

Abstract

A differentiable manifold having a torsion-free connection ∇ and a conformal class C[g] of metrics which is preservedby ∇ is called a Weyl manifold. The condition involved in this definition can be expressed as ∇g = 2(g ⊗ w) for some1-form w [1] .

It is well known that Einstein’s tensor G for a Riemannian manifold defined by Gβα = Rβ

α− 12 δβ

αR, Rβα = gβγRαγ where

Rβα and R respectively the Ricci tensor and the scalar curvature of the manifold , plays an important part in Einstein’s

theory of gravitation as well as in proving some basic theorems in Riemannian geometry [2].In this work , we obtain the generalized Einstein’s tensor for Weyl manifolds by using the second Bianchi identity for

such manifolds obtained in [3] . Then, we deduce the following results :(a) Any 2-dimensional Einstein-Weyl manifold has a vanishing generalized Einstein’s tensor,(b) A Weyl manifold and its Liouville transformation have the same generalized Einstein’s tensor,

(c) If the 1-form w for an Einstein-Weyl manifold is locally a gradient, then the scalar curvature of the manifold is

prolonged covariant constant.

References[1] A.Norden, Affinely connected spaces,Nauka , Moscow, (1976).

[2] J.C.H.Gerretsen, Lectures on tensor calculus and differential geometry, P.Noordhoff N.V., Groningen, (1962).

[3] E.O.Canfes, A.Ozdeger, Some applications of prolonged covariant differentiation in Weyl spaces, J.Geom.60(1997), 7-16 .

2000 Mathematics Subject Classification. 53A30, 53A40Key words and phrases. Weyl manifold, Einstein-Weyl manifold , Einstein’s tensor, generalized Einstein’s tensor, Liouvilletransformation.

64


Tests for Trend: a Simulation Study

Abdullah Almasri

Department of Economics and Statistics Vxjo University,Sweden

[email protected]

Abstract

In this study we use the wavelet analysis to construct a test statistic to test for the existence of a trend in the series.

We also propose a new approach for testing the presence of trend based on the periodogram of the data. Since we are also

interested in the presence of a long-memory process among the data, we study the properties of our test statistics under

different degrees of dependency. We compare the results when using the band periodogram test and the wavelet test with

results obtained by applying the ordinary least squares (OLS) method under the same conditions.


65


A Note on Comparison Between Laplace and Sumudu

Transfoms

Adem Kılıcman, Hassan Eltayeb, Kamel Ariffin Bin Mohd Atan

Department of Mathematics and Institute for Mathematical Research,

Universiti Putra Malaysia, 43400 UPM, Serdang, Selangor, Malaysia

[email protected]

Abstract

In the literature there are several works on the theory and applications of integral transforms by changing the kernelin the integral transform one can have several different transform such as Laplace, Fourier, Mellin, Hankel, to name a few,but very little on the power series transformation such as Sumudu transform, probably because it is little known, and notwidely used yet. Recently, the Sumudu transform was proposed originally by Watugala see [1] and defined by

F (u) =1

u

∫ ∞

0e−( t

u)f(t)dt, (1)

over the set of the functions

A =

f(t) | ∃M, τ1, τ2 > 0, |f(t)| < Me

tτj , if t ∈ (−1)

j × [0,∞)

where f(t) is a function which can be expressed as a convergent infinite series, see [2] and similarly the double Sumudutransform is defined by

F (v, u) = S2 [f(t, x); (v, u)] =1

uv

∫ ∞

0

∫ ∞

0e−( t

v+ x

u)f(t, x) dt dx, (2)

see [1], or [3]. Further this new integral transform generalized and applied by Kılıcman and Eltayeb to the linear second

order partial differential equations with non-constant coefficients as well as to generalized functions, for more details see

[4]. In this paper, we discuss existence of the double Sumudu transform and established some relationship between Laplace

and Sumudu transforms. Further, we apply two transforms to solve the linear ordinary differential equations with non

constant coefficients, in special case, we provide some examples related to the second order differential equations having

non-constant coefficients.

References[1] Watugala, G.K., Sumudu Transform - a new integral transform to solve differential equations and control engineering problem. Int.

J. Math. Educ.Sci. Technol. 1993.

[2] Watugala, G.K., The Sumudu transform for function of two variables, Mathematical Engineering in Industry, 8(4)(2002), 293–302.

[3] Jean M. Tchuenche and Nyimvua S. Mbare. An application of the double Sumudu transform. App. Math. Sci. 1(1)(2007), 31–39.

[4] H. Eltayeb and A. Kılıcman. Note On The Sumudu Transform and Generalized Functions, submitted for publication.

2000 Mathematics Subject Classification.35G15, 44A85,44A35.Key words and phrases. Integral transforms, Sumudu transform, convolution

66


Some Properties in Nonsmooth Analysis of

Perturbation Function in Vector Optimization

Agamali Agamaliyev1, Serkan Ilter2

1Azerbaijan University, Mathematics Department, Baku, Azerbaijan

[email protected]

2Istanbul University, Mathematics Department, Istanbul, Turkey

[email protected]

Abstract

We consider in this paper the following vector optimization problem

max f(x) = (f1(x), ...fk(x)) ,

subjectto gi(x) ≤ yi, i = 1, ..., m, (1)

hj(x) = yj , j = m + 1, ..., p,

where f : Rn → Rk , each gi : Rn → R, each hj : Rn → R , the variables y ∈ Rp are perturbations near y = 0 . For each y ,the set of feasible solutions is

S(y) =

.x ∈ Rn: .gi(x) ≤ yi, hj(x) ≤ yj , i = 1, ..., m, j = m + 1, ..., p.

.

We assume that the objective and constraint functions of the problem (1) are smooth. The solution concepts for (1) thatwe will be concerned with is the notion of an ideal maximal (or strongly efficient) point.

Our main aim in this paper is to investigate some properties in nonsmooth analysis of perturbation function (or marginal

function).

References[1] J.Gauvin, The generalized gradient of a marginal function in mathematical programming, Math. of Operations Res.,4,4,458-463,1979

[2] J.Gauvin and J.W.Tolle, Differential Stability in Nonlinear Programming, SIAM J. Control Optimization, 15,294-311,1977

[3] J.Gauvin, A necessary and sufficient regularity condition to have bounded multipliers in nonconvex, Math. Program. 12(1),136-138,1977

[4] F.H.Clarke, Optimization and nonsmooth analysis, Wiley-Interscience, 2000

[5] F.H.Clarke, Generalized gradients and applications, Trans. of the American Math. Soc., 205, 247-262, 1975

[6] F.H.Clarke, Yu.S.Ledyaev, R.J.Stern, P.R Wolenski, , Nonsmooth Analysis and Control Theory, Springer, 1998

[7] O.L.Mangasarian and S.Fromovitz, The Fritz John necessary optimality conditions in the presence of equality and inequality con-straints, J. Math. Anal. Appl.,17,37-47,1967

[8] G.Giorgi, A.Guerraggio, J.Thierfelder, Mathematics of Optimization: Smooth and Nonsmooth Case, Elsevier, 2004

2000 Mathematics Subject Classification. 78M50Key words and phrases. Vector optimization, Nonsmooth analysis, Perturbation function

67


Prediction In A Trivariate Normal Distribution Via A

Linear Combination Of Order Statistics

Ahad Jamalizadeh*, Mina Habibi**

*Shahid Bahonar University, Department of Statistics, Kerman, Iran

[email protected]

**Shahid Bahonar University, Department of Statistics, Kerman, Iran

[email protected]

Abstract

In this paper, by considering a trivariate normal distribution, we derive the exact joint distribution of one variable and

a linear combination of order statistics from the other two variables. We show that this joint distribution is a mixture

of unified bivariate skew-normal distributions. This mixture for them enables us to predict the variable based on a linear

combination of order statistics from the other two variables. We finally illustrate the usefulness of these results by using a

real-life data.

2000 Mathematics Subject Classification.62H05, 62H10, 62E10, 62E15Key words and phrases.Skew-normal distribution; Unified multivariate skew-normal distribution; Order Statistics

68


Solving Capacitated Vehicle Routing Problem with a

Rank-based Ant Colony System

Ahmad Nejoomi-Markid, Ardeshir Dolati

Department of Mathematics, Shahed University, Tehran, Iran

[email protected]

Department of Mathematics, Shahed University, Tehran, Iran

[email protected]

Abstract

This study considers the application of Ant Colony Optimization (ACO) to the Capacitated Vehicle Routing Problem

(CVRP), in which customers of known demand are supplied by a homogeneous fleet of vehicles from a single depot.

Vehicles are subject to a weight limit, and each customer must be assigned exactly once to a vehicle. We use a combination

of Ant Colony System with Rank based Ant System hybridized with saving heuristic and local search methods to solve

CVRPs. Numerical experiments indicate that the proposed approach is competitive with other ACO algorithms, Simulated

Annealing (SA) and Genetic Algorithm (GA). We also introduce a new best solution with route structure for CVRP instance

G-n262-k25.

References[1] Baker B. M., Ayechew M. A., (2000), A genetic algorithm for the vehicle routing problem, Computers and Operations Research 30,

pp. 787-800.

[2] Bullnheimer B, Hartl RF, Strauss C. An improved Ant System algorithm for the Vehicle Routing Problem. Annals of OperationsResearch 1999; 89:319-328.

[3] Dolati A., Nejoomi-Markid A., A Hybrid Ant Colony Optimization for Capacitated Vehicle Routing Problem, FRONTIERS SCIENCESERIES, 2007, num 49, UNIVERSAL ACADEMY PRESS, (ICOTA7), pages 99-100.

[4] Dolati, A., Nejoomi-Markid, A., (2008). Solving CVRP via Rank Based ACS, 1st International Conference of Iranian OperationsResearch Society, Kish, Iran.

[5] Dorigo M, Stutzle T. Ant Colony Optimization. MIT Press. 2004.

[6] Funke B, Grunert T. Local Search for Vehicle Routing and Scheduling Problems: Review and Conceptual Integration. Journal ofHeuristics 2005; , 11:267-306.

[7] Mazzeo S, Loiseau I. An Ant Colony Algorithm for the Capacitated Vehicle Routing. Electronic Notes in Discrete Mathematics 2004;18:181-186.

[8] Oppen J, Løkketangen A. Arc routing in a node routing environment. Computers and Operations Research 2006; 33:1033-1055.

[9] Osman IH. Metastrategy simulated annealing and tabu search algorithms for the vehicle routing problem. Annals of OperationsResearch 1993; 41:421-451.

[10] Toth P, Vigo D, editors. The vehicle routing problem. Philadelphia: Society for Industrial and Applied Mathematics; 2002.

[11] Wassan NA. A reactive tabu search for the vehicle routing problem. Journal of the Operational Research Society 2006; 57:111-116.

2000 Mathematics Subject Classification. 90C27, 90B06, 68T27, 90C59Key words and phrases. Vehicle Routing Problem, Ant Colony Optimization, Local search, Saving heuristic

69


The Effects Of Web Supported Instruction And Use Of

Instructional Materials On Students’ Mathematics

Anxieties, Attitudes And Achievements

Ahmet Arslan, Ahmet Sukru Ozdemir


Abstract

The purpose of this study is to investigate the effects of web supported instruction and use of instructional materialson primary education students’ mathematics anxieties, attitudes and achievements. In line with this purpose, the effectsof web supported instruction and use of instructional materials on anxiety, attitude and achievement were investigated ingroups matched in terms of mathematics achievement, mathematics anxieties, mathematics attitudes, computer attitudesand gender. Being of an experimental nature, this study was conducted with total of 90 students at the Mehmet Akif ErsoyPrimary School located in the Sultanbeyli town of the Istanbul province. The Mathematics Achievement Test, MathematicsAnxiety Scale, Mathematics Attitude Scale, Computer Attitude Scale and Personal Information Form, are the instrumentsused for data collection. All the instruments were tested for validity and reliability. Following the matching activities carriedout with these instruments, application activities were performed and the Mathematics Achievement Test, MathematicsAnxiety Scale and Mathematics Attitude Scale were re-applied as the post-test, and the hypotheses were tested. Then, forthe purpose of testing the permanency of the applications, the aforementioned tests were re-applied eight weeks later, anddata obtained at three different times were compared with each other.

Two of the total of fifteen hypotheses in the study were rejected and thirteen were adopted as a result of their statistical

investigation. As a result of the hypotheses tests, it was concluded that both web supported instruction and use of

instructional materials have significant and permanent effect on anxiety and achievement. However, it was also seen that

the different teaching environments in the study had no significant effect on student’s mathematics attitudes.

2000 Mathematics Subject Classification. 97C40Key words and phrases. Web Supported Instruction, Use of Instructional Material, Mathematics Anxiety, Mathematics Attitude,Mathematics Achievement

70


The Effect Of Teaching With The Mathematics Activity

Based On Purdue Model On The Achievement Of

Non-Gifted Students

Ahmet Sukru Ozdemir, Esra Altıntas

Marmara University, Department of Mathematics

[email protected]


hoca [email protected]

Abstract

The purpose of this study- by introducing Purdue 3- stage model which is used in training of gifted students- was todesign example activity about ”Informed Consumer Arithmetic” lesson at 7 th grade non -gifted students in our countryand to investigate the effects of this activity to the mathematics achievement of these students.

The universe of the study was formed of the students who studied at 7 th grade in Primary schools in Fatih district ofIstanbul and the sample of the study formed of 22 students who were in 7-B and 7-C classes in a Primary School in Fatihdistrict. In this study, we used pre-final test model with a control group. The study has been made by researcher for 8weeks. The lesson has been made by using the activity based on Purdue model on the experimental group and by usingthe activities related to the lesson in National Education Curriculum on the control group.

After being applied the pre-test to two classes, the data obtained were analyzed by using appropriate tests, there

was seen that there wasn’t a significant difference between the averages of two groups and by random testing groups was

determined as ” control” and ”experimental”. The final test was the same with pre-test. The pre-final tests belong to

experimental and control group were analyzed by using t-test. As a result, which way is the best has been discussed.

2000 Mathematics Subject Classification. 97D40Key words and phrases. Mathematics Education, Purdue 3-stage enrichment model, gifted student, non-gifted student

71


Developing ASAB Cryptology Technique with

Irrational Numbers Perspective

Ahmet Sukru Ozdemir*, Ahmet Bilal Yaprakdal**

* Marmara University, Department of Mathematics

[email protected]

** Marmara University, Computer & Instructional Tech.

[email protected]

Abstract

Cryptography (or cryptology) is the science of information security and also the practice and study of hiding information.The word is derived from the Greek kryptos, meaning hidden. Cryptography’s aim is to construct schemes or protocolsthat can still accomplish certain tasks even in the presence of an adversary.

In modern times cryptography is considered a branch of both mathematics and computer science, and is affiliated closelywith information theory, computer security and engineering. It is based on some specific areas of mathematics, includingnumber theory, linear algebra, and algebraic structures. As a result, it is considered as a main branch of both mathematicsand computer science. It is used in applications present in technologically advanced societies; examples include the securityof ATM cards, computer passwords and electronic commerce which all depend on cryptography.

This study develops ASAB cryptology technique (presented by authors at Proceedings of the Third International

Conference on Modeling, Simulation and Applied Optimization’09) with the last ideas and perspectives. The new developed

technique, which we called ”ASAB-2” (Initial of the names of authors), is based on infinite and periodical continued fractions

with irrational numbers.

2000 Mathematics Subject Classification. 11J70Key words and phrases. Number theory, continued fractions, infinite continued fractions, irrational numbers, cryptology, ASAB-2,ASAB-2 technique

72


The Effects of The Lessons Plans Prepared on The

Multıple Intellıgence Approach to Mathematical

Achivement

Ahmet Sukru Ozdemir, Fatmagul Durmus


[email protected]


[email protected]

Abstract

The acceptance of the multiple intelligence approach to mathematics teaching by today’s mathematics teachers is a

positive step for those who are in search of new approaches towards the teaching of mathematics. In the present study,

the main aim is to investigate the effects of the lessons plans prepared based on the multiple intelligences approach.

The study uses a pretest-posttest design. The pretest scores were used to verify that the levels of knowledge of the two

groups of students are equal prior to the intervention. At the end of the intervention a post test was delivered to both

groups whose content covered all the subjects that were taught during this period. Other data collection instruments are:

multiple intelligences inventory, mathematics achievement tests, personal information inventory and mathematics attitude

inventory. The experimental group received teaching based on the lesson plans based on the multiple intelligence approach

and the control group was taught with the traditional method by their own teachers. Data were analyzed using the SPSS

10.00 computer software. The correlation in between mathematics achievement and attitude towards mathematics was

investigated. Multiple regression results of achievement -attitude were also investigated. The findings indicate that in the

experimental group there is an increase in the achievement levels and there is a significant positive improvement in their

retention levels and attitudes towards mathematics.

2000 Mathematics Subject Classification.97C40Key words and phrases. Multiple intelligences, Mathemathics Education, Lesson Plans

73


An analytical approach to the fractional foam drainage

equation

Ahmet Yıldırım, Huseyin Kocak

Ege University, Department of Mathematics, 35100

Abstract

In this study, we used the variational iteration method and the homotopy perturbation method to give a rational ap-

proximation solutions of the foam drainage equation with time- and space- fractional derivatives. The fractional derivatives

are described in the Caputo sense. Numerical examples are given to demonstrate the effectiveness of the present meth-

ods. Results show that the proposed schemes are very effective and convenient for solving lineaer and nonlinear fractional

differential equations with high accuracy.

2000 Mathematics Subject Classification. 35C10Key words and phrases. Homotopy perturbation method; Variational iteration method; Caputo fractional derivative; Fractionaldifferential equations; Foam drainage equation.

74


2-Edge Connected Subgraph Problem, Complete

Description

Aider Meziane, Aoudia Lamia

USTHB, Dpartement de Recherche Oprationnelle, Alger, Algerie

[email protected]

USTHB, Dpartement de Recherche Oprationnelle, Alger, Algerie

[email protected]

Abstract

Our work focus on node weighted 2-edge connected subgraph problem defined by Baiou [?]. Given a graph G = (V, E),a node r ∈ V and cost (weight) function on nodes and edges, the r-2-edge connected subgraph problem consists on findinga 2-edge connected subgraph in G containing r whose total cost (weight) on both nodes and edges is minimized. We studya class of graphs for which the polytope associated to the r-2-edge connected subgraph problem is completely described bythe trivial inequalities and the inequalities so called generalized cut inequalities. After that, we investigate a class of validinequalities given by Baiou and Correa in the case of cordless multi-cycle graphs.

2000 Mathematics Subject Classification. primary: 54Dxx secondaries: 54D05Key words and phrases. valid inequality, face, facets

75


Fuglede-Putnam Theorem For (p, k)-Quasihyponormal

And Class (Y )Operators

Aissa Nasli Bakir

University Of Chlef, Algeria

[email protected]

Abstract

Let A and B be normal operators on a complex separable Hilbert space H. The equation AX = XB implies A∗X = XB∗

for some operatorX on H ino itself is known as the familiar Fuglede-Putnam theorem. An operator A ∈ B(H) is said to

be log-hyponormal if A is invertible and log(A∗A) ≥ log(AA∗), class (Y ) if there exist α ≥ 1 and kα > 0 such that

|AA∗ − A∗A|α ≤ k2α (A− λ)∗ (A− λ) for all λ ∈ C, dominant if ran(A− λ) ⊆ ran(A− λ)∗ for all λ ∈ σ(A) where σ(A)

denotes the spectrum ofA. A is called (p, k)-quasihyponormal if A∗k((A∗A)p − (AA∗)p)Ak ≥ 0, k ∈ N, 0 < p ≤ 1.

In this talk, we’ll give an extension of Fuglede-Putnam’s result to the case when either 1) A is log-hyponormal operator

and B∗ is a class (Y ) operator 2) A is (p, k)-quasihyponormal operator with ker A ⊆ ker A∗ and B∗ is dominant. Other

results are also given.

References[1] A. Aluthge, On p-hyponormal operators for 0 < p < 1, Int. Eq. Op. Th., 13 (1990), 307-315.

[2] I.H. Kim, On (p, k)-quasihyponormal operators, Math. Ineq. Appl, 7(2004), 629-638.

[3] I.H. Kim, The Fuglede-Putanm theorem for (p, k)-quasihyponormal operators, J. Ineq. Appl,(2006), article ID 47481, page 1-7.

[4] A. Uchiyama and K. Tanahashi, Fuglede-Putanm’s theorem for log-hyponormal or p-hyponormal operators, Galsgow Math. J,44(2004), 397-410.

[5] A. Uchiyama and T. Yoshino, On the class Y operators, Nihonkai Math. J, 8(1997), 179-194.

2000 Mathematics Subject Classification. 47B47, 47A30, 47B20,47B10.Key words and phrases. log-hyponormal operators, class (Y ) operators, Theorem of Fuglede-Putnam.

76


A Certain Subclass Of P-Valently Analytic Functions

Of Bazilevic Type

Ajab Akbarally*, Maslina Darus**

*Department of Mathematics, Faculty of Computer and

Mathematical Sciences, Universiti Teknologi MARA,

40450 Shah Alam, Selangor, Malaysia

[email protected]

**School of Mathematical Sciences, Faculty of Science and

Technology, University Kebangsaan Malaysia, 43600

Bangi, Selangor, Malaysia

[email protected]

Abstract

Using extended Ruscheweyh [2] derivatives we define a new subclass M(n, p, α, β) of p-valently analytic functions whichare of Bazilevic [1] type. A function f which is p-valently analytic is said to be in the subclass M(n, p, α, β) if it satisfies

Re

(pDn+pf(z)

Dn+p−1f(z)

(Dn+p−1f(z)

zp

)α)> β

where z ∈ U, U = z : |z| < 1, α > 0 and 0 ≤ β < p. Dn+pf(z) and Dn+p−1f(z) are extensions of the familiar operator

Dnf(z) of Ruscheweyh Derivatives [2], n ∈ N0 = N ∪0. These operators were considered by Sekine, Owa and Obradovic

[3]. We find some sufficient conditions and angular properties for functions belonging to the subclass M(n, p, α, β).

References[1] I.E. Bazilevic, Uber einen fall der integrierbarkeit in der gleichung von Lowner-Kufarev, Maths. Sb. 37 (1955), 471-476.

[2] S. Ruscheweyh, New criteria for univalent functions. Proc. Amer.Math. Soc. 49 (1975), 109-115.

[3] T. Sekine, S. Owa & M. Obradovic, A certain class of p-valent functions with negative coefficients, Current Topics in AnalyticFunction Theory. Srivastava, H.M. & Owa, S. (Eds.): World Scientific Publishing Co. Pte Ltd. (1992).

2000 Mathematics Subject Classification.primary:30C45 secondaries:30C55Key words and phrases. Analytic functions, Ruscheweyh derivatives, Bazilevic typeThis work is fully supported by the Universiti Teknologi MARA under the research grant 600-RMI/ST/FRGS 5/3/Fst (21/2008)

77


A new form to Newton-Pade approximants

Alexey Lukashov, Cevdet Akal

Department of Mathematics, Fatih University,

34500 Buyukcekmece,Istanbul, Turkey


Abstract

M.B. Balk proved an assertion about uniform convergence of Pade approximants. Newton- Pade (or multipoint Pade)

approximants solve more general interpolation problems than Pade approximants. Usually Newton- Pade approximants

have only nominators in Newton form. We propose to use Newton form for the denominators also. Using that special form

of Newton- Pade approximants Balk’s method was extended to the case of more general rational interpolation functions.

References[1] M.B.Balk, Interpoliatzionnyi protzess Padeh dlia nekotorykh analiticheskikh funktzii, Issledovaniya po sovremennym problemam

teorii funktzii kompleksnogo peremennogo. Markushevich, A.I. (Ed.): Moscow, Fizmatlit (1960), 234-257.

2000 Mathematics Subject Classification. 41A21, 41A05Key words and phrases. Pade approximants, Interpolation.

78


Minimizing Makespan in a Two-Machine Stochastic

Flowshop

Ali Allahverdi*, H. Aydilek**

*Department of Industrial and Management Systems Engineering,

College of Engineering and Petroleum Kuwait University,

P.O. Box 5969, Safat, Kuwait

[email protected]

**Department of Natural Sciences and Mathematics

Gulf University for Science and Technology, P.O. Box 7207, Hawally 32093

[email protected]

Abstract

The two-machine flowshop scheduling problem is usually addressed where processing times are assumed to be determin-

istic for which Johnson’s algorithm can be used to solve the problem. For many scheduling environments, the assumption

of deterministic processing times is not valid. Hence, the random variation in processing times has to be taken into account

while searching for a solution. Some researchers addressed the flowshop problem where job processing times follow certain

probability distributions. For some scheduling environments, it is hard to obtain exact probability distributions for random

processing times, and therefore assuming a specific probability distribution is not realistic. Usually, solutions obtained after

assuming a certain probability distribution are not even close to the optimal solution. It has been observed that, although

the exact probability distribution of job processing times may not be known, upper and lower bounds on job processing

times are easy to obtain in many cases. Hence, this information on the bounds of job processing times should be utilized

in finding a solution for the scheduling problem. In this paper, we address the two-machine flowshop scheduling problem of

minimizing makespan where jobs have random processing times which are bounded between a lower and an upper bound.

The probability distributions of job processing times within intervals are not known. The only known information about

job processing times are the lower and upper bounds. The decision about a solution of the problem has to be made based

on these bounds. Different heuristics using the bounds are proposed, and the proposed heuristics are compared by using

simulation. The simulation results have shown that the proposed heuristics perform well with an overall average error of less

than one and half percent for all heuristics. One of the heuristics performs as the best with an overall average percentage

error of less than one percent.

2000 Mathematics Subject Classification.90B36, 68M20, 60K30Key words and phrases.Scheduling, flowshop, makespan, random processing times, simulation.

79


Minimizing Average Job Completion Time in a

Two-Stage Assembly Flowshop with Setup Times

Ali Allahverdi*, Fawaz S. Al-Anzi**

*Department of Industrial and Management Systems Engineering

Kuwait University, P.O. Box 5969, Safat, Kuwait

[email protected]

**Department of Computer Engineering Kuwait University,


[email protected]

Abstract

The two-stage assembly flowshop problem consist of two stages where there are m machines at the first stage while there

is only a single assembly machine at the second stage. There are n jobs to be scheduled and each job has m +1 operations.

For each job, the first m operations are conducted at the first stage by m machines in parallel and a final operation in the

second stage by the assembly machine. The last operation at the second stage may start only after all m operations at

the first stage are completed. The two-stage assembly scheduling problem has many applications in industry, and hence,

has received an increasing attention of researchers recently. We address the two-stage assembly scheduling problem with

the objective of minimizing average job completion time. This objective is particularly important in real life situations

where reducing inventory or holding cost is of primary concern. Setup times are treated as separate from processing times.

This problem is NP-hard since its special case, when setup times are ignored and m = 1 (which is a regular two-machine

flowshop problem), is NP-hard. Therefore, we present a dominance relation and present three heuristics. The heuristics are

evaluated based on randomly generated data. One of the proposed heuristics is known to be the best heuristic for the case

of zero setup times while another heuristic is know to perform well for such problems. A new version of the latter heuristic

is proposed and shown to perform much better than the other two heuristics.

2000 Mathematics Subject Classification.Key words and phrases.Scheduling, flowshop, average completion time, heuristic, dominance relation.

80


Polytopes of majorization and g-majorization

Ali Armandnejad

Department of Mathematics, Faculty of Sciences,

Vali-E-Asr University of Rafsanjan.

P.O.Box: 7713936417, Rafsanjan, Iran.


Abstract

Let Mn and Mn,m be the vector spaces of all n × n and n ×m matrices respectively with entries in the field of realnumbers. A nonnegative (or not necessarily nonnegative) matrix R ∈ Mm is called row stochastic (or g-row stochastic)if Re = e where e = (1, ..., 1)t ∈ Mn,1 . For matrices A, B ∈ Mn,m , it is said that A is majorized (or g-majorized) byB from right if there exists a row stochastic (or g-row stochastic) matrix R ∈ Mm such that A = BR. The polytopes ofmajorization and g-majorization for given matrices A, B ∈ Mn,m denoted by P (A ≺ B) and P (A ≺g B) respectively anddefined as the following convex sets:

P (A ≺ B) := R : R is a row stochastic matrix and A = BR,

P (A ≺g B) := R : and R is a g-row stochastic matrix and A = BR.

In this paper, we investigate some properties of polytopes of majorization and g-majorization for some special types of

matrices A, B ∈ Mn,m . Also we will find the dimension of the linear vector spaces generated by P (A ≺ B) or P (A ≺g B)

.

References[1] G. Dahl, Mjorization Polytopes, Linear Algebra and its Applications. 297 (1999) 157-175.

[2] A. Armandnejad and H. Heydari, Polytopes of g-majorization. Preprint.

2000 Mathematics Subject Classification. 15A03, 15A48Key words and phrases.polytopes , majorization , g-majorization, stochastic matrices.

81


Generalization of Clark’s derivation and subdifferential

Ali Farajzadeh

Islamic Azad University-Kermanshah Branch, Iran

[email protected]

Abstract

In this talk, we first introduce some new concepts of nonsmooth analysis for locally convex topological vector spaces

and then by using these definition we obtain some results. Moreover we generalizes Lebourg’s mean value theorem to locally

convex spaces.

References1. F. H. Clarke, Yu. S. Ledyaev, R. J. Stern, P. R. Wolenski, Nonsmooth analysis and control theory, Springer-Verlag, 1998.

2. W. Rudin, Functional Analysis, MacGraw-Hill book company, United States of America, 1973.

2000 Mathematics Subject Classification.49J40, 90C33.Key words and phrases. Locally Lipschitz mapping; Clarke subdifferential; Lebourg’s mean value theorem.

82


Triangle matrix and infinite linear systems of

differential equations

Ali Fares1, Bruno de Malafosse2

1 LMAH-Universite du Havre

[email protected]

2 LMAH-Universite du Havre I.U.T Le Havre BP 4006

76610 Le Havre. France.

[email protected]

Abstract

In this work we deal with the solvability of infinite systems of differential equations of the form X′ (t) = TX (t) + B

where T is one of the well known triangles ∆ (λ), C (λ), or the weighted mean matrix Nq and B is a given infinite column

matrix t(b1, b2, ...., bn, ...). We use Matlab to represent our solutions.

2000 Mathematics Subject Classification.Key words and phrases. Infinite linear systems of differential equations, systems of linear equations, Laplace operator.

83


An Operational Method for Solving Non-linear Volterra

Integro-Differential Equations

Ali Khani*, Sedaghat Shahmorad**

*Faculty of science, Department of Mathematics,

Azarbaijan University of Tarbiat Moallem, Tabriz, Iran

[email protected]

**Department of Applied Mathematics, University of Tabriz,

Tabriz, Iran

[email protected]

Abstract

In this paper we will develop a new method to find a numerical solution for the general form of the Non Linear Volterra

Integro-Differential Equations (NVE). To this end, we will present our method based on the matrix form of the (NVE). The

corresponding unknown coefficients of our method have been determined by using the computational aspects of matrices.

Finally the accuracy of the method has been verified by presenting some numerical computation.

References[1] M.K. EL-Daou, H.G. Khajah, Iterated solutions of linear operator equations with the Tau method, Math. Comput. 66 (217) (1997),

207-213.

[2] D. Gottlieb, S.A. Orszag, Numerical analysis of spectral methods, theory and applications (1977).

[3] S.M. Hosseini, S. Shahmorad, Numerical solution of a class of integro-differential equations by The Tau method with an errorestimation, Appl. Math. Comput 136 (2003), 559-570.

[4] S.M. Hosseini, S. Shahmorad, Tau numerical solution of Fredholm integro- differential equations with arbitrary polynomial bases,Appl. Math. Modelling 27 (2003), 145-154.

[5] S.M. Hosseini, S. Shahmorad, A matrix formulation of the Tau for Fredholm and Volterra linear integro-differential equations, TheKorean J. Comput. Appl. Math. Vol. 9, NO.2 (2002), 497-507.

[6] C. Lanczos, Trigonometric interpolation of empirical and analytical functions, J. Math. Phys. 17 (1938), 123 - 199.

[7] K.M Liu, E.L. Ortiz, Eigenvalue problems for singularly perturbed differential equations, in J.J.H. Miller (Ed.), Proceeding of theBAIL II conference, Boole press, Dublin, (1982) 324-329.

[8] K.M. Liu, E.L. Ortiz, Approximation of eigenvalues defined by ordinary differential equations with the Tau method, in B. Ka gestrm,A. Ruhe (Eds). Matrix pencils, Springer, Berlin, (1983) 90-102.

[9] K.M. Liu, E.L. Ortiz, Tau method approximation of differential eigenvalue problems where the spectral parameter enters nonlinearly,J. Comput. Phys. 72 (1987), 299-310.

[10] K.M. Liu, E.L. Ortiz, Numerical solution of ordinary and partial function-differential eigenvalue problems with the Tau method,Computing (wien) 41 (1989), 205-217.

[11] K.M. Liu, E.L. Ortiz, Numerical solution of eigenvalue problems for partial differential equations with the Tau-lines method, Comp.Math. Appl. B 12 (5/6) (1986) 1153-1168.

[12] K.M. Liu, E.L. Ortiz, K.S. Pun, Numerical solution of steklov’s partial differential equation eigenvalue problem, in J.J.H. Miller(Ed.), Computational and asymptotic methods for boundary and interior layers III, Boole Press, Dublin, (1984) 244-249.

[13] E.L. Ortiz, H. Samara, An operational approach to the Tau method for the numerical solution of non-linear differential equations,Computing 27 (1981), 15-25.

[14] E.L. Ortiz, H. Samara, Numerical solution of differential eigenvalue problems with an operational approach to the Tau method,Computing 31 (1983), 95-103.

2000 Mathematics Subject Classification. 65R20Key words and phrases.Volterra Integro-Differential Equations, Matrix Forms, Numerical Solutions

84


[15] E.L. Ortiz, K.S. Pun, Numerical solution of nonlinear partial differential equations with Tau method, J. Comp. Appl. Math. 12/13(1985), 511-516.

[16] E.L. Ortiz, K.S. Pun, A bi-dimensional Tau-elements method for the numerical solution of nonlinear partial differential equationswith an application to Burgers’equation, Comp. Math. Appl. B 12 (5/6) (1986), 1225-1240.

[17] E.L. Ortiz, H. Samara, Numerical solution of partial differential equations with variable coefficients with an operational approach

to the Tau method, Comp. Math. Appl. 10 (1) (1984), 5-13.

85


The existence of the optimal control of systems with

quadratic quantity criterium.

Ali Mahmud Ateiwi*, Iryna Volodymyrivna Komashynsk**

*Department of Mathematics and Statistics, Faculty of Science,

Al-Hussein Bin Talal University P.O. Box (20), Ma’an-Jordan

[email protected]

**Department of Mathematics and Statistics, Faculty of Science,

Al-Hussein Bin Talal UniversityP.O. Box (20), Ma’an-Jordan

iryna [email protected]

Abstract

Consider optimal control problem in Rn with quadratic in control quality criterium:

dx

dt= f(x, t)B(t)u (1)

x(s) = y

I(s, y, u) = ϕ(τ, x(τ)) +

∫ τ

s

[Ψ(t, x(t)) + (N(t)u(t), u(t))] dt → inf (2)

Here t ∈ [0, T ], x ∈ Rn, Q0 = (0, T )× Rn, Q is bounded sub domain of Q0 with the boundary ∂Q. We assume that :

1) The functions ϕ(t, x) and Ψ(t, x) are nonnegative, smoth in their arguments in Q, morover, ∂Ψ∂x is Lipshitz in x in Q

(Q is the closure of Q)

2) f(t, x) is smooth in Q and ∂f∂x is Lipshitz in x in Q.

3) n×m is dimensional matrix B(t) is smooth in t in Q.

4) m×m is dimensional matrix N(t) is positive definite in Q. and smooth in t

The bellman’s equation of the problem (1) , (2) is

∂V

∂t+

(f(t, x),

∂V

∂t

)+ Ψ(t, x)− 1

4

(B(t)N

−1(t)B ∗ (t)

∂V

∂t,

∂V

∂t

)= 0

With the boundary condition. THEOREM 1. If the hyper surface ∂Q is correctly embedded into Rn+1, and the conditions

(1)-(4) hold , then the boundary value problem (7), (8) has the unique solution in Q, which is continuous together with it’s

partial derivative up to the second order.

2000 Mathematics Subject Classification.Key words and phrases.optimal control, quadratic quantity criterium.

86


Differentiation in a new viewpoint

Ali Parsian

Department of Mathematics, University of Tafresh,

Paradise of Amirkabir university of Technology, Tafresh, Iran.

[email protected]

Abstract

In the theory of functions the domain of the differentiable functions needs to be locally connected and the derivative ofa single variable function with variable x,for a particular value of x is a number given by the

limh→0f(x + h)− f(x)

h

Provided that this limit exists. This definition requires the values of the function f for all of the elements of its domain which

are sufficiently near the point x.Here we introduce a new generalized form of the derivative definition in which the values of

at most countably many points of the domain of the function near the x, i.e., the elements of a sequence which approaches

to x,is needed, the situation which is hold with connivance in the region of all of sciences. Moreover this definition is done in

such a way that all of the theorems of this theory are valid yet. First we generalized the concept of continuity of functions

and show the validity of all of the theorems of this section of calculus and then use of them for extending the basic theory.

References[1] K. Knopp,infinite sequences and series ,English translation by, F.Bagemihl,Dover publication,inc.(1928)148-150.

[2] J.W.Milnor, Topology from the differentiable viewpoint, The University Press of Virginia. Charlottes-vile.(1972)23-25.

[3] W.Rudin,principles of Mathematical analysis ,3d ed.,McGraw-Hill Book Company,New York.(1976)103-113.

[4] S.C.Saxena, S.M.Shah,Introduction to Real variable theory, prentice Hall on India, New Delhi.(1980)130-159.

[5] M.Spivak,Calculus on manifolds,W.A. Benjamin,Inc,New York.(1956)71-73.

[6] S.Strenberg , Lectures on Differential Geometry, Prentice Hall,Inc,New, York.(1964)45-47.

[7] A.Zygmund,Trigonometric series vol.1,2, Cambridge University Press,London.(1959)10-14.

2000 Mathematics Subject Classification. 35E15,58C05,26A06,28A10.Key words and phrases. Intermediate value Theorem, Sard,s Theorem, Taylor,s theorem, measure.**This research was supported by Scientific Research Project Commission of the University of Tafresh,Paradise of Amirkabiruniversity of Technology of Iran.

87


On common Periodic Points Conjecture, History and

Some Related Questions

Aliasghar Alikhani-Koopaei

Department of Mathematics, Pennsylvania State University,

Reading, PA 19610-6009


Abstract

From 1954 to 1969 there was a rather well known conjecture, namely the common fixed point conjecture, that if fand g are continuous functions from the closed unit interval to itself which commute, meaning f(g(x)) = g(f(x)), thenthey have a common fixed point. In [2] and [3], W.M. Boyce and J.P. Huneke answered this question independently by theconstruction of a pair of commuting continuous functions which have no fixed point in common. This conjecture led us tointroduce the common periodic point conjecture (see [1]) which reads as:

Conjecture. If f and g are continuous functions from [0, 1] to itself which commute (i.e. f(g(x)) = g(f(x))),then they must have a common periodic point.

In fact we conjectured that typically commuting continuous self-maps of closed intervals do not share a periodic point.

In this talk we give the history of this conjecture as well as some related results and some open questions.

References[1] A. A. Alikhani-Koopaei, On common fixed and periodic points of commuting functions, International Journal of Mathematics and

Mathematical Sciences, Vol. 21 No. 2 (1998) 269-276.

[2] W. M. Boyce, Commuting functions with no common fixed point, Trans. Amer. Math. Soc. 137(1969),77-92.

[3] J. P. Huneke, On common fixed points of commuting functions on an interval, Trans. Amer. Math. Soc. 139 (1969),371-381.

2000 Mathematics Subject Classification.primary:26A16 secondaries:47H10Key words and phrases.Fixed points, Periodic points, Typical property, Self-maps.

88


Optimization of the EDM process with multiple

performance characteristics based on the orthogonal

array and grey relational analysis method

Alireza Abdi1, Mehdi Eskandarzade2, Ali Naser3

1 Faculty of Engineering, Urmia University, Urmia, West Azerbaijan Province, Iran

2 Faculty of Engineering, Urmia University of Technology, Urmia,

West Azerbaijan Province, Iran

3 Faculty of Engineering, Urmia University, Urmia,

West Azerbaijan Province, Iran

Abstract

This paper describes application of the grey relational analysis with Taguchi methods to optimize the electrical dis-

charge machining process with multiple performance characteristics. An orthogonal array, grey relational generating, grey

relational coefficient, grey relational grade and grey relational graph analysis of variance are applied to study the perfor-

mance characteristics of the machining process. In this paper, levels of machining parameters including pulse on time,

discharge current, discharge voltage, and duty factor are optimized with respect to multiple performance characteristics

including material removal rate, electrode wear ratio, and surface roughness. Experimental results show that this approach

can help to optimize the electrical discharge machining process with multiple process responses.

2000 Mathematics Subject Classification. 78M50Key words and phrases. Electric discharge machining, Taguchi method, Grey relational analysis, Multiple response, Optimization

89


Group Theory on Some Chemical Nanostructures

Alireza Gilani*, Ali Moghani**

*Department of Mathematics, Islamic Azad University,

South Tehran branch, Iran

a [email protected]

**Departmen of Color Physics, Institute for Colorants

Paints and Coating, Iran

[email protected]

Abstract

Shinsaku Fujita, to enumerate isomers of molecules introduced some definitions like maturity and the Q-conjugacy

character table of a finite group. In this paper at first, we provide a new simple method to specify how a given finite group

with big symmetry and complicated structure is maturated or unmaturated, then, to verify our derived theorem some useful

nanostructures are considered.

References[1] A. Moghani, J. Serb. Chem. Soc. 73, 189 (2008).

[2] M. R. Darafsheh and A. Moghani, Bull. Chem Soc Jpn. 81 (8), 979 (2008).

[3] A. Moghani, S. Naghdi, A. R. Ashrafi and A. Ahmadi, London Math. Soc. 340, 630 (2007).

[4] GAP, Groups, Algorithms and Programming, http://www.gap -system.org, Lehrstuhl De fur Mathematik, RWTH, Aachen, 1995.

[5] M. Yavari and A. R. Ashrafi, Int. J. Mol. Sci. 8, 1 (2007).

[6] K. Balasubramanian, Chem. Phys. Letters 398, 15 (2004).

[7] M. R. Darafsheh, A. Moghani and S. Naghdi Sedeh, Acta Chim. Slov.55, 602 (2008).

2000 Mathematics Subject Classification.Key words and phrases.Automorphism, Conjugacy Class, Permutation, Character.

90


Well-Posedness of Basset Difference Equations

Allaberen Ashyralyev

Department of Mathematics, Fatih University

34500 Buyukcekmece, Istanbul,Turkey [email protected]

Abstract

The stable difference scheme for the approximate solution of the initial value problem

du(t)

dt+ D

12t u(t) + Au(t) = f(t), 0 < t < 1, u(0) = 0 (1)

for the fractional differential equation in a Banach space E with the strongly positive operator A is presented. The

well-posedness of the difference scheme in difference analoques of spaces of smooth functions is established. In practice,

the coercive stability estimates for the solution of difference schemes for the fractional parabolic equation with nonlocal

boundary conditions in space variable and the multidimensional fractional parabolic equation with Dirichlet condition in

space variables and the 2m-th order multidimensional fractional parabolic equation are obtained.

References[1] I. Podlubny, Fractional Differential Equations, Academic Press, New York, (1999).

[2] A. Ashyralyev, A note on fractional derivatives and fractional powers of operators, Journal of Mathematical Analysis and Applications357 (2009)232-236.

2000 Mathematics Subject Classification. 65N12, 65M12Key words and phrases. fractional parabolic equation, Basset problems, well-posedness, coercive stability, difference scheme

91


A Note On Fractional Schr¨odinger Differential And

Difference Equations

Allaberen Ashyralyev, Betul Topcu


34500 Buyukcekmece, Istanbul, Turkey


Abstract

The initial value problem for the fractional differential equation

i dudt + Au +

t∫0

α (s) D1/2s u (s) ds = f (t) , 0 < t < 1,

u (0) = 0

(1)

in a Hilbert space H with a self adjoint positive definite operator A is considered. The stability estimates for the solution

of this problem and its first derivative under the condition |α (s)| <M1

s1/2are established. In practice, the mixed problems

for one dimensional fractional Schrodinger differential equation with nonlocal boundary conditions in space variable and

multidimensional fractional Schrodinger differential equation with Dirichlet condition in space variables are considered. The

stability estimates for the solution and first order of derivative of the solution of these problems are obtained. The first

order of accuracy difference scheme for the approximate solution of this initial value problem is presented. The stability

estimate for the solution of this difference scheme and its first order of difference derivative are established. The application

of this abstract result to the mixed problems considered above is presented. The stability estimates for the solution and

first order of difference derivative of the solution of these difference schemes for these problems are obtained.

References[1] A. Ashyralyev, A note on fractional derivatives and fractional powers of operators, Journal of Mathematical Analysis and Applications

357 (2009) 232-236.

[2] A. Ashyralyev and A. Sirma, ”Nonlocal boundary value problems for the Schrodinger equation”, Computers and Mathematics with

Applications 55 (3) (2008) 392-407.

2000 Mathematics Subject Classification. 65J10, 65M06, 26A33Key words and phrases. fractional Schrodinger equation, difference scheme, stability.

92


On The Numerical Solution Of Parabolic Stochastic

Differential Equation

Allaberen Ashyralyev*, Mehmet Emin San**

*Department of Mathematics, Fatih University, 34500, Istanbul, Turkey


**Department of Mathematics, Fatih University, 34500, Istanbul, Turkey


Abstract

We are interested in studying the stable difference schemes for the approximate solutions of the nonlocal boundaryvalue problem for parabolic stochastic differential equation

du(t) + Au(t)dt = f(t)dωt (0 ≤ t ≤ T ), u(0) = u(T ) + ϕωT

in a Hilbert space H with self-adjoint positive definite operator A. Here, Wt is a standard Wiener process given on theprobability space (Ω; F ; P ).

In the present paper the first and second orders of accuracy difference schemes for approximately solving this non-

local boundary value problem are presented. The convergence estimates for the solution of these difference schemes are

established. A numerical method is proposed for solving the stochastic parabolic partial differential equation with nonlocal

boundary condition. The first and second order of accuracy difference schemes are presented. A procedure of modified

Gauss elimination method is used for solving these difference schemes in the case of a one-dimensional stochastic parabolic

partial differential equation. The method is illustrated by numerical examples.

References[1] A. Ashyralyev and I. Hasgur, Linear stochastic differential equations in a Hilbert space, Abs. of Statistic Conference-95, Ankara, Turkey, 1995, 6p.

[2] A. Ashyralyev and G. Michaletsky, The approximation of solutions of stochastic differential equations in Hilbert space by the difference schemes, Trudynauchno-prakticheskoy konferencii ” Differencialniye uravneniya i ih prilozheniya” , Ashgabat, 1, 85-95, 1993.

[3] A. Ashyralyev and P.E. Sobolevskii, New Difference schemes for Partial Differential Equations, Birkhuser Verlag, Basel, Boston, Berlin,Operator Theoryand Appl., 148, 2004.

[4] E. Hausenblas, Numerical analysis of semilinear stochastic evolution equations in Banach spaces, Journal of Computational and Applied Mathematics,147, 2, 485-516, 2002.

[5] G. Da Prato, Regularity properties of a stochastic convolution integral, Analisi Matematica, 217-219, 1982.

[6] G. Da Prato and J. Zabczyk, Stochastic equations in in.nite dimensions, Encyclopedia of Mathematics and its Applications, vol.44, Cambridge UniversityPress, Cambridge, 1992.

[7] T. Shardlow, Numerical methods for stochastic parabolic PDEs, Numer. Funct. Anal. Optim., 20, 121-145, 1999.

2000 Mathematics Subject Classification.Key words and phrases.Stochastic parabolic equation, Dierence scheme, Convergence.

93


On the parabolic inverse problem with an unknown

source function

Allaberen Ashyralyev, Oznur Demirdag, Abdullah S. Erdogan



[email protected]



[email protected]



[email protected]

Abstract

Let Ω be the unit open cube in the n−dimensional Euclidean space Rn(0 < xk < 1, 1 ≤ k ≤ n) with boundary

S, Ω = Ω ∪ S. In [0, 1]× Ω we consider the mixed boundary value problem for the multidimensional parabolic equation

∂v(t, x)∂t−n∑

r=1∂∂xr (αr(x)∂v(t, x)∂xr) = f(t, x) + p(x),

x = (x1, . . . , xn) ∈ Ω, 0 < t < 1,

v(0, x) = ϕ(x), v(1, x) = ψ(x), x ∈ Ω,

v(t, x) = 0, x ∈ S,

(1)

where αr(x) (x ∈ Ω), ϕ(x), ψ(x) (x ∈ Ω) and f(t, x) (t ∈ (0, 1), x ∈ Ω) are given smooth functions and αr(x) ≥ a > 0. The

first and second orders of accuracy stable difference schemes for the approximate solution of (1) are presented. Stability,

almost coercive stability and coercive stability estimates are obtained. Numerical techniques are developed and algorithms

are tested on an example.

References[1] Y.S. Eidelman, The boundary value problem for differential equations with a parameter, Differentsial’nye Uravneniya 14 (1978)

1335-1337.(English transl. Differential Equations 14 (1978))

[2] Y.S. Eidelman, Two-point boundary value problem for differential equations with a parameter, Dopovidi Akademii Nauk UkrainskoiRSR Seriya A-Fiziko-Matematichni ta Technichni Nauki no.4 (1983) 15-18.(Russian)

[3] A. I. Prilepko, Inverse problems of potential theory, Mat. Zametki 14 (1973) 755-767. (English transl Math. Notes 14 (1973))

[4] A. I. Prilepko, A. B. Kostin, On certain inverse problems for parabolic equations with final and integral observation, Mat. Sb 183no. 4 (1992) 49-68. (English transl Russian Acad. Sci. Sb. Math 75 (1993))

[5] A. I. Prilepko, I. V. Tikhonov, Uniqueness of the solution of an inverse problem for an evolution equation and applications to thetransfer equation, Mat. Zametki 51 no. 2 (1992) 77-87. (English transl Math. Notes 51 (1992))

2000 Mathematics Subject Classification.34K29, 35K35, 65N12Key words and phrases.inverse problems, parabolic equations, stability

94


Wave Approach in Dynamical Discrete-Continuous

Systems

Amalia Pielorz

Faculty of Management and Computer Modelling,

Chair of Mathematics, Kielce, Poland

[email protected]

Abstract

The paper deals with the dynamics of discrete-continuous systems consisting of elastic elements connected by means

of rigid bodies. They belong to a certain class of discrete-continuous systems, namely to those where the motion of elastic

elements with a constant cross-section is described by means of the classical wave equation, [1-3]. The discussed systems

can be longitudinally or torsionally deformed. In the discussion a wave method using the solution of the d’Alembert type

is applied, what leads to solving equations with a retarded argument.

After a short description of the approach applied, detailed considerations are done for two nonlinear discrete-continuous

systems. The first one consists of three noncoaxial rods longitudinally deformed, two rigid bodies and a local nonlinearity

having characteristics of a hard type as well as of a soft type. In systems with a hard type characteristic amplitudes jumps

are observed while in systems with a soft type characteristic solutions amplitudes can diverge to infinity. The second one is

a multi-mass system torsionally deformed with rigid bodies having variable mass moments of inertia. Local nonlinearities

and variable inertia in such systems are justified by engineering solutions in many machines and mechanisms. Moreover,

it is shown that in linear cases analytical solutions can be derived in the form of series consisting of exponential functions

and polynomials.

References[1] Pielorz A., Skora M., Modeling of multimass systems torsionally deformed with variable inertia, Differential Equations and Nonlinear

Mechanics, Vol. 2006, ID 20758, 1-11

[2] Pielorz A., Nonlinear equations with a retarded argument in discrete-continuous systems, Mathematical Problems in Engineering,Volume 2007, ID 28430, 1-11

[3] Pielorz A., Skora M., Analytical approach in torsional multi-mass discrete-continuous systems with variable inertia, Meccanica, 44,2009, 121-131

2000 Mathematics Subject Classification. 34C20, 34C25, 93C10Key words and phrases. dynamical systems, waves, discrete-continuous models, nonlinear oscillations

95


Introduction to a method for solving a kind of Integrals

Amin Daneshmand Malayeri

Hamedan University Of Technology,

Faculty Of Computer Engineering, Islamic Republic Of Iran

[email protected]

Abstract

Some kinds of integrals have a special way for solving. These are mostly applicated integrals . we can find some

discovered methods for these integrals.But when you do not have an unique way for solving an integral, finding an answer

for this kind is usually with hardnesses.in this paper we present a new method for solving a kind of applicated integrals by

introducing a table which its name is ”table of coefficients”.this table let us find answer of a specific kind of integrals.this

method can decrease errors in our usual calculates in finding an answer of integrals.

2000 Mathematics Subject Classification.Key words and phrases.Polynomial integrals,specific table, table of coefficients,sequence of coefficients.

96


Simulation in Math and Its Effects On Education



Faculty Of Computer Engineering, Islamic Republic Of Iran

[email protected]

Abstract

Different ways of problem solving let us experiment them and choose the best way for the best education. Our researches

show that simulating and making partners for problems can provide better solutions than the other ways for students.

Presenting new models of simulating and new partners will encourage students for better thinking and finding the best path

for receiving the answer. At this paper,the Results of this experiment has been presented.

2000 Mathematics Subject Classification.Key words and phrases.Simulation, partnership education, Simulated models, answer recycling.

97


Introduction to a Sequence in Natural Numbers With

Logical Properties



Faculty Of Computer Engineering, Iran

[email protected]

Abstract

Today, mathematical science in computer is a very basical course in math.the base of the computer science is on Logical

operating. All of the functions which has been defind for Digital computing are depending on logical mathematics. At

this paper we Introduce a new sequence with logical properties.By this sequence,we can define new functions with logical

elements.some properties are useful for designing new models of circuits with interesting and unique applications.The best

property of this sequence is easy learning for interested students in basic computer science.this sequence can produce logical

unique codes for each state.

2000 Mathematics Subject Classification.Key words and phrases.binary sequence,binary coding,logical pyramid,code of sequence.

98


A new non-linear optimization of parameters in

Michaelis-Menten kinetics

Amir Heydari

Chemical Engineering Department,

University of Mohaghegh Ardabili, Ardabil, Iran

[email protected]

Abstract

A new non-linear optimization of parameters in Michaelis-Menten equation has been developed. This method is based

on special mathematical form of Michaelis-Menten equation and finding best fitting line of R versus S/ (S +Km). By trying

to tend the intercept to zero, the proper Km will be obtained. At the founded Km, the slope is equal to Vm. In this method

a non-linear, two-parameter optimization is changed into finding a root of non-linear equation. Generated data set is used

to introduce this new method. Data set from literature is used to illustrate accuracy of this technique in comparison with

linearization methods. Results show that accuracy of the mentioned method is better than Lineweaver-Burk, Eddie and

Hanes methods.

2000 Mathematics Subject Classification.B09-119Key words and phrases.Michaelis-Menten, Enzyme kinetics, Non-linear optimization, Least squares line.

99


The search method based on soft computing for linear

cryptanalysis of block ciphers

Amir Tabatabaei

Sadra Institute of Higher Educations, Tehran, Iran

[email protected]

Abstract

Optimization, combinatorial and in general modeling methods are the concepts in applied mathematics which if con-

sidered alone and purely they can not be used in solving real problems. The better establishing a relation with other fields

the more applications can be gained. In this article two kinds of optimization methods which have a lot of applications in

cryptography will be proposed: The first one is dealing with the advantages of using high performance Genetic Algorithm

in comparison to some analytic methods in cryptanalysis of block ciphers and the second one is a model represented by

a weighted graph which must be optimized by some soft computing methods because of its high complexity. At the end

of this article some other useful applications of these ideas along with a practical done example on a block cipher will be

represented.


100


A Survey on Search Methods Based on Soft Computing

for Cryptanalysis of Block Ciphers

Amir Tabatabaei

Sadra Institute of Higher Educations, Tehran, Iran

[email protected]

Abstract

In this paper, a survey on the applications of soft computing in cryptanalysis of block ciphers along with some case

studies is presented. The nature of cryptanalysis problems is involved with huge search domain which is a key point in

providing the security of primitives. Regarding to this property, tracing analytic solutions will frustrate the attacker due

to complexity theory. We propose two kinds of optimization models which have a lot of applications in cryptography: The

first one is dealing with a high performance Genetic Algorithm in comparison to some analytic methods in cryptanalysis

of block ciphers and the second one is a model represented by a weighted graph which must be optimized by some soft

computing methods because of its high complexity. We will show the results gained by suggested methods in finding the

differential and linear characteristics of a well-known block cipher. The cost of time, memory, and data complexity of the

proposed method in comparison to analytic methods validates the priority of them.

2000 Mathematics Subject Classification. 90C30, 68W40.Key words and phrases. Block cipher; Linear attack; Differential attack; Neural Networks; Cryptanalysis; Genetic Algorithm.

101


2-orthogonal polynomials and linear “2–generalized”

birth and death processes

Ammar Boukhemis 1, Ebtissem Zerouki 2

1 Dept. Math., Fac. Sci., University of Annaba,

B.P. 12, Annaba 23000 (Algeria).

[email protected]

2 Dept. Math., Fac. Sci., University of Annaba,

B.P. 12, Annaba 23000 (Algeria).

[email protected]

Abstract

We show that the linear ”2-generalized” birth and death processes (i.e. the processes defined from two death rates and

one birth rate) could be generated by the 2-orthogonal polynomials sets. In particular, we give a characterization of these

processes when their related 2-orthogonal polynomials are Sheffer-Meixner type. Also, we show that in one particular case,

it is possible to give an integral representation of the measures of orthogonality. In the general case, we give the integral

equations satisfied by the measures of orthogonality.

References[1] W. A. Al-Salam, On a characterization of Meixner’s polynomials, the quart, J. Math. (Oxf)(2) 17 (1966), 7-10.

[2] R. P. Jr. Boas, The Stieltjes moment problem for functions of bounded variation, Bull. Amer. Math. Soc., 45 (1939), 399-404.

[3] A. Boukhemis, On the classical 2-orthogonal polynomials sequences of Sheffer-Mexner type, Cubo A Mathematical Journal, vol 7(2), (2005), 39-55.

[4] A. Boukhemis and P. Maroni, Une caracterisation des polynomes strictement 1/p orthogonaux de type Sheffer. Etude du cas p = 2,J. Approx. Theory 54 (1988), 67-91.

[5] S. Karlin and J. McGregor, The differential equation of birth and death processes and the Stieltjes moment problem, Trans. Amer.Math. Soc. 86 (1957), 489-546.

[6] P. Maroni, L’orthogonatite et les recurrences des polynomes d’ordre superieur a deux, Ann. Fac. Sci. Toulouse 10, (1989),no 1105-139.

[7] E. Zerouki et A. Boukhemis, On the 2-orthogonal polynomials and the generalized birth and death processes, IJMMS, vol 2006,(2006) Article ID 28131, pages 1-12.

[8] E. Zerouki, Sur les polynomes 2-orthogonaux et les processus de naissance et de mort generalises, These d’Etat, Univ. Badji Mokhtar,

Annaba, Algerie, (2007).

2000 Mathematics Subject Classification. 33C47, 60G20 and 60H10Key words and phrases. Orthogonal Polynomials, Birth and Death Processes, Transition Probabilities, Sheffer-Meixner Polyno-mials.

102


A New Approach To Numerical Algorithms

Ana Paula Lopes, Antonio Jose Pascoal

Institute of Accounting and Administration of Oporto ISCAP

Polytechnic Institute of Oporto IPP

[email protected]

Universidade Portucalense - Oporto - Portugal

[email protected]

Abstract

The problem of computing eigenvalues, eigenvectors and invariant subspaces is always present in areas as diverse as

Engineering, Physics, Computer Science and Mathematics. Considering the importance of these problems in many practical

applications, it is not surprising that has been and continues to be the subject of intense research. We developed a new

Lanczos algorithm on the Grassmann manifold. This work comes in the wake of the article by A. Edelman, T. A. Arias and

S. T. Smith, The geometry of algorithms with orthogonality constraints, where they presented a new conjugate gradient

algorithm on the Grassmann and Stiefel manifolds. These manifolds which are based on orthogonality constraints, yields

penetrating insight into many numerical algorithms of linear algebra. They have developed an approach to numerical

algorithms involving orthogonality constraints. As the Lanczos method and the method of conjugate gradients are closely

related, and one of the main problems of the Lanczos method is the loss of orthogonality, arose the idea of checking whether

it would be possible to get a Lanczos algorithm on the Grassmann manifold.

References[1] P.-A Absil, R. Sepulchre, P. Van Dooren and R. Mahony, (2004), Cubically convergent iterations for invariant subspace computation,

SIAM J. Matrix Analysis, vol 26, 1, 70-96.

[2] A. Edelman, T. A. Arias and S. T. Smith, (1998), The geometry of algorithms with orthogonality constraints, SIAM J. Matrix Anal.Appl. 20, n 2, 303-353.

[3] A.P. Lopes, O metodo de Lanczos na Variedade de Grassmann, PhD theses, Universidade Portucalense, 2006.

[4] B. N. Parlett, (1998), The symmetric eigenvalue problem, Prentice Hall series in Computational Mathematics.

2000 Mathematics Subject Classification. 15A, 65F, 15A18, 15A75, 65F10, 65F15, 65F25Key words and phrases. Lanczos Method, Grassmann Manifold, Stiefel Manifold, Invariant Subspaces, Eigenvalues and Eigen-vectors.

103


Using Moodle As A Tool For Learning And Developing

Math Skills

Ana Paula Lopes, Lurdes Babo, Jose Azevedo, Cristina Torres

Institute of Accounting and Administration of Oporto

ISCAP olytechnic Institute of Oporto - IPP - Oporto - Portugal

[email protected]


ISCAP Polytechnic Institute of Oporto - IPP Oporto - Portugal

[email protected]



[email protected]



[email protected]

Abstract

MatActiva is a Mathematics project based on the platform Moodle, which is being developed in the Institute of

Accounting and Administration of Porto - ISCAP. The main objective of this project is to motivate students, encourage

them to overcome theirs difficulties through an auto-study, giving them more confidence and making students keen on

Mathematics. The adequacy of the courses to the Bologna process has created new challenges, such as the management of

hours per class, and also the methods and types of activities proposed. MatActiva provides a variety of materials, which

include theoretical notes, multiple choice tests that can be done online and automatically provide quantitative results and

the feedback for each question when the student misses, forum of doubts moderated by the teachers that are responsible

for the project, challenges, etc. As ISCAP receives many students through the ERASMUS program, the MatActiva also

includes a range of materials in English. This project wishes to be a real advantage in teaching/learning of mathematics at

higher education level.

2000 Mathematics Subject Classification. 97-XX; 97U70; 97D40; 97B40Key words and phrases. Mathematics Education; Educational material and media; Educational technology; Moodle.

104


Comparison of speeds of convergence in some families of

summability methods for functions

Anna Sheletski

Tallinn University Narva Road 25, 10120 Tallinn, Estonia

[email protected]

Abstract

Speeds of convergence in certain family of summability methods for functions are compared in the talk. The resultsintroduced here extend the results proved in [1] for ”matrix case” to ”integral case” and are partly published in [2].1. Let us denote by X the set of all functions x = x(u) defined for u ≥ 0, bounded and measurable by Lebesgue onevery finite interval [0, u0]. Suppose that A is a transformation of functions x = x(u) (or, in particular, of sequencesx = (xn)) into functions Ax = y = y(u) ∈ X. If the limit limu→∞ y(u) = s exists then we say that x = x(u) isconvergent to s with respect to the summability method A, and write x(u) → s(A).One of the basic notions in our talk is the notion of speed of convergence. Let λ = λ(u) be a positive function from Xsuch that λ(u) → ∞ as u → ∞. We say that a function x = x(u) is convergent to s with speed λ if the finite limitlimu→∞ λ(u) [x(u) − s] exists. We say that x is convergent with speed λ with respect to the summability method A ifthe function Ax = y = y(u) ∈ X is convergent with speed λ.2. We discuss a Riesz-type family Aα of summability methods Aα where α > α0 and α0 is some fixed number andwhich transform functions x = x(u) into functions Aαx = yα(u). This family is defined with the help of relation Aβ =Cγ,β Aγ (β > γ > α0), where Cγ,β is certain integral transformation (see e.g. [2]). For example, the Riesz methods(R, α) and certain generalized Norlund methods (N, pα(u), q(u)) form Riesz-type families.It is important to be able to compare the speed of convergence of x = x(u) with respect to different methods in familyAα For a given speed λ = λ(u) and a fixed number γ > α0 the speeds λβ = λβ(u) and λδ = λδ(u) can be found (see[2]) such that for all β > δ > γ the next implications are true:

λ(u) [yγ(u)− s] → t =⇒ λβ(u) [yβ(u)− s] → t,

λ(u) [yγ(u)− s] = O(1), λβ(u) [yβ(u)− s] → t =⇒ λδ(u) [yδ(u)− s] → t.

References[1] U. Stadtmuller, A. Tali. Comparison of certain summability methods by speeds of convergence, Analysis Mathematica, 29 (2003),

227–242.

[2] A. Seletski, A. Tali. Comparison of speeds of convergence in Riesz-type families of summability methods, Proc. Estonian Acad. Sci.,

57 (2008), 70–34.

2000 Mathematics Subject Classification.40C10, 40C15, 40G05, 40G10.Key words and phrases.summability methods for functions, speed of convergence, Riesz methods, generalized integral Norlundmethods, Borel-type methods.

105


On families of generalized Norlund matrices as bounded

operators on lp

Anne Tali

Tallinn University Narva Road 25, 10120 Tallinn, Estonia

[email protected]

Abstract

Let lp (p ≥ 1) be the Banach space of all complex sequences x = (xn) (n ∈ N0), and let B(lp) be the Banach algebra ofall bounded linear operators on lp. Any operator from B(lp) can be represented in form of a matrix A = (ank) (n, k ∈ N0)but, of course, not any matrix is in B(lp). The question how to characterize the matrices in B(lp) (by means of conditionsthat are not difficult to apply) has been discussed in a number of papers. Different types of conditions (mostly sufficient)for A to be in B(lp) in general and, in particular, for Norlund, Riesz and Hausdorff matrices has been proved, also theestimates for norms ‖A‖p has been found (see e.g. [1] for references).

We consider certain generalized Norlund matrices A = (ank) = (N, pn, qn), defined with the help of two non-negativesequences (pn) and (qn) (such that p0, q0 > 0 and rn =

∑nk=0 pn−kqk 6= 0 for any n ∈ N0) as follows:

ank =

pn−k qkrn

if 0 ≤ k ≤ n,

0 if k > n .

In this paper we find some sufficient conditions for generalized Norlund matrices A = (N, pn, qn) to be in B(lp), andcalculate the evaluates for norms ‖A‖p. These sufficient conditions base on paper [1] and on construction of matrices. Asa result, we come to certain families of generalized Norlund matrices

Aα = (N, pαn, qn)

where α is a continuous or discrete parameter (see e.g. [2]).

References[1] D. Borwein. Simple conditions for matrices to be bounded operators on lp, Canad. Math. Bull. 41 (1998), 10–14.

[2] U. Stadtmuller, A. Tali. Comparison of certain summability methods by speeds of convergence, Analysis Mathematica 29 (2003),227–242.

2000 Mathematics Subject Classification. 47B37, 47A30, 40G05Key words and phrases. Banach space lp, bounded linear operators, generalized Norlund matrices, Norlund, Riesz, Cesaro andEuler-Knopp matrices.

106


Some Notes On Improvement Of Convergence By

Regular Matrices

Ants Aasma

Department of Economics, Tallinn University of Technology,

Kopli 101, 11712 Tallinn, Estonia

[email protected]

Abstract

We consider some aspects of convergence acceleration by regular matrices M = (mnk) with real or complex entries.Classically a matrix M is called accelerating the convergence if the relation

∣∣∑k mnkxk − limn

∑k mnkxk

∣∣|xn − limn xn|

→ 0 for n →∞

holds for every convergent sequence x = (xn) . Besides the classical concept of comparing and estimating the speeds of

convergence of sequences and series we use weakened criterion, called improvement of convergence ([1]). As an application

regular matrices are used for increasing the order of approximation of Fourier expansions and Zygmund means of Fourier

expansions in certain Banach spaces.

References[1] Aasma, A. On the acceleration of convergence by regular matrix methods. Proc. Estonian Acad. Sci., 2008, 57, 3-17.

2000 Mathematics Subject Classification. 40A05, 40C05, 40G99, 41A25, 42C15Key words and phrases. convergence acceleration, matrix methods, Fourier expansions, order of approximation

107


The Almost Everywhere Convergence Of The

Fourier-Laplace Series

Anvarjon Ahmedov

Department of Process and Food Engineering, Faculty of Engineering

Institute for Mathematical Research, Universiti Putra Malaysia

[email protected]

Abstract

In this paper we study the almost everywhere convergence of the spectral expansions related to the self-adjoint extension

of the Laplace-Beltrami operator on the unit sphere. The sufficient conditions for summability of the Fourier-Laplace series

is obtained. We have established the positive results on the almost everywhere convergence of Fourier-Laplace series by

Riesz means of critical order N−12 . The more general properties and representation in terms of eigenfunction expansion of

the Laplace-Beltrami operator is used. We have constructed different method for investigating the convergence problems

of Fourier-Laplace series, which based on the theory of spectral decompositions property of self-adjoint Laplace-Beltrami

operator on unit sphere.

References[1] Alimov Sh.A., Ashurov R.R., Pulatov A.K., Multiple Fourier Series and Fourier IntegralsCommutative Harmonic Analysis -IV,

Springer-Verlag, 1992, 1-97.

[2] Anvarjon, Ahmedov, The principle of general localization on unit sphere, Journal of Mathematical Analysis and ApplicationsVolume 356, Issue 1, 1 August 2009, Pages 310-321

[3] Akhmedov, A.A., About the almost everywhere convergence of the spectral expansions of functions from Lα1 (SN ), Uzbek Mathe-

matical Journal, N. 4, 1997, pp. 17-25. arXiv:0806.4761v1 [math.FA]

[4] Akhmedov, A.A., About summability of Fourier-Laplace series , Uzbek Mathematical Journal, N. 4, 1996, pp. 20-27.arXiv:0808.0352v1 [math.FA]

[5] A.A. Ahmedov. Conditions of localization averages of Riesz on spectral decomposition of the operator Laplace - Beltrami onsphere of distributions, International Science Journal, Science. Education. Engineering., Osh, Kyrgyzstan - N.3, 2006, pp. 36-40.

[6] A.A. Ahmedov. About convergence spectral expansions of functions from Liuovill class, Natural and Technical science, Russia,Moscow, 2006, N.5 (25), pp.12-17.

[7] Ashurov, R.R., Summability almost everywhere of fourier series in Lp with respect to eigenfunctions (1983) Mathematical Notesof the Academy of Sciences of the USSR 34 (6), pp. 913-916

[8] Bastis, A.I., Almost-everywhere convergence of expansions in eigenfunctions of the Laplace operator on the sphere MathematicalNotes of the Academy of Sciences of the USSR 33 (6), pp. 440-443

[9] Bonami, A., Clerc, J.L.,Sommes de Cesa‘ro et multiplicateurs des de‘velopments en harmonique sphe’rique, Trans. Amer. Math.Soc. 183 (1973) 223-263.

[10] Carleson L., On convergence and growth of partial sums of Fourier series, Acta. Math., 116 (1966), 135-157; MR, 33, 7774

[11] Dai, F., Wang, K.Y. Summability of Fourier-Laplace Series with the Method of Lacunary Arithmetical Means at Lebesgue Points,Acta Mathematica Sinica, English Series 17 (3), 2001, pp. 489-496

[12] Huang, R., Wang, K.Y. A covering lemma on the unit sphere and application to the Fourier-Laplace convergence Acta Mathe-matica Sinica, English Series 23 (7),2007, pp. 1327-1332

[13] Hermander L, On the Riesz means of spectral functions and eigenfunction expansions for elliptic differential operators, Recentadvances in the Basic Sciences, (Proc. Annual Sci. Conf. Belfer Grad. School Sci. 2, (Yeshiva Univ. New York), 1965-1966, 155-202; MR, 41, 2239

[14] Lasuriya, R.A.. Summation of Fourier-Laplace series in the space L(Sm ) ,Ukrainian Mathematical Journal 57 (4),2005, pp. 600-609

[15] Li, L., Yu, C. Convergence rate of Cesa?ro means of Fourier-Laplace series,Journal of Mathematical Analysis and Applications325 (2), 2007, pp. 808-818

[16] Lin, C.-C., Wang, K.. Convergence rate of Fourier-Laplace series of L2-functions ,Journal of Approximation Theory 128 (2),2004,pp. 103-114

[17] Luoqing Li, Chunwu Yu, Convergence rate of Cesro means of FourierLaplace series Journal of Mathematical Analysis and Appli-cations, Volume 325, Issue 2, 15 January 2007, 808-818

[18] Ping, T. On linear summation methods of Fourier-Laplace series. II ,Analysis Mathematica 24 (2), 1998, pp. 151-162

2000 Mathematics Subject Classification. 35P10, 42B05Key words and phrases. Fourier-Laplace series, Operator Laplace-Beltrami, Almost everywhere convergence**This research has been supported by Institute for Mathematical Research Universiti Putra Malaysia under Science Fund GrantScheme (SF), Project number is 06-01-04-SF0256.

108


[19] Rakhimov, A.A., On the summability of multiple trigonometric fourier series of distributions Doklady Mathematics 62 (2), 2000,pp. 163-165

[20] Rakhimov, A.A., Summability of the spectral expansions of distributions, connected with the elliptic partial differential operators,Thesis of Doctor Science Degree,2004, Tashkent.

[21] Sjolin P, Convergence almost everywhere of certain singular integrals and multiple Fourier series, Ark. Mat., 9 (1971), 65-90;MR, 40, 998

[22] Stein E. M., Localization and summability of multiple Fourier series, Acta Math., 100 (1958), 93-147; MR, 21, 433

[23] Stein E. M., and Weiss G., Introduction to Fourier analysis on Euclidean spaces, Princeton Math. Series No. 32, (University Press,Princeton, N.J.), 1971; MR, 46 (1974), 4102;

[24] Zhizhiashvili, L.V., Topuriya, S.B. Fourier-Laplace series on a sphere ,Journal of Soviet Mathematics 12 (6),1979, pp. 682-714

109


A New Approach to Quantile Regression

Arash Ardalan1, H. A. Mardani-Fard2

1 Shiraz University, Department of statistics, Shiraz, Iran

[email protected]

2 Shiraz University, Department of statistics, Shiraz, Iran

h [email protected]

Abstract

In this paper, we present a new approach to the quantile regression context that combine classical quantile regression

approach given by Koenker and Bassett (1978) which estimates quantiles by specialized linear programming techniques,

with expectile regression given by Efron (1991) and Newey and Powell (1987) which is very much related to the classical

quantile regression. We try to compare these three methods. It is known that the quantiles also coincide with the maximum

likelihood solution of the location parameter in a class of asymmetric distribution. In this regard, we present a new class

of asymmetric distributions and investigate the properties and asymptotic behavior of maximum likelihood estimators of

the parameters.

References[1] B. Efron, Regression percentiles using asymmetric squared error loss. Statist.Sinica, 1(1) 93, (1991).

[2] R. Koenker, and G. Jr. Bassett, Regression quantiles. Econometrica, 46(1) 33, (1978).

[3] W. K. Newey, and J. L. Powell, Asymmetric least squares estimation andtesting. Econometrica, 55(4) 819, (1987).

2000 Mathematics Subject Classification. 62H12, 62H10, 62G20Key words and phrases. Asymmetric Laplace distribution; Asymmetric normal distribution; Quantile regression; Maximumlikelihood estimation, Asymptotic normality

110


Exponential family and special entropy relation

Arman Beitollahi

Islamic Azad University-Roudehen branch,

Department of statistics, Tehran, Iran

email:arman [email protected]

Abstract

In this article ,we derive Taneja’s entropy formula for exponential family so that the derived formula by Menendez(2000) is a special case of it. We will obtain proper Taneja’s entropy formulas for Gamma, Beta and Normal distributions.

At last we will review the asymptotic distribution of(

HT (θ)−HT (θ))

in regular exponential models. Let x, βx, Pθ, θ ∈ Θ

be a statistical space where Θ is an open subset of Rm. We consider that there exist p.d.f. fθ(x) for the distribution Pθ

with respect to a σ-finite measure µ. In 1975 Taneja introduced the generalized entropy as follows:

HT (θ) = −2r−1

∫

x

frθ (x) log fθ(x)dµ(x)

which by taking r = 1, Shannon’s entropy is obtained. Salicru et al. [2] defined (h, ϕ)-entropy associated to fθ(x) asfollows:

Hhϕ(fθ(x)) = h

(∫

x

ϕ(fθ(x))dµ(x)

)

where eitherϕ : [0,∞) → R is concave and h : R → R is an increasing and concave or ϕ is convex and h is a decreasingand concave. Furthermore we assume that h and ϕ are in C3 (functions with continuous third derivatives) . If we

putϕ(x) = xr log x andh(x) = −2r−1x then the Taneja’s entropy formula is obtained. The exponential family of k-parameter distribution is:

fθ(x) = exp

k∑

j=1

Tj(x)θj − b(θ)− R(x)

(1)

Theorem: Let fθ(x) be a density of the form [1] with R(x) = 0, then:

HT (θ) = −2r−1

[exp−rb(θ) + b(rθ)]

k∑

j=1

θj

(∂b(rθ)

∂θj

)− b(θ)

Pasha et. al [1] obtained the formula of divergnce measure by use of Taneja’s entropy in exponential family.

References[1] E. Pasha, A. Beitollahi and M. Khodabin, Divergence measure and testing statistical hypothesis, Pakistan Journal of Statistics.

23(3) (2004) 205-220.

[2] M. Salicru, M. L. Menendez, D. Morales and L. Pardo, Asymptotic distribution of (h, ϕ)-entropies, Commun. In Stat.(Theory and

Methods). 27(7) (1993) 2015-2031.

2000 Mathematics Subject Classification.Key words and phrases.Taneja’s entropy, Regular exponential family , Asymptotic distribution.

111


The arithmetic foundations of mathematics:

constructing new mathematics with negative numbers

beyond infinity

Armen G. Bagdasaryan

Institution of the Russian Academy of Sciences,

V. A. Trapeznikov Institute for Control Sciences,

65 Profsoyuznaya, 117997, Moscow, Russia

[email protected]

Abstract

The basic and fundamental concept underlying the foundations of mathematics is the notion of natural number. Negativenumbers had been introduced to extend natural numbers to the set of all integers. Some properties of negative numbershad long been remaining unclear, in particular, the order relation between positive and negative numbers. There existed atleast two approaches: (1) negative numbers are less than ”nothing” (zero), −1 < 0 (Descartes, Girard, Stifel), (2) negativenumbers are ”greater” than infinity, −1 > ∞ (Wallis, Euler, and probably Pascal) [1].

We present theoretical statements of a new mathematical conception underlying the construction of a new theory [2]based on: (1) a new method for ordering the integers (first introduced, but in other form, in [3]): let a, b ∈ Z, then

a ≺ b ⇔ −1a < −1

b , thus getting Z = [0, 1, 2, ...,−2,−1]; the set Z can be geometrically represented as cyclically closed; (2)

a new class of real regular functions f(·) and the definition of∑b

a f(·) that extends the classical definition to the case b < a:

let Za,b = [a, b] if a ¹ b and Za,b = Z\(b, a) if a Â b, Z\(b, a) = [a,−1]∪[0, b], then ∀a, b ∈ Z,∑b

k=a f(k) =∑

k∈Za,bf(k);

(3) a set of conditions imposed on regular functions. From these we define a new regular method for infinite series summationand find a unified approach to summation of divergent series, and to determination of limits of unbounded and oscillatingfunctions.

In this new setting we recently elementarily evaluate the zeta function and the zeta alternating function at integer

points [4-5]. We discover various surprising phenomena and unexpected results concerning some areas of mathematics,

obtained within the framework of this new theoretical background, which is being futher developed. We also discuss some

aspects of future research which will be based on the theory to be formulated as a paradigm.

References[1] D. J. Struik, Abriss der Geschichte der Mathematik. Berlin, 1963; S. Gunther, H. Wieleitner, Geschichte der Mathematik. Berlin,

1939.

[2] R. R. Varshamov, A. G. Bagdasaryan, On one number-theoretic conception: towards a new theory, arXiv:0907.1090 [math.NT]

[3] R. R. Varshamov, Some issues of projective arithmetic, Doklady Akad. Nauk 331 (1993) 263-268.

[4] A.G. Bagdasaryan, An elementary and real approach to values of the Riemann zeta function, Physics of Atomic Nuclei (to appear),arXiv:0812.1878 [math.NT].

[5] A.G. Bagdasaryan, Elementary evaluation of the Riemann zeta function, in preparation

2000 Mathematics Subject Classification. 26A03, 40C15secondaries: 40A05, 11B05, 11M06, 11B68, 54A05, 54F05, 26A09, 00A05Key words and phrases. integers ordering, limits of functions, summation of series

112


Some Results on an Advanced Impulsive Differential

Equation with Piecewise Constant Argument

Arzu Ogun1, Gizem Seyhan2, Huseyin Bereketoglu3

1,2,3 Ankara University, Department of Mathematics, Ankara, Turkey


[email protected]

Abstract

In this paper, we consider the following first order advanced impulsive differential equation with piecewise constantargument

x′(t) + a(t)x(t) + b(t)x([t + 1]) = 0 t 6= n (1)

∆x(n) = dnx(n) n ∈ N = 0, 1, 2, ..., (2)

and the initial conditionx(0) = x0 (3)

where a, b : [0,∞) → R are continuous functions, dn : N → R , ∆x(n) = x(n+) − x(n−), x(n+) = limt→n+ x(n),

x(n−) = limt→n− x(n), and [.] denotes the greatest integer function. Throughout this paper it is assumed that the solution

x(t) is right continuous at [t], t ∈ [0,∞). We established the exact solution of (1)-(3) on the interval [0,∞) and we study

the existence of oscillatory and periodic solutions of the same equation.

References[1] A. R. Aftabizadeh, J. Wiener, J. Ming Xu, Oscillatory and periodic solutions of delay differential equations with piecewise constant

argument, Proc. Of American Math. Soc. 99 (1987) 673-679.

[2] H. Bereketoglu, M. Pituk, Asymptotic constancy for nonhomogeneous linear differential equations with unbounded delays, Discreteand Continuous Dynamical Systems, Supp. Vol. (2003) 100-107.

[3] K.L. Cooke, J.Wiener, Retarded differential equations with piecewise constant delays, J. Math. Anal. Appl. 99 (1984) 265-297.

[4] F. Karakoc, H. Bereketoglu, Some results for linear impulsive delay differential equations, Dynamics of Cont. Discrete and ImpulsiveSystems Series A: Mathematical Analysis 16, (2009) 313-326.

2000 Mathematics Subject Classification. 34K11, 34K13, 34K45Key words and phrases. Impulsive differential equation, Differential equation with piecewise constant argument, Oscillatorysolution, Periodicity.

113


Some Forms Of The Banach-Steinhaus Theorem In The

Locally Convex Cones

Asghar Ranjbari

Faculty of Mathematical sciences, University of Tabriz, Tabriz, Iran

[email protected]

Abstract

A cone is a set P endowed with an addition and a scalar multiplication for non-negative real numbers. The addition is

associative and commutative, and there is a neutral element 0 ∈ P. For the scalar multiplication the usual associative

and distributive properties hold. We have 1a = a and 0a = 0 for all a ∈ P. A preordered cone is a cone with a reflexive

transitive relation ≤ which is compatible with the algebraic operations. A subset V of the preordered cone P is called an

(abstract) 0-neighborhood system, if V is a subcone without zero directed towards 0. We call (P, V) a full locally convex

cone, and each subcone of P, not necessarily containing V, is called a locally convex cone. We require the elements of a

locally convex cone to be bounded below, i.e. for every a ∈ P and v ∈ V we have 0 ≤ a + ρv for some ρ > 0. We verify

some forms of the Banach-Steinhaus Theorem in the locally convex cones.

2000 Mathematics Subject Classification. 46A03.Key words and phrases. locally convex cone, Banach-Steinhaus Theorem.

114


N-dimensional Moment invariants Based Aprroach for

the analysis of Mammography Images using GRID

Azir Aliu*, Margita Konpoposka**

*South East European University- Tetovo Ilindenska bb -Tetovo, Macedonia

[email protected]

**Institut of Informatics, Faculty of Science and Mathematics,

Ss Cyril and Methodius University, Skopje, Macedonia

[email protected]

Abstract

Mathematical morphology is a well-known image and signal processing technique. Mammography is among the most

popular imaging techniques used in the diagnosis of breast cancer. The use of computer to assist clinicians in Digital

mammography image screening has advantages over traditional methods. Computer Algorithms can enhance the appearance

of the images and highlight suspicious areas. This paper describes the concept of digital mammography, its principles,

moment invariants and a novel combination method for computer aided detection (CAD) that identifies structures of

interest from medical images. Also descibes expected advantages using Grid capability for mammogram image processing.

Grids computing promises to resolve many of the difficulties in facilitating medical image analysis to allow clinicians

to collaborate without having to colocate. In this technique, some digital image processing methods such as contrast,

enhancement and segmentation are used for beter processing the image in the next stage and for feature extraction stage of

patter recognition approach. This proposed recognition method includes four stages. In first stage, a preprocessing system

is realized for analyzing and sorting the images. In second stage localization of Region of Interest (ROI). In third stage,

extraction mechanism and obtaining unique features from the same group of patterns. In forth stage, an adaptive system

is used for recognition process. Fast method for computing moment function, for gray-level images are also constructed.

References[1] Tamas Hauer, Richard McClatchey, Mohammed Odeh, Tony Solomonides, Requirements for Large-Scale Distributed Medical Image

Analysis

[2] www.imageprocessingbook.com - Gonzalez, Woods: Digital Image

[3] Azir Aliu, Margita Konpoposka, Grid Infrastructure in Macedonia and Tools for Grid-based Medical Platform, 3rd EGEE Forum

[4] P. K. Saha, J. K. Udupa, E. F. Conant, D. P. Chakraborty, and D. Sullivan. Breast tissue density quantification via digitized

mammograms. IEEE Transactions On Medical Imaging, 20(792-803):575-580, august 2001.

2000 Mathematics Subject Classification.Key words and phrases.Digital mammography, moment, GRID, Computer-Aided Detection, Algorithm

115


Analysis of a System of Multi-term Fractional

Differential Equations with Polynomial Coefficients

Azizollah Babakhani

Department of Basic Science, Babol University of Thecnology , Bobol-Iran.

[email protected]

Abstract

In this paper we present analysis of the system of fractional differential equations:

D

αn −n−1∑

j=1

pj(t)Dαn−j

[x(t)− x(0)] = Ax(t), x(0) = x0,

where 0 < αj < 1, Dαj is the standard Riemann-Liouville fractional derivative and pj(t) =∑Nj

k=0 ajktk , j = 1, 2, · · · , n−1.Further we discuss the initial value problem for nonlinear system:

D

αn −n−1∑

j=1

pj(t)Dαn−j

[x(t)− x(0)] = f(t, x(t)), x(0) = x0,

where f : W (⊂ R × Rm) −→ Rm. It is shown that for f bounded, continuous and Lipschitz in the second variable,there exists unique solutions. The dependence of solutions on initial conditions has also been discussed. Riemann-Liouvillefractional derivative/integral are defined below.Let f ∈ C[a, b], the expression

Iαa+f(x) =

1

Γ(α)

∫ x

a

(x− t)α−1

f(t) dt, x > a,

is called as left-sided fractional integral of order α and the left-sided Riemann-Liouville fractional derivatives of order α isdefind,

Dαa+f(x) =

dn

dxn

I

n−α

a+ f(x)

, n− 1 ≤ α < n, n ∈ N.

References[1] I. Poudlubny, Fractional differential equations, Academic Press (1999).

[2] A. Babakhani and V. Daftardar-Gejji, Analysis of system of fractional differential equation, J. Math. Anal. Appl, 293 (2004) 511 -522.

[3] A. Babakhani and V. Daftardar-Gejji, Existence of positive solutions for multi-term non-autonomous fractional differential equations

with polynomial coefficients, Electronic Journal of Differential Equations, 129 (2006) 1-12.

2000 Mathematics Subject Classification. 34GXXKey words and phrases. Fractional derivative/Integral, Sup norm, Gamma function, Voltra integral equation.**This research was supported by Babol University of Technology, Babol, IRAN.

116


New Dynamic Hysteresis Model by Means of Soft

Computing Approach

B. Boudjema1, M. Mordjaoui1, M. Bouabaz2 and R. Daira1

1 LRPCSI Laboratory, University of Skikda,

BP:26 Skikda, 21000. Algeria,

Boudjema [email protected], Mordjaoui [email protected]

2 ILMGHU Laboratory, University of Skikda,

BP 26, Skikda, 21000. Algeria

[email protected]

Abstract

The study and calculation of magnetic field in electrical machines required dynamic hysteresis model. On the basis

of fuzzy clustering and Neuro-fuzzy identification capability of any kind of nonlinear, continuous functions represented by

its discrete set of measured data, a new modeling technique for dynamic magnetic hysteresis is presented and compared

with measured data. Four technique are study and compared, the first one is based on neuro-fuzzy technique by using

an adaptive neuro-fuzzy system identification and the others are based in Gustafson-Kessel, Gath- Geva and EM fuzzy

clustering algorithm. Very accurate prediction of dynamic hysteresis loops is observed, proving that the clustering and

Neuro-fuzzy techniques are suitable for hysteresis modeling.

2000 Mathematics Subject Classification. 81T80Key words and phrases. Anfis, Gustafson-Kessel algorithm, Magnetic hysteresis, Fuzzy clustering, Model identification.

117


Asymptotically Central Net in Semigroup Algebras and

Inner Invariant Extensions of Dirac Measures

B. Mohammadzadeh

Department of Basic Science,

Babol University of Thecnology , Bobol-Iran.

[email protected]

Abstract

Let S be a locally compact semigroup with identity e and Ma(S) be the semigroup algebra of all complex Radon

measures on S with continuous translations. In this paper, we study the existence of quasi-central and asymptotically

central nets in Ma(S) of a locally compact semigroup S. We also, study inner invariant extensions of Dirac measures at e.

2000 Mathematics Subject Classification. 43A07, 43A10, 43A20, 46H05.Key words and phrases. Asymptotically central net, inner amenability, inner invariant mean, locally compact semigroup, quasi-central net.

118


A Comparative Study On The Response Of Prismatic

And Non-Prismatic Timoshenko Beams To Accelerating

Loads

B. Omolofe

Department of Mathematical Sciences, Federal University of Technology,

Akure Ondo State, Nigeria.

babatope [email protected]

Abstract

The Dynamic response of Timoshenko beams of uniform and non-uniform cross-sections resting on elastic foundation

whose rigidity is of a linear function and subjected to fast traveling concentrated loads of constant and varying magnitude

is scrutinized using an elegant analytical approach. In particular, the spectral generalized Galerkin’s method in conjunction

with Integral transform method is used to treat the problem of the coupled system of partial differential equations describing

the transverse motion of the vibrating system. The specific aim is to compare the dynamic stability of Timoshenko beams

of uniform and non-uniform cross-sections when under the actions of moving concentrated loads of constant and varying

magnitudes. The closed-form solutions for both beam problems are obtained. Analytical and numerical Results show

that as the foundation parameter K0 increases the response amplitudes for both beam decrease. Results also show that

foundation parameter K0 produces a more noticeable effect on the deflection of a non-uniform beam than on a uniform

beam when subjected to variable magnitude loads. It is equally established that, for higher values of foundation modulus,

the risk of resonance is sufficiently reduced for both uniform and non-uniform Timoshenko beams resting on variable elastic

foundation and under the actions of concentrated moving loads of any magnitude.

2000 Mathematics Subject Classification.74H45, 74K10Key words and phrases.Dynamic response, Dynamic Stability, Foundation parameter, Transverse motion, Timoshenko beam,Concentrated loads, Galerkin’s method, Resonance.

119


A Criterion Of Optimization Of A Modified Green’s

Function In Two Dimensional Elastic Waves

B. Sahli, L. Bencheikh

Dept.of mathematics University of Ferhat Abbas Setif, Algeria

[email protected]

Abstract

In the work [*] an optimal choice of the multipoles coefficients is determined in a circular case of border. These complexfactors involved in the modification of the Green’s function, who plays the role of the kernel of the modified integraloperator’s in elasticity.

In this note, it is intended to identify relatively simple expressions of this coefficients for the particular case of circularborder. And then to find an estimate of the norm of the modified integral operator’s in elasticity.

For this, we consider a domain D of circular border ∂D ( ∂D is a cercle for radius ′a′ ), using the orthogonality

proprieties between some vectors F σ%m σ,%=1:2

m=0:∞ who are involved in the definition of the modified Green’s function G1(p, q),and the expressions of optimal choice for the coefficients of multipoles for a general domain’s obtained in [*], and taking into

account the fact that the scalar product of vectors F σ%m σ,%=1:2

m=0:∞ in this case, is a calculation of integral in circle of radius’a’. We obtain a relatively simples expressions for optimal choice of the coefficients of multipoles, and thereafter, and byreplacing the values of this coefficients in the expression of the modified integral operator’s K1, and using a developementof the modified Green’s function G1(p, q), given by [*]:

G1(p, q) = 12

[GD(p, q) + GN (p, q)

]

Where GD and GN are the Green’s functions for the Dirichlet and Neumann problems respectively. We prof that

the norm of the modified integral operator’s K1 is zero. The interest of this result (‖K1‖ = 0) is that the more we rely

on approximate method to solve the integral equation obtained from the use of the integral representations method for

the bounded problem defined in [*], at the moment we have more integral equation to be solved, because the fact that

(‖K1‖ = 0) drive then directly to the solution of the bounded problem.

References[1] B. SAHLI, ’Optimizing multipoles coefficients of the modified Green’s function by minimization of the norm of the modified integral

operator’s in elasticity’, Master thesis, Department of Mathematics, University of Batna, Algeria, 1999.

2000 Mathematics Subject Classification. 65N38Key words and phrases. multipoles coefficients, Green’s function, integral equations, elastic waves.

120


Boundary value problem for the linear Elasticity

equations

Benabderrahmane Benyattou*, Abita Rahmoune**

*Department of Mathematics, Faculty of Sciences,

University of Laghouat (03000), Algeria

[email protected]

**Department of Mathematics, Faculty of Sciences,

University of Laghouat (03000), Algeria

[email protected]

Abstract

In this paper, we consider a non linear boundary value problem governed by the equations that describe the evolution

of an elastic body. Using the Faedo Galerkin techniques as well as a result of compactness we demonstrate the existence of

a weak solution of the problem considered by passing to the limit. The unicity of the solution is demonstrated by removing

a heavy enough hypothesis that has been considered by an other authors.

2000 Mathematics Subject Classification.37L65, 47J35Key words and phrases.Compacity, Elasticity, Faedo Galerkin, Gronwalle, Holder inequality, Non linear problem, Young inequality.

121


Mathematical Methods for Modeling of Lightning and

Thunderstorm Electrification

Beyza C. Aslan, William Hager

University of North Florida, Department of Mathematics and Statistics

UNF Drive, Bldg 14/2731, Jacksonville, FL 32224

[email protected]

University of Florida, Department of Mathematics, 358 Little Hall

Gainesville, FL 32611

[email protected]

Abstract

The change in the electric potential due to lightning is evaluated. The potential along the lightning channel is a

constant which is the projection of the pre-flash potential along a piecewise harmonic eigenfunction which is constant along

the lightning channel. The change in the potential outside the lightning channel is a harmonic function whose boundary

conditions are expressed in terms of the pre-flash potential and the post-flash potential along the lightning channel. The

expression for the lightning induced electric potential change for the continuous equations are based on the properties of

the eigenvalues and eigenfunctions of a generalized eigenproblem. The forcing term in the equation which is associated with

the movement of charged particles by the wind can be estimated using the balloon-borne electric field sensors (Esonde).

The data from the Esonde can be combined with simultaneous Lightning Mapping Array (LMA) measurements of VHF

pulses emitted during lightning breakdown processes to estimate the charge transport associated with lightning. Using these

techniques, we analyze lightning charge transport for a thunderstorm which occurred on August 18, 2004, near Langmuir

Laboratory, New Mexico. The analysis yields the three dimensional current generator structure of the thunderstorm.

References[1] W. W. Hager, B. C. Aslan, R. G. Sonnenfeld, J. D. Battles, Michael Holborn, and Ruth Ron, Three Dimensional Discharging

Structure of a Mountain Thunderstorm, J. Geophys. Res., submitted, 25 December 2008.

[2] B. C. Aslan, W. W. Hager, and S. Moskow, A generalized eigenproblem for the Laplacian which arises in lightning, J. Math. Anal.Appl., 341 (2008), 1028 - 1041.

[3] W. W. Hager and B. C. Aslan, The change in electric potential due to lightning, M2AN Math. Model. Numer. Anal. (ESAIM:M2AN),42 (2008), 887 - 901.

[4] W. W. Hager, R. G. Sonnenfeld, B. C. Aslan, G. Lu, W. P. Winn, and W. L. Boeck, Analysis of Charge Transport During LightningUsing Balloon Borne Electric Field Sensors and LMA, J. Geophys. Res., 112 (2007), D18204,

2000 Mathematics Subject Classification. 35, 65, 86Key words and phrases. lightning, charge transport, Laplacian, eigenfunction**This research was supported by National Science Foundation

122


Role of noncompatible and discontinuous mappings to

prove coincidence and common fixed point theorems in

various spaces

Bhavana Deshpande

Department of Mathematics Govt. Arts and Science

P. G. College Ratlam (M. P.) India

[email protected]

Abstract

In this talk, we will discuss single valued and hybrid pair of noncompatible mappings. As applications of noncompatible

mappings we will discuss some coincidence and fixed point theorems in metric spaces, fuzzy metric spaces, Menger spaces

and intuitionistic fuzzy metric spaces etc. We will point out that continuity of any mapping is not necessary for the existence

of common fixed point for noncompatible mappings. We will give some examples to validate our results. We will discuss

some recent results and applications.

2000 Mathematics Subject Classification. 47H10, 54H25.Key words and phrases. Noncompatible maps, Fuzzy metric spaces, Menger spaces, Intu- itionistic fuzzy metric spaces, Intuition-istic Menger space, Common fixed point.

123


Modeling and Optimization in Estimating and

Budgeting Projects Using Gath and Geva Fuzzy

Clustering Approach

Bouabaz Mohamed1, Belachia Mouloud1, Boudjema Bouzid2,

Mordjaoui Mourad2

1LMGHU, University of Skikda, BP 26, Skikda, 21000, Algeria,


2LRPCSI, University of Skikda, BP 26, Skikda, 21000, Algeria,

Boudjema [email protected], Mordjaoui [email protected]

Abstract

In this paper, a new modeling technique for estimating and budgeting project management is presented using a Gath

and Geva fuzzy clustering approach. The Partition Coefficient (PC), the Dunn’s Index (DI) and the Alternative Dunn index

(ADI) indices were used for validation of clusters number. The optimization of the number of clusters is significant for

subsequent in modeling. However, cost estimates are to be used for bidding purposes; a poor estimation may have negative

financial consequences. A cost over estimation bears the risk of making the firm uncompetitive and losing a customer, while

underestimating the cost leads to winning a contract but incurring a financial loss. Furthermore, a precise knowledge of

prospective resources utilization is critical for project management purposes when passing to the conceptual phase. The

proposed model was tested on a set of twenty projects. Very accurate result was achieved, showing that, the clustering

technique is more appropriate in modeling and financial budgeting of project management.

References[1] Abonyi, J. Clustering and data analysis toolbox. (2005).

[2] Babuska and H. B. Verbruggen. (1995). Identification of composite linear models via Fuzzy Clustering, Proc. European ControlConference, Rome, Italy, (1995) 1207-1212.

[3] Bezdek, J.C. and Dunn, J.C., Optimal fuzzy partition: A heuristic for estimating the parameters in a mixture of normal distributions.IEEE Trans. C-24 (1975) 835-838.

[4] Gath, I. and Geva, A.B., Unsupervised optimal fuzzy clustering. IEEE Trans Pattern and Machine Intell, vol. 11 no. 7, (1989)773-781.

[5] Takagi, T, M.Sugeno, Fuzzy identification of systems and its application to modelling and control, IEEE transactions on systems,

man, and cybernetics. 15(1), (1985) 116-132.

2000 Mathematics Subject Classification. 81T80Key words and phrases. Fuzzy clustering, Optimization, Simulation, Validity indices, Cost modeling, Project management.

124


On Idealized Electromagnetic Singularities in Arbitrary

Nonrelativistic Motion

Burak Polat

Uludag University, Faculty of Science and Letters,

Department of Mathematics, Gorukle 16059, Bursa, Turkey

[email protected]

Abstract

In this talk we present the distributional derivatives in space (gradient, divergence, curl and Laplacian) and in time

of generalized functions whose singular parts are concentrated on an arbitrary surface, an arbitrary space curve or a point

in arbitrary nonrelativistic motion. Such generalized functions are described in a Schwartz-Sobolev space setting and

represent arbitrary sources or field quantities in the equations of mathematical physics. Their regular components are

locally integrable functions in the Lebesgue sense and their singular components are assumed to be constructed via the

temporal and spatial derivatives of the Dirac-delta distribution of every order. We illustrate the applications of these

mathematical tools to the field equations of classical electrodynamics under the postulation that they apply in the sense of

distributions. The results cover initial, boundary/continuity, edge and tip conditions for concentrated sources in arbitrary

nonrelativistic motion.

References[1] B. Polat,”A Distributional Approach to Classical Electromagnetism” - a series of papers to appear in the Journal of Generalized

Functions.

[2] B. Polat, ”On Poynting’s Theorem and Reciprocity Relations for Discontinuos Fields”, IEEE Antennas and Propagation Magazine,49 (2007) No. 4, 74-83

[3] B. Polat, ”Remarks on the Fundamental Postulates on Field Singularities in Electromagnetic Theory” IEEE Antennas and Propa-gation Magazine 47 (2005) No.5, 47-54.

[4] B. Polat, ”A Note Regarding ”Remarks on the Fundamental Postulates on Field Singularities in Electromagnetic Theory””, IEEEAntennas and Propagation Magazine 48 (2006) 3, p.105.

[5] R. Estrada and R.P. Kanwal, Higher Order Fundamental Forms of a Surface and Their Applications to Wave Propagation andDistributional Derivatives, Rend.Cir.Mat.Palermo 36 (1987), 27-62.

[6] R. Estrada and R.P. Kanwal, Applications of Distributional Derivatives to Wave Propagation, J.Inst.Math.Appl. 26 (1980), 39-63.

2000 Mathematics Subject Classification. 78A02, 46A11Key words and phrases. Dirac-delta distributions, electrodynamics, initial, boundary, edge, tip conditions.

125


Stability and Optimal Control

C.C. Remsing

Department of Mathematics (Pure and Applied), Rhodes University,

PO Box 94, Grahamstown 6140, South Africa

[email protected]

Abstract

We consider the problem of minimizing a quadratic cost functional J = 12

∫ T0

(c1u2

1 + · · ·+ c`u2`

)dt over the trajec-

tories of a left-invariant control system Σ evolving on a matrix Lie group G, which is affine in controls. The final timeT > 0 is fixed and there are no restrictions on the values of the control variables.

Each such invariant optimal control problem defines the appropriate Hamiltonian H on the dual g∗ of the Lie algebra

of G through the Pontryagin’s Maximum Principle. The integral curves of the corresponding Hamiltonian vector field ~H(with respect to the minus Lie-Poisson structure on g∗) are called extremal curves. In this paper we are concerned withregular extremal curves. When the Lie algebra g admits a non-degenerate invariant bilinear form 〈·, ·〉 : g × g → R, theHamilton equations take a more familiar form. This is always possible if g is semisimple.

Lyapunov stability of Hamiltonian equilibria is investigated by using the energy-Casimir method. Explicit computations

are done in the special case of the rotation group SO (3).

2000 Mathematics Subject Classification. Primary 49J15, 93D05; Secondary 22E60, 53D17Key words and phrases. Invariant control system, Lie-Poisson structure, Lyapunov stability, the energy-Casimir method

126


Nonparametric regression: a brief overview and recent

developments

C.J. Swanepoel

North-West University, Potchefstroom Campus, South Africa

[email protected]

Abstract

A regression curve describes a general relationship between two or more quantitative variables. In a multivariate situ-ation vectors of explanatory variables as well as response variables may be present. For the simple case of one-dimensionalexplanatory and response variables, n data points S := (Xi, Yi), i = 1, 2, . . . , n are collected. The regression relationshipcan be modeled by Yi = m(Xi) + εi, i = 1, 2, . . . , n, where m(x) = E(Y |X = x) is the unknown regression function andthe εi’s are independent random errors with mean 0 and unknown variance σ2.

Nonparametric methods relax on traditional assumptions and usually only assumes that m belongs to an infinite-dimensionalcollection of smooth functions.

Several popular nonparametric estimators are discussed, mostly of the form m(x) = 1n

n∑

i=1

Wn,i(x)Yi, where Wn,ini=1

denotes a sequence of weights depending on the explanatory variables. Several kernel and nearest neighbour approaches tothe weight functions are considered. Each of these estimators depends on a smoothing parameter and the issue of estimatingit is discussed briefly.

The performance of m(x) is assessed via methods involving the mean squared error (MSE) and the mean integrated squarederror (MISE).

Two recent developments of improving the performance of m(x) are discussed, namely “boosting” and ‘bagging”, whichare respectively an iterative computer intensive method, and an averaging method involving the generation of bootstrapsamples. These methods, together with variations of these methods, for example the method referred to as “bragging”, areillustrated.

2000 Mathematics Subject Classification. 62G08, 62G09,62E20Key words and phrases. nonparametric regression, smoothing, kernel estimation, bootstrap

127


On Curvature inheriting symmetry in Finsler space

C. K. Mishra* and Gautam Lodhi**

*Department of Mathematics and Statistics Dr. R.M.L.

Avadh University Faizabad-224001 (U.P.), India.

[email protected]

Abstract

K. L. Duggal[1] has studied Curvature inheritance symmetry in Riemannian space with application of fluid space time

and also Ricci curvature inheriting symmetry of semi-Riemannian manifolds were introduced by K. L. Duggal and R. Sharma

[2]. In this paper we have study on Curvature inheritance symmetry and Ricci-Inheriting symmetry in Finsler space and

investigated some results.

References[1] K. L. Duggal, Curvature inheritance symmetry in Riemannian space with application of fluid space time. J. Math. phys. 33(9), (1992).

[2] K. L. Duggal & R. Sharma, Ricci curvature inheriting symmetry of semi-Riemannian manifolds, Contemporary Mathematics 170,

(1994).

2000 Mathematics Subject Classification.53B40Key words and phrases.Finsler space, curvature & relative curvature tensor, curvature inheritance, Ricci inheritance, projectivemotion, CI projective motion.

128


Adaptive Error Estimation for Linear Functionals

Approximation and Applications

Chin-Yun Chen

Department of Applied Mathematics, National Chiayi University

300 University Rd., Chiayi 600, Taiwan


Abstract

While concerning numerical approximation to bounded linear functionals, the approximate errors are generally discussed

by derivatives of the highest orders regarding the exactness degrees of the approximate functionals. This approach, however,

is only valid for functions with sufficient smoothness. For less smooth functions, the Peano/Sard kernels theorems are known

to be useful tools. Actually, the Peano/Sard theorems supply error representations of full orders, including the highest

order representation. Therefore, depending on the smoothness of the underlying functions, there can be more alternatives

to represent an approximation error. It thus makes adaptive local error estimation possible. These important mathematical

results have no more only the theoretical values, by automatic differetiation and interval arithmetic, the kernels method

finally can be realized in numerical computation on computers. One critical task prior to their applications is the nontrivial

calculation of Peano Sard constants. The talk will present all these aspects and their applications in numerical integration.

References[1] C.-Y. Chen, Verified Computed Peano Constants and Applications in Numerical Quadrature, BIT 47(2), 297–312, 2007.

[2] C.-Y. Chen, Computing Interval Enclosures for Definite Integrals by Application of Triple Adaptive Strategies, Computing 78(1),81–99, 2006.

[3] C.-Y. Chen, Bivariate product cubature using Peano kernels for local error estimates, J. Sci. Comput., 36(1):69–88. 2008.

[4] C.-Y. Chen, A Sard kernels theorem based automatic error estimation and its application to non-product cubature, Preprint.

[5] P. J. Davis and P. Rabinowitz, Methods of Numerical Integration, 2nd. ed., Academic Press, NY, 1984.

[6] H. Engels, Numerical Quadrature and Cubature, Academic Press, NY, 1980.

[7] A. H. Stroud, Approximate Calculation of Multiple Integreals, Prentice-Hall, NJ, 1971.

2000 Mathematics Subject Classification. 41A80, 41A55, 41A44, 41A63, 41-04, 65D30, 65D20, 65G20, 65G30Key words and phrases. Peano Sard kernels, Peano/Sard constants, interval arithmetic, Taylor arithmetic, numerical integration.

129


Fixed points and fuzzy stability of a quadratic-quartic

functional equation

Choonkil Park

Department of Mathematics, Hanyang University,

Seoul 133-791, Republic of Korea

[email protected]

Abstract

Using the fixed point method, we prove the generalized Hyers-Ulam stability of the following quadratic-quartic functionalequation

f(2x + y) + f(2x− y) = 4f(x + y) + 4f(x− y) + 2f(2x)− 8f(x)− 6f(y)

in fuzzy Banach spaces.

2000 Mathematics Subject Classification.Primary 46S40, 39B72; Secondary 39B52, 46S50, 26E50, 47H10.Key words and phrases.fuzzy Banach space, fixed point, generalized Hyers-Ulam stability, quadratic-quartic functional equation.

130


Semilinear Evolution Equations on Discrete Time

Claudio Cuevas, Carlos Lizama

Universidade Federal de Pernambuco, Departamento de Matematica,

Av. Prof. Luiz Freire, S/N, Recife-PE, CEP. 50540-740, Brazil.

[email protected]

Universidad de Santiago de Chile, Departamento de Matematica,

Facultad de Ciencias, Casilla 307-Correo 2, Santiago-Chile.

[email protected]

Abstract

This work deals with the existence and stability of solutions for semilinear equations on Banach spaces by using recent

characterizations of discrete maximal regularity. As application we examine the asymptotic behavior of discrete control

systems.

References[1] H. Amann, Quasilinear parabolic functional evolution equations. In: M. Chipot, H. Ninomiya (editors), Recent Avdances in Elliptic

and Parabolic Issues. Proc. of the 2004 Swiss - Japanese Seminar, World Scientific, (2006), 19 - 44.

[2] W. Arendt, Semigroups and evolution equations: functional calculus, regularity and kernel estimates, Evolutionary equations.Vol. I, 1-85, Handb. Differ. Equ., North-Holland, Amsterdam, 2004.

[3] S. Blunck, Maximal regularity of discrete and continuous time evolution equation, Studia Math., 146 (2) (2001), 157-176.

[4] S. Blunck, Analyticity and discrete maximal regularity of Lp-spaces, J. Funct. Anal., 183 (1) (2001), 211-230.

[5] C. Cuevas, C. Lizama, Maximal regularity of discrete second order Cauchy problems in Banach spaces, J. Differ. Equ. Appl., 13(12) (2007), 1129-1138.

[6] S. Elaydi, An introduction to difference equations, Undergraduate Texts in Mathematics, 3rd. ed. Springer Verlag, 2005.

[7] M. Geissert, Maximal Lp regularity for parabolic difference equations, Math. Nach., (16) 279 (2006), 1787-1796.

[8] D. Guidetti and S. Piskarev. Stability of the Crank-Nicolson scheme and maximal regularity for parabolic equations in Cθ(Ω)spaces, Numer. Funct. Anal. Optim., 20 (3-4) (1999), 251-277

[9] V.B. Kolmanovskii, E. Castellanos-Velasco, J.A. Torres-Munoz, A survey: stability and boundedness of Volterra difference equa-tions, Nonlinear Anal., 53 (7) (2003), 861-928.

[10] J.P. LaSalle, The Stability and Control of Discrete Processes, Springer-Verlag, New York, 1986.

[11] V.N. Phat, J. Jiang, Stabilization of nonlinear discrete-time systems via a digital communication channel, Int. J. Math. Sci., 1(2005), 43-56.

[12] P. Portal, Discrete time analytic semigroups and the geometry of Banach spaces, Semigroup Forum, 67 (2003), 125-144.

2000 Mathematics Subject Classification. 39A12, 39A11, 47D06Key words and phrases.

131


Fractional Differential Equations in term of Comparison

Results and Lyapunov Stability with Initial Time

Difference

Coskun Yakar

Gebze Institute of Technology Department of Mathematics

Gebze-Kocaeli 141-41400 Turkey

[email protected]

Abstract

The qualitative behaviour of a perturbed fractional differential equation that differs in initial position and initial time

with respect to the unperturbed fractional differential equation have been investigated. We compare the classical notion

of stability to the notion of initial time difference stability for fractional differential equations. We present a comparison

result which again gives the null solution a central role in the comparison fractional differential equation when establishing

initial time difference stabilty of the perturbed fractional differential equation with respect to the unperturbed fractional

differential equation.

References[1] Brauer, F. and Nohel, J., The Qualitative Theory of Ordinary Differential Equations, W.A. Benjamin, Inc., New York 1969.

[2] Lakshmikantham, V. and Leela, S., Differential and Integral Inequalities, Vol. 1,Academic Press, New York 1969.

[3] Lakshmikantham, V. and Vatsala, A.S., Differential inequalities with time difference and application, Journal of Inequalities andApplications 3, (1999) 233-244.

[4] Shaw, M.D. and Yakar, C., Generalized variation of parameters with initial time differenceand a comparison result in term Lyapunov-like functions, International Journal of Non− linear Differential Equations−Theory−Methods and Applications 5, (1999)86-108.

[5] Shaw, M.D. and Yakar, C., Stability criteria and slowly growing motions with initial time difference, Problems of NonlinearAnalysis in Engineering Systems 1,(2000) 50-66.

[6] Yakar C. and Shaw, M.D., A Comparison Result and Lyapunov Stability Criteria with Initial Time Difference. Dynamics of Contin-uous, Discrete and Impulsive Systems. A: Mathematical Analysis. Volume 12, Number 6 (2005) (731-741).

[7] Yakar C. and Shaw, M.D., Initial Time Difference Stability in Terms of Two Measures and Variational Comparison Result. Dynamicsof Continuous, Discrete and Impulsive Systems. Series A: Mathematical Analysis 15 (2008) 417-425.

[8] Yakar, C. Boundedness Criteria in Terms of Two Measures with Initial Time Difference. Dynamics of Continuous, Discrete andImpulsive Systems. Series A: Mathematical Analysis. Watam Press. Waterloo. Page: 270-275. DCDIS 14 (S2) 1-305 (2007). ISSN1201-3390. Editors: Zhaosheng Feng, Xinzhi Liu, Lokenath Debnath.

[9] Yakar C., Strict Stability Criteria of Perturbed Systems with respect to Unperturbed Systems in term of Initial Time Difference.

Proceedings of the Conference on Complex Analysis and Potential Theory. World Scientific Publishing. Page: 239-248 (2007). ISBN:

13 978-981-270-598-3 Editors: Tahir Aliyev Azeroglu and Promarz M. Tamrazov.

2000 Mathematics Subject Classification.34D10, 34D99.Key words and phrases.fractional differential equation, perturbed fractional differential systems, initial time difference stability.

132


Inverse System in the category of Sostak Fuzzy

Topological Spaces

Cigdem Gunduz (Aras)

Department of Mathematics, Kocaeli University, Kocaeli, 41380-Turkey

[email protected]

Abstract

The aim of the talk is to introduce and study inverse system and series of its properties in the category of Sostakfuzzy topological spaces. Let SFTS be the category of Sostak fuzzy topological spaces and J be direct poset (consider asa category).

Definition 1. Any functor D : Jop → SFTS is called an inverse system in SFTS, the limit of D is called an inverse limitof D.Theorem 2. Every inverse system in the category of SFTS has a limit, and this limit is unique.Theorem 3. Let Inv(SFTS) be a category of all inverse systems in SFTS and all mappings between them. Then lim

←operation is a functor from the category of Inv(SFTS) to the category of SFTS.

Theorem 4. If

((IXi , τi, τ∗i

)i∈J

,−→p i′

i

i≺i′

)is an inverse system of Smooth fuzzy compact Hausdorff spaces, then

lim←

IXi is a Smooth fuzzy compact space.

References[1] S. –G. Li, Inverse limits in category LTop (I)1, Fuzzy Sets and Systems 108 , 235- 241(1999)

[2] T.K. Mondal, S.K.Samanta, On intuitionistic gradation of openness, Fuzzy Sets and Systems 131 ,323-336 (2002)

2000 Mathematics Subject Classification. 54A40, 08A05, 18A30, 18A35Key words and phrases. Inverse system; Sostak fuzzy topological space; Mapping of inverse system; Limit of inverse system,Bitopological fuzzy spaces; Sum and product operations; Smooth compactness.

133


Time Optimal Control Problem Via Differential

Inclusions

D. Affane

Departement de Mathematiques, Universite de Jijel, Algeria

[email protected]

Abstract

We prove existence of solution to the second order differential inclusion of the form

u(t) ∈ F (u(t), u(t)) , u(0) = u(1) = 0 (1.1)

An application to a time optimal control problem is given under conditions that are weaker than the usual assumptions of

convexity.

References[1] A. Cellina; G. Colombo, On a classical problem of the calculus of variations without convexity assumptions , Anal. Inst0. H.

Poincarre, Anal. non lineaire, 7, (1990), 97-106.

[2] L. Cesari, Optimization theory and applications, Springer-Verlag, NewYork, 1983.

[3] A. F. Fillipov, On certain questions in the theory of optimal control, , Vestnik Moskov univ; Ser. Mat. Mech. Astr., 2 (1959), 25-32;

translated in Siam J. Control; 1 (1962).

2000 Mathematics Subject Classification. 34A60, 49J52Key words and phrases. Differential inclusion, autonomouse case, optimal control.

134


Semi-analytical Solution of the First and Second Kind

Abel Integral Equations Using Fractional Differential

Transform Method

D. Nazari, S. Shahmorad

Faculty of Mathematical Science, University of Tabriz, Tabriz-Iran

[email protected]

Abstract

In this paper, we present a method for solving Abel integral equations of the first and second kinds, which is based on

the Fractional Differential Transform method. Performance of the method is illustrated on some examples that verify the

excepted accuracy.

2000 Mathematics Subject Classification. 65R20Key words and phrases. Fractional differential transform method (FDTM), Abel integral equations.

135


A Specific Artificial Neural Network based Model for

the Identification of Pollution Sources

Dalila Acheli, Abdelmalek Kouadri2, Abdallah Namoune

2 Applied Control Laboratory, University of Boumerdes-Algeria

a [email protected]

Abstract

The aim of the present work is to suggest an original approach based on the concept of training of an artificial neural

network input or IT-Net in order to predict the possible sources of pollution. The IT-Network is composed of three layers

of neurons of which one is hidden. The output layer contains m neurons corresponding to the dimension of pollutant

concentration noted x. The input layer is composed of one neuron corresponding to the distance between the sources of

pollution and the pollutant concentration sensor. Instead of proceeding to a phase of training with five layers of neurons,

it appears more interesting to only apply the same phase of training to a part of the network involving three layers. This

approach is promising as it extends the back-propagation algorithm as long as the error function is well-defined. The

difference between this form in the input training network and multi-layers perceptron is that the input is not necessarily

known because it represents sources of pollution searched in a river for example. Therefore during the phase of training, it

becomes necessary to adjust not only the external parameters of the network but also the values of the input by minimizing

the error of the network output. The training of an IT-Net enables determining the existing relationship between sources

of pollution and data of pollutant concentration.


136


Exemples of differential games with stochastic

perturbations associated with solutions of Nash

equilibrum and open loop strategies

Daniela Ijacu

Academy of Economic Studies- Faculty CSIE- Calea

Dorobanti no.15-17 sect 1 Bucharest Romania

[email protected]

Abstract

This paper contained some exemples of differential games with stochastic perturbations associated with solutions of

Nash equilibrum and open loop strategies.The necessary conditions for Nash equilibrum solutions can be obtained using

variation calculus and Hamilton-Jacobi equations associated with optimal control problem. An optimal control problem,

usually, is defined by the same elements as a differential game with open loop strategies, with the difference that, this time,

we have just one functional which must be minimized in comparison with admissible comands.

References[1] Daniela Ijacu, C. Varsan, Smooth mapping and non adapted solutions associated with Hamilton Jacobi stochastic equations, IFIP

Proceedings ”Analysis and Optimization of Differential Systems”, Kluwer Academic Publisher, 2003

[2] Daniela Ijacu, I. Molnar and C. Varsan, On some parabolic SPDE involving gradient representation of stochastic flows, Rev.Roum. de Math. Pures et Appl.tom LI, nr 4, 2006

[3] C. Varsan, On evolution system of differential equations with stochastic perturbation, Preprint IMAR nr 4 /2001

2000 Mathematics Subject Classification. 60H15Key words and phrases. differential games with stochastic perturbation.

137


Transitive Designs Constructed From Finite Groups

Dean Crnkovic*, Vedrana Mikulic**, Andrea Svob***

*Department of Mathematics, University of Rijeka, Croatia

[email protected]

**Department of Mathematics, University of Rijeka, Croatia

[email protected]

***Department of Mathematics, University of Rijeka, Croatia

[email protected]

Abstract

Let G be a finite group. We describe a construction of 1-designs admitting an automorphism group isomorphic to G.

The designs are constructed by defining incidence structures on conjugacy classes of subgroups of the group G. The group

G acts transitively on the set of points and the set of blocks of the constructed design. Some of the constructed 1-designs

are also 2-designs. We apply this method to construct transitive 2-designs from some finite simple groups. One can use this

method to construct other combinatorial structures aditting transitive automorphism group, e.g. strongly regular graphs.

2000 Mathematics Subject Classification. 05B05, 05B20, 05E30Key words and phrases.combinatorial design, strongly regular graph*This research was supported by Scientific Research Project 319-0000000-3037 Commission of Ministry of Science, Educatuonand Sports of the Republic of Croatia

138


He’s Homotopy Perturbation Method for a General

Riccati Equation

Deniz Agırseven, Turgut Ozis

Trakya University, Faculty of Arts and Sciences

Department of Mathematics, 22030 Edirne, Turkey

Ege University, Science Faculty, Department of Mathematics

35100 Bornova-Izmir, Turkey

Abstract

The factorization method of the Hamiltonian in Quantum Mechanics involves solving a particular type of Riccati

equation. In this paper, He’s homotopy perturbation method is applied to a general Riccati equation. The solutions

introduced in this paper are in recursive sequence forms which can be used to obtain the closed form with the property

of being exactly solvable. This property generally means that one can solve the eigenvalue problem completely for the

Hamiltonian operator. The method is tested on various examples which are revealing the effectiveness and the simplicity

of the method.

References[1] M. A. El-Tawil, A. Bahnasawi, A. Abdel-Naby, Solving Riccati differential equation using adomian’s decomposition method, Appl.

Math. Comput. 157 (2004) 503-514

[2] H. Bulut, D.J. Evans, On the solution of the Riccati equation by the decomposition method, Int.J. Comput. Math. 79 (2002) 103-109

[3] S. Abbasbandy, Homotopy perturbation method for quadratic Riccati differential equation and comparison with Adomian’s decom-position method, Appl. Math. Comput. 172 (2006) 485-90

[4] S. Abbasbandy, Iterated He’s homotopy perturbation method for quadratic Riccati differential equation, Appl. Math. Comput. 175(2006) 581-589

[5] Y. Tan, S. Abbasbandy, Homotopy analysis method for quadratic Riccati differential equation, Commun. Nonlin. Sci. Numer. Simul.13(2008) 539-546

[6] B. Batiha, M. S. M. Noorani, I. Hashim, application of variational iteration method to a general Riccati equation, Internationalmathematical Forum, 2 (56) (2007) 2759-2770

[7] He, JH, Non-Perturbative Methods for Strongly nonlinear Problems,dissertation.de-verlag im Internet GmbH, Berlin, 2006

2000 Mathematics Subject Classification. 65L99, 34L30Key words and phrases. homotopy perturbation method, Riccati equation, nonlinear equations.

139


Introduction Of A Circular Number Line

Dharmendra Kumar Yadav

Department Of Applied Mathematics,

HMR Institute Of Technology & Management G.T.Karnal Road,

Hamidpur, Delhi-36, India

[email protected]

Abstract

The present paper introduces a circular number line, the superset of imaginary number line previously given by Yadav[1]

and an imaginary circular plane, the superset of circular complex plane given by Yadav[2]. It also introduces the new

concepts of imaginary circles and imaginary spheres. Taking different values of n, the natural numbers in in, we find that it

takes all the values on the imaginary number line. Giving in the geometrical meaning as the sum of arithmetical distances,

we find that the values of in lie on a circle and the imaginary number line lies on this circle, which gives the concept of

circular number line. This circular number line is not a straight line but is a circle of imaginary radius. At last some axioms

of Elliptical geometry and Euclidean geometry have been observed true in the paper. These axioms have been observed

on the imaginary sphere and imaginary circle. The circular number line, imaginary circle and imaginary sphere will play a

major role in explaining the concepts of Elliptical geometry and Hyperbolic geometry as well as they will be very helpfull

in explaining the universe geometrically. In fact the author has given D- theory of Universe by combining different theories

of the universe.

2000 Mathematics Subject Classification.14H50, 14H45, 30A99, 97B60, 51M10, 51M09, 51M30.Key words and phrases.Real Numbers, Real number Line, Imaginary Unit ’i’, Imaginary Numbers, Imaginary Number Line,Imaginary Circle, Imaginary Sphere, Axioms of Elliptical Geometry, Hyperbolic Geometry and Euclidean Geometry etc.

140


Domination dot-critical on a Harary graph

Doost Ali Mojdeh∗†, Somayeh Mirzamani∗, Roslan Hasni†

∗Department of Mathematics, University of Mazandran, Babolsar, Iran

[email protected]

†School of Mathematics, Universiti Sains Malaysia,

11800 Penang, Malaysia

[email protected]

Abstract

A set of vertices S in a graph G is a dominating set if every vertex of G−S is adjacent to some vertex of S. If S has the

smallest possible cardinality of any dominating set of G, then S is called a minimum dominating set-abbreviated MDS. The

cardinality of any MDS for G is called the domination number of G and is denoted by γ(G) [3]. More generally, we say that

a set of vertices A dominates the set B if every vertex of B−A is adjacent to some vertex in A. A vertex v of G is critical if

γ(G− v) < γ(G). A graph G is vertex-critical if every vertex of G is critical. We denote the set of critical vertices of G by

G′. In [2], Burton et al. introduced a new critical condition for the domination number. A graph is domination dot-critical

(hereafter, just dot-critical) if identifying any two adjacent vertices (i.e., contracting the edge comprising those vertices)

results in a graph with smaller domination number. If identifying any two vertices of G causes the domination number to

decrease, then we say that G is totally dot-critical. For a pair of vertices a, b of G, we denote by G.ab the graph obtained

by indentifying a and b. When we say that G is k-edge-critical, k-vertex-critical, k-dot-critical, or totally-k-dot-critical, we

mean that it has the indicated property and that γ(G) = k, for more, see [1, 2, 5]. Given k ≤ n, place n vertices around a

circle, equally spaced. If k is even, form Hk,n by making each vertex adjacent to the nearest k2 vertices in each direction

around the circle. If k is odd and n is even, form Hk,n by making each vertex adjacent to the nearest k−12 vertices in

each direction and to the diametrically opposite vertex. In each case, Hk,n is k-regular. When k and n are both odd we

construct Hk,n from Hk−1,n by adding an edge between vertices i andi+(n−1)

2 for each 1 ≤ i ≤ (n+1)2 . The graph Hk,n

in each case is known as Harary graph H that V (G) = 1, 2, · · · , n ([6]). Domination number in Harary graphs have

been studied in ([4]). In this note, we investigate the critical, dot-critical and totally dot-critical of the first type of Harary

graphs, that is, H2m,n(k = 2m).

References[1] T. A. Burton, Domination dot-critical graphs, PhD Dissertation, University of South Carolina, 2001.

[2] T. A. Burton, D. P. Summner, Domination dot-critical graphs, Discrete Mathematics, 306 (2006), 11–18.

[3] T. W. Haynes, S. T. Hedetniemi, P. J. Slater (Eds.), Fundamentals of Domination in Graphs, Marcel Dekker, Inc. NewYork, 1998.

[4] A. Khodkar, D. A. Mojdeh, A. P. Kazemi, Domination in Harary graphs, Bulletin of the ICA, Volume 49 (2007), 61 − 78.

[5] D.A. Mojdeh and S. Mirzamani, On the diameter of dot-critical graphs, Opuscula Mathematicae (to appear).

[6] D. B. West, Introduction to gragh theory, (2nd edition), Prentice Hall USA (2001).

2000 Mathematics Subject Classification.05C69Key words and phrases.Harary graph, domination, dot-critical

141


Acceptance Single Sampling Plan with Fuzzy Parameter

E. Baloui Jamkhaneh*, B. Sadeghpour-Gildeh**, G. Yari***

*Ph.D Student, Science and Research Branch, Islamic Azad University, Tehran, Iran.

e baloui2008@ yahoo.com

**Department of Statistics, Faculty of Basic Science,

University of Mazandaran Bablosar, Iran [email protected]

***Iran University of Science and Technology, Tehran, Iran

[email protected]

Abstract

Single sampling plan for acceptance or rejecting a lot is an important subject in statistical quality control. This plan

is one of the sampling method for acceptance or rejection which is along with classical attribute quality characteristic.

This plan has a sample size n and acceptance number c. If the number of defective items is less than or equals to c,

the lot will be accepted. However, the fraction of defective items (quality characteristic) in a lots is not often exact and

certain. Estimations and personal judgments are the useful response for inexactness and ambiguity. In different acceptance

sampling plan the fraction of defective items (p), is considered as a precise value, but this precision is not true in real world

and decision making problems, and there also exist some uncertainty in the value of p obtained from experiment, personal

judgment or estimation. The theory of fuzzy sets is widely used in solving problems in which parameter or quantities cannot

be expressed precisely. The theory is a powerful and well-known tool to formulate and analyze the uncertainty resulting

from ambiguity and personal judgment. In dealing with the above problem we tried to restore the uncertainty existing in

the problem by defining the imprecise parameter as a fuzzy number, and achieve a result with a higher certainty. With

this definition, the number of defective items in the sample has a fuzzy binomial probability distribution. In this paper

we discuss the acceptance single sampling plan when the fraction of nonconforming products is a fuzzy number. We have

shown that the operating characteristic (OC) curve of the plan is like a band having high and low bounds whose width

depends on the ambiguity proportion parameter in the lot when that sample size and acceptance number is fixed. When

the acceptance number equals zero, this band is convex for different n s and for large n, the convexity will be more. Finally

we have given some examples and then compared the OC bands for some values of c.

2000 Mathematics Subject Classification. 62p30Key words and phrases.Statistical quality control, acceptance single sampling, fuzzy number.

142


Defining sets of Combinatorial Designs: Recent

Developments

E. Sule Yazıcı

Koc University

[email protected]

Abstract

In this talk, the defining set problem will be defined for combinatorial designs. Loosely speaking a defining set of a

combinatorial design D is a partial design S contained in the design such that D is the unique completion of S to a design

with the given parameters. The emphasis of this talk will be on defining sets of full designs and their connections with the

defining sets other t-designs. The new found families of minimal defining sets of full designs will be given. And final results

on spectrum of minimal defining sets of these designs will be presented.


143


Silver graphs

Ebadollah S. Mahmoodian

Department of Mathematical Sciences

Sharif University of Technology Tehran, I.R. Iran

[email protected]

Abstract

A problem was given in the International Mathematical Olympiad in 1997 (IMO97–Problem 4) on “silver matrices”. Itcame from a research problem in graph colorings called defining sets and in latin squares critical sets, Mahdian and Mahmoodian[2]. In a given graph G, a set of vertices S with an assignment of colors is called a defining set of the (proper) k–coloring if thereexists a unique extension of the colors of S to a k–coloring of the vertices of G. A defining set with minimum cardinalityis called a minimum defining set and its cardinality is the defining number, denoted by d(G, k). Existence of a silver matrixof order n is equivalent to d(Kn¤Kn, 2n − 1) = n2 − n. Recently we have studied silver d–cubes [1], that is when we have

d(

d︷︸︸︷Kn¤Kn¤ · · ·¤Kn, dn − d + 1) = nd − nd−1. Silver d–cubes are attractive, challenging to construct, and appear to be

connected with classical combinatorics, including coding theory and projective geometry.

In general a silver graph is defined as follows. Let c be a proper (r + 1)-coloring of an r-regular graph G. A vertex x

in G is said to be rainbow with respect to c if every color appears in the closed neighborhood N [x] = N(x) ∪ x. Given a

maximum independent set I of G, the coloring c is said to be silver with respect to I if every x ∈ I is rainbow with respect to

c. We say G is silver if it admits a silver coloring with respect to some diagonal. If all vertices of G are rainbow, then c is

called a totally silver coloring of G and G is said to be totally silver. In this talk we will discuss silver graphs and its relation

with some concepts in combinatorics and graph theory and at the end some unsolved problems will be stated.

References[1] M.Ghebleh, L.A. Goddyn, E.S. Mahmoodian, and M.Verdian-Rizi, Silver cubes, Graphs Combin., 24 (2008), 429–442.

[2] M.Mahdian and E.S. Mahmoodian, The roots of an IMO 97 problem, Bull. Inst. Combin. Appl., 28 (2000), 48–54.

2000 Mathematics Subject Classification. 05C15, 05B25Key words and phrases. graph colorings, defining set, unique coloring*This research was supported by The Research Office of the Sharif University of Technology.

144


The Characterisation of Compact Operators on Spaces

of Stongly Summable and Bounded Sequences

Eberhard Malkowsky

Department of Mathematics, University of Giessen, Arndtstrasse 2,

D-35392 Giessen, Germany

Faculty of Information Technologies, Taduesa Koscuska 63,

11000 Belgrade, Serbia

[email protected]

Abstract

We use the characterisations of the classes of all infinite matrices that map the spaces of sequences which are strongly

summable or bounded by the Cesaro method of order 1 into the spaces of null or convergent sequences, given by Basar,

Malkowsky and Altay in [Publ. Math. 73(1-2)(2008), 193–213], and the Hausdorff measure of noncompactness to charac-

terise the classes of all compact operators between those spaces.

2000 Mathematics Subject Classification. 46A45, 40H05Key words and phrases. Spaces of strogly bounded and summable sequences, matrix transformations, compact operators, Haus-dorff measure of noncompactnessThe author wishes to express his thanks to TUBITAK for supplying the financial support by BIDEB Programme during thepreparation of the present work. Research also supported by the research project ]144003 of the Serbian Ministry of Science,Technology and Development

145


On weak nil-Armendariz rings

Ebrahim Hashemi

Department of Mathematics Shahrood University of Technology

Shahrood, Iran

eb [email protected]

Abstract

Rege and Chhawchharia introduce the notion of an Armendariz ring. A ring R is Armendariz if whenever f(x)g(x) = 0where f(x) = a0 + a1x + · · ·+ anxn and g(x) = b0 + b1x + · · ·+ bmxm ∈ R[x], then aibj = 0 for each i and j. The nameof the ring was given due to E. Armendariz who proved that reduced rings (i.e. rings without nonzero nilpotent elements)satisfied this condition. Armendariz rings are thus a generalization of reduced rings, and therefore, nilpotent elements playan important role in this class of rings. There are many examples of rings with nilpotent elements which are Armendariz.

A ring is weak Armendariz if whenever the product of two polynomials is zero then the product of their coefficients isnilpotent. This further motivates the study of the nilpotent elements in this class of rings.

We call a ring R weak nil-Armendariz if whenever f(x)g(x) ∈ nil(R)[x] where f(x) = a0 + a1x + · · · + anxn andg(x) = b0 + b1x + · · ·+ bmxm ∈ R[x], then a0bj ∈ nil(R) for each j.

We prove that if R is a nil-Armendariz ring, then the set of nilpotent elements of R is a subring without unit of R. This

allows us to study the conditions under which the polynomial ring over a nil-Armendariz ring is also nil-Armendariz. These

conditions are strongly connected to the question of Amitsur of whether or not a polynomial ring over a nil ring is nil.

2000 Mathematics Subject Classification. 16S36; 16S50; 16U99Key words and phrases. Armendariz ring; Nil-Armendariz ring; Polynomial ring; Nilpotent elements

146


An Extension of the Poisson-Lindley Distribution and

its Applications

Eisa Mahmoudi

Faculty of Mathematics, Department of Statistics, Yazd University, Yazd, Iran.

[email protected]

Abstract

An extended version of the compound Poisson distribution is obtained by compounding the Poisson distribution with

the generalized two-parameter Lindley distribution. This paper offers a three-parameter generalized Poisson-Lindley dis-

tribution, which generalizes Poisson-Lindley distribution, as a model for count data. This distribution provides enough

flexibility for analyzing different types of count data. The study examines various properties of this model. The behavior of

the density function, the expressions for the moments, the distribution of the sums of random variables and truncated and

weighted versions of this distribution is obtained. Estimation of the parameters is discussed using the method of moments

and maximum likelihood estimators. A simulation study is carried out to investigate the average bias and average mean

square error (MSE) of the simulated estimates. An application of this distribution, including several examples of the fitting

of this distribution to data, and comparing with other discrete distributions, are given.

References[1] M. E. Ghitany, B. Atieh, S. Nadarajah, Lindley distribution and its application, Math. Comput. Simul. 78 (2008) 493-506.

[2] M. E. Ghitany, D. K. Al-Mutari, S. Nadarajah, Zero-truncated Poisson-Lindley distribution and its application, Math. Comput.Simul. 79 (2008) 279-287.

[3] N. L. Johnson, A. W. Kemp, S. Kotz, Univariate discrete distributions, Inc., Hoboken, New Jersey, 2005.

[4] D. V. Lindley, Fiducial distributions and Bayes’ theorem, Journal of Royal Statistical Society. B 20 (1958) 102-107.

[5] C. R. Rao, On discrete distributions arising out of methods of ascertainment, In classical and contagious discrete distributions, G.P.Patil (editor), Pergamon Press and Statistical Publishing Society, Calcutta. (1965) 320-332.

[6] M. Sankaran, The discrete Poisson-Lindley distribution, Biometrics. 26 (1970) 145-149.

2000 Mathematics Subject Classification. primary: 62E10, 62E15 secondaries: 62F10, 62F12Key words and phrases. Poisson-Lindley distribution, Truncated distributions, Weighted distributions

147


On some new sequence spaces with an index defined by

a modulus function

Ekrem Savas , Hamdullah Sevli

Department of Mathematics, Istanbul Ticaret University

Uskudar-Istanbul, Turkey

[email protected]

Department of Mathematics, Yuzuncu Yil University

Van, Turkey

[email protected]

Abstract

In this paper we define the following sequence spaces by using a modulus function

wp(f) =

x :

∑

k

kp−1

f(|dkm − dk−1,m|

)converges uniformly in m

ˆwp(f) =

x : supm

∑

k

kp−1

f(|dkm − dk−1,m|

)< ∞

,

where p ≥ 1 and

dkm = dkm(x) =1

(n + 1)

n∑

k=0

tkm(x).

We also get some inclusion relations. Note that if f(x) = x, then we get wp(f) = wp and ˆwp(f) = ˆwp. If p = 1, then

wp = w, which was defined in [1].

References[1] G. Das, S. K. Sahoo, On some sequence spaces, J. Math. Anal. Appl., 164 (1992) 381-398.

2000 Mathematics Subject Classification. 40H05, 46A45Key words and phrases. Sequence spaces, Modulus function, Almost convergence

148


On Double Lacunary ∆σ-Statistical Convergence of

sequences of Fuzzy numbers

Ekrem Savas

Istanbul Ticaret University, Department of Mathematics,Uskudar, Istanbul- Turkey

[email protected]

Abstract

Quite recently, Savas and Mursaleen [1] defined the statistical analogue for double sequences X = Xk,l of fuzzynumbers as follows: A double sequences X = Xk,l is said to be P-statistically convergent to X0 provided that for eachε > 0

P − limm,n

1

mn numbers of(j, k) : j ≤ m and k ≤ n, d(Xj,k, X0) ≥ ε = 0.

In this paper we introduce and study double lacunary ∆σ-statistical convergence for sequences of fuzzy numbers and

also we get some inclusion theorems.

References[1] Savas, E.; Mursaleen, On statistically convergent double sequences of fuzzy numbers. Inform. Sci. 162 (2004), no. 3-4, 183–192.

[2] Savas, E. A note on double sequence of Fuzzy numbers, Turk J. Math., 20(1996), 175-178.

[3] Savas, E. A note on sequence of Fuzzy numbers, Information Sciences, 124(2000), 297-300.

[4] Savas, E. On strongly λ− summable sequences of Fuzzy numbers, Information Sciences, 125(2000), 181-186.

[5] Savas, E. On statistically convergent sequence of Fuzzy numbers, Information Sciences,137(2001), 272-282.

[6] Savas, E., On Lacunary statistically convergent double sequences of fuzzy numbers. Appl. Math. Lett. 21(2008),134-141.


149


The algorithms of the program control construction for

some classes of the dynamic systems

Elena Chalykh

Pacific National University, Khabarovsk,

Department of mathematical modeling and control processes, Russia

[email protected]

Abstract

In this article the program control tracing algorithm is considered for some dynamic systems, which evolve on thedynamic varieties. These algorithms are based on the differential equation systems construction, which have given inadvance the collection of the first integrals . The first algorithm is used the stochastic systems and the second is for thedeterminate systems. The main idea of these algorithms is based on the first integral of SDE system definition, given byprof. V.Doobko [1].

The program control of the stochastic system with the probability equaled to 1

Let us consider the SDE system with control:

dx(t) = [P (t;x(t)) + Q(t;x(t)) · s(t;x(t))] · dt + R(t;x(t)) · dw(t), (1)

where x(t) is a n-dimensional stochastic process, w(t) – is a m-dimensional standard Wiener process. The solution x(t) =x(t; 0;xo, s) of the stochastic system (1) is called a program motion if it allows to stay on the given integrated varietyu(t;x(t;xo); ω) = u(0;xo) with the probability equaled to 1 for all time t at some s. This variety defines the first integrals

of the equations dx(t) = A(t, x(t))dt + B(t, x(t)) dw(t) with the given initial condition x(t;xo)∣∣∣t=0

= xo. Thus we shall

name the non-random function s = s(t;x(t)) as the program control for the dynamic stochastic system. The theory of thefirst integral of SDE system in the prof. Doobko’s sense [1] allows to construct the new SDE system. In this system thecoefficients A and B are determined through the given dynamic variety surface for the system. This surface is invariantfor the system (1) with the probability equaled to 1, and it may be considered as the first integral collections of this SDEsystem [2]. The congruence of the coefficients of the equations (1) and new equation make possible define the controls(t; x(t)) = (s1, . . . , sn)∗ and the reaction on random effect B(t;x(t)).

The continuous program control of the determinate system

As a rule definition of the program control of determinate systems is considered for the discreet points only, whichdefine the system position by the given periods of time. The specificity of our approach is that the controlled system is onthe given dynamic variability at any time.

We construct the class of the differential equations similar to [1]

dx(t) = A(t;x(t)) dt, which have the given first integrals collection

ul(t;x)N

l=1, N ≤ n. Then the program control

s(t;x(t)) for systemdx(t) = [P (t;x(t)) + Q(t;x(t)) · s(t;x(t))] dt

is as the solution of equation A(t;x(t)) = P (t;x(t))+Q(t;x(t))·s(t;x(t)). The conditions for the matrix Q and the invariant

surfaces are defined for the different dimensions control s.

References[1] V. A. Doobko, Averaging for a class of stochastic differential equations, Ukrainian Mathematical Journal, Vol. 30, No 4, (1978)

399-403.

[2] E. Chalykh, The construct of the program control with probability is equaled to 1 for the some class of stochastic systems, Journal

of Ubiquitous Convergence Technology (JUCT), Vol. 2, No 2 (2008) 105-108.

2000 Mathematics Subject Classification.primary:93C10, secondaries:37A50, 93E03Key words and phrases.program control, dynamic variety, stochastic and determined system

150


Optimal Control of The Elliptic Type Differential

Inclusions with Dirichlet and Neumann

Boundary Conditions

Elimhan N. Mahmudov1, Ozkan Deger2

1 Industrial Engineering Department, Faculty of Management

Istanbul Technical University, 34367 Macka, Istanbul, Turkey

[email protected]

2 Mathematics Department, Faculty of Science, Istanbul University

34134, Vezneciler, Istanbul, Turkey

[email protected]

Abstract

The talk deal with optimization the Dirichlet and Neumann Problems for differential inclusions where the right-hand

side is governed by set-valued mapping. The set-valued mapping depends not only of required function, but also the first

partial derivatives of these functions. This generalization is very important and the results obtained can’t be deduced from

the results considered before [2]. Formulations of sufficient conditions are based on the discretization idea of continuous

problem and equivalence theorems [1]. Thus in the form of Euler-Lagrange inclusion sufficient conditions for optimality

are derived for which are used locally adjoint mappings. In general, we establish necessary and sufficient conditions for

so-called discrete approximation problem on a uniform grid. These conditions take an intermediate place between discrete

and continuous problems.

References[1] B.N. Pshenichnyi , Convex Analysis and Extremal Problems, Nauka , Moscow, (1980).

[2] E.N. Mahmudov, Necessary and Sufficient Conditions for discrete and differential inclusions of elliptic type, J. Math. Anal. Appl.,323, 768-789, (2006).

2000 Mathematics Subject Classification. 49K20, 49K24Key words and phrases. Differential inclusions, nonsmooth analysis, discrete approximation, locally adjoint mapping, necessaryand sufficient conditions

151


Optimal Control of Discrete and Differential Inclusions

in Gradient Form

Elimhan N. Mahmudov, Murat Unal

Industrial Engineering Department, Faculty of Management


[email protected]

Industrial Engineering Department, Faculty of Management


[email protected]

Abstract

This talk is dedicated to optimization of so-called first order differential inclusions in gradient form on a square domain.

As a supplementary problem, discrete-approximation problem is considered. In the Euler-Lagrange form, necessary and

sufficient conditions are derived for problems and partial differential inclusions, respectively. The results obtained are based

on a new concept of locally adjoint mappings. The duality theorems are proved and duality relation is established.

References[1] B.N. Pshenichnyi , Convex Analysis and Extremal Problems, Nauka , Moscow, (1980).

[2] Locally adjoint mappings and optimization of the first boundary value problem for hyperbolic type discrete and differential inclusions.Nonlinear Anal. 67 (2007), no. 10, 2966–2981..

2000 Mathematics Subject Classification.Key words and phrases. Locally adjoint mappings, discrete and differential inclusions, discrete approximation, necessary andsufficient conditions, duality theorems

152


The New Numerical Algorithms For Solving

Multiplicative Differential Equations

Emine Mısırlı1, Yusuf Gurefe2

1 Ege University, Department of Mathematics, Izmir, Turkey

[email protected]

2 Ege University, Department of Mathematics, Izmir, Turkey

[email protected]

Abstract

The mathematical modelling of most phenomena in science and engineering are based on differential equations. But,one can observe that this is not possible to define some problems through classical concepts. While one problem can beeasily expressed in one calculus, the same problem can not be expressed as easily as the others. From the point of view of M.Grossmann and R. Katz some new calculi were alternatively defined. Multiplicative calculus and multiplicative differentialequations involving multiplicative derivatives become very important in recent studies.

In this study, we define multiplicative Adams Bashforth-Moulton algorithms using the exponential Newton backward

division formula for solving multiplicative differential equations. Afterwards, a problem is solved and the error estimations

are considered. Solutions are compared with analytic ones.

References[1] A.E. Bashirov, E.M. Kurpinar, A. Ozyapici. Multiplicative calculus and its applications Journal of Mathematical Analysis and

Applications, (2008) 337(1):36-48.

[2] D. Aniszewska. Multiplicative runge-kutta methods. Nonlinear Dynamics, (2007) 50(1-2): 265-272.

[3] M. Grossmann. Bigeometric Calculus, A System with a Scale-free Derivative. Archimedes Foundation, Rockport, 1983.

[4] M. Grossman and R.Katz. Non-Newtonian Calculus. Lee Press, Pigeon Cove, Massachusats, 1972.

[5] M. Riza, A. Ozyapici, E. Misirli. Multiplicative Finite Difference Methods. Quarterly of Applied Mathematics (in press).

[6] E. Suli, D.F. Mayers. An Introduction to Numerical Analysis. Cambridge University Press, Cambridge, United Kingdom, 2003.

[7] J.C. Butcher. Numerical Methods for Ordinary Differential Equations. Wiley, Chichester, England, 2003.

2000 Mathematics Subject Classification.Key words and phrases. Multiplicative calculus, multiplicative backward division formula, adams methods

153


On New Inequalities Via Convex Functions

Erhan Set

Ataturk University, K.K. Education Faculty, Department of Mathematics,

Erzurum, Turkey

[email protected]

Abstract

The aim of the present note is to establish some new inequalities for convex functions by using a fairly elementary

analysis.

References[1] S. S. Dragomir, C. E. M. Pearce, Selected Topic on Hermite-Hadamard Inequalities and Applications, RGMIA Monographs, Victoria

University, 2000.

[2] D.S. Mitrinovic, J.E. Pecaric, A.M. Fink, Classical and New Inequalities in Analysis, Kluwer Academic Publishers (1993).

2000 Mathematics Subject Classification. Primary 26A51, Secondary 26D07, 26D15Key words and phrases. Convex functions, convexity, inequalities.

154


On optimal vertex colorings of graphs

Esmaeil Parsa

Faculty of Sciences, Islamic Azad University( Parand Branch), Tehran, Iran

[email protected]

Abstract

Let c be a k-coloring of a graph G, then the number of different colors which appear in N(v) is called the coloring

degree of v with respect to c and denoted by Cdc(v). K-coloring index of G is denoted by Cik(G) and defined as Cik(G) =

Min∑v∈V (G) Cdc(v) which, the minimum is over all k-colorings of G. A coloring c is called an optimal coloring of G if∑v∈V (G) cdc(v) 6 Cik(G), ∀k. In this paper we provide some essential conditions for coloring c to be an optimal coloring

and provide an algorithm to create an optimal coloring of a graph G as a conjecture along with some open problems.

2000 Mathematics Subject Classification. 05C15Key words and phrases. graph coloring,degree coloring, coloring index, optimal coloring.*This research was supported by Islamic Azad University (Parand Branch)

155


Linear Operator on univalent Function of Complex

Order

Essam Aqlan

Department of Mathematics, Hodeidah University, Hodeidah, Yemen

essam [email protected]

Abstract

In the present paper, the outher obtaoin the sharp Fekete-Szego Inequalities for new class defiend on the open unit

disk. The outher also obtain some properties of this class which defined by linear operators.

References[1] O. P. Ahuja and M. Jahangiri, Fekete-Szego Problem for a Uni?ed Class of Analytic functions, PanAmerican Math. J. 7(1997),no.

2, 67-78.

[2] B. C. Carlson and D. B. Shaffer, Starlike and prestarlike hypergeometric function, SIAM J. Math. Anal. 15(1984), 737-745.

[3] A.W. Goodman, Univalent functions and nonanalytic curves, Proc. Amer. Math. Soc. 8 (1957), 598-601.

[4] I. S. Jack, Functions starlike and convex of order α, J. London Math. Soc. (2) 3(1971), 469-474.

[5] F.R. Keogh and E.P. Merkes, A coeffcient inequalty for certain classes of analytic functions, Proc. Amer. Math. Soc. 20 (1969),8-12.

[6] Jin-Lin Liu and H. M. Srivastava, A linear operator and Associated families of meromorphically multivalent functions, J. Math.Anal. and Appl. 259 (2001), 566-581.

[7] M. L. Mogra, Meromorphic multivalent functions with positive coeffcients, I and II, Math. Japon., 35 (1990), 1-11, 1089-1098.

[8] M.S. Rebertson, Quasi subordination functions, In Mathematical Essay dedicated to A.J. Maclntyre Vol.(Ohio University, 1967),311.

[9] H. M. Srivastava and S. Owa, Some characterization and distortion theorems involving fractional calculus, generalized hypergeo-

metric functions, Hadamard product, linear operators, and certain subclasses of analytic functions, Nagoya Math. J. 106 (1987),

1-28.

2000 Mathematics Subject Classification.30C45, 30C50.Key words and phrases.Subordination, Fekete-Szego Inequalities, Linear Operator.

156


Dynamics for hyperbolic non-invertible maps

Eugen Mihailescu

Institute of Mathematics of the Romanian Academy, P.O Box 1-764, RO 014700

Bucharest, Romania

[email protected]

Abstract

We will talk about methods and results in the dynamics of hyperbolic non-invertible maps. One important direction

is that of applying thermodynamical formalism (entropy, pressure, inverse pressure) to study various metric properties

of fractals obtained from iterations of hyperbolic maps on basic sets. For example inverse pressure helps us estimate the

Hausdorff dimension of fractal intersections in the basic set. Another direction is the ergodic study of the invariant measures

supported on such sets, in particular the equilibrium measures, and their conditional measures relative to various partitions.

2000 Mathematics Subject Classification.37C, 37D, 37F.Key words and phrases.dynamics of hyperbolic non-invertible maps, ergodic theory.

157


Modified Atkinson method: Forward Search algorithm

F.M.O. Hamed

Department of Statistics, University of Garyounis, Benghazi, Libya

fathi [email protected]

Abstract

The method discussed in this paper is Atkinson’s Forward Search Algorithm (Atkinson, 1994). This is a powerful robuststatistical method for detecting multiple outliers. Multiple outliers can have a strong influence on the model fitted to data.

The Forward Search seeks to distinguish a larger ”clean” part, which is called the ”good” class, from outlier data, the”bad” class. When there are two separated groups in the data, it rejects one of the groups in favour of the other. Themain strategy is to separate ”good” from ”bad” data, where the ”good” data lie in one of the clusters and the ”bad” liein the remaining clusters. Real data however might contain more than one class of ”good” data in addition to the outliersgroup. In this paper the standard method will be extended and applied sequentially. That is, the method is applied on thedata to identify a ”good” group in the data, then remove this group and apply the method again to get the next ”good”group from the rest of the data, and so on until all the observations are classified into their groups and one of these groupis the outliers class. The main problem, in this case, is that the first ”good” data may only contain a small portion of theobservations. This matter will be discussed in detail in this work and some applications on different data are presented.

2000 Mathematics Subject Classification. 62-09Key words and phrases. Atkinson method, Least Median Square, Outliers, stalactite.

158


Advanced Thermal Imaging and Measurement

Techniques: Application to a Printed Circuit Board

F.A. Mohammadi1, F. Farrokhi2, M.C.E. Yagoub3

1 Department of Electrical and Computer Engineering,

Ryerson University, 350 Victoria St. M5B 2K3, Toronto, ON, Canada.

[email protected]

2 Department of Electrical and Computer Engineering,

Ryerson University, 350 Victoria St. M5B 2K3, Toronto, ON, Canada.

3 University of Ottawa, School of Information Technology

and Engineering, 161 Louis Pasteur, K1N 6N5, Ottawa, ON, Canada.

Abstract

Thermal management is vital to the successful design, manufacturing and operation of the most modern electronic

systems. The objective of this paper is to describe an experimental setup using an infrared camera system to characterize

thermal behavior of the electronic components. A comparison is given for the use of two different coatings to create a

uniform surface emissivity within a variety of experimental situations. New oil based heat sink has been implemented. The

effect of oil flow regime has also been presented. In addition, three dimensional thermal simulation of the device under test

has been performed and the results obtained were compared to experimental test results.


159


Numerical solutions of NBSP for elliptic equations

F.S.O. Tetikoglu

Department of Mathematics, Fatih University, Istanbul, Turkey

[email protected]

Abstract

In present paper joint with Prof. Allaberen Ashyralyev, Fatih University, we consider the Neumann Bitsadze Samarskiitype problem for the multidimensional elliptic equation

−utt −n∑

r=1(ar (x) uxr )xr

+ δu = f (t, x) ,

0 < t < 1, x = (x1, · · · , xn) ∈ Ω,

ut (0, x) = ϕ (x) , x ∈ Ω,

ut (1, x) = βut (λ, x) + ψ (x) , x ∈ Ω, |β| ≤ 1, 0 ≤ λ < 1,∂u(t,x)

∂~u

∣∣∣x∈S

= 0, 0 ≤ t ≤ 1.

(1)

with ψ (x) , ϕ (x)(

x ∈ Ω)

and f (t, x) (t ∈ (0, 1) , x ∈ Ω) are smooth functions. Here Ω is the unit open cube in the

n-dimensional Euclidean space Rn (0 < xk < 1, 1 ≤ k ≤ n) with boundary S, Ω = Ω ∪ S, δ is a large positive constant.

We are interested in studying the stable difference schemes for the numerical solution of the nonlocal boundary value

problem (1). The first and second orders of accuracy difference schemes are presented. A modified Gauss elimination

method is used for solving these difference schemes for the two-dimensional elliptic differential equation. The method is

supported by numerical examples.

References[1] A.V. Bitsadze, A.A. Samarskii, On some simplest generalizations of linear elliptic problems, Dokl. Akad. Nauk SSSR 185 (1969).

[2] A. Ashyralyev, A note on the Bitsadze-Samarskii type nonlocal boundary value problem in a Banach space, Journal of MathematicalAnalysis and Applications 344(1)(2008) 557-573.

[3] A. Ashyralyev and E. Ozturk, Numerical solutions of Bitsadze-Samarskii problem for elliptic equation, Further progress in analysis:Proceedings of the 6th International ISAAC Congress Ankara, Turkey 13 - 18 August 2007, World Scientific (2009)698-707.

[4] D. G. Gordeziani, On a method of resolution of Bitsadze-Samarskii boundary value problem, Abstracts of reports of Inst. Appl.

Math. Tbilisi State Univ. 2 (1970) 38-40.

2000 Mathematics Subject Classification. 65M06, 65J10Key words and phrases. elliptic equation, difference scheme, stability.

160


An Algorithm for Robot Path Planning in

Environments with Flashing Off-On Obstacles, Using

Cellular Automata

Farid Alaghmand1, Vahid Ahmadi2, Nesa Najafi3, H.Haji Seyyed Javadi4

1 Department of Algorithms and Computations, College of Engineering,

University of Tehran

[email protected]

2 Department of Software Engineering, Azad University of Arak

[email protected]

3 Department of Mathematics and Computer Science, University of shahed

[email protected]

4 Department of Mathematics, University of shahed, Tehran, P.O.Box,

18151-159, Iran

[email protected]

Abstract

This paper presents a new algorithm based on Cellular Automata (CA) for robot path planning. The main novelty

in our algorithm is that it can handle the path planning of environments that contain not only stationary obstacles, but

also contain flashing on-off obstacles with different fixed flashing periods. Using flashing on-off obstacles with different

periods, combined with stationary obstacles, we can model numerous interesting real world path planning problems. Herein

the path computation is performed by successive application of some simple transition functions and the proofs show both

progress and safety properties are preserved by algorithm. That means algorithm ”finally converges” and ”no bad” situation

happens. Verification against safety property is crucial, because unlike environments that only contain stationary obstacles,

in environments where some obstacles flash on and off, we have to ensure that robot never collides with any stationary and

flashing obstacles. We used linear temporal logic to formally specify the problem, safety and progress properties. Finally

some interesting case studies inspired from real world problems have been tested by algorithm. The results are promising

and indicate that the algorithm is time and space efficient in application.

2000 Mathematics Subject Classification. 68W30, 68N15,00A69, 37B15Key words and phrases. Multilayered Cellular Automata, Path planning, temporal logic, Safety, Progress, Pigeonhole law

161


Multiple-Criteria Assembly Flowshop Scheduling

Problem

Fawaz S. Al-Anzi*, Ali Allahverdi**

*Department of Computer Engineering Kuwait University,


[email protected]

**Department of Industrial and Management Systems Engineering

Kuwait University, P.O. Box 5969, Safat, Kuwait

[email protected]

Abstract

Different performance measures are considered in the scheduling research. These performance measures may be classified

as completion time related or due date related. Makespan (Cmax), a completion time related performance measure, is one

of the most widely used performance measures. Minimizing makespan is important in situations where a simultaneously

received batch of jobs is required to be completed as soon as possible. For example, a multi-item order submitted by

a single customer needs to be delivered as soon as possible. The makespan criterion also increases the utilization of

resources. Minimizing maximum lateness (Lmax) is a widely used due date related measure. This objective is particularly

important in situations where there is a penalty to complete a job beyond its due date and the penalty increases with the

gap between the two. We consider a two-stage assembly flowshop scheduling problem with the objective of minimizing

a weighted sum of makespan and maximum lateness. The problem is known to be NP-hard, and therefore, we propose

heuristics to solve the problem. The proposed heuristics are Tabu search (Tabu), particle swarm optimization (PSO), and

self-adaptive differential evolution (SDE). An extensive computational experiment is conducted to compare the performance

of the proposed heuristics. The computational experiment reveals that both PSO and SDE are much superior to Tabu.

Moreover, it is statistically shown that PSO perform better than and SDE. The computation time of both PSO and SDE

are close to each other and it is less than 45 seconds for the largest size problem considered.

2000 Mathematics Subject Classification.Key words and phrases.Assembly flowshop, bicriteria, makespan, maximum lateness, heuristic.

162


On Three New Functions Which Determine The

Equation Of The Ruled Surface

Filiz Kanbay

Department of Mathematics, Faculty of Arts and Science,

Yıldız Technical University, 34210 Esenler, Istanbul, Turkey

[email protected]

Abstract

It is known that a ruled surface in three-dimensional Euclidean space, E3 , is determined by three functions β , α,

D which are called the distribution parameter, the abscissa of the central point and the function that determined the

director-cone of the ruled surface, respectively. But, it is not focused on the question how the equation of the ruled surface

is written by these functions; because it is too hard to find the equation of the ruled surface by using them. This work

answers this question; in other words, three new functions which are sufficient to take place the equations ,β , α , D , are

found. By using the three new functions, it can be written the equation of the ruled surface easily.

References[1] Eisenhart, L. P. ”A Treatise On The Differential Geometry Of Curves And Surfaces” Dover Publications, Inc. 347 New York pp.

28-29 and pp. 241-249 (1960).

[2] Struik Dirk J., ”Lectures on Analytic and Projective Geometry” Addison-Wesley Publishing Company, Inc. pp.193 (1953)

[3] Kanbay, F. ”Bonnet Ruled surfaces” Acta Mathematica Sinica, English Series June, Vol. 21, No3, pp. 623-630 (2005).

2000 Mathematics Subject Classification. 53A05Key words and phrases. Ruled surface, distribution parameter, central point, director-cone, natural equation

163


Application of Least Square Method to Numerical

Solution of Second-Order Boundary Value Problems

G. B. Loghmani

Department of Mathematics, University of Yazd, Yazd, Iran.

[email protected]

Abstract

The numerical solution of second order linear and nonlinear boundary value problems with a general Sturm-Liouville

boundary conditions is considered. A second degree B-spline functions is used to construct the numerical method. E.H.Twizell,

H.N.Caglar and S.H.Caglar used a collocation method and B-spline functions of one degree higher of order of boundary

value problems. But we use B-spline functions of same degree of the order of boundary value problems we will show that

for every ε > 0, there exist an approximate solution vε such that the least square error is less than ε > 0 and vε satisfies

the exact boundary conditions.

References[1] [1]. A. R. Aftabizadeh, N. H. Pavel, and Y. K. Huang, Anti-periodic oscillations of some second order differential equations and

optimal control problem, J. Comput. Appl. Math. 52 (1994), No.1-3, 3-21.

[2] [2]. M. Ahmadinia and G. B. Loghmani, Application of Least Square Method to Some Anti-periodic Boundary Value Problems,Submitted.

[3] [3]. H. N. Caglar, S. H. Caglar and E. H. Twizell, The Numerical Solution of Third-Order Boundary-Value Problems with Fourth-Degree B-Spline functions, Intern. J. Computer Math71(1999)373-381.

[4] [4]. I. Daubecheis, Orthonormal bases of compactly supported wavelets, Comm. Pure Appl. Math. 41 (1988) 909-996.

[5] [5]. C. De Boor, A practical Guide to splines, Springer-Verlag, New York (1978).

[6] [6]. S. Effati and A. V. Kamyad, Solution of boundary value problems for linear second order ODE’s by using measure theory, J.Anal.6 (1998) 139-149.

[7] [7]. M. Gachpazan, A.Kerayechian and A. V. Kamyad, A new method for solving nonlinear second order partial differential equations,Korean J. Comput. Appl. Math. bf 7 (2000),No.2 333-345.

[8] [8]. M. Radjabalipour, Application of Wavelet to Optimal Control Problems, in: International Conference on Scientific Computationand Differential Equations (UBC, Vancouver, July 29-August 3, 2001) .

[9] [9]. J. Stoer and R. Bulirsch, Introduction to Numerical Analysis, Springer-Verlag, Berlin(1993).

2000 Mathematics Subject Classification. 65L99, 34A45Key words and phrases. Least square method, B-Splines, boundary value problems.

164


Fuzzy troubleshooting of a complex desalination /

dehydration plant

G. Zahedi*, S. Saba**

*Simulation and Artificial Intelligence Research Centre,

Chemical Engineering Department , Razi University, Kermanshah, Iran.

**Simulation and Artificial Intelligence Research Centre,

Chemical Engineering Department , Razi University, Kermanshah, Iran.

Abstract

Oil desalination / dehydration plant is very complex and its operation and troubleshooting knowledge is very difficult.

This paper tries to represent a fuzzy troubleshooting method in order to use expert knowledge and handle this complexity

of plant. For this purpose firstly, problematic instrument, were identified then according to the manual information fuzzy

membership functions were constructed and related fuzzy rules were generated. Subsequently, a fuzzy troubleshooting

program which shows the normality degree of each part work was created. This program is able to show the faulty

instrument in a plant which could be the root of some fault in other part of the plant.

2000 Mathematics Subject Classification.Key words and phrases.oil desalination / dehydration, fuzzy, troubleshooting, membership functions, fuzzy rules

165


The Baer criterion for acts over semigroups

Gh. Moghaddasi

Department of Mathematics

Tarbiat Moallem University of Sabzevar

Sabzevar, Iran

[email protected]

Abstract

It is known that although the Baer Criterion for injectivity holds for modules over rings with unit, it is not true for

acts over an arbitrary monoid. Recently, the present author, together with M. Ebrahimi and M. Mahmoudi, published a

paper (Comm. Algebra 35 (2007), 3912-3918) giving for the acts over some classes of semigroups, the Baer Criterion is true.

In this paper we find another classes of monoids such that for acts over them the Baer Criterion hold. We also construct

injective hull of separated acts over another classes of semigroups. Finally we charactrize the subdirectly irreducible of acts

over some classes of semigroups.

References[1] Berthiaume, P., The injective envelope of S-sets, Canad. Math. Bull. 10 (1967), 261-273.

[2] M. Ebrahimi; M. Mahmoudi; Gh. MoghaddasiInjective hulls of Acts over left zero semigroups, Semigroup Forum, vol. 75 (2007)212-220 .

[3] Ebrahimi, M.M.; Mahmoudi, M.; Gh. Moghaddasi On the Baer criterion for acts over semigroups, Communication in Algebra, 35:3912-3918,(2007).

[4] Kilp, M.; Knauer, U.; and Mikhalev, A. Monoids, Acts and Categories, Walter de Gruyter, Berlin, New York, 2000.

[5] M. Mahmoudi; Gh. Moghaddasi. Sequential Injective hulls of Acts over idempotent semigroups, Semigroup Forum vol. 74 (2007)240-246.

2000 Mathematics Subject Classification. 08A60, 08B30, 08C05, 20M30Key words and phrases. S-act, complete, injective hull, subdirectly irreducible, Baer Criterion.

166


The Greeks of Indonesian Call Option

Gunardi*, J.A.M. Vander Weide**

*Department of Mathematics, Gadjah Mada University

Sekip Utara, Yogyakarta, Indonesia, Postcode 55281

[email protected]

**Delft Institute of Applied Mathematics

TU Delft The Netherlands

Abstract

Indonesian Stock Exchange has started to trade option at September 9th, 2004. The option can be considered as anAmerican style barrier option with immediate (forced) exercise if the price hits or crosses the barrier before maturity. Thepayoff of the option is based on a Weighted Moving Average (WMA) of the price of the underlying stock. The barrier isfixed at the strike price plus or minus a 10 percent. The option is automatically exercised when the underlying stock hitsor crosses the barrier and the difference between strike and barrier is paid immediately. We will refer to type of this optionas Indonesian option.

To calculate price of Indonesian option contracts, we have to model the WMA price. This is not easy. In this paper we

study the pricing of Indonesian call option when WMA is replaced by stock price in a Black-Scholes model. We will derive

analytic approximations for the Greeks of the option.

2000 Mathematics Subject Classification. 62P05, 62P20Key words and phrases. Indonesian option, barrier option, Black-Scholes model, The Greeks.

167


Determination of Sintering Kinetics of Mullite by

Differential Dilatometry

H. Belhouchet*, M. Hamidouche**, N. Bouaouadja***,

V. Garnier***, G. Fantozzi****

*Department of physics, Mohamed Boudiaf University, 28000, M’sila, Algeria

[email protected]

**Laboratoire des Matriaux Non Mtalliques, Dpartement d’O.M.P.,

Facult des Sciences de l’Ingnieur, Universit Ferhat Abbas 19000 Stif, Algrie

*** Universit de Lyon, INSA-Lyon, MATEIS CNRS-UMR 5510, 69621

Villeurbanne, France

Abstract

Reaction sintering of zircon and alumina is an easy inexpensive route to obtain homogeneous mullite-zirconia composites

with enhanced mechanical properties. In the present paper we studied the crystallization behaviour of the zircon and

boehmite (as alumina source) mixtures. The powder of boehmite was obtained from partial dehydration of a gibbsite. As-

received raw materials were weighed to produce the 3:2 alumina: silica stoichiometric mixture. All raw powders have been

ball milling and then isostatically pressed followed by sintering at different temperatures. The non-isothermal activation

energies for mullite crystallization were calculated by the Kissinger method using differential dilatometry. Analysis of the

results showed of mullite crystals that bulk nucleation was dominant in mullite crystallisation followed by three-dimensional

growth of mullite crystals with polyhedron-like morphology controlled by diffusion from a constant number of nuclei.

References[1] W.S. Young, I.B. Cutler, Initial sintering with constant rates of heating, J. Am. Ceram. Soc., 53 (11-12) (1970) 659-663.

[2] J.L. Woolfrey, M.J. Bannister, Nonisothermal techniques for studying initial-stage sintering, J. Am. Ceram. Soc., 55 (8) (1972)390-394.

[3] E. Morales, N. Alvarez, J. Leiva, L. Castellaanos, C. Villar, R. Hernandez, Kinetic theory of the overlapping phase transformations:case of the dilatometric method, Acta Materialia. 52 (2004) 1083-1088.

[4] S.C. Vieira, A.S. Ramos, M.T. Vieira, Mullitization kinetics from silica- and aalumin-rich wastes, Ceramics Inter. 33 (2007) 59-66.

2000 Mathematics Subject Classification.74N25Key words and phrases.Mullite, Kinetics of formation, Phase transformation, Activation energy, differential dilatometry.

168


Singularity of the solutions of some transmission

problems in a dihedral

H. Benseridi*, M. Dilmi**

*Department of the Mathematics, Faculty of Sciences,

University of F. Abbas, Setif, 19000, Algeria.

m [email protected]

Abstract

In this paper we prove the existence and uniqueness results for the weak solution of Lame system in a three -dimensional

domain Q non homogeneous composed of two homogeneous bodies Q+ and Q− for various boundary value problems. Using

[2] and [9], we show that the study of singularities of the solutions of problems at the neighborhood of edge A in the spatial

case becomes a study of two problems: a problem of plan deformation and the other is of antiplan deformation.

References[1] H. Benseridi, Regularite de quelques problemes aux limites lineaires et non lineaires dans des domaines non reguliers et non

homogenes, These de Doctorat, Univ- Ferhat Abbas de Setif, Algerie, Juil.(2005).

[2] H. Benseridi, B. Merouani, Quelques problemes de transmission lies au systeme de Lame dans un polyedre pour une classed’espaces de Sobolev a doubles poids, Rev. Roum. Sci. Techn.- Mec. Appl., Tome 48, no 1- 6, Bucarest (2003), pp. 21-34.

[3] H. Benseridi, M. Dilmi, Regularite des solutions de quelques problemes aux limites dans un domaine de R2 non homogene, Anal.Univ. Oradea, fasc. Math. Tom XII (2005), pp. 221-235.

[4] B. Merouani, Solutions singuliers du systeme de l’elasticite dans un polygone pour differentes conditions aux limites, MaghrebMaths. Rev., Vol. 5, Nos 1 & 2, (1996), pp. 95- 112.

[5] H. Benseridi, B. Merouani, Regularity of the solution of a nonlinear boundary value problem governed by Lame operator in anirregular domain, Far East J. Appl. Math. 16(3) (2004), pp. 305-314.

[6] H. Benseridi, M. Dilmi, Boundary value problems in plan sector with corners for a class of Sobolev spaces of double weight. J.Appl. Funct. Anal. (JAFA), Accepted feb (2007).

[7] P. Grisvard, Boundary value problems in plan polygons, Instruction for use, E.D.F, Bulletin de la Direction des etudes et Recherche,serie C, Mathematique no.1, (1986), p 21-59.

[8] V. Parton, Methodes de la theorie Mathematique de l’elasticite, Moscou, (1983).

[9] O.K. Aksentian, Singularitties of the stress-strain state of a plate in the neighborhood of edge, PMM. Vol. 31, No. 1, (1967), pp.

178-186.

2000 Mathematics Subject Classification. 35B40, 35B65, 35C20.Key words and phrases.Dihedral, Elasticity, Singularity, Transcendental function, Edge, Sobolev spaces.

169


Completion Of Cone Metric Spaces

Huseyin Cakallı*, Ayse Sonmez**

*Maltepe University, Department of Mathematics, Istanbul, Turkey

[email protected]

**Istanbul University, Istanbul, Turkey

ayse [email protected]

Abstract

In case of ordinary metric spaces, completion of a metric space is well-known. In 2007, the concept of cone metric space

was introduced by Huang Long-Guang and Zhang Xian. In this note, we construct completion of cone metric spaces, and

prove that any cone metric space can be completed.

References

[1] ] Huang, Long-Guang; Zhang, Xian. Cone metric spaces and fixed point theorems of contractive mappings. J. Math. Anal. Appl.

332 (2007), no. 2, 1468-1476. MR2324351 (2008d:47111).

2000 Mathematics Subject Classification. primary:54 H25,secondaries: 47H10Key words and phrases.Cone metric spaces, completion.

170


Completion Of Cone Normed Spaces



[email protected]



Abstract

In case of ordinary normed spaces, completion of a normed space is well-known. In 2007, the concept of cone metric

space was introduced by Huang Long-Guang and Zhang Xian. Recently Sonmez introduce the concept of cone normed space.

In this note, we construct completion of cone normed spaces, and prove that any cone normed space can be completed.

References[1] Huang, Long-Guang; Zhang, Xian. Cone metric spaces and fixed point theorems of contractive mappings. J. Math. Anal. Appl. 332

(2007), no. 2, 1468-1476. MR2324351 (2008d:47111).

[2] Sonmez, A. Ph D thesis, May 2009

2000 Mathematics Subject Classification. primary:54 H25, secondaries:47H10Key words and phrases.Cone metric spaces, completion.

171


Some Topological Properties Of Cone Metric Spaces



[email protected]



Abstract

In 2007, the concept of cone metric space was introduced by Huang Long-Guang and Zhang Xian. Recently Sonmez

introduce the concept of cone normed space. Some topological properties of cone metric spaces was recently given by

Turkoglu, D. and Abuloha M. In this note, we give some more properties of cone metric spaces and prove related theorems.

References[1] Huang, Long-Guang; Zhang, Xian. Cone metric spaces and fixed point theorems of contractive mappings. J. Math. Anal. Appl. 332

(2007), no. 2, 1468-1476. MR2324351 (2008d:47111).

[2] Sonmez, A. Ph D thesis, May 2009

[3] Turkoglu, D. and Abuloha M, cone metric spaces and fixed point theorems in diametrically contractive mappings, to appear

2000 Mathematics Subject Classification. primary:54 H25, secondaries: 47H10Key words and phrases.Cone metric spaces, topological spaces.

172


Approximating the p.d.f of α-stable distribution by

using Pade and Spline Interpolation

H. Fallahgoul, S.M. Hashemiparast

Department of Mathematics, Faculty of Science, K. N.

Toosi University of Technology, P. O. Box 16765− 165, Tehran, Iran

h−[email protected]

Department of Mathematics, Faculty of Science, K. N.

Toosi University of Technology,P. O. Box 16765− 165, Tehran, Iran

[email protected]

Abstract

Improvements in numerical evaluation of α-stable distribution are presented, the proposed approach is mainly based on

Pade and Spline interpolation, for approximating the p.d.f of α-stable distribution a procedure is presented, the algorithm

for the approximation of α-stable densities is developed, and the results are compared with the other methods and the

accuracy of the algorithm is verified. finally numerical example are presented for illumination.

References[1] J.P. Nolan and B. Rajput, Calculation of multidimensional stable densities, Commun. Statist.-Simula. 24, 551-556, (1995).

[2] V.M. Zolotarev, One-Dimensional Stable Distributions, (Translation of 1983 Russian original), American Math. Society, Providence,

RI, (1986).

2000 Mathematics Subject Classification. 62XXKey words and phrases. α-Stable; Density Function; Pade Approximation; Spline Approximation

173


Common Fixed Points of New Iterations for Two

Asymptotically Nonexpansive Nonself-Mappings in

Banach Spaces

H. Kızıltunc*, M. Ozdemir**, S. Akbulut***

Faculty of Sciences Department of Mathematics

Ataturk University 25240 Erzurum Turkey

*[email protected], **[email protected]

***[email protected]

Abstract

In this paper, we introduce a new two-step iterative scheme for two asymptotically nonexpansive nonself-mappings in

a uniformly convex Banach space. Weak and strong convergence theorems are established for the new two-step iterative

scheme in a uniformly convex Banach space.

References[1] Chidume, C.E., Ofoedu, E.U., Zegeye, H., Strong and weak convergence theorems for asymptotically nonexpansive mappings, J.

Math. Anal. Appl., 280 (2003) 364–374.

[2] Wang, L., Strong and weak convergence theorems for common fixed points of nonself asymptotically nonexpansive mappings, J.Math. Anal. Appl., 323 (2006) 550–557.

[3] Tan, K.K., Xu, H.K., Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process, J. Math. Anal. Appl.,178 (1993), 301-308.

[4] Xu, H.K., Inequalities in Banach spaces with applications, Nonlinear Anal., 16(1991), 1127-1138.

[5] Shahzad, N., Approximating fixed points of non-self nonexpansive mappings in Banach spaces, Nonlinear Anal., 61 (2005), 1031-1039.

[6] Khan, S.H., Takahashi W., Approximanting common fixed points of two asymptotically nonexpansive mappings, Sci. Math. Japon.,53 (1) (2001), 143-148.

[7] Thianwan, S., Weak and strong convergence theorems for new iterations with errors for nonexpansive nonself-mapping, Thai Journalof Math., special Issue (Annual Meeting in Mathematics, 2008), 27-38.

[8] Suantai, S., Weak and strong convergence criteria of Noor iterations for asymptotically nonexpansive mappings, J. Math. Anal.Appl., 311 (2005), 506-517.

[9] Opial, Z., Weak convergence of successive approximations for nonexpansive mappins, Bull. Amer. Math. Soc., 73 (1967), 591-597.

[10] Senter, H.F., Dotson, W.G., Approximating fixed points of nonexpansive mappings, Proc. Amer. Math. Soc., 44 (1974), 375-380.

[11] Cho, Y. J., Zhou, H.Y., Guo, G., Weak and strong convergence theorems for three-step iterations with errors for asymptoticallynonexpansive mappings, Comput. Math. Appl., 47 (2004), 707-717.

[12] Kiziltunc, H., Ozdemir M. and Akbulut S., S., On common fixed points of two nonself nonexpansive mappings in Banach spaces,Chiang Mai J. Sci., 2007; 34(3) : 281-288.

[13] Khan S.H., Fukhar-ud-din H., Weak and strong convergence of a scheme with errors two nonexpansive mappings, Nonlinear Anal.,61 (2005) 1295-1301.

[14] Maiti, M., Ghosh M.K., Approximating fixed points by Ishikawa iterates, Bull. Austral. Math. Soc., 40 (1989) 113-117.

2000 Mathematics Subject Classification. 47H10, 47H09Key words and phrases.Asymptotically nonexpansive nonself-mapping, Weak and strong convergence, Common fixed points.

174


Cone D-Metric Spaces With ∆-Distance And Fixed

Point Theorems Of Contractive Mappings

H.Lakzian, E. Agheshte Moghadam

Department of Mathematics Payame Noor

University of Sabzevar

[email protected]

Department of Mathematics Guilan University, Iran

Abstract

Naoki Shioji, Tomonari Suzuki and Wataru Takahashi in 1995 describe the relationship between weakly contractivemappings and weakly Kannan mappings. They discuss characterizations of metric completeness which are connected withthe existence of fixed points for mappings and then they showed that a metric space is complete if it has the fixed pointproperty for Kannan mappings. Huang Long-Guang, Zhang Xian in 2007 introduced cone metric space and then theyproved some fixed point theorems of contractive mappings on cone metric spaces. Recently, Dhage in 1992 introduced theconcept of D-metric. Afterwards Y.J.Cho and R.Saadati in 2006 introduced a ∆-distance on a D-metric space which is ageneralization of the concept of w-distance due to Kada, Suzuki and Takahashi in 1995. This generalization is non trivialbecause a D-metric doesn’t always define a topology, and even when it does, this topology is not necessarily Hausdorff .In this paper, we first introduce cone D-metric spaces with ∆-distance. Then we describe the relationship between weaklycontractive mappings and weakly Kannan mappings on this spaces. We discuss characterizations of cone D-metric spaceswith ∆-distance completeness which are connected with the existence of fixed points for mappings and then we show thata cone D-metric spaces with ∆-distance is complete if it has the fixed point property for Kannan mappings.

References[1] Y. J. Cho and R. Saadati, A fixed point theorem in generalized D-metric spaces, Bull. Iranian Mathematical society Vol. 32 No.

2(2006), pp 13-19.

[2] B. C. Dhage, Generalized metric spaces and mapping with fixed point, Bull. Calcutta Math. Soc.84 (1992), 329-336.

[3] L.-G. Huang, X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl. 332 (2007)1468-1476.

[4] O. Kada, T. Suzuki and W.Takahashi. Nonconvex minimization theorems and fixed point theorems in complete metric spaces. Math.

Japonica, 44 (1996) 381-591.

2000 Mathematics Subject Classification. 54H25, 47H10Key words and phrases. fixed point, Kannan mappings, D-metric, ∆-distance

175


Cone Metric Spaces With w-Distance And Fixed Point

Theorems Of Contractive Mappings

H.Lakzian, F.Arabyani

Department of Mathematics Payame Noor

University of Sabzevar

[email protected]

Department of Mathematics; University of Birjand

f [email protected]

Abstract

Osama Kada, Tomonari Suzuki, And Wataru Takahashi in1996 first introduced the concept of w-distance on a metric

space and improved Carist’s fixed point theorem, and the nonconvex minimization theorem accoding to Takahahi. Further

they proved a fixed point theorem in a complete metric space . Huang Long-Guang, Zhang Xian in 2004 has introduced

cone metric space without w-distance and then proved some fixed point theorems of contractive mappings on cone metric

spaces. Naoki Shioji, Tomonari Suzuki, and Wataru Takahashi in 1998 study the relationship between weakly contractive

mappings and weakly Kannan mappings and then discuss characterization of metric completeness which are connected with

the existence of fixed points for mappings and they show that a metric space is complete if it has the fixed point property

for Kannan mappings. We compose these concepts together and introduce cone metric space with w-distance and then we

prove a few fixed point theorems. In this paper, we introduce cone metric spaces with w-distance on X. Then we prove

fixed point theorems of weakly contractive, weakly Caristi and weakly Kannan mappings.

2000 Mathematics Subject Classification. 54H25, 47H10Key words and phrases. Mcone metric space with w-distance, p-Cauchy, p-convergent, weakly contractive, weakly Kannan.

176


Weighted Function Algebra on Weighted Flows,

Compactifications of Weighted Flows, Existence and

None Existence

H. Lakzian 1, R. Jahanpanah 2

1 Department of Mathematics University of Guilan

[email protected]

2 Department of Mathematics University of Guilan

[email protected]

Abstract

During the past decade harmonic analysis on weighted semigroups has enjoyed considerable attention, and a good dealof results have been proved in this connection. H A M Dzinotyiweyi in 1984 first introduced the concept of weightedfunction algebra on groups and semigroups. Let S be a locally compact Hausdorff semitopological semigroup. A mappingwS : S → (0,∞) is called a weight function on S if wS(st) ≤ wS(s)wS(t). Khadem-Maboudi A A and Pourabdollah M A in1999 study the relationship between semigroups and weighted semigroups with the introduce means, homomorphisms, andcompactifications of weighted semitopological semigroups. They also show that these compactifications do not retain allthe nice properties of the ordinary semigroup compactifications unless we impose some restrictions on the weight functions.In this paper, we introduce a weight function on flow (S, X, σ) as follows: Let X is a locally compact Hausdorff topologicalspace and a mapping wX : X → (0,∞) is called a weight function on X if wX(sx) ≤ wX(s)wx(x). Then transform it toweighted flow ((S, wS), (X, wX), σ). We define them corresponding to weighted flows compactifications. We also show thatthese compactifications do not retain all the nice properties of the ordinary flow compactifications unless we impose somerestrictions on the weight functions.

2000 Mathematics Subject Classification. 22A20, 22A25, 43A60.Key words and phrases. weighted flow, weighted LUC-compactifications, weighted AP-compactifications, weighted WAP-compactifications.

177


Prediction of technical state of petrol equipments

(thermic motor case)

H. Meglouli*, E. Bouali F.Ait Hocine**

*Laboratoire de recherche d’electrification d’entreprises industrielles.

Faculte des hydrocarbures et de la chimie. Universite de Boumerdes.

[email protected]

Abstract

The improvement of the exploitation accuracy of petrol equipments is possible by the prediction of their technical state,

this operation can insure their rational use, and permit to avoid unexpected damages of the equipments by enlarging in one

hand the average time between the reparation that is reduced by consequence the time and the volumes of the reparations.

In the resolution of the prediction problem of parameters variations which characterize the state of entities functioning of

petrol equipments in time.

We determine the mutual relation between future gaps of parameters and retrospective values. The observation, of pa-

rameters variations characterising petrol equipments state, shows that they are uncertain functions. The knowledge of

distribution laws of these uncertain functions is not enough and it must know also the uncertain functions values for some

values of time argument. The distribution laws present a certain difficulty for speaking. For this we use for the uncertain

processes description, their moments to be known: Mathematical expectation, the variety, the moments of correlation. As

a particular case of study, we consider diesel motors. A lot of parameters characteterize the state of entities and their

functioning of diesel motors, they are function of work time. We consider particularly the value and the uniformity of

the flow of pump motor-fuel at high pressure of the system (motor diesel).These letters vary in the time according to the

variation of temperature conditions or of usury of mechanical pieces, and cinematical couples that constitute the pump.

2000 Mathematics Subject Classification.Key words and phrases.Mathematical expectation; prediction problem; function work time; petrol equipments.

178


Detecting and adjusting inconsistencies through a

graphical and optimal approach in AHP

H. Navidi*, M. Ahmadi**

*Department of Applied Mathematics, Shahed University,


[email protected]

**Department of Applied Mathematics, Shahed University,


[email protected]

Abstract

It is difficult to rank the alternatives in an ordinal or/and cardinal inconsistent AHP model. There is an iterative

method to detect and adjust inconsistencies. In this study it is improved, lots of conditions omitted and it is confirmed

by the numerical results by MATLAB. Gower Plot upon the singular value decomposition of paired comparisons matrix

is used to detect inconsistencies. The improved optimization model provides suggested adjustments satisfying the bounds

determinate by decision maker. After observing suggested numerical changes and Gower Plot the decision maker may revise

iteratively the preferences to improve inconsistencies.

2000 Mathematics Subject Classification.90B50, 91C99, 62C05Key words and phrases.AHP, Inconsistency, Gower Plot, Paired Comparisons, Singular Value Decomposition.

179


A Summability Factor Theorem By Using An Almost

Increasing Sequence

H. Nedret Ogduk

[email protected]

Abstract

When given an infinite series∑

an with the partial sums (sn) and a normal matrix A = (anv), i. e. a lower triangularmatrix of non-zero diagonal entries, A defines the sequence-to-sequence transformation, mapping the sequence s = (sn) toAs = (An(s)), where

An(s) =n∑

v=0

anvsv , n = 0, 1, ...

In this case, by | A |k summability of this infinite series we mean the convergence of the series∑

nk−1 | ∆An(s) |k, by

Tanovic-Miller in [5], where k ≥ 1 and ∆An(s) = An(s)− An−1(s).Let (pn) be a sequence of positive numbers such that Pn =

∑nv=0 pv →∞ as n →∞, (P−i = p−i = 0, i ≥ 1). Sulaiman

in [4] defined | A, pn |k summability of the series. Specifically, when anv = pvPn

, | A, pn |k summability is equivalent to

| N, pn |k summability which was introduced by Bor in [1].

Bor in [2] proved the sufficient conditions for | N, pn |k summability of the series∑

anλn, later Mazhar in [3] alsoproved under weaker conditions by using an almost increasing sequence.

The object of this paper is to show that these two results can be generalized to a wide class of summability methods.

References[1] Bor, H., On two summability methods, Math. Proc. Camb. Phill. Soc., 97 (1985) 147-149.

[2] Bor, H., On absolute summability factors, Proc. Amer. Math. Soc., 118 (1993) no.1, 71-75.

[3] Mazhar, S. M., Absolute summability factors of infinite series, Kyungpook Math. J., 39 (1999) 67-73.

[4] Sulaiman, W. T., Inclusion theorems for absolute matrix summability methods of an infinite series (IV), Indian J. Pure Appl.Math., 34 (11) (2003) 1547-1557.

[5] Tanovic-Miller, N., On strong summability, Glasnik Mathematicki, 34 (14) (1979) 87-97.

2000 Mathematics Subject Classification.Key words and phrases.Absolute summability, summability factors, infinite series

180


Topological Left Almost Convergence and Extreme

Points of Amenable Locally Compact Semigroups

H. P. Masiha


K. N. Toosi University of Technology,

P.O. Box 16315− 1618, Tehran, Iran.

[email protected]

Abstract

In this talk, the extreme points and topological left almost convergence in the set of all topological left invariant means

of locally compact semigroups are considered, which are the generalization of the results of S. P. Lloyd.

References[1] S. K. Berberian, Measure and integration, New York: Chelsea, (1985).

[2] J. Conway, A course in functional analysis, Graduate texts in Math. 96, Springer-Verlag, (1985).

[3] M. M. Day, Amenable semigroups, Illinois J. Math. 1 (1957) 509-544.

[4] E. E. Granirer, Extremely amenable semigroups, Math. Scand. 17 (1965) 177-179.

[5] E. E. Granirer, Extremely amenable semigroups II, Math. Scand. 20 (1967) 93-113.

[6] E. Hewitt, K. Ross, Abstract harmonic analysis I, 2nd.ed., Springer-Verlag, Berlin (1979).

[7] J. Kelley, I. Namioka et al., Linear topological spaces, Van Nostrand, New York (1963).

[8] J. M. Ling, Extremely amenable locally compact semigroups, Far East J. Math. Sci. (FJMS) 1 (4) (1999) 533-559.

[9] S. P. Lloyd, A mixing condition for extreme left invariant means, Trans. Amer. Math. Soc. 125 (1966) 461-481.

[10] T. Mitchell, Constant functions and left invariant means on semigroups, Trans. Amer. Math. Soc. 119 (1965) 244-261.

[11] I. Namioka, FØlner’s conditions for amenable semigroups, Math. Scand. 15 (1964) 18-28.

[12] J.-P. Pier, Amenable locally compact groups, Wiley-Interscience, New York, (1984).

[13] A. Riazi and H. P. Masiha, Topological lumpy subsets of a locally compact semigroup and topological extreme amenable, Far EastJ. Math. Sci. (FJMS) 5(3) (2002) 289-310.

[14] J. C. S. Wong, Invariant means on locally compact semigroups, Proc. Amer. Math. Soc. 31(1) (1972) 39-45.

[15] J. C. S. Wong, Abstract harmonic analysis of generalized function in locally compact semigroups with applications to invariant

means, J. Austral Math. Soc. Ser A. 23 (1977) 84-94.

2000 Mathematics Subject Classification.46H20, 43A07, 43A10Key words and phrases.Extreme point,Mean, Topological left almost convergence, Extreme amenability.

181


A Simultaneously Determination Of The Optimal

Trajectory And Control For Vibrating Shell Systems By

Measures

H. R. Sahebi, S. Ebrahimi, A. Fakharzadeh J.


Ashtian Azad University and Member of Young Researcher Club, Iran

[email protected]


Ashtian Azad University and Member of Young Researcher Club, Iran

s [email protected]

Department of Mathematics, Shiraz University of Technology, Shiraz, Iran

a [email protected]

Abstract

In the recent decade, a considerable number of optimal control problems have been solved successfully based on the

properties of the measures. This method, called embedding method, has many useful benefits like finding the global solution,

a linear treatment even for the strong nonlinear problems and also easy calculations in the numerical schemes. But, in

general, the method is not able to determine the optimal trajectory and control at the same time; moreover, it rarely

uses the advantages of the classical solutions of the involved systems. In this article, for a wave control system governed

by vibrating shell equations, we are going to present a new solution path by applying this method and also using the

trigonometric series. First by considering all conditions, the problem is represented in a variational format in which the

trajectory is shown by a trigonometric series with the unknown coefficients. Then the problem is converted into a measure

theoretical optimization one that the unknowns are the mentioned coefficients and a positive radon measure. It is also

proved that the new problem has the optimal solution and how one be able to identify the optimal trajectory and control

simultaneously form the solution of a finite linear programming problem. In this manner some numerical examples are also

given.

2000 Mathematics Subject Classification.49Q10, 49Q20, 49J20Key words and phrases. vibrating shell, trigonometric series, Radon measure, optimal control, linear programming.

182


Evaluating A Novel Cellular Automaton Based Energy

-Conservating Solution In Mobile Wierless Sensor

Networks

H. Haj Seyyed Javadi*, Se. Adabi**, A. Rezaee***

*Department of Mathematics, Shahed University,

Tehran, P.O. Box: 18151-159, Iran.

[email protected]

**Computer Engineering Department, Islamic Azad University,

North Tehran Branch, Tehran, Iran.

[email protected]

***Member of Young Research Club, Islamic Azad University,

Science and Research Branch, Tehran, Iran.

[email protected]

Abstract

According to the traditional definition of wireless sensor networks (WSNs), static sensors have limited the feasibility of

WSNs in some kind of approaches, so the mobility was introduced in WSN. Mobile nodes in a WSN come equipped with

battery and from the point of deployment; this battery reserve becomes a valuable resource since it cannot be replenished.

Hence, maximizing the network lifetime by minimizing the energy is an important challenge in mobile WSN. Energy

conservation can be accomplished by different approaches. One approach is utilizing the low-power stand-by mode supported

by the wireless devices and adjusting the transmission range on each node. In this paper, an energy conservation solution

based on cellular automata is presented. The main objective of this approach is based on dynamically adjusting the

transmission range and switching between operational states of the sensor nodes.

2000 Mathematics Subject Classification. 37B15, 68Q80, 90B18Key words and phrases. Cellular Automata, Energy Conservation, Mobile Wireless Sensor Networks

183


Growth of Solutions of Linear Differential Equations

With Entire Coefficients Having the Same Order and

Type

H. Saada

University of Mostaganem, Algeria

[email protected]

Abstract

The value distribution theory of a meromorphic function founded by R. Nevanlinna play an important role in the

study of the growth and oscillation of solutions of linear differential equations in the complex plane. The question which

arises in this domain is when and how many independent solutions of finite order may appear. Partial results have been

available since a paper of Frei [2]. In its generality, the problem remains oppen. Recently, Jin Tu and Cai- Feng Yi [5]

have investigated the case when the coefficients have the same order and different types. In this paper, we will improve

this result by taking coefficients having the same order and type.

References[1] B. Belaıdi, S. Hamouda; Orders of solutions of an n-th order linear differential equations with entire coefficients, Electron. J. Diff.

Eqns, 61 (2001), 1-5.

[2] M. Frei, Sur l’ordre des solutions entieres d’une equation differentielle lineaire, C. R. Acad. Sci. Paris, 236 (1953), 38-40.

[3] G. G. Gundersen; Finite order solutions of second order linear differential equations, Trans. Amer. Math. Soc. 305 (1988), 415-429.

[4] I. Laine, and R. Yang; Finite order solutions of complexe linear differential equations, Electron. J. Diff. Eqns, 65 (2004), 1-8.

[5] J. Tu, Z. X. Chen, X. Zheng; Growth of solutions of complex differential equations with coefficients of finite iterated order, Electron.

J. Diff. Eqns, 54 (2006), 1-8.

2000 Mathematics Subject Classification. 34M10, 30D35Key words and phrases.Growth of solutions, entire coefficients, order of growth

184


Existence and uniqueness results of some fractional

BVP

H. Seddiki, S. Mazouzi

Department of Mathematics, University Badji Mokhtar,

P.O.Box 12, Annaba 23000, Algeria.

Abstract

In recent years the fractional derivatives have considerably received a great interest of a lot of investigators. As amatter of fact they have been successfully applied in several fields of science and engineering such as viscoelastic materials,electrotechnical processes as well as signal processing.

Actually, the concept of fractional derivatives is a systematic generalization of the classical derivatives to non integralorders which gives reliable models in engineering and other fields of science better than those based on the ordinaryderivatives. Our contribution in this matter is the investigation of the existence and uniqueness of the fractional boundaryvalue problem

cDα0 y(t) = f(t, y(t), y′ (t)), 0 < t < T, 1 < α ≤ 2,

a1y(0) + a2y(T ) = c1,

b1y′(0) + b2y′(T ) = c2,

where cDα0 is Caputo’s fractional derivative, f : [0, T ] × R × R → R is a continuous function, a1, a2, b1, b2, c1, and c2

are given real constants. By using the Banach fixed point theorem we establish the existence of a unique continuously

differentiable solution to the above BVP.

2000 Mathematics Subject Classification.26A33, 65L10Key words and phrases.Boundary value problem, fractional differential equation, fixed point theorem.

185


Copulas Pareto: Characterizations and Dependence

Measures

Hakim Bekrizadeh

Faculty member of Department of Statistics, Ilam Payame Noor University, Iran

h [email protected]

Abstract

A bivariate copula can be statistically interpreted as a bivariate distribution function with uniform marginals. Sklar

(1959) argues that for any bivariate distribution function, say H with marginals F and G, there exists a copula functional,

say C, such that H(x, y) = C[F (x), G(y)], for (x, y)T in the support of H. This article provides Copulas pareto using Sklar

theorem and new characterizations and dependence measures Kendall’s tau and Spearman’s rho of the Copulas pareto.

2000 Mathematics Subject Classification.Key words and phrases. Copulas, bivariate pareto, Kendall’s tau, Spearman’s rho

186


The Importance of Using The “Omega Calculus” in

Computer Algebra

Halil Snopce*, Ilir Spahiu**, Azir Aliu***

*Fac. of Contemporary Sciences and Technologies, Tetovo,R.Macedonia

[email protected]

**University of ”Ss. Cyril and Methodius”, Fac.of Pedagogy, Skopje, R.Macedonia

[email protected]

***Fac. of Contemporary Sciences and Technologies, Tetovo,R.Macedonia

[email protected]

Abstract

In his book ”Combinatory Analysis”, Percy A. MacMahon developed the so called ”Omega calculus”. In this contribu-

tion we emphasize the importance of the ”Omega Calculus”. Using the properties of this tool, we investigate the possible

aplication in computer algebra.We investigate how the methods presented by Macmahon’s can be applied to the problem of

enumerating lattice points in convex polyhedron. A lot of Scientific and Engineering problems require the solution of large

systems of linear equations of the form Ax=b in an effective manner. LU-Decomposition offers good choices for solving this

problem. QR Factorization has implementation in various problems of linear algebra. Discrete Fourier transformation can

be implemented in different problems regarding the signal and image processing, pattern recognition etc. We investigate a

possible optimization of these problems finding the lower bound of processing elements (PEs) required by a schedule as a

function of n. From a given algorithm, defining a corresponding index space, we consider that the elements of that index

space are lattice points inside 3-dimensional convex polyhedron. The faces of the polyhedron are defined by the inequalities

which are the consequence of the given algorithm. From these inequalities augmenting by the condition of linear schedule

for the corresponding dag, we convert the geometrical interpretation of the problem, into a combinatorial interpretation,

exactly into finding of solutions to the system of Diophantine equations. Then we run the Mathematica program Diophan-

tineGF.m. This program calculates the generating function from which is possible to find the number of solutions to the

system of Diophantine equalities, which in fact gives the lower bound for the number of processors needed for achieving a

given schedule. We give a mathematical explanation and then we confirm the conclusion taking a random example.

References[1] P. Cappello, Omer Egecioglu, Processor lower bound formulas for array computations and parametric Diophantine systems, Int. J.

Found. Comput. Sci. 9 (4) (1998) 351-378

[2] Snopce H., Spahiu I., An implementation of McMahon’s partition analysis in ordering the number of lattice points in convex

polyhedron with examples for systolic arrays, Proc. of the ITI 2009 31st int. conf. pp. 659-664

2000 Mathematics Subject Classification. 11Y50Key words and phrases.Omega calculus, generating function, system of diophantine equations, lattice points, convex polyhedron,lower bound of PEs.**This research was supported by Scientific Research Committee of SEE-University, Tetovo

187


An Approach for Simultaneously Determining the

Optimal Trajectory and Control of a Heating System

Hamid Reza Sahebi*, Sara Ebrahimi**

*Department of Mathematics

Islamic Azad Ashtian University, Ashtian,Iran

[email protected]

**Department of Mathematics

Islamic Azad Ashtian University, Ashtian,Iran

s [email protected]

Abstract

In the recent decade, a considerable number of optimal control problems have been solved successfully based on the

properties of the measures. Even the method, has many useful benefits, in general, the method is not able to determine the

optimal trajectory and control at the same time; moreover, it rarely uses the advantages of the classical solutions of the

involved systems.

In this article, for a one -dimensional heat wave control system. we are going to present a new solution path. First, by

considering all necessary conditions, the problem is represented in a variational format in which the trajectory is shown by

a trigonometric series with the unknown coefficients. Then the problem is converted into a new one that the unknowns are

the mentioned coefficients and a positive radon measure. It is proved that the optimal solution is exited and . it is also

explained how the optimal pair would be identified from the results deduced by a finite linear programming problem. In

this manner ,a numerical examples is also given.

References[1] Fakharzadeh J., A. and Rubio, J. E. Global Solution of Optimal Shapes Design Problems. ZAA Journal for Analysis and its

Applications. vol.16, No.1, p.143-155, 1999.

[2] Fakharzadeh J., A., Determining the best domin for a nonlinear wave system, JAMC J. Of Applied Mathematics and computations,Vol13, No.1-2, pp.183-194, 2003.

[3] Farahi, M. H., The Boundary Control of the Wave Equation. PhD thesis, Dept. of Applied Mathematical Studies, Leeds University,April 1996.

[4] Farahi, M. H., Mehneh, H. H. and Borzabadi, A. H., Wing drag minimization by using measure theory. J. Optimization Methodaand Software, pp.1-9, 2005.

[5] Farahi, M.H., Mehne H.H. and Borzabadi A.H., Wing drag minimization by using measure theory. Optimization Methods andSoftware Vol.00, No. 00, Month, 1-9, 2005.

[6] Friedman, A., Foundations of Modern Analysis. Rinehart and Winston, New York, 1970.

[7] Kamyad, A. V. Rubio, J. E. and Wilson, D. A., The optimal control of multidimensional diffu-sion equation. JOTA, 1(70), pp.191-209, 1991.

[8] Wyliy, C. R., Advance Engineering Mathematics. John Wiley and Sons , 1979.

[9] Mikhailov, V. P., 1978, Partial Differential Equations. MIR, Moscow.

[10] Rosenbloom, P.C., Qudques Classes de Problems Exteremaux., Bulletin de Societe Mathema-tique de France, 80:183-216, 1952.

[11] Rubio, J. E., Control and Optimization: the linear treatment of nonlinear problems. Manch-ester University Press, Manchester,1986.

[12] Rubio, J. E., 1993 The global control of nonlinear elliptic equation. Journal of Franklin Insti-tute, 330(1), p.29-35.

[13] Rudin, W. Real and Complex Analysis Advance. McGraw-Hill series in higher mathematics(3ed edition), 1987.

[14] Wyliy, C. R. and Barrett, L. C, Engineering Mathematics. McGraw-Hill , 1985.

2000 Mathematics Subject Classification. 49QJ20, 49J45, 49M25, 76D33Key words and phrases.optimal control, trigonometric series, optimal trajectory, finite linear programming

188


An Equity-efficiency Location of a Noisy Facility in a

continuous plane

Hamidreza Navidi1, Ruhollah Heydari2, Saeed Safari Moghadam3

1 Industrial Engineering Department, Shahed University, Tehran, Iran

[email protected]


[email protected]


[email protected]

Abstract

Production engineers are often faced with the problem of placing a noisy but necessary piece of equipment, process,

material, or facility in general, into a working environment. Such semi-obnoxious facilities are defined here as facilities that

could introduce hazards into the workplace. Similarly, urban planners are often faced with the challenging task of placing

in a city a fire department, an airport or a shopping center. These public service facilities should be placed close to the

residential area they serve but not too close to prevent noise pollution. In this paper, a new model for the noisy facility

location problem in a continuous plane is introduced. The new model is composed of a minisum function to represent the

transportation costs and a maximin function to represent the obnoxious effects of the facility by maximizing the distance

of the nearest inhabitant from new facility. Although transportation is managed into a network approximately could be

supposed as rectangular roads, intensity of noise inversely depends on the squared euclidean distance of the inhabitants

from noise source, so the formulation includes rectangular minisum and squared euclidean maximin criteria problem. Using

some mathematical theories, the problem dimension is decreased from three to two and then efficient points on this two-

dimensional space are searched. An algorithm that constructs the entire nondominated vectors and efficient sets is presented

and it is illustrated in an example problem.

References[1] R.L. Francis, J.A. White, Facility layout and location: an analytical approach., Prentice-Hall, 1974.

[2] D. Halliday, R. Resnick, J. Walker, Fundamentals of Physics, John Wiley - Sons, Inc. 2001.

[3] E. Melachrinoudis, Z. Xanthopulos, Semi-obnoxious single facility location in Euclidean space, Comput. Oper. Res. 30 (2003) 2191-2209.

[4] E. Melachrinoudis, Bicriteria location of a semi-obnoxious facility, Comput. Ind. Eng. 37 (1999) 581-593.

[5] H. Yapicioglu, A.E. Smith, G. Dozier, Solving the semi-desirable facility location problem using bi-objective particle swarm, Eur. J.Oper. Res. 177 (2007) 733-749.

2000 Mathematics Subject Classification. 60K30, 90C90, 90B85, 90C29, 90C30Key words and phrases. Location, Noisy Facility, Semi-obnoxious Facility, Efficient Set, Nondominated Set

189


Holditch-Type Theorems

for The 1-Parameter Closed Motions

Using Lorentzian Matrix Multiplication

Handan Yıldırım1, Salim Yuce2, Nuri Kuruoglu3

1 Istanbul University, Faculty of Science, Department of Mathematics,

34134, Vezneciler, Istanbul, Turkey

[email protected]

2 Yıldız Technical University, Faculty of Arts and Science,

Department of Mathematics, 34210, Esenler, Istanbul, Turkey

[email protected]

3 University of Bahcesehir, Faculty of Arts and Science,

Department of Mathematics Computer Sciences, 34100, Besiktas, Istanbul, Turkey

[email protected]

Abstract

In [6], a new matrix multiplication was defined in Rmn × Rn

p by using Lorentzian inner product in Rn, where Rmn is the

set of matrices with m rows and n columns.

In this study, under the 1-parameter closed motion in Lorentzian 3-space L3, Holditch-Type Theorems are given by

means of this Lorentzian matrix multiplication and the areas of the closed projection curves of the closed space curves onto

Euclidean plane.

References[1] H. Holditch, Geometrical Theorem, Q.J. Pure Appl. Math., 2 (1858) 38.

[2] W. H. Greub, Linear Algebra, 3rd ed., Springer-Verlag and Academic Press, New York, (1967).

[3] H. R. Muller, Erweiterung des Satzes von Holditch fur geschlossene Raumkurven, Abh. Braunschw. Wiss. Ges. 31 (1980) 129-135.

[4] B. O’ Neill, Semi-Riemannian Geometry, Academic Press, New York, (1983).

[5] J. J. Dzan, Trigonometric Laws on Lorentzian Sphere S21 , Journal of Geometry, 24 (1985) 6-13.

[6] H. Gundogan, O. Kecilioglu, Lorentzian matrix multiplication and the motions on Lorentzian plane, Glasnik Matematicki, 41 (61)(2006) 329-334.

2000 Mathematics Subject Classification. 53A17, 53B30, 53B50Key words and phrases. Lorentzian matrix multiplication, Lorentzian motion, Holditch-Type Theorems**The first author thanks TUBITAK-BAYG for their financial supports during her doctorate studies.

190


Optimal Control For High Order Pdes

Hanif Heidari, Alaeddin Malek



[email protected]



[email protected]

Abstract

In this paper we consider linear high order PDEs with nonhomogeneous boundary conditions. Our goal is to find some

control functions that acts in a part of boundary such that desired state is reached in the given time T . At first, solution

of high order PDE is calculated, then we construct a moment problem for solving optimal control problem. The moment

problem can be solved by choosing appropriate optimization algorithm.

References[1] S. Boyd, L. Vandenberghe,Convex Optimization, Cambridge University Press, 2004.

[2] S. Micu, E. Zuazua, Controle non lineaire et applications: An Introduction to the Controllability of Partial Differential Equations,Sari, T., ed., Collection Travaux en Cours Hermann, Paris, 2004.

[3] A. D. Polyanin, Handbook of Linear Partial Differential Equations for Engineers and Scientists, Chapman & Hall/CRC Press,Boca RatonLondon, 2002.

[4] J. N. Reddy, Introduction to Functional Analysis, John Wiley and sons, 1998.

2000 Mathematics Subject Classification. 49J20, 35E99, 47F05Key words and phrases. Optimal control; High order PDEs; Moment problem

191


Counting of the distinct fuzzy subgroups of the dihedral

group D2pn

Hassan Naraghi

Department of Mathematics, Islamic Azad University,

Ashtian Branch. P. O. Box 39618-13347, Ashtian, Arak, Iran.

[email protected]

Abstract

In this paper, by using of an equivalence relation on fuzzy subgroup, we determine the number of distinct fuzzy sub-groups of the dihedral group of order 2pn such that p is a prime and p ≥ 3. A fuzzy subset of a set X is mappingµ : X → [0, 1]. Fuzzy subset µ of a group G is called a fuzzy subgroup of G if(G1) µ(xy) ≥ µ(x) ∧ µ(y)∀x, y ∈ G;

(G2) µ(x−1) ≥ µ(x)∀x ∈ G.The set of all fuzzy subgroup of a group G denoted by F (G). Let G be a group, and µ, ν ∈ F (G). Defined three equivalencerelation as follow respectively:(i) We say that µ is equivalence ν, written as µ ≈ ν if Fµ = Fν .(ii) We say that µ is equivalent to ν, written as µ ∼ ν if

1. µ(x) > µ(y) ⇔ ν(x) > ν(y), for all x, y ∈ G.

2. µ(x) = 0 ⇔ ν(x) = 0, for all x ∈ G.

(iii) We say that µ is equivalence ν, written as µ 't ν if there exists an isomorphism f from suppµ to suppν such that forall x, y ∈ suppµ,

µ(x) > µ(y) ⇔ ν(f(x)) > ν(f(y))

Let G be a group and µ, ν ∈ F (G). We say that µ is equivalence ν, written as µ ∼t ν, if and only if Fµ = Fν andsuppµ = suppν.The set of all fuzzy subgroups µ of G such that µ(e) = 1 denoted by F1(G) . The number of equivalence classes ∼ on F1(G)will be denoted by r?

G.

Theorem. Suppose that p be a prime and p ≥ 3. If G is a dihedral group of order 2pn, then r?G =

n−1∑i=1

pir?(D

2pn−i ) +

pn−pp−1 + 2n+2 + 4pn − 1.

References[1] P.S.Das, Fuzzy groups and level subgroups, Math. Appl.8(1981)264-269.

[2] C.Degang and J.Jiashang, Some notes on equivalence fuzzy sets and fuzzy subgroups,Fuzzy sets and systems.152(2005)403-409.

[3] M.Mashinchi and M. Mukaidonon, On fuzzy subgroups classification, Research Report of Meiji University, Japan.9(65)(1993)31-36.

[4] John N. Mordeson, Kiran R. Bhutani and Azriel Rosenfeld, Fuzzy Group Theory, Springer-Verlag Berlin Heidelberg.(2005).

[5] V.Murali and B.B. Makamba,On an equivalence of fuzzy subgroups I ,Fuzzy sets and systems.123(2001)259-264.

[6] V.Murali and B.B. Makamba, Counting the number of fuzzy subgroups of an abelian group of order pnqm,Fuzzy sets and sys-tems.144(2004)459-470.

[7] A.Rosenfeld, Fuzzy groups, J.Math.Anal.Appl.35(1971)512-517

[8] Zhang Yunji and Kaiqizou, A not on an equivalence relation on fuzzy subgroups,Fuzzy Sets and Systems,95(1998)243-247.

[9] Zadeh, L.A, Fuzzy sets,information and control8(1965) 338-353.

2000 Mathematics Subject Classification.20N25.Key words and phrases.Fuzzy subgroups, Dihedral group, Equivalence relation

192


Analyzing Near-Normal Data Using A New Class Of

Skew Distributions

Hassan Elsalloukh

University of Arkansas at Little Rock,

Department of Mathematics and Statistics, Little Rock, Arkansas, USA

[email protected]

Abstract

A family of distributions, which was first introduced by OHagan and Leonard in 1976 for Bayesian analysis of normal

means and was later investigated in detail by Azzalini in 1985 and 1986, is modified leading to a new class of asymmetric

distributions. A new score test is derived for detecting non-normality within the new class of asymmetric distributions.

Then, the new score test is applied on two examples of real data sets within the new class of asymmetric distributions to

detect non-normality. Maximum likelihood estimators are used to fit the data with a skew distribution and compared to

studies in which researchers used the normal distribution.

References[1] R. B. Arellano-Valle, H. W. Gmez, and F. A. Quintana, Statistical inference for a general class of asymmetric distributions. Journal

of Statistical Planning and Inference 128 (2005), no. 2, 427-443.

[2] M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions. New York: Dover Publications, 1965.

[3] A. Azzalini, A Class of Distributions Which Includes the Normal Ones. Scand. J. Statist., 12(1985), 171-178.

[4] A. Azzalini, Further Results on a Class of Distributions Which Includes the Normal Ones. Statistica, 46(1986), 199-208.

[5] G. E. P. Box, A Note on Regionns of Kurtosis. Biometrika, 40(1953), 465-468.

[6] D. R. Cox and D. V. Hinkley, Theoretical Statistics. London: Chapman and Hall, 1974.

[7] H. Elsalloukh, J. H. Guardiola, and D. M. Young, The Epsilon-Skew Exponential Power Distribution Family. Far East Journal ofTheoretical Statistics 17(1) (2005), 97-112.

[8] G. S. Mudholkar and A. D. Hutson, The Epsilon-Skew-Normal Distribution for Analyzing Near-Normal Data. Journal of StatisticalPlanning and Inference, 83(2000), 291- 309.

[9] A. OHagan, and T. Leonard, Bayes Estimation Subject to Uncertainty about Parameter Constraints. Biometrika, 63(1976), 201-202.

[10] D. J. Poirier, D. Tello, and E. Zin, A diagnostic Test for Normality Within the Power Exponential Family, Journal of Business andEconomic Statistics, 4(1986), 359-373.

[11] J. C. W. Rayner and D. J. Best, Smooth Tests of Goodness of Fit, Oxford: Oxford University Press, Reprinted in Small Data Sets,P. 123.

[12] J. R. Serfling, Approximation Theorems of Mathematical Statistics, New York: Wiley, 1980.

[13] S. D. Silvey, The Lagrangian Multiplier Test. Ann. Math. Statist., 30(1954), 389-407.

[14] J. W. Tukey, Exploratory Data Analysis. Addison-Wesley, Reading, MA, 1977.

2000 Mathematics Subject Classification.60E05Key words and phrases. Skewness, Normal distribution, Skew Normal distribution, Score tests

193


Common zeros of exponential polynomials and Shapiro

conjecture

Hassane Abbas*, Ahmed Hajj-Diab**

*Lebanese University, Faculty of Sciences-1,

Department of mathematics, Hadeth Beirut-Lebanon

[email protected]

**Lebanese University, Faculty of Sciences-1,

Department of mathematics, Hadeth Beirut-Lebanon

Abstract

Shapiro conjectured that if two exponential polynomials have infinitely many zeros in common, they have a non trivial

common factor. In this paper we prove this conjecture in many particular cases where the coefficients of the polynomials

are algebraic and the frequencies are linear combination with rational coefficients of two algebraic numbers.

2000 Mathematics Subject Classification. 11L03, 11L07, 11C08Key words and phrases. Zeros of exponential polynomial, Shapiro conjecture.

194


What Are Copulas?

Heydar Ali Mardani-Fard*, Arash Ardalan**

*Department of Statistics, Shiraz University, Shiraz, Iran

h [email protected]

**Department of Statistics, Shiraz University, Shiraz, Iran

[email protected]

Abstract

A copula is, in fact, a multivariate distribution function with standard uniform margins. Sklar (1959) proved that fora d−variate distribution function F with univariate margins F1, . . . , Fd, there exists a d−copula, CF , such that

F (x) = F (x1, . . . , xd) = CF (F (x1), . . . , F (xd)), for all x ∈ Rd.

Studying multivariate distribution functions with given margins coincides with studying copulas. For example, looking forbounds on a specified class of multivariate distribution functions with given margins coincides with trying to find boundson a class of copulas with related conditions. Also,CF can be stand for the joint information of F , against its marginalinformation (that are all in its marginal distribution functions). As a result, in the studying of association of two randomvariables, it is useful to restrict our attentions to the copula-based measures.

In this work we give some interpretations and properties of copulas and present some ways to construct a copula. Also,

some applications of copulas were presented. In many parts of this work, the particular case d = 2 is discussed.

References[1] Joe, H., Multivariate Models and Dependence Concepts, Chapman & Hall, London, 1997.

[2] Mardani-Fard, H. A., Sadooghi-Alvandi, S. M., and Shishebor, Z., Bounds on bivariate distribution functions with given marginsand known values at several points, Communications in Statistics: Theory and Methods, (2009), Submitted.

[3] Nelsen, R. B., An Introduction to Copulas, Springer, New York, 2006.

[4] Sklar, A., Fonctions de repartition a n dimensions et leurs marges, Publ. Inst. Statist. Univ. Paris, 8, (1959), 229-231.

2000 Mathematics Subject Classification. 62E15Key words and phrases.Copula, Multivariate Distribution Functions, Dependence Measures, Quasi-Copula.

195


Congruence relations on generalized fuzzy

subsemimodules

Hossein Hedayati

Department of Mathematics, Babol University of Technology, Babol, Iran

[email protected]

Abstract

In this paper, the notion of interval valued intuitionistic fuzzy subsemimodules of a semimodules, by different examples,

are introduced. We generalize this notion by considering t−norms and s−norms. Also some basic properties such as

homomorphic image and inverse image are investigated. Finally, by the help of the congruence relations on semimodules,

new interval valued intuitionistic fuzzy subsemimodules are constructed.

2000 Mathematics Subject Classification. 16D10, 08A72Key words and phrases. semimodule, subsemimodule, congruence relation, interval valued intuitionistic fuzzy subsemimodule

196


U-statistic Testing in Competing Risk Models in

Two-Sample Cases

Hossein Jabbari Khamnei*, Hadise Akbari**

*Department of Statistics, Faculty of Mathematical Sciences,

University of Tabriz, Tabriz, Iran

h [email protected]

**Department of Statistics, Faculty of Mathematical Sciences,

University of Tabriz, Tabriz, Iran

[email protected]

Abstract

In this paper we consider a situation in which two systems are subject to failure from competing risks or could be

censored from an independent censoring process. A procedure, based on a U-statistics, is proposed for testing the equality

of two systems with respect to two failure rates in the competing risk set in each sample. Under independence assumptions,

the asymptotic distribution of the statistic is given and used to construct the test.

References[1] E.A.A. Aly, S.C. Kochar, I.W. McKeague, Some tests for comparing cumulative incidence functions and cause-specific hazard rates,

J. Amer. Statist. Assoc. 89 (1994) 994-999.

[2] G. Aras, J.V. Deshpande, Statistical analysis of dependent competing risks, Statistics and Decisions 10 (1992) 323-336.

[3] I. Bagai, J.V. Deshpande, S.C. Kochar, Distribution free tests for stochastic ordering in the competing risks model, Biometrika 76(1989) 776-781.

[4] C.L. Chiang, Introduction to Stochastic Processes in Biostatistics, Wiley, New York, NY, (1968).

[5] M.J. Crowder, Classical Competing Risks, CRC Press, Boca Raton, FL, (2001).

[6] W. Hoeffding, A class of statistics with asymptotically normal distribution, Ann. Math. Statist. 19 (1948) 293-325.

[7] N. Keyfitz, S.H. Preston, R. Schoen, Inferring probabilities from rates: extension to multiple decrements, Skandinavisk Aktuarietid-skrift (1972) 1-13.

[8] N. Molinari, A U-statistic test in competing risk models, C. R. Acad.Sci. Paris, Ser. 1 341 (2005) 317-322.

[9] P. Yip, K.F. Lam, A class of non-parametric tests for the equality of failure rates in a competing risks model, Commun. Statist. -

Theory and Methods 21 (1992) 2541-2556.

2000 Mathematics Subject Classification. primary:60E15 secondaries:60K10Key words and phrases.U-statistic, competing risks, censored, failure rates

197


Generalized Cauchy problem: Caputo type

Hossein Parsian

Buali Sina University, Hamadan, Iran,

[email protected]

Abstract

Fractional derivatives, or more precisely derivatives of arbitrary orders, have played a significant role in engineering,

sciences, pure and applied mathematics in recent years. Several types of fractional derivative and integral have proposed.

These definitions include Riemann-Liouville fractional derivative and integral. Grunwald-Letnikov, Weyl-Marchaud, Caputo

and Riesz fractional derivative. In this research work we will generalize Cauchy problem to fractional derivative. We will

introduce generalized cauchy problem (GCP) as two faces, left side GCP and right side GCP. In next section we will

generalize numerical Euler method to GCP. The generalized numerical Euler method (GNEM) reduces to numerical Euler

method (NEM) when GCP reduce to CP.

References[1] F. Riewe, Nonconservative Lagragnian and Hamiltonian mechnics, Phys, Rev. E 53(1996), 1890-1899.

[2] F. Riewe, Mechanics with fractional derivative, Phys, Rev. E 55(1997), 3582-3592.

[3] S.G. Samko, A.A. Kilbas, O.I. Marichev, Fractional integrals and derivative- Theory and applications, Gordon and Breach,Longhorne, PA, (1993).

[4] I. Podlubny, Fractional Differential Equations, Academic Press, New york, 1999.

[5] P.L. Butzer, U. Westphal, An introduction to fractional calculus, in: R. Hilfer(Ed.), Applications in Fractional Calculus in Physics,World Scientific, New Jersey, 2000, pp.1-85.

[6] F. Mainardi, Fractional calculus: Some basic problems in continuum and statistical mechanics, in: A. Carpinteri, F. Mainardi(Eds.)Fractals and Fractional Calculus in Continuum Mechanics, Springer-Verlag, New York, 1997 pp. 291-348.

[7] R.L. Bagley, P.J. Torvik, On the fractional calculus model of viscoelastic behavior, J. Rheology 30(1986)133-155.

[8] A. M. A. El-Sayed, M. Gaber, On the Finite Caputo and Finite Riesz Derivatives, Elec. Jour. of Theoritical physics, 3 No. 12 (2006),

81-95.

2000 Mathematics Subject Classification. 26A33, 78M25.Key words and phrases. Differential equation, Fractional calculus, Numerical method.

198


The Projective Quarter Symmetric Metric Connections

and Reccurent Projective Curvature Tensor

Hulya BagdatlıYılmaz, Aynur Uysal

University of Marmara, Department of Mathematics

Istanbul,Turkey

[email protected]

University of Dogus, Department of Mathematics

Istanbul, Turkey

[email protected]

Abstract

In 1970, Yano, studied Riemannian manifolds admitting semi-symetric metric connections whose curvature tensors

vanish. In 1980, Misra and Pardey , studied quarter symmetric metric connections in Riemannian, Kaehlerian and Sasakian

manifolds and found some properties of curvature tensors of them. In 1982, Yano and Imai , gave the most general form of

quarter symetric metric connections and studied its applications. In 2008, Zhao, investigated the properties of projective

semi-symmetric metric connections of a Riemannian manifold and gave some interesting results with respect to this semi

-symmetric connection. In the present paper, after describing the projective quarter symmetric metric connection D, we

define a projective recurrent manifold M with respect to D and study some properties of it.

References[1 ]. R. S. Mishra and S. N. Pandey, On quarter symmetric metric F-connection, Tensor N.S., Vol. 34(1980).

[2 ]. Z. Peibiao, Some properties of projective semi-symmetric connections, International mathematical forum, 3 , no 7, (2008), 341-347.

[3 ]. N. Pusic. , On concircular and projective curvature tensors of a certain Weyl-Otsuki space of second kind, Review of research,Faculty of Science, University of Novi Sad, Mathematics series, 15,1(1985).

[4 ]. K. Yano and T. Imai, Quarter symmetric metric connections and their curvature tensors, Tensor N.S., Vol. 38(1982).

[5 ]. K. Yano, On semi-symetric metric connection, rev., Roum., Math., Pureset Appl., 15(1970), 1579-1586.

2000 Mathematics Subject Classification. 53B, 53CKey words and phrases.Projective quarter symmetric metric connection, projective reccurent tensor

199


A Fixed Point Theorem Without Convexity

Hulya Duru

Istanbul University Faculty of Science


Vezneciler-Istanbul, 34134, Turkey

[email protected]

Abstract

In this paper we give the Schauder fixed point theorem for compact and connected subset of a strictly convex space

imposing a mild condition on the set. The results of this paper are completely original.

References[1] L.E. Brouwer, Uber abbildungen von mannigfaltigkeiten, Math.Ann.71(912), 97-115.

[2] J.Schauder, Der fixpunktsatz in funktionalraumen, Studia Math. 2(1930),171-180.

2000 Mathematics Subject Classification. 47H09, 47H10Key words and phrases. Fixed point,Brouwer fixed point theorem, Schauder, continuous mapping, compact, connected, convexity

200


On Computing The Eigenvectors Of Structured

Matrices

Hulya Kodal Sevindir

University of Kocaeli, Department of Mathematics,

Kocaeli, Turkey

[email protected]

Abstract

A numerical method for computing the eigenvectors of symmetric tridiagonal matrices is studied in this paper. This

method can easily be adapted for other classes of matrices, e.g. semiseparable matrices, as long as a step of the QR method

requires O(n) floating point operations. A real symmetric matrix of order n has a full set of orthogonal eigenvectors. The

most used approach to compute the spectrum of such matrices reduces first the dense symmetric matrix into a symmetric

structured one, i.e., tridiagonal matrices or semiseparable matrices. This step is accomplished in O(n3) operations. Once

the latter symmetric structured matrix is available, its spectrum is computed in an iterative fashion by means of the QR

method in O(n2) operations. In principle, the whole set of eigenvectors of the latter structured matrix can be computed

by means of inverse iteration in O(n2) operations.

References[1] I.S. Dhillon, B.N. Parlett, Multiple representations to compute orthogonal eigenvectors of symmetric tridiagonal matrices, Linear

Algebra Appl. 387 (2004) 128.

[2] G.H. Golub, C.F.Van Loan, Matrix Computations, second ed, The Johns Hopkins University Press, Baltimore, MD, 1989.

[3] J. Liesen, Z. Strakos, Convergence of GMRES for tridiagonal toeplitz matrices, SIAM J. Matrix Anal. Appl. 26 (1) (2004) 233251.

[4] N. Mastronardia, M. Van Barel, E. Van Campb, R. Vandebril, Journal of Computational and Applied Mathematics 189 (2006)580591

[5] B.N. Parlett, The Symmetric Eigenvalue Problem, Classic ed, SIAM, Philadelphia, PA, 1998.

2000 Mathematics Subject Classification.Key words and phrases. Symmetric matrix, Eigenvectors, Semiseparable matrix.

201


On The Relationship Between Regression Analysis and

Mathematical Programming

I. Mufit Giresunlu1, Esra Ertan2

1 Istanbul University, Science Faculty, Mathematics Department, Turkey

[email protected]

2 Istanbul University, Science Faculty, Mathematics Department, Turkey

[email protected]

Abstract

In the development of the underlying theories in statistical methods, it has been face to face with a optimization

problem. For example, for the aim of regression problem estimates the β parameters that makes minimum the objective

function according as structure of functions, is a optimization problem. Least Squares Method and Minimizing Mean

Absolute Deviations (MINMAD) are at most using approaches in this problem. Although it has long been popular to utilize

the Least Squares estimation procedure for fitting the linear regression model to observed data, with the development of

Mathematical Programming, solving the MINMAD regression problem with Simplex Method has been a robust alternative

to Least Squares Method (LS). In this study solving the MINMAD regression problem with Simplex Method has been given.

References[1] ARTHANARI, T.S., DODGE, Y., 1993, Mathematical Programming in Statistics, John Wiley&Sons Inc., New York, 0-471-59212-9

[2] GASS, Saul I., 1985, Linear Programming Methods and Applications, 5th edition, McGraw Hill Inc., USA, 0-7895-0333-6

[3] WAGNER, H:M., 1959, Linear Programming Techniques for Regression Analysis, Journal of the American Statistical Association,Vol.54, No.285, pp. 206-212.

2000 Mathematics Subject Classification. 62J05Key words and phrases. Lineer Programming, Regression Analysis, Statistics, Simplex Method

202


Solutions of the topological structure in the early

universe via conformal motions

I. Yılmaz, I. Turkyılmaz, C. Camcı, C. Aktas, M. Sahin, M. Battaloglu

Canakkale Onsekiz Mart University, Faculty of Science and Arts

Department of Physics, C. anakkale, Turkey

Canakkale Onsekiz Mart University, Faculty of Engineering and Architecture

Department of Computer Engineering, C. anakkale, Turkey


Department of Mathematics, C. anakkale, Turkey.


Department of Mathematics, C. anakkale, Turkey.

Canakkale Onsekiz Mart University, Faculty of Engineering and Architecture

Department of Computer Engineering, C. anakkale, Turkey

Canakkale Onsekiz Mart University, Canakkale Vocational School

Department of Economic and Administrative Programs, C. anakkale Turkey.

Abstract

In this article Einstein’s field equations are solved for topological structures in the early universe (spherical space-time)

by using conformal motions. Also the features of the obtained solutions are discussed

2000 Mathematics Subject Classification. 83F05, 83C05Key words and phrases. Conformal Motions, Einstein’s Field Equations

203


Tauberian theorems for (A)(C, α) summability method

Ibrahim Canak, Yılmaz Erdem, Umit Totur

Adnan Menderes University Department of Mathematics 09010 Aydın, Turkey

[email protected]


[email protected]


[email protected]

Abstract

Using Tauberian theorems for Abel summability method by Hardy [1], Littlewood [2] and Pati [3], we have given several

Tauberian theorems for (A)(C, α) summability method. Also in this work some theorems given by Pati [3] are generalized

and new Tauberian conditions are introduced.

References[1] G. H. Hardy, Theorems relating to the summability and convergence of slowly oscillating series, Proc. London Math. Soc. 8 (1910)

301-320.

[2] J. E. Littlewood, The converse of Abel’s theorem on power series, Proc. London Math. Soc. 9 (1911) 434-448.

[3] T. Pati, On Tauberian Teorems, Sequences, Summability and Fourier Analysis, 84-96, edited by D. Rath and S. Nanda, NarosaPublishing House, 2005.

2000 Mathematics Subject Classification. 40E05Key words and phrases. Tauberian theorems, summability.

204


Some Tauberian theorems for Borel summability

methods

Ibrahim Canak, Umit Totur


[email protected]


[email protected]

Abstract

We investigate the conditions needed for a Borel summable sequence to be convergent. The results of this paper extend

and improve the well known result of Hardy and Littlewood [Proc. London Math. Soc. 11 (1913), 1-16].

References[1] D. Borwein, T. Markowich, A Tauberan theorem concerning Borel-type and Cesaro methods of summability, Canad. J. Math. 40

(1988), 228-247.

[2] I. Canak, M. Dik, F. Dik, On a theorem of W. Meyer-Konig and H. Tietz, Int. J. Math. Math. Sci. 15 (2005), 2491-2496.

[3] F. Dik, Tauberian theorems for convergence and subsequential convergence with moderately oscillatory behavior, Math. Morav. 5(2001), 19-56.

[4] M. Dik, Tauberian theorems for sequences with moderately oscillatory control modulo, Math. Morav. 5 (2001), 57-94.

[5] G H. Hardy, J. E. Littlewood, The relations between Borel’s and Cesaro’s method of summation, Proc. London Math. Soc. 11 (1913),1-16.

[6] G H. Hardy, J. E. Littlewood, Theorems concerning the summability of series by Borel’s exponential method, Rend. Palermo, 41(1916), 36-53.

[7] G H. Hardy, J. E. Littlewood, On the Tauberian theorems for Borel summability, J. London Math. Soc. 18 (1943), 194-200.

[8] G. H. Hardy, Divergent Series, 2nd edition, Oxford University Press, Oxford, 1949.

[9] A. Jakimovski, Some relations between the methods of summability of Abel, Borel, Cesaro, Holder and Hausdorff, J. Analyse Math.3 (1954), 346-381.

[10] B. Kwee, An improvement on a theorem of Hardy and Littlewood, J. London Math. Soc. 28 (1983), 93-102.

[11] R. D. Lord, On some relations between the Abel, Borel and Cesaro methods of summation, Proc. London Math. Soc. 38 (1935),241-256.

[12] M. R. Parameswaran, Some Tauberian theorems for the circle family of summability methods, Math. Z. 143 (1975), 199-201.

[13] C. T. Rajagopal, On a theorem connecting Borel and Cesaro summabilities, J. Indian Math. Soc. (N.S.) 24 (1961), 433-442.

[14] O. Szasz, On products of summability methods, Proc. Amer. Math. Soc. 3 (1952), 257-262.

[15] K. Zeller, W. Beekmann, Theorie der Limitierungsverfahren, Springer, Ergebn. Math. u. Grenzgebiete, vol 15, 1970.

2000 Mathematics Subject Classification. 40E05Key words and phrases. Borel summability, general control modulo, Tauberian conditions, slow oscillation

205


On Tauberian theorems for (A, k) summability method

Ibrahim Canak, Umit Totur, Mehmet Dik


[email protected]


[email protected]

Rockford College, 5050 E. State Street, 61108, Rockford, IL, USA

[email protected]

Abstract

Let (un) be a sequence of real numbers which is (A, k) summable. In this work, several new Tauberian theorems for

(A, k) summability methods will be given in terms of generating sequences of (un).

References[1] M. Dik, Tauberian theorems for sequences with moderately oscillatory control modulo, Math. Morav. 5 (2001) 57-94.

[2] F. Dik, Tauberian theorems for convergence and subsequential convergence with moderately oscillatory behavior, Math. Morav. 5(2001), 19-56.

[3] I. Canak, U. Totur, A Tauberian theorem with a generalized one-sided condition, Abstr. Appl. Anal. 2007 (2007) 12 (Article ID60360).

[4] G. H. Hardy, J. E. Littlewood, Tauberian theorems concerning power series and Dirichlet’s series whose coefficients are positive,Proceedings of the London Mathematical Society, 13 (1914) 174-191.

[5] C. V. Stanojevic, V. B. Stanojevic, Tauberian retrieval theory, Publ. Inst. Math., Nouv. Ser. 71 (2002) 105-111.

[6] I. Canak, U. Totur, Tauberian theorems for Abel limitability method, Cent. Eur. J. Math. 6 (2008) 301-306.

2000 Mathematics Subject Classification. 40E05, 40G10Key words and phrases. General control modulo, regularly generated sequence, slow oscillation, (A, k) summability, moderateoscillation

206


Some Characteristics of Systolic Arrays

Ilir Spahiu*, Halil Snopce**, Azir Aliu***

*University of ”Ss. Cyril and Methodius”, Fac.of Pedagogy,

Skopje, R.Macedonia

[email protected]

**Fac. of Contemporary Sciences and Technologies,

Tetovo,R.Macedonia

[email protected]

***Fac. of Contemporary Sciences and Technologies,

Tetovo,R.Macedonia

[email protected]

Abstract

We investigate a possible optimization of some linear algebra problems which can be solved by parallel processing using

the special arrays called systolic arrays. In this paper are used some special types of transformations for the designing of

this arrays. We show the characteristics of each one giving the examples of their implementation as well. The main focus

is on discussing the advantages of these arrays in parallel computation of matrix product, with special approach to the

designing of systolic array for matrix multiplication and discrete Fourier transformation. Multiplication of large matrices

requires a lot of computational time and its complexity is O(n3). There are developed many algorithms (both sequential

and parallel) with the purpose of minimizing the time of calculations. Systolic arrays are good suited for these purpose.

In this paper we show that using a appropriate composite function, the given index space can be mapped in another index

space suitable for systolic array. This mapping implicates in finding more optimal arrays for doing the calculations of this

type. We show that this can be implemented on the designing of optimal systolic array for Discrete Fourier transformation.

References[1] M.P. Bekakos, Highly Parallel Computations-Algorithms and Applications, Democritus University of Thrace, Greece, pp. 139-209,

2001.

[2] Milentijevic, I.Z., Milovanovic, I.Z., E.I. and Stojcev, M.K., The Design of Optimal Planar Systolic Arrays for Matrix Multiplication,Comput. Math. Appl., pp. 17-35, 1997

[3] Bekakos, M.P., Milovanovic, E.I., Milovanovic, I.Z. and Milentijevic, I.Z., An Efficient Systolic Array for Matrix Multiplication,Proc. of the Fourth Hellenic European Conference on Computer Mathematics and its Applications (HERCMA ’98), Athens ’98, pp.298-317, 1999

[4] Snopce, H., Elmazi, L., Reducing the number of processors elements in systolic arrays for matrix multiplication using linear trans-

formation matrix, Int. J. of Computers, Communications and Control, Vol. III (2008), Suppl. issue: Proceedings of ICCCC 2008,

pp. 486-490

2000 Mathematics Subject Classification. 65Y05Key words and phrases. Systolic arrays, matrix multiplication, Fourier transformation, data dependences, optimization.**This research was supported by Scientific Research Committee of Pedagogical Faculty of University of ”Ss. Cyril and Method-ius”, Skopje.

207


Solution of the Cauchy Problem for a Degenerate

Parabolic Equation

Iryna Volodymyrivna Komashynsk

Department of Mathematics and Statistics, Faculty of Science,

Al-Hussein Bin Talal University. Box (20), Ma’an-Jordan ,

iryna [email protected]

Abstract

We consider a degenerate parabolic equation and investigate conditions of the existence of a solution of the Cauchy

problem .

2000 Mathematics Subject Classification.Key words and phrases. Degenerate parabolic equation, Cauchy problem, diffusion matrix

208


Control Adaptive for Binary Time series

Isaac Almasi*, Reza Jalilian**

*Department of Mathematics, Ilam University,

PO Box 69315-516, Ilam, Iran

isaac [email protected]

**Department of Mathematics, Ilam University,

PO Box 69315-516, Ilam, Iran

[email protected]

Abstract

The model ARMAX provides a complete framework for stochastic difference equation. in this paper we will extend this

methodology to cover binary time series. A particular example is the adaptive control of Markov processes with tow states.

By employing a logistic model we will analyze a recursive estimator procedure and an adaptive control law. This enables

the observer to regulate the transition probabilities system. These indicate that the proposed control law is asymptotically

optimal with respect to a certain criterion. The paper terminates with illustrate some important points by simulations

binary time series with inputs according a first order autoregressive process.

2000 Mathematics Subject Classification.Key words and phrases.control adaptive, models input- output, Markov chain, model logistic**This research was supported by Ilam University

209


Solution of mixed B.V.P including a first order three

dimensional P.D.E with nonlocal and global boundary

conditions

J. Ebadpour , D.Jabbari Sabegh


payam-e-noor University, Iran

[email protected]

Abstract

In this paper solution of mixed complex boundary value problem of first order is considered. The basic term in theproblem with respect to space variables. has Cauchy-Riemann operator. We first use Laplace transformation to introducespectral problem. Then we investigate corresponding for Fredholms type.

The spectral problem here is different from classical boundary value problems. Here boundary conditions are nonlocal

and global and dependent functionals to boundary conditions are in general linear. At the end for the solution of spectral

problem which depends on unknown complex parameter. We find asymptotic expansion. With the help of this asymptotic

expansion we prove existance and uniqueness of mixed problem.

2000 Mathematics Subject Classification.Key words and phrases. Mixed problem. Nonlocal and global boundary conditions.. Singularity. Dependent boundary valueconditions to general complex functionals. Regularization. Fredholms type. Asymptotic expansion.

210


Rational approximation on closed curves

J.I. Mamedkhanov

Baku State University, Depart. of Mech.-Math.,

Z.Khalilov, 23, P.O.Box AZ-1148, Baku, Azerbaijan

[email protected]

Abstract

A problem an approximation of classes of function determined only on the boundary of domain takes important placesimultaneously with studying approximation by means of polynomials analytic in the domain G and with some conditionson the boundary Γ of functions.

Obviously, generally speaking, it is impossible to approximate such classes of function by means of polynomials. There-fore, in this case, usually different forms of rational functions or so called generalized polynomials are used as approximationaggregate. My followers D.Israfilov, I.Botchaev and me studied problems on approximation of function determined only onthe boundary of domain by means of rational functions of the from Rn(z) = Pn(z, 1

z ).

In the given report, we consider a rational function of the form

Rn(z) = Pn(z, z) as an approximate aggregate. For this case, analogies of Jackson’s direct theorems on closed curves

of complex plane are proved.

References[1] J.Wolsh, Interpolation and approximation by rational functions in the complex domain, M., IL, (1961) (Russian).

[2] J.I.Mamedkhanov and I.B.Dadashova, Analogue of Jackson–Bernstein theorem in Lp on closed curves in a complex plane, Furtherprogress in analysis, Proceedings of the 6th International ISAAC Congress, Ankara, Turkey 13-18 August (2007), 260-267.

[3] V.K.Dzjadyk, Introduction to the theory of approximation of functions by polynomials, ”Nauka”, M., (1977) (Russian).

2000 Mathematics Subject Classification. primary: 41A17 secondary:41A20Key words and phrases. Jackson’s direct theorems, closed curve, polynomial approximation, continuity modulus, rational func-tions.

211


Estimation of stochastic differential equations with

applications in finance

J.A. Shali1, K. Aghajani2

1 Islamic Azad University, Shabestar Branch, Shabestar-Iran

[email protected]

2 Center of Economics and finance, Bank Sepah, Tabriz-Iran

[email protected]

Abstract

In this note, we will present a new simple method for constructing the approximate solutions of nonlinear stochasticdifferential equations (sde). We shall consider solutions w : [0, T ]× Rd 7→ R to the following problem

−∂w

∂t+ aw =

q∑

i=1

µi(t, x)∂w(t, x)

∂xi

+1

2

q∑

i,j=1

σ2ij(t, x)

∂2w(t, x)

∂xixj

+ c, (0.1)

for known functions a : [0, T ] × Rd 7→ [0,∞), c : [0, T ] × Rd 7→ R, µ : [0,∞) × Rd 7→ Rd and σ2 : [0,∞) × Rd 7→ Rd×d

be given. By using the Feynman-Kac Representation, a direct link between the solution to (0.1) and a conditional momentinvolving the process Xt solving the following nonlinear sde

dXt = µ(t, Xt)dt + σ(t, Xt)dBt, 0 ≤ t ≤ T, (0.2)

where Bt is Brownian motion. Equation (0.2) on [t0, T ], may be linearized as follows

dx(t) = (f∗(t) + F

∗(t)x(t))dt +

m∑

j=1

[g∗j (t) + G

∗j (t)x(t)]dBj(t) (0.3)

where F∗(.), G∗(.) are d× d-matrix-valued functions, f∗(.), g∗j (.) are Rd-valued functions. Equations (0.3) is a linear sdewhose analytical solution may be written as

x(t) = Φ(t)(xn +∫ t

tnΦ−1(s)[f∗(s)−∑m

j=1 G∗j (s)g∗j (s)]ds

+∑m

j=1

∫ ttn

Φ−1(s)g∗j (s)dBj(s)),(0.4)

where Φ(t) is the fundamental matrix of the homogeneous. If a solution to (0.2) exist, then we define the generalizedsolution wF K as

wF K(t, x) = Et,x[b(XT ) exp[−∫ T

t

a(s, Xs)ds]] + Et,x[

∫ T

t

c(s, Xs) exp[−∫ s

t

a(u, Xu)du]ds], (0.5)

where Et,x[.] = E[.|Xt = x]. In some cases Xt (exact solution of (0.2)) may not exist, then by using the (0.4), we can

obtain the approximate solution of the PDE (0.1).

References[1] G.N. Milstein, Numerical Integration of Stochastic Differential Equations, Kluwer Academic Publishers, 1988.

[2] Peter E. Kloeden and Eckhard Platen, Numerical Solution of Stochastic Differential Equations, Springer-Varlag Berlin Heidelberg,1992.

[3] Xuerong Mao, Stocastic Differential Equations and Applications, Horwood Publishing Limited, 1997.

[4] Bernt Øksendal, Stocastic Differential Equations, An Introdction with Applicationc, Fifth Edition, Springer-Varlag Heidelberg NewYork 2000.

2000 Mathematics Subject Classification. 65C30, 60H10Key words and phrases. Stochastic differential equation, Partial differential equations

212


A Semi Numerical-Analytical Method for Solving

Nonlinear Integro-Differential Equations

Jafar Ahmadi Shali, Parviz Darania

Islamic Azad University, Shabestar Branch,Shabestar-Iran

[email protected]

Department of Mathematics and Computer Science,

University of Tabriz, Tabriz-Iran

[email protected]

Abstract

In this paper, we present a new scheme based on Taylor series to convert high-order nonlinear Volterra-Fredholm

integro-differential equations to a M-order linear differential equations which may be integrated using classical methods.

Also, the objective of this paper is to assess both the applicability and the accuracy of linearization method in several

problems of general high-order nonlinear Volterra-Fredholm integro-differential equations. This method provides piecewise

linear differential equations which can be easily integrated. It is shown that the accuracy of linearization method can be

substantially improved by employing variable steps which adjust themselves to the solution. Numerical examples are used

to illustrate the preciseness and effectiveness of the proposed method.

References[1] P. Darania, A. Ebadian and A.V. Oskoi, Linearization method for solving nonlinear integral equations, Mathematical Problem in

Engineering, 1 (2006), 1-11.

[2] P. Darania and A. Ebadian, Development of the Taylor expansion approach for nonlinear integro-differential equations, Int. J.Contemp. Math. Sciences, 1 (2006), 651-664.

[3] H. Brunner, Implicitly linear collocation methods for nonlinear Volterra integral equations, Appl. Numer. Math., 9 (1992), 235-247.

[4] T. Tang, S. McKee and T. Diogo, product integration method for an integral equation with logarithmic singular kernel, App. Numer.Math. 9 (1992), 259-266.

[5] A.T. Diogo, S. McKee and T. Tang, A Hermite-type collocation method for the solution of an integral equation with a certain weaklysingular kernel, IMA J. Numer. Anal., 11 (1991), 595-605.

[6] A. M. Wazwaz, S. M. El-Sayed, A new modification of the Adomian decomposition method for linear and nonlinear operators, App.Math. Comput., 122 (2001), 393-404.

2000 Mathematics Subject Classification. 45J05, 47G20Key words and phrases. Taylor polynomials, integro-differential equations, Numerical treatments, Linearization method, Nonlin-ear Volterra integral equations.**This research was supported by Scientific Research Project Commission of Islamic Azad University, Shabestar Branch,Shabestar-Iran

213


Gardner’s Mathematical Intelligence Theory To

Measure Managers Mathematical Intelligence And

Organizational Effectiveness In East Azerbaijan’s Gas

Company

Jafar Beikzad, Mohammad Reza Noruzi

Public Management, PhD, Islamic Azad University, Bonab, Iran

beikzad [email protected]

Executive MBA, Islamic Azad University, Bonab, Iran

[email protected]

Abstract

Increasing recession and emergence of new markets and various customers on the other hand caused the world encounter

lots of sophisticated and complicated changes. If the trend continues, chaos will emerge; although we can touch chaos now

in today’s economic conditions and markets[1]. In today economy we can not expect that the sea will be calm tomorrow,

but probably we could do that in the past and could plan exactly the outcome and process but can we do this for the

current activities? May be the answer is No[2]. Should we be panicked in this downturns or be smarter and find ways

to outperform our competitor? What is the duty of science here? The aim of this paper is to study the relationship

between Gardner’s Mathematical Intelligence among managers with Stephen Robbins organizational effectiveness in East

Azerbaijan Gas Company. This is based on a project studies empirically and concluded that there is a relationship between

Mathematical Intelligence and organizational effectiveness

References[1] Gardner, H, (1999), Intelligence Reframed, New York: Basic books, P.33.

[2] Martin, H, (1996) Multiple Intelligence in the mathematics classroom P.15 .

2000 Mathematics Subject Classification. M: 10Key words and phrases. Mathematical Intelligence, Organization, Effectiveness

214


A Description Of 3-Place Functions Of Idempotent

Algebras

Jafar Pashazadeh

Islamic Azad University of branch Bonab, Bonab, Iran

jm [email protected]

Abstract

An algebra is idempotent if and only if for every algebraic operation f the equation f(x,x,...,x)=x holds for every x. In

[4], K.Urbanik characterize the set of all binary operations of idempotent algebras that has no essentially n-ary algebraic

operation for some n > 2. In this paper we characterize the set of all ternary algebraic operations of idempotent algebras

that has no essentially n-ary algebraic operation for some n > 3 and show that this set is finite and costruct a ternary

algebra.

References[1] J. Pashazadeh, Yu. M. Movsisyan On the representation of Boolean Algebras, FJMS, vol. 26, No 3 (2007), 789-794.

[2] J.Pashazadeh, A characterization of De Morgan bisemigroup of binary functions,Int.J.Algebra and computation,vol 18, No5(2008),951-956.

[3] K. A. Zaretskii, Matematicheskie Zametki,Abstract characteristics of bisemigroups of binary operations, vol. 1, No 5, 525–530 (1967).

[4] K.Urbanik, On algebraic operations in idempotent algebras,Colloquium Mathematicum,vol 13(1964-1965),129-157.

[5] V. D. Belousov, On conjugate operations, studies in General Algebra [in Russian], Kishinev, 37–52 (1965).

[6] S. L. Bloom , Z. Esik and E. G. Manes, A Cayley theorem for Boolean algebras, Amer. Math. Monthly 97 (1990), 831–833.

[7] Z. Esik, A Cayley theorem for ternary algebras, Int. J. Algebra computation 8(3) (1998), 311–316.

2000 Mathematics Subject Classification. 62H05, 14H05, 62E10Key words and phrases. Algebraic operation, idempotent algebra, boolean algebra, ternary algebra, 3-place function.

215


Bootstrap-based tests for two measures of association

Jan W.H. Swanepoel, James S. Allison

North-West University, Potchefstroom, South Africa

[email protected]

North-West University, Potchefstroom, South Africa

[email protected]

Abstract

We propose two new bootstrap-based tests for both Spearmans rho and Kendalls tau. The first test is a semiparametric

test based on copulas, while the second is a nonparametric test. The efficiency of the various tests are investigated by

means of a Monte-Carlo study. It is found that they perform very satisfactorily as far as size and power are concerned.

Some recommendations regarding the practical use of the new tests are made.

2000 Mathematics Subject Classification. 62G09, 62G10, 62G30Key words and phrases. Spearmans rho, Kendalls tau, copula,bootstrapThis research was supported by the National Research Foundation of South Africa

216


Common fixed points of nonlinear contraction in

Menger spaces

Javid Ali, M. Imdad

Department of Mathematics and Statistics,

Indian Institute of Technology Kanpur 208 016, India

[email protected]

Department of Mathematics, Aligarh Muslim University

Aligarh 202 002, India

[email protected]

Abstract

In this paper, we introduce the notion of common property (E.A) in Menger spaces. We prove a result which shows the

relation between property (E.A) and common property (E.A). Using common property (E.A), some common fixed point

theorems proved for self mappings satisfying Ciric-type and f-type contractions in Menger PM spaces. Our results generalize

many known results in Menger as well as metric spaces. Some related results and illustrative examples are also furnished.

2000 Mathematics Subject Classification. 54H25, 47H10.Key words and phrases. Menger spaces, common property (E.A), weakly compatible mappings and t-norm Cone metric space,completion.

217


Conditions for Uniqueness of Fractional Powers

Javier Pastor

Departament de Matematica Aplicada,

Universitat de Valencia, 46100 Burjassot, Valencia, Spain

[email protected]

Abstract

It is well-known the important role that plays, in relation to Cauchy problems associated to an operator A, the factthat A has an additive family of closed operators Att>0, A1 ≡ A, such that the operator −At is the generator of asemigroup of bounded linear operators for small exponents t.

The need of considering the inverse, the closure or the adjoint of single-valued linear operator leads in a natural wayto deal with multivalued linear operator. Applications of multivalued methods to degenerated evolution equations can befound in [1]. A theory of fractional powers for nonnegative multivalued linear operators in a complex Banach space wasintroduced in [4].

This work is devoted to the study of uniqueness of a continuous semigroup of fractional powers for a nonnegativemultivalued linear operator A. In [3] we can find several uniqueness results in the single-valued case. Very recently, in[1], it has been established a uniqueness result analogous to the presented here, but only for injective single-valued andnonnegative linear operators.

More specifically, we prove that there exists a unique family Att>0 of closed multivalued linear operators satisfying

(i) A1 = A,

(ii) AtAt = At+s (s, t ≥ 0),

(iii) there exists 0 < ε ≤ 1, such that, for all u ∈ D(A), the set-valued map t ∈]0, ε] → Atu is lower semicontinuous,

(iv) At is a sectorial operator of angle tw (tw < π, A is sectorial of angle w).

This result is proved in two different ways. One method is based on the property of multiplicativity for the fractional

powers Att>0 introduced in [4], that is, (At )s = Ats. The other one is to prove uniqueness of 2n roots of A thanks to

be unique the solution of the incomplete Cauchy problem of second order associated to A. From this second method, that

makes no appeal to multiplicativity, we provide also a new and simple proof of the multiplicativity for the fractional powers

of a multivalued linear operator.

References[1] R. deLaubenfels and J. Pastor, A semigroup approach to fractional powers, Semigroup Forum (2008) 76, 385-426.

[2] A. Favini and A. Yagi, Degenerate Differential Equations in Banach Spaces, Marcel Dekker Monographs and Textbooks in Pure andApplied Mathematics, Vol. 215 (1999)

[3] C. Martınez and M. Sanz, The Theory of Fractional Powers of Operators, North-Holland Mathematics Studies,Vol. 187 (2001).

[4] C. Martınez, M. Sanz and J. Pastor, A functional calculus and fractional powers for multivalued linear operators, Osaka J. Math.,

37 (2000), 551-576.

2000 Mathematics Subject Classification. 47A06,47D06Key words and phrases. Multivalued linear operators, Semigroups of linear operators, Fractional powers*This research is supported by Universitat de Valencia, Grant UV-AE-09-5915

218


Minimization Theorems And Fixed Point Theorems For

A Generalized Metric

Jeong Sheok Ume

Department of Applied Mathematics, Changwon National University

Changwon 641-773, Korea

[email protected]

Abstract

We prove new minimization theorems, fixed point theorems and variational principles on a S-complete quasi-metric

space. Using these theorems, we extend, improve and unify many known results due to Caristi, Ekeland, Ciric, Kada-

Suzuki- Takahashi, Ume and others.

2000 Mathematics Subject Classification. 547H10Key words and phrases. Fixed point theorem, minimization theorem, quasi-metric space

219


Hereditary orders in the quotient ring of a skew

polynomial ring

John S. Kauta

Department of Mathematics, Faculty of Science, Universiti Brunei Darussalam,

Bandar Seri Begawan BE1410, Brunei

[email protected]

Abstract

Let K be a field, and let σ be an automorphism of K of finite order, say n. One can form a skew polynomial ringK[X, σ] over K with the usual rules of multiplication defined by the commutation rule: Xa = σ(a)X ∀ a ∈ K. Let K(X, σ)denote the skew field of quotients of K[X, σ]. If F is the fixed field of σ, then K(X, σ) is a cyclic algebra of degree n withcenter F (Xn). If V is a valuation ring of F (Xn) containing F , and S is the integral closure of V in K(Xn), then any orderof K(X, σ) with center V can be written as a “crossed-product V -algebra”:

Af =

n−1∑

i=0

Sxσi ,

with the multiplication rule xσis = σi(s)xσ for all s ∈ S, 0 ≤ i < n and xσixσj = f(σi, σj)xσi+j , where f : G×G 7→ S\0is some normalized 2-cocycle, and G is the Galois group of the cyclic extension K(Xn)/F (Xn).

Let H = σi | f(σi, σ−i) ∈ U(S), where U(S) denotes the group of the multiplicative units of the ring S. Then H isa subgroup of G. On G/H, one can define a partial ordering by the rule

σiH ≤ σ

jH if f(σ

i, σ

j−i) ∈ U(S).

Then “≤” is well-defined, and depends only on the cohomology class of f over S. Further, H is the unique least element.We call this partial ordering on G/H the graph of f.

The aim of the talk is to determine the conditions on the graph of f that would guarantee that Af is a hereditary order.

2000 Mathematics Subject Classification. 16H05, 16S35, 16S36, 16W60.Key words and phrases. skew polynomial ring, crossed product, hereditary orders, valuation rings.

220


Extensional Flows With Viscous Heating

Jonathan Wylie1, Huaxiong Huang2

1 City University of Hong Kong, Kowloon Tong, Hong Kong.

[email protected]

2 York University, Toronto, Canada.

[email protected]

Abstract

In this talk we will investigate the role played by viscous heating in extensional flows of viscous threads with temperature-

dependent viscosity. We will show that there exists an interesting interplay between the effects of viscous heating, which

accelerates thinning, and inertia, which prevents pinch-off. We will first consider the steady drawing of a thread that is

fed through a fixed aperture at given speed and pulled with a constant force at a fixed downstream location. For pulling

forces above a critical value, we will show that inertialess solutions cannot exist and inertia is crucial in controlling the

dynamics. We will also consider the unsteady stretching of a thread that is fixed at one end and pulled with a constant

force at the other end. In contrast to the case in which inertia is neglected, the thread will always pinch at the end where

the force is applied. Our results show that viscous heating can have a profound effect on the final shape and total extension

at pinching.


221


On a size-structured two-phase population model with

infinite states-at-birth

Jozsef Z. Farkas1,Peter Hinow2

1 Department of Computing Science and Mathematics,

University of Stirling, Stirling, FK9 4LA, United Kingdom

2 Institute for Mathematics and its Applications,

University of Minnesota, 114 Lind Hall, Minneapolis, MN 55455, USA

[email protected]

Abstract

We introduce and analyze a linear size-structured population model with infinite states-at-birth. We model the dynamics

of a population in which individuals have two distinct life-stages: an “active” phase when individuals grow, reproduce and

die and a second “resting” phase when individuals only grow. Transition between these two phases depends on individuals’

size. First we show that the problem is governed by a positive quasicontractive semigroup on the biologically relevant

state space. Then we investigate, in the framework of the spectral theory of linear operators, the asymptotic behavior of

solutions of the model. We prove that the associated semigroup has, under biologically plausible assumptions, the property

of asynchronous exponential growth.

2000 Mathematics Subject Classification. 92D25, 47D06, 35B35Key words and phrases. Size-structured populations, positivity, quasicontractive semigroups, spectral methods, asynchronousexponential growth

222


Solution of the system of tenth-order boundary value

problems using Non-polynomial spline

K. Farajeyan

Islamic Azad University of Bonab,

Department of Mathematics, Bonab, Iran

[email protected]

Abstract

Non-polynomial spline is used for the numerical solution of the tenth-order linear boundary value problems.we show

that the present method gives an approximation which are better that those produced by order finite difference and spline

methods.The end condition consistent with the boundary value problems , are also derived. a example are considered for

the numerical illustration of the method developed.

References[1] R.P. Agarwal, Boundary-Value Problems for Higher Order Differential Equations, World Scientific, Singapore, 1986.

[2] H.N. Caglar, S.H. Caglar, The numerical solution of fifth-order boundary-value problems with sixth-degree B-spline functions, Appl.Math. Lett. 12 (1999) 25-30.

[3] S.S. Siddiqi, E.H. Twizell, Spline solutions of linear tenth order boundary value problems, Int. J. Comput. Math. 68 (1998) 345-362.

2000 Mathematics Subject Classification.65L10Key words and phrases. tenth-order boundary-value problem; Non-polynomial spline functions; End conditions.

223


On Commutative Distributive Algebras with Division

Operations

K. Shahbazpour1, M. Soltani2

1 Dept. of Maths, University of Urmia, Urmia, I.R. Iran

[email protected]

Abstract

A binary algebra < Q, Σ > called q-algebra, if there exists an invertible operator of binary type in Σ. In [8, p.115-189]

q-algebras with nontrivial hyperidentities of distributivity are described. In this article we prove analogical results for

algebras < Q, Σ > with commutative division operations.

References[1] V. D. Belousov, On Structure of Distributive Quasigroups, Mat. Sbornik 50, 267-298 (1960), in Russian.

[2] R. H. Bruck, A survey of binary systems, springer-verlag Company, Gottingen Heidelberg (1958).

[3] T. Kepka, J. Jezek, Medial Groupoids, Praha 1983.

[4] T. Kepka, J. Jezek, P. Nemec, Distributive Groupoids, Praha 1981.

[5] T. Kepka, P. Nemec, Notes of Distributive Groupoids, Comment. Math. Univ. Carolinae 24(1983), 237-249.

[6] T. Kepka, Distributive Division Groupoids, Math. Nacher. 876(1979), 103-107.

[7] Yu. M. Movsisyan, S. S. Davidov On Algebras with Distributive Hyperidentities, Mejvozbcky sb. Mathematica, Yerevan, N3(1985),5-26 (in Russian).

[8] Yu. M. Movsisyan, Hyperidentities in algebras and varieties, Uspekhi Mat. Nauk. 53 (1998), 61–114 (in Russian).

[9] A. B. Romanowska, J. D. Smith, Post-Modern Algebra, John Wiley and Sons, Inc, (1999)

[10] Kh. Shahbazpour On Quasigroups Isotopic to Groups, Armenian Algebra & Geometry Conference (2007), p.20.

2000 Mathematics Subject Classification. 20N05, 08B26Key words and phrases. q-algebras, hyperidentity, variety, division operation

224


A condition for points and compact subsets of C(X) to

be Gδ Subsets of RX

Kelaiaia Smail

Department of Mathematics University of Annaba, Algeria

[email protected]

Abstract

It was given in [6], a condition for points and compact subsets of C(X) to be Gδ Subsets of RX , the set of all real-valued

functions defined on a topological space X, when it is equipped with a compact-open topology. It was also shown in the

same paper that if C(X) contains a non empty Gδ Subset of RX , then X is the topological sum of a σ−compact space and

a discret space. In this talk it will be shown that these two results remain valid in the frame work of a set-open topology

more general then the consedered compact-open topology.

References[1] Engelking R. ”General topology”, Polish Scientific Publishing, (1977).

[2] McCoy R.A ”Complete function spaces”, Internat. J. Math. Sci. Vol. 6, N2, 271-278, (1983).

[3] McCoy R.A & Ntantu I. ”Campleteness properties of function spaces”, Top. and Appl. 2, 191-206, (1986).

[4] Oxtoby J. C. ”Cartesian prducts of Baire spaces”, Fund. Math. 49(1961), 157-166.

2000 Mathematics Subject Classification. 54C35Key words and phrases. Compact-open topology, set-open topology, Pseudocompleteness, σ−compacity, Gδ sets

225


Estimate Of The Parameters Of The Stochastic

Differential Equations. Balck-Scholes Model

Khaled Khaldi, Samia Medahi

Boumerdes University, Department of Mathematics, Boumerdes 35000, Algeria.

[email protected]

Boumerdes University, Department of Mathematics, Boumerdes 35000, Algeria.

[email protected]

Abstract

In this paper, one treats the techniques of estimate of the parameters of the Black - Scholes model. These techniques are

based on the function of probability. The ”discrete” method considers the function of density of transition from the process

of diffusion normal log. The second method proposes the estimate of the parameters of the model via the observation of the

time of first passage of the process through a constant terminal of which the density is known. One treats an application

of the action Toyota MTR.

References[1] F. Black, M. Scholes, The Pricing of Options Liabilties. The Journal of Political Economy, Vol.81, No 3, (1973) 637-654.

[2] P. Gross, Parameter Estimation for Black-Scholes Equation. Springer (2006) 2006.

[3] J, Janssen, M. Saib, T. Khamiss, Techniques d’Estimation pour le Modele de Black et Scholes. AFIR Colloquium Nurnberg, Germany(1996).

[4] D. Lamberton, B. Lapeyre, Introduction to Stochastic Calculus Applied to Finance. Springer. (2007) 208.

[5] E. Peirano, D. Talay, Domain Decomposition by stochastic Methods. Fourtheen International Conference on Decomposition Methods.Editors Herrera I., Keyes D. E., Widlund O. B., Yates R., (2003) 131-147.

2000 Mathematics Subject Classification. 60H15, 60H30, 62M10, 62M20, 62P05Key words and phrases. Estimate parameters, discrete method, time of the first passage

226


Corner Detection Based On Uncalibrated Images

Khaled Al-Shalfan

Artificial Intelligence Laboratory,

College of Computer & Information Sciences,

Al-Imam Muhammad Ibn Saud University, Riyadh, Saudi Arabia

[email protected]

Abstract

Precise determination of object corners in an image is very important in applications of robotics and computer vision,such as pattern recognition and 3-D reconstruction. The corners of a polygonal object plane, e.g. roof, wall, etc. in animage, can be determined by detecting image corners bounding the plane edges. An automatic system for locating imagecorners is likely to produce many corners do not represent corners of a polygonal object, and so despite many studies in thefield of boundary recognition, the question of whether the detected corner in the image of a 3-D scene corresponds to anobject point still merits further investigation. The aim of the research presented in this paper is to propose an image systemcapable of detecting image corners and then show the ones that correspond to polygonal object planes for a variety of typesof subject. A review of the existing literature suggested that a two-camera approach based on uncalibrated images wouldoffer the most flexible potential solution. The method is based on rectified images obtained from a pair of uncalibratedimages utilizing the epipolar constraint, and is illustrated with images of several scenes captured using a digital camera.

2000 Mathematics Subject Classification.Key words and phrases. Computer vision, image rectification, stereo vision, object detection, corner detection.

227


Studies on Sensitivity of Clock and Data Recovery

Circuits to Power Supply Noise

Khalil I. Mahmoud, R. Rajasekar, J. Dhurga Devi, P.V. Ramakrishna

Department of ECE, College Of Engineering Guindy,

Anna University. Chennai, India

khalil [email protected]

Abstract

This paper deals with the study of the impact of power supply noise on the performance of CMOS Clock and Data

Recovery (CDR) Circuits. The sensitivity of the various blocks of the dual loop CDR circuit to power supply noise is first

studied and then it is demonstrated that insertion of suitable Low Dropout Regulators (LDO) can enhance the performance

of the CDR system with respect to power supply noise. Based on extensive simulations, it was observed that while the

system can tolerate only about 20 mV/10MHz noise on the power supply, incorporation of LDOs enables it to tolerate

200mV/10MHz noise without degradation in performance.


228


Scatter Search for Vehicle routing

Kheffache Rezika*, Ouafi Rachid **

*Department of Mathematics, USTHB University, Algiers, Algeria

[email protected]

**Department of Mathematics, USTHB University, Algiers, Algeria

rachid [email protected]

Abstract

In our work, we are interested in the scatter search method that was described by Glover in 1977. The approach

comes from research strategies for the creation of decision rules and constraints substitution. Recent studies demonstrated

the practical benefits of this approach for solving various optimization problems. Scatter search operates on a set of

reference solutions to generate new ones by weighted linear combinations of structured subsets of solutions. The reference

set is required to be made up of high-quality and diverse solutions and the goal is to produce weighted centers of selected

subregions that project these centers into regions of the solution space to be explored by auxiliary heuristic procedures.

In this paper, we illustrate how this method can be effectively used for the solution of general permutation problems that

involve the determination of optimal cycles (or circuits) in graph theory and combinatorial optimization and we identify a

general conception to resolve the vehicle routing problem.

References[1] F. Glover, M. Laguna and R. Marti, Scatter Search, 2000.

[2] F. Glover, Scatter Search and Path relinking. New Ideas in Optimiation, (Fevrier 1999), 297–316.

[3] M. Laguna, Scatter Search, (Aout 1999), pp.14.

2000 Mathematics Subject Classification. 90C59Key words and phrases.Combinatorial optimization, Metaheuritics, Scatter search, Vehicle routing.

229


Simultaneous Quadruple Series Equations Involving

Generalized Bateman-K Functions

Kuldeep Narain

Dept. of Mathematics The University of Fiji Saweni,

Lautoka, Fiji Islands

Abstract

In this paper a closed form solution has been obtained for the simultaneous Quadruple Series equations involving

generalized Bateman -K functions.


230


On Identification of Distribution for Two Independent

Markov Chains to the Subject Reliability Criterion

Leader Navaei

Payame Noor University(PNU), Faculty of Mathematics and Probability, Iran

ashkan [email protected]

Abstract

Ahlswede and Haroutunian in [1] formulated an ensemble of problems on multiple hypotheses testing for many objects

and on identification of hypotheses under reliability requirement. The problem of many (L > 2) hypotheses testing on

distributions of a finite state Markov chain is studied in [5] via large deviations techniques. In this paper we solve the

problem to identification of distributions of many hypotheses for two independent objects by usage of simple homogeneous

stationary finite states of Markov chains.

References[1] Ahlswede R. F. and Haroutunian E. A., “On logarithmically asymptotically optimal testing of hypotheses and identification”. Lecture

Notes in Computer Science, vol. 4123. “General Theory of Information Transfer and Combinations”, Springer, pp. 462-478, 2006.

[2] Csiszar I., “ Method of types”, IEEE Trans. Inform. Theory, vol. 44. no. 6. pp. 2505-2523, 1998.

[3] Dembo A. and Zeitouni O., “ Large Deviations Techniques and Applications ”, Jons and Bartlet. Publishers, London, 1993.

[4] Haroutunian E. A., “ On asymptotically optimal testing of hypotheses concerning Markov chain”, (in Russian). Izvestia Acad. NaukArmenian SSR. Seria Mathem. vol. 22, no. 1. pp. 76-80, 1988.

[5] Navaei L., “ Application of LDT to many hypotheses optimal testing for Markov chain”, Mathematical Problems of ComputerScience, vol. 31, pp. 73-78, 2008.

[6] Navaei L., “ Large deviations techniques for error exponents to many hypotheses LAO testing”, Journal of Modern Applied StatisticalMethods, USA, vol. 6, No. 3. pp. 487-491, 2007.

2000 Mathematics Subject Classification. 62M02Key words and phrases. Identification, error probability, hypotheses testing,two independent Markov chains

231


On Identification Of Distributions For Multiple Lao

Hypotheses Testing

Leader Navaei



Abstract

Applications of information-theoretical methods in mathematical statistics are reflected in the monographs by Kullback[5], Csiszar and Korner [2], Gutman [3] and others.

In [1] Ahlswede and Haroutunian formulated an ensemble of new problems on multiple hypotheses testing for many

objects and on identification of hypotheses. The problem of many (L > 2) hypotheses testing on distributions of a finite

state Markov chain is studied in [6] via large deviations techniques.

In this paper we solve the problem to identification of distributions of many hypotheses for one object by usage of simple

homogeneous stationary finite states of Markov chains.

References[1] R. F. Ahlswede R. F. and E. A. Haroutunian E. A., “On logarithmically asymptotically optimal testing of hypotheses and identi-

fication”. lecture Notes in Computer Science, vol. 4123. “General Theory of Information Transfer and Combinations” Springer. pp.462-478, 2006.

[2] Csiszar I. and Korner J., “ Information Theory: Coding Theorem for Discrete Memoryless Systems ”, Academic press, NewYork,1981.

[3] Gutman M., “Asymptotically optimal classification for multiple test with empirically observed statistics”, IEEE Trans. Inform.Theory, vol. 35, no. 2. pp. 401-408, 1989.

[4] Haroutunian E. A., “ On asymptotically optimal testing of hypotheses concerning Markov chain”, (in Russian). Izvestia Acad. NaukArmenian SSR. Seria Mathem. vol. 22, no. 1. pp. 76-80, 1988.

[5] Kullback S., “ Information Theory and Statistics”, Wiley, New York, 1959.

[6] Navaei L., “ Application of LDT to many hypotheses optimal testing for Markov chain”, Mathematical Problems of Computer

Science, vol. 31, pp. 73-78, 2008.

2000 Mathematics Subject Classification. 62M02Key words and phrases. Hypotheses testing, error probability, type

232


Hypotheses Optimal Testing Via Large Deviations

Techniques

Leader Navaei



Abstract

The problem of many hypotheses testing for a model consisting of L > 2 hypotheses on distribution of a Markov chainis studied. We apply large deviations techniques (LDT) and the method of types to the empirical distributions of finitestates of Markov chain.

It is proved that this method of investigation in solving the problem of logarithmically asymptotically optimal (LAO)hypotheses testing is easier than the procedure that was introduced by Haroutunian.

The matrix of exponents E = El|m, m, l = 1, L of error probabilities of the LAO test El|m(φ) = limN→∞

− 1N log αl|m(φN ), where

αNl|m(φN ) for l 6= m is the probability to accept the hypothesis l, when the hypothesis m is true, is determined.

References[1] Csiszar I., “ Method of types”. IEEE Trans. Inform. Theory, vol. 44. no. 6. pp. 2505-2523, 1998.

[2] Haroutunian E. A., “Haroutunian M. E and Harutyunyan A. S. “ Reliability criteria in Information Theory and in StatisticalHypothesis testing”,Foundations and trends in communications and Information Theory vol. 4, no.2-3, 2007.

[3] Kullback S., “ Information Theory and Statistics”, Wiley, New York, 1959.

[4] Natarajan S., “ Large deviations, hypotheses testing , and source coding for finite Markov chain”, IEEE Trans. Inform. Theory, vol.31, no. 3, pp. 360-365, 1985.

[5] Navaei L., “ On many hypotheses LAO testing via the theory of large deviations”, Far East Journal of Mathematical Sciences, vol.25,

no. 2, pp.335-344, 2007.

2000 Mathematics Subject Classification. 62M02Key words and phrases. Large Deviation Techniques (LDT), Markov chain, Logarithmically asymptotically optimal (LAO)hypotheses testing, reliability matrix.

233


The Subdifferential of a Convex Functional on regulated

function space

Luis Antonio Fernandes de Oliveira, Roseli Arbach

Departament of Mathematics - UNESP - Ilha Solteira, Al. Rio de Janeiro,

266, 15385-000 - Ilha Solteira - Brasil

[email protected]



[email protected]

Abstract

We treat here about the utilization of classic tools of Convex Analysis in the study of optimality conditions in theoptimal control convex process for a Volterra-Stietjes linear integral equation in the Banach space G([a, b], X) of theregulated functions in [a, b], that is, the functions f : [a, b] → X, X a Banach space, that have only discontinuity of firstkind, in Dushnik (or interior) sense, and with an equality linear restriction. In this work we report the initial investigation ofthe subdifferentiability of the lower-semicontinuous convex functional Lβ,f (x) of Nemytskii type, we had already introduced.This notion is related with the properties of directional derivative and with the notion of Gateaux differentiability. Thennatural the investigation of its subgradients and the duality aspects, because the classical result on characterization of itsglobal minimum in x0 by the condition 0 ∈ ∂Lβ,f (x0).

References[1] V. Barbu, and T. Precupanu, “Convexity and Optimization in Banach Spaces“, Sijthoff and Noordhoff, Publishing House of Romanian

Academy, Bucharest, 397 p. (1978).

[2] L. D. Berkovitz, Lower Semicontinuity of Integral Functionals, Transactions of the American Mathematical Society, Volume 192,(1974), 51-57.

[3] L.A.O. Fernandes, and R. Arbach, “Lower-semicontinuity and optimization of Convex Functionals“, International Journal of Pureand Applied Mathematics, vol. 51, No. 2, p. 189-194 (2009).

[4] L.A.O. Fernandes, Convex Functionals on the Regulated Function Space G([a, b], X), 49o Brasilian Seminar of Analysis, Campinas,(1999), 767-772.

[5] C.S. Honig : Volterra-Stieltjes Integral Equations, Math. Studies 16, North Holland Publ. Company, Amsterdam, 1975, 157 p.

[6] C.S. Honig : The Adjoint Equation of a Linear Volterra-Stieltjes Integral Equation with a Linear Constraint, Lecture Notes inMathematics 957, 110-125, Springer, 1982.

[7] R.T. Rockafellar, Integrals wich are Convex Functionals, Pacific Journal of Mathematics 24, no. 3 (1968), 525-539.

[8] M. Tvrdy: Linear Bounded Functionals on the space of Regular Regulated Functions, Tatra Mountains Mathemathical Publications8 (1996), 203-210.

2000 Mathematics Subject Classification. 45D05Key words and phrases. Subdifferentiability, Convex Optimization, Regulated Functions

234


Computation of Expected Interference Between FSS

and Imt-Advanced for Fixed and Mobile Users in

Deferent Malaysian Environments

Lway Faisal Abdulrazak1, Tharek Abd. Rahman2

1 Wireless Communication Center (WCC), Universiti Teknologi Malaysia 81310 UTM Skudai

[email protected]

Wireless Communication Center (WCC), Universiti Teknologi Malaysia 81310 UTM Skudai

[email protected]

Abstract

The impact of single and aggregates cases of IMT-Advanced (4G) systems on Fixed Satellite Services (FSS) earth

station (ES) was conducted in this research paper for deferent Malaysian environments. The study initiated within detailed

calculations of the most useful formulas for path loss effect and clutter loss by using the existing parameters of FSS and

the most expected parameters for the IMT-Advanced. Site shielding, isolation, off-Axis, and in-band have been concluded,

analyzed and simulated using Matlab software for several scenarios. Numerical formulas to calculate the power of the

interference signal received at the FSS ES when IMT-Advanced base stations (BS) are operated is presented. Simulation

results indicate that the proposed mitigation scheme is highly efficient in terms of reducing the separation distance as well

as robust against DOE estimation errors. The study also used the propagation model of Rec. ITU-R P.525 to see the effect

of terrain profile on the separation distance of the two systems for frequency sharing. Finally, the frequency sharing results

are analyzed in the co-channel with respect to minimum separation distance, possible FSS elevation angle, and direction of

FSS-ES (DOE).

References[1] Lway Faisal Abdulrazak and Thaek Abd. Rahman, ”Introduce the FWA in the band 3300-3400 MHz”, Proceedings of World Academy

of Science, Engineering and Technology (PWASET), Volume 36, December 2008 ISSN 2070-3740.

[2] Lway Faisal Abdulrazak, Zaid A. Shamsan - Tharek Abd. Rahman. (June 2008). Potential Penalty Distance between FSS Receiverand FWA for Malaysia. International Journal Publication in WSEAS Transactions on COMMUNICATIONS, Issue 6, Volume 7,pp637-646, June 2008, ISSN: 1109-2742.

[3] ITU-R Document,”Draft New Report on Sharing Studies Between IMT-Advanced Systems and Geostationary Satellite Networks inthe Fixed Satellite Service in the 3 400-4 200 and 4 500-4 800 Mhz Frequency Bands”, Kyoto, May 2007.

[4] ASIA-PACIFIC TELECOMMUNITY, The 3rd Interim Meeting of the APT Wireless Forum, ”Co-existence of broadband wirelessaccess networks in the 3400-3800MHz band and fixed satellite service networks in the 3400-4200MHz band,” , Thailand, Bangkok,13 January 2007.

[5] CEPT ECC Report 100,”Compatibility Studies in the Band 3400- 3800 MHz between Broadband Wireless Access(BWA) Systemsand other Services” Feb. 2007.

[6] Inter Inter-American Telecommunication Commission, ”Use of 3.4 - 4.2 GHz Frequency Bands for Fixed-Satellite Service and Ter-restrial Broadband Applications,” organization of American states, Regional Dialogue, 12 February 2007.

[7] ITU-R SF.1486, ”Sharing methodology between Fixed Wireless Access Systems in the Fixed Service and Very Small ApertureTerminals in the Fixed-Satellite Service in the 3 400-3 700 MHz Band,” ITU-R R WP4-9S, Geneva, November 2000.

[8] ITU-R WP 8F/TEMP 432 rev.2, ”Working document towards a PND report on sharing studies between IMT-ADVANCED and the

Fixed Satellite Service in the 3 400- 4 200 and 4 500-4 800 MHz bands”, ITU-R Working Party 8F, August 2006

2000 Mathematics Subject Classification. 78A55Key words and phrases. Antenna, WLAN, RWSA, SMA connector, Bandwidth

235


Kanan Fixed Point Theorem On Generalized Metric

Space With Extended Kind Of Contraction

M. Alimohammady, M. Ramzannezhad

Department of Mathematics, University of Mazandaran

Babolsar, Iran

[email protected]

Department of Mathematics, University of Mazandaran

Babolsar, Iran

[email protected]

Abstract

Here, we obtain sufficient conditions for existence of fixed point of extension of Kannan type mappings defined on a

generalized metric space.

References

[ 1] A. Azam and M. Arshad, Kannan fixed point theorem on generalized metric spaces, J. Nonlinear Sci. Appl, 1/1 (2008), 45-48.

[2] M. Berinde and V. Berinde, On a general class of multi-valued weakly Picard mappingts, J. Math. Anal. Appl. 326 (2007),

772-782.

[3] A. Branciari, A fixed point theorem of Banach-Caccippoli type on a class of generalized metric spaces, Publ. Math. Debrecen, 57

1-2(2000), 31-37.

[4] K. Goebel and W. A. Kirk, Topics in metric fixed point theory, Cambridge University Press, Cambridge (1990) 1.

[5] R. Kannan, Some results on fixed points, Bull. Calcutta. Math. Soc., 60 1-2(1968), 71-76.

[6] B. E. Rhoads, A comparison of various definitions of cotractive mappings, Trans. Amer. Math. Soc., 26 (1977), 257-290.

2000 Mathematics Subject Classification. 47H10; 54H25.Key words and phrases. Generalized metric; Kannan fixed point theorem; Contractive type mapping.

236


Some mapping properties of strongly p−summing

M. Belaib*, D. Achour**

*Department of Mathematics, Setif University, 19000, Setif, Algeria

[email protected]

**Department of Mathematics, M’sila University, 28000, M’sila, Algeria

[email protected]

Abstract

We prove that if X is a Banach space type 2, Y is a Banach space and T : X → Y is strongly 2−summing if and only

if T takes members of Rad(X) into members of l2⊗Y.

References[1] Q. Bu and J. Diestel, Observations about the projective tensor product of Banach spaces, Quaestiones Math. 24 (2001) 519-533.

[2] J.S. Cohen, Absolutely p−summing, p−nuclear operators and their conjugates. Math. Ann. 201, 177-200(1973)

[3] J. Diestel, H. Jarchow and A. Tonge, Absolutely summing operators, Cambridge University Press, 1995.

[4] A. Pietsch, Absolut p−summierende Abbildungen in normierten Raumen. Studia Math. 28, 333-353, 1-103(1967)

2000 Mathematics Subject Classification.46B28, 47B25, 46M05Key words and phrases.Absolutely p−summing , strongly p−summing operator.

237


Some Results About Algebraic Properties Of

Generalized Cellular Automata

M. K. Dadsetani*, H. Haj Seyyed Javadi**, Sa. Adabi***

*Department of Computer Engineering,

Science and Culture University, Tehran, Iran

[email protected]

**Department of Mathematics, Shahed University, Tehran,

P.O. Box: 18151-159, Iran

[email protected]

***Computer Engineering Department, Islamic Azad University,

North Tehran Branch, Tehran, Iran

[email protected]

Abstract

Let G : RA → RA be a cellular automaton where R is a ring and A is an R-module. In module structure point of

view no attempt was made to classify cellular automata (CA). In this presentation we will discuss some properties of linear

CA. We prove that if R is a countable ring, G an R-module epimorphism and its restriction to finite configurations is a

monomorphism then G is isomorphism.

2000 Mathematics Subject Classification. 37B15, 68Q80Key words and phrases.Cellular Automata, Ring, Module, Garden of Eden Configuration.

238


Classification of Systems of Nonlinear ODEs:

Multi-Species Interaction

M.H. Rahmani Doust, M. N. Modoodi


University of Ilam, Ilam, 69315-516 Iran

m [email protected]

Department of Studies in Environmental Sciences

University of Mysore, Mysore, 570 006 (India)

[email protected]

Abstract

In this paper, we study one class of multi-species interaction including predator-prey, competition and coexistence

model; each which can be divided into three cases depending upon “the density changes of each species leads to either

diminish or increase the growth rate of another species”. Furthermore, we study the general Lotka-Volterra equations,

Lotka-Volterra equations for food chain, and Kolmogorove equations in the last section.

References[1] H. Edwards, D. Penny, “Differential Equations and Boundary Value Problems”,Pearson Education (Singapore), Indian Branch Delhi,

2005.

[2] J. D. Murray, “Mathematical Biology” ,Volume I, An Introduction, Springer Verlag, New York, 2002.

[3] J. Hofbauer, K. Sigmund, “The Theory of Evolution and Dynamical Systems”, Cambridge University Press, Cambridge, 1988.

[4] M.H. Rahmani Doust, “Analysis of a System of Coexistence Equations”, Journal of Ultra Scientist of Physical Sciences, Vol. 19, No.1, 2007.

[5] M.H. Rahmani Doust, “Analysis of a System of Competition Equations”, Journal of Ultra Scientist of Physical Sciences, Vol. 19,No. 2, 2007.

[6] M.H. Rahmani Doust and R. Rangarajan, “A Global Analysis of Lotka-Volterra Predator-Prey Model with Interaspecies Competi-tion”, Journal of Analysis and Computational,Vol. 4, No. 1, 2008.

[7] P. F. Verhulst, “Recherche Mathematiques Sur Le Loi D’accroissement De La Population”, Nouveau Memoires De L’Academie RoyaleDes Sciences et Belles Lettres De Bruxelles, 18, pp. 3-38, 1845.

[8] Volterra, “Variations and Fluctuations of The Number of Individuals in Animal Species Living Together”, Translated from 1928edition by R. N. Chapman. Animal ecology. Arno, New York, 1931.

[9] T. R. Malthus “An Essay on The Principle of Population”, Reprinted from 1798 edition, Johnson, London, as Malthus-Population:the first essay. Ann Arbor Paperbacks, University of Michigan, Ann Arbor, Michigan, 1959.

2000 Mathematics Subject Classification. 34A34, 37N25, 92B05, 92D25Key words and phrases. Multi-Species, Nonlinear Systems of ODEs, Predator-Prey, Competition, Coexistence

239


Quasirecognition by the prime graph of the group Cn(2)

M. Foroudi Ghasemabadi*, Ali Iranmanesh**

*Department of Mathematics, Tarbiat Modares University,


[email protected]

**Department of Mathematics, Tarbiat Modares University,


[email protected]

Abstract

If G is a finite group, we denote by π(G) the set of all prime divisors of |G| and by ω(G) the spectrum of G; i.e., the set

of element orders of G. The prime graph (or Gruenberg-Kegel graph) Γ(G) of G is the graph with vertex set π(G) where

two distinct vertices p and q are adjacent by an edge (we write (p, q) ∈ Γ(G)) if p.q ∈ ω(G).

A finite simple nonabelian group P is called quasirecognizable by its prime graph, if each finite group G with Γ(G) = Γ(P )

has a unique nonabelian composition factor isomorphic to P . In this paper, we show that the simple group Cn(2), where

n is an odd number and n ≥ 9, is quasirecognizable by its prime graph.

References[1] A. Khosravi and B. Khosravi, Quasirecogniton by prime graph of the simple group 2G2(q) , Siberian Math. J., 48 (2007), No. 3,

570-577.

[2] A. V. Vasil’ev and I. B. Gorshkov, On recognition of finite simple groups with connected prime graph, Siberian Math. J., 50 (2009),No. 2, 233-238.

[3] A. V. Vasil’ev and E. P. Vdovin, An adjacency criterion for the prime graph of a finite simple group, Algebra and Logic, 44 (2005),

No. 6, 381-406.

2000 Mathematics Subject Classification.primary:20D05 secondaries: 20D06Key words and phrases.uasirecognition, prime graph, simple group, element order.

240


A Set Theory Based Centralized Diagnosability in

Discrete Event Systems

M. Ghasemzadeh, M. Shirmohammadi

Yazd University, Yazd, Iran

[email protected]

Abstract

This paper addresses a new set theory based model of centralized diagnosability in discrete event systems. Thisresearch improves the efficiency of Sampaths approach as a reference framework. The proposed model meets the necessaryand sufficient conditions of diagnosability and it benefits from ZBDD (Zero-suppressed Binary Decision Diagram ) in settheory representations. The CUDD - Colorado University Decision Diagrams package was used to implement the relatedalgorithms, and we have also derived a formal proof which shows the superiority of the proposed method in space and timecomplexity to former existing methods.

Mainly we address centralized diagnosability in discrete event systems (DESs). DESs have discrete states and events. Byoccurring a certain event, DESs’s state is changed. Diagnosability, first was introduced by [1] who considered its propertiesin the framework of DESs. In summary, the sequencing of events uses to determine whether a system is operating as desiredor whether a failure may have occurred. A methodology for building DESs models for failure diagnosis is also providedand a model-based approach for detecting failure events using diagnosers is presented, which state necessary and sufficientconditions for a language to be diagnosed. Jiang [2] is one of the related research works. Then, the researchers like Yoofocused on polynomial tests of failure diagnosability [3], and such a new direction like timed discrete event systems wheresequencing and timing of events are considered. After all decentralized and distributed diagnosability have been introduced.In these two latter concepts, there are more than one observer in large and distributed systems. If the observers do not speakwith each other, the decentralized diagnosability is considered, and if they do speak each other, the distributed diagnosabilityis considered. Since Diagnosability is important in large complex systems, so it has been received considerable attentionsin scientific and industrial literatures.

References[1] F. Lin, Diagnosability of discrete event systems and its applications, Discret Event Dynamic System, Theory Appl., Vol. 4, 1 (1994)

197-212.

[2] S. Jiang, R. Kumar, and H.E. Garcia, Diagnosis of repeated intermittent failures in discrete event systems, IEEE Transaction onRobot. Autom., 19 (2003) 310-323.

[3] T.S. Yoo and S. Lafortune, Polynomial-time verification of diagnosabilityof partially observed discrete-event systems, IEEE Trans-action on Automatic Control, 47 9 (2002) 1491-1495.

2000 Mathematics Subject Classification. 68Q15, 68W40Key words and phrases. Discrete Event Systems, ZBDD, BDT, Finite State Automata

241


Two-Dimensional Mechanical Stresses in a Hollow FGM

Sphere

M. Jabbari1, A.H. Mohazzab2

1 Islamic Azad University-South Tehran Branch, Tehran, Iran

2 Islamic Azad University-South Tehran Branch, Tehran, Iran

Abstract

This paper studied the analytical solution for two-dimensional steady-state mechanical stresses in hollow functionallygraded spheres. Material properties of the sphere are graded continuously across the thickness as power function in radialdirection. Displacements and stresses are derived due to the general mechanical boundary conditions as function of radialand circumferential directions. The Navier equations are solved analytically, using Taylor and Legendre series. The directmethod of solving Navier equations is presented.

Functionally graded materials are very advanced and nonhomogeneous material where changed continuously from metalsurface to ceramic surface. Spherical vessels are very applicable and useful in petroleum industrials, gasoline industrialsand power plants.

In this work by using direct method for solving Navier equations, we obtain general relations that we can apply many

complicated mechanical boundary conditions on them, and see the behavior of FG sphere in each problem. These relations

are evaluated analytically and are exact solution generally, not in special case and not numerically. And at the end of paper

an example is solved and results are shown by two, three-dimensional figures and are discussed.

References[1] Zimmerman, R.W., and Lutz, M.P., 1999, ”Thermal Stresses and Thermal Expansion in a Uniformly Heated Functionally Graded

Cylinder,” J. Thermal Stresses, vol. 22, no. 2, pp. 177–188.

[2] ] M.R. Eslami, M.H. Babaei, and R. Poultangari, Thermal and Mechanical Stresses in a Functionally Graded Thick Sphere, Int. J.Pressure Vessel and Piping 82, 522–527 (2005).

[3] Jabbari, M., Sohrabpour, S., Eslami, M. R., 2003, ”General Solution for Mechanical and Thermal Stresses in a Functionally GradedHollow Cylinder Due to Nonaxisymmetric Steady-State Loads,” J. Appl. Mech., vol. 70, pp. 111–118.

[4] Jabbari, M., Sohrabpour, S., Eslami, M. R., 2002, ”Mechanical and Thermal Stresses in a Functionally Graded Hollow Cylinder Dueto Radially Symmetric Loads,” Int. J. Pressure Vessel and Piping, vol. 79, pp. 493–497.

[5] Mohazzab, A.H., Mohammadi, S., Jabbari, M., 2008, ”Analytical Solution for One-Dimensional Stresses in a Hollow FGM Cylinder

With Heat Source,” Proc 2th Int. Conf. Functional Materials - Devices (ICFMD), Kuala Lumpur, Malaysia, June 16-19.

∗This research work is supported by Iranian Telecommunication Research Center (ITRC)2000 Mathematics Subject Classification.

Key words and phrases.

242


Genetic Algorithm based on Fuzzy System for

Uncapacitated P-Median Problem

M. Jalali Varnamkhasti

Laboratory of Applied and Computational Statistics, Institute for

Mathematical Research, University Putra Malaysia,

43400 UPM Serdang, Selangor, Malaysia

[email protected]

Abstract

In this paper for solving uncapacitated p-median location problem a genetic algorithm is considered. In this genetic

algorithm is using fuzzy system to control probability of crossover and mutation. In this fuzzy system two membership

functions for each chromosome is considered. One membership function for minimizing the weighted average distance

traveled from demand point to facility sites and other, for amount of covering demand points by facilities. A sexual

selection is considered and during the sexual selection, the male and female chromosomes are selected randomly. When

a parent is selected the fuzzy system considers membership functions and a probability of crossover for this parent is

introduced. And after crossover fuzzy system calculated a probability for mutation and introduce to genetic algorithm. In

order to assess the performance of the techniques used in this study, the benchmark problems available in open literature

are used.

2000 Mathematics Subject Classification.Key words and phrases. uncapacitated p-median location problem, genetic algorithm, fuzzy system, sexual selection

243


On Regularized Quasi-Semigroups and the Evolution

Equation

M. Janfada

Department of Mathematics,

Sabzevar Tarbiat Moallem University, Iran

m [email protected]

Abstract

In this note we introduce the notion regularized quasi-semigroups of bounded linear operators on a Banach space, asa generalization of regularized semi-groups of operators and its generator. After some examples of such semigroups theproperties of this notion will be studied. Also some application of regularized quasi-semigroups in the abstract evolutionequation will be considered.

References[1] D. Brcenas, H. Leiva, A. Tineo Moya, Quasisemigroups and evolution equations, IJEvE, in press.

[2] E. B. Davies and M. M. H. Pang, The Cauchy problem and a generalization of the Hille-Yosida approximation, Proc. London Math.Soc. (3)55 (1987) 3181-208.

[3] R. deLaubenfels, it C-semigroups and the Cauchy problem, J. Func. Analysis 111 (1993) 44-61.

[4] Y.-C. Li and S.-Y. Shaw, On Characterization and perturbation of local C-semigroups, Proc. of Amer. Math. soc. Vol.135, 4 (2006)1097-1106.

[5] N. Tanaka and I. Miyadera, Exponentially bounded C-semigroups and integrated semigroups, Tokyo J. of Math.12 (1989) 99-115.

[6] N. Tanaka and I. Miyadera, C-semigroups and the Cauchy problem, J. Math. Analysis and Appl. 170 (1992) 196-206.

2000 Mathematics Subject Classification. 47D60, 46D06Key words and phrases. Quasi-semigroup, generatos, evolution equation.

244


Fuzzy 2-Normed Spaces and its Fuzzy I-Topology

M. Janfada1, A. Nezhadali2

1 Department of Mathematics,

Sabzevar Tarbiat Moallem University, Iran

m [email protected]

Abstract

In this paper a fuzzy 2-norm on a vector space is introduced and a fuzzy I-topology generated with this concept is

constructed. After making our elementary observations on this fuzzy topology, fuzzy continuity of functions on these spaces

is studied. Next continuity of the operations of vector space under this topology is discussed and it is proved that this

structure is not an I-topological vector space with respect to the I-topology.

References[1] N.F. Das, P. Das, Fuzzy topology generated by fuzzy norm, Fuzzy Sets and Systems 107 (1999) 349-354.

[2] J.-X. Fang, On I-topology generated by fuzzy norm, Fuzzy Sets and Systems 157 (2006) 2739-2750.

[3] Jin-Xuan Fang, Cong-Hua Yan, Induced I (L)-fuzzy topological vector spaces, Fuzzy Sets and Systems 121 (2001) 293-299.

[4] C. Felbin, Finite dimensional fuzzy normed linear spaces, Fuzzy Sets and Systems 48 (1992) 239-248.

[5] S. Gahler, Lineare 2-normierte Raume, Math. Nachr. 28 (1964), 1-43.

[6] Z. Lewandowska, Linear operators on generalized 2-normed spaces, Bull. Math. Soc. Sci. Math. Roumanie 42 (4) (1999), 353-368.

[7] M. Mizumoto, J. Tanaka, Some properties of fuzzy numbers, in: M.M. Gupta et al. (Eds.), Advances in Fuzzy Set Theory andApplications, North-Holland, New York, 1979, pp. 153-164.

[8] Guo-Hua Xu, Jin-Xuan Fang, A new I-vector topology generated by a fuzzy norm, Fuzzy Sets and Systems 158 (2007) 2375-2385.

[9] J. Xiao, X. Zhu, On linearly topological structure and property of fuzzy normed linear space, Fuzzy Sets and Systems 125 (2002)

153-161.

2000 Mathematics Subject Classification. 54A40, 46S40, 74S40Key words and phrases. Fuzzy topology, fuzzy 2-norm, I-topology, fuzzy topological vector spaces.

245


On the basis number of the lexicographic product of

two graphs and some related problem

M.M.M. Jaradat, M.K. Al-Qeyyam

Department of Math., Qatar University, Doha-Qatar

[email protected]

Department of Mathematics, Yarmouk University, Irbid-Jordan

[email protected]

Abstract

For a given graph G, the set E of all subsets of E(G) forms an |E(G)|-dimensional vector space over Z2 with vectoraddition X⊕Y = (X\Y )∪ (Y \X) and scalar multiplication 1.X = X and 0.X = ∅ for all X, Y ∈ E. The cycle space, C(G),of a graph G is the vector subspace of (E,⊕, .) spanned by the cycles of G. Traditionally there have been two notions ofminimality among bases of C(G). First, a basis B of G is called a d-fold if each edge of G occurs in at most d cycles of thebasis B. The basis number, b(G), of G is the least non-negative integer d such that C(G) has a d-fold basis; a required basisof C(G) is a basis for which each edge of G belongs to at most b(G) elements of B. Second, a basis B is called a minimumcycle basis (MCB) if its total length

∑B∈B |B| is minimum among all bases of C(G).

The lexicographic product G[H] has the vertex set V (GρH) = V (G)×V (H) and the edge set E(G[H]) = (u1, v1)(u2, v2)|u1 =u2 and v1v2 ∈ H, or u1u2 ∈ G.

In this work, we give an upper bound of the basis number for the lexicographic product of two graphs. Moreover, in a

related problem, construct a minimum cycle bases for lexicographic product of the same.

2000 Mathematics Subject Classification. 05C38; 05C75Key words and phrases. Cycle space; Minimum cycle basis; Basis number; Lexicographic product.

246


Application of Graph Theory in Stability of Nonlinear

Complex Dynamic Systems

M. Kidouche1, H. Habbi2

1 Kidouche [email protected]

2 habbi [email protected]

Abstract

In this paper we follow a graph theoretic approach to develop a decomposition tool which exploits the structure of the

directed graphs associated with a nonlinear dynamical system. Through this structural exploitation a new stability results

for a nonlinear complex systems described by time varying ordinary differential equations are established. The present

results make use of directed graph to transform complex systems into an interconnection of strongly connected subsystems

(SCS). The stability is then accomplished in terms of the subsystems and in terms of the interconnection structure of

the complex systems. To demonstrate the applicability of these results to physical systems, a damped transiently driven

pendulum is considered as a specific example.

2000 Mathematics Subject Classification. 62P10Key words and phrases. Complex Dynamical systems, Control theory, Decomposition, Graph theory, Stability.

247


Applications of Numerical Solution Method HPM

M. Matinfar

Department of Mathematics, University of Mazandaran, Babolsar

47416− 1468, Iran

[email protected]

Abstract

In this Letter, approximate solution of Kawahara equation is obtained by the known homotopy perturbation method

(HPM) and the approximate solution has been compared with their known theoretical solution and result obtained via

variational iteration method (VIM) in [8]. Using this method, it is possible to find the exact solution or an approximate

solution of the problem.

References[1] J.H. He, A coupling method of a homotopy technique and a perturbation technique for non-linear problems, International Journal

of Non-Linear Mechanics. 35(1) (2000) 37–43.

[2] J.H. He. Application of homotopy perturbation method to nonlinear wave equations, Chaos, Solitons and Fractals. 26 (2005) 695–700.

[3] J.H. He. Homotopy perturbation method for solving boundary value problems, Physics Letters A. 350 (2006) 87–88.

[4] J.H. He. Limit cycle and bifurcation of nonlinear problems, Chaos, Solitons and Fractals. 26 (2005) 827–833.

[5] J.H. He. The homotopy perturbation method for nonlinear oscillators with discontinuities, Applied Mathematics and Computation.151 (2004) 287–292.

[6] J.K. Hunter, J. Scheurle, Physica D. 32 (1988) 253.

[7] T.J. Kawahara, Phys. Soc. Jpn. 33 (1972) 260.

[8] M. Matinfar, H. Hosseinzadeh and M. Ghanbari. Exact and Numerical Solution of Kawahara Equation by the Variational IterationMethod, Applied Mathematical Sciences. 2(43) (2008) 2119–2126.

2000 Mathematics Subject Classification. 65L80,65L05Key words and phrases. Homotopy perturbation method, Varietional iteration method, Kawahara equation

248


Discrete First-Order Four-Point Boundary Value

Problem

M. Mohamed, M. S. Jusoh

Universiti Teknologi MARA Kampus Arau, Perlis, Malaysia

[email protected]

Universiti Teknologi MARA Kampus Arau , Perlis, Malaysia

[email protected]

Abstract

We establish existence results for solutions to four-point boundary value problems for systems of first-order difference

equations associated with systems of first-order ordinary differential equations.

2000 Mathematics Subject Classification.Key words and phrases. Discrete four-point boundary value problem, Contraction mapping theorem, Brouwer fixed point theorem.

249


Serial-Parallel Access Method (SPAM) for Instruction

Cache Performance Improvement

M. Mohtashamzadeh, M. Fathy, M. Soryani

Department of Computer Engineering,

Iran University of Science and Technology, Tehran, Iran.

[email protected], [email protected], [email protected]

Abstract

Achieving to high fetch bandwidth and low power consumption are the more important challenges in cache performance.The approach to achieve these goals is to use way prediction in associative caches. Although this technique satisfies theabove mentioned goals but it enforces some hardware complexities which could not be neglected. There are other techniquessuch as serial and parallel that have some advantages and disadvantages.

In this paper we are introducing a method that is the combination of serial and parallel techniques which is named

Serial-Parallel Access Method (SPAM). Performance and power consumption of proposed method has been compared to

serial and parallel architecture. The results show that our proposed combined technique in comparison with serial increases

Instruction Per Cycle (IPC) and power consumption. Also the results of comparing parallel and combined techniques show

decreasing both in IPC and power consumption. Although the former decrease doesn’t look good, but the latter is more

important especially in systems which power consumption is critical for.

References[1] Brooks D, Tiwari V and Martonosi M (2000) Wattch: a framework for architectural level power analysis and optimizations, 27th

Annual International Symposium on Computer Architecture. Vancouver, Canada, pp. 83-94.

[2] Montanaro J (1997), A 160 MHz 32b 0.5W CMOS RISC microprocessor. Digital Technical Journal.Vol, 9(1): 49-62.

[3] Inoue K, Moshnyaga V G, Marakani K (2002). Trends in high performance, low power cache memory architectures, IEICE Transac-tions on Electronics, 85(2): 304-314.

[4] Reinman G, Calder B (2004). Using a serial cache for energy efficient instruction fetching, EUROMICRO Journal, 50(11): 675-685.

[5] Burger D, Austin T M, Keckler S W (2004). Recent extensions to SimpleScalar tool suite, ACM Sigmetrics Performance EvaluationReview, 31(4): 4-7.

[6] Tarjan D, Thaziyoor S, Jouppi N P (2006). CACTI version 4.0, Technical Report Hewlett-Pakard Development Company, availableat: http://www.hpl.hp.com/techreports/2006/.

[7] Kaxiras S, Martonosi M (2008). Architectural techniques for low power, Morgan and Claypool Publishers, 119-120.

2000 Mathematics Subject Classification. 65L99, 34A45Key words and phrases. Cache access method, Multi component cache, Way prediction.

250


Applying the WKB Method to The Bifurcation of an

Everted Spherical Shell Made of Elastic Varga Material

M.S. Pour1, M.Vakilian2

1 University Sistan and baluchestan, Departement of Mathematics, Zahedan, Iran

[email protected]

2 University Sistan and baluchestan, Departement of Mathematics, Zahedan, Iran

vakili [email protected]

Abstract

The WKB method is a powerful tool to obtain solutions for Eigenvalue problems. We apply the WKB method to the

bifurcation analysis of everted a spherical shells composed of Varga material. Incompressible cases are considered. The

method is degenerate but we obtain explicit bifurcation criteria and compare with previous numerical approximations.

References[1] Alen , W , Bush , Perturbation Methods for Engineers and Sciencetist .school of Coputing and Mathematics Teeside polytechnic

Middlesbrough ,u,k. (1992).

[2] Haughton, D. M. and Orr, A. On the eversion of incompressible elastic cylinders, Int. J.Non-Linear Mech. 30 (1995), 81-95.

[3] Chen, Yi-chao, and Haughton, D. M. On the existence of exact solutions for the eversion of elastic cylinders J. Elasticity 49 (1997),79-88.

[4] Haughton, D. M. and Chen, Yi-chao, On the eversion of incompressible elastic spherical shells ZAMP 50 (1999), 312-326.

[5] Sanjarani Pour, M. S. Application of the WKB method to some of the buckling problems in finite elasticity Ph. D. Thesis Keele,(2001).

[6] Fu, Y. and Pour, M. S., WKB method with repeated roots and its application to the buckling analysis of an everted cylindrical tube,SIAM Journal of Applied Mathematics 62 (2002),1856-1876.

[7] Ogden, R. W., Non-Linear Elastic Deformations. Dover Publications. New York (1997).

2000 Mathematics Subject Classification. 73C, 73G, 73HKey words and phrases. Elastic, spherical shells, eversion , bifurcation, asymptotic, WKB method

251


Application Of Generalized Purcell Method For Real

Eigenvalue Problems

M. Rahmani*, S. H. Momeni-Masuleh**

*Technology Development Institute, ACECR,


[email protected]

**Department of Mathematics, Shahed University,


[email protected]

Abstract

In numerical linear algebra, the singular value decomposition (SVD) is an important factorization of a rectangular real

or complex matrix, with several applications in signal and image processing, image compression and statistics. A new

method based on generalized Purcell method for real eigenvalue problem and QR decomposition of an arbitrary matrix is

proposed. The method in comparison to the inverse power method generates better results and has less computational cost.

In addition, the method obtains directly the rank of a matrix and gives linearlly independent eigenvectors corresponding

to an eigenvalue.

2000 Mathematics Subject Classification. 65F05, 65F10, 65F15Key words and phrases. Eigenvalue problem, Singular value decomposition, QR decomposition

252


Design, Manufacture And Optimization Of Intelligent

Cane For Blinds By Avr Microcontroller

M. Reza*, A. Malek**

*Technology Development Labs, Iranian Research Organization for

Science and Technology (IROST), Tehran, Iran

[email protected]



[email protected]

Abstract

Sight is one of the most important blessing of God that in case privation of it, there are many problems for blindpersons. Blind persons use of white cane for informing of obstacles and for finding suitable route, but application of it isnot enough for their requests, so they are confronted with many dangers.

The aim of this article is design, manufacture and optimization of electronic circuits in intelligent cane with advancedfeatures and better application. In these electronic circuits we can determine distance and depth by ultrasonic waves. Aftersending waves by transmitter circuit and their encounter with an obstacle, receiver circuit receives return waves, then AVRmicrocontroller processes data, auditory alarms become active and LCD shows distance to an obstacle and the depth ofhole. The basis of distance distinction is given by X = V t. X stands for distance, V is velocity of sound and t is the timeof transmitting and receiving ultrasonic waves. The velocity of sound is 330 m/s - 340 m/s, but its changes depends ontemperature and properties of matter in air.

In this article we use of AVR ( ATMEGA8 ) microcontroller and have designed, manufactured and optimized transmit-

ting and receiving circuits. Distance distinction is computed with our written program.

2000 Mathematics Subject Classification. 93A, 94CKey words and phrases.Circuit, Control.

253


Monomial Irreducible sln(C)-Modules

M. Shahryari

Islamic Azad University, Sarab Branch, Sarab, Iran.

[email protected]

Abstract

In this talk, we introduce monomial irreducible representations of the special linear Lie algebra sln(C). We will showthat, this kind of representations have bases for which the action of the Chevalley generators of the Lie algebra on the basiselements can be given by a simple formula.

Let L be a finite dimensional complex simple Lie algebra. For any functional integral dominant weight λ, we denotethe associated irreducible module byL(λ). One of the most important problems concerning representations of simple Liealgebras, is considered in this talk: to find an ordered basis for L(λ), such that one can obtain the matrix representationsof elements of L with respect to this ordered basis. It is trivial that handling with matrix representations are more flexiblethan working with L-modules, especially in practise.

It is the aim of this talk to introduce such a suitable basis for L(λ). In the present work we do this for monomialweights of the Lie algebra sln(C). Note that every dominant integral weight λ is associated with a partition π. We saythat λ is monomial, iff χπ, the corresponding character of π, is monomial character. In this case, by a paper of me and A.Madadi, (see [2]), there is a subgroup G ≤ Sm and a linear character χ of G, such that

L(λ) ∼= Vχ(G),

where Vχ(G) is symmetry class of tensors associated with G and χ over V = Cn.The symmetry class of tensors Vχ(G) has an orthonormal basis, consisting of decomposable symmetrized tensors, say

E = |α〉 : α ∈ ∆

such that |ασ〉 = χ(σ−1)|α〉, for all σ ∈ G. This is just the basis we need, because for Chevalley generators of sln(C), wewill prove that

Hi.|α〉 = µα|α〉,

Xi.|α〉 =m∑

r=1

δi+1,αr χ(σ−1r )|(α− εr)

σr 〉.

References[1] M. Shahryari, Monomial Irreducible sln(C)-Modules, Turkish J. of Math. Submitted.

[2] A. Madadi, M. Shahryari, Symmetry classes of tensors sln(C)-modules, Linear and Multilinear Algebra, Vol. 55, 2008.

2000 Mathematics Subject Classification.Primary: 15A69, Secondary 20C15.Key words and phrases.Symmetric group, Character theory, Representations of Lie algebras, Symmetry classes of tensors.

254


Multiple Confounded and Orthogonal Replicated Full

Factorial BIB Designs

M. Shamsuddin 1, M. Albassam2

1 Department of Statistics, King Abdulaziz University Saudi Arabia


Abstract

The sn factorial design, where s is a prime number like 2, 3, 5, etc., generally confounds a set of different orthogonal

factorial effects with sr blocks (n > r > 1) under one replicate. Thus there will be a complete set of orthogonal replicates of

different group of orthogonal factorial effects for constructing a partially confounded sn factorial design in sr blocks. The

factorial design, in general, when it partially confounds different orthogonal sets of different groups of orthogonal factorial

effects under the complete set of different orthogonal replicates constitutes a BIB design having their individual properties,

same result and detailed information of all factorial effects. The procedure is illustrated with some examples and one

practical application.


255


Fractional sn−k Factorial BIB Designs

M. Shamsuddin 1, M. Albassam2



Abstract

The partially confounded different sn−k fractional factorial designs under complete orthogonal replicates of different

groups of factorial effects constitute different BIB designs with detailed but same factorial and BIB result. The method

with some examples of different levels and one application are given..


256


Multi-Stage Multi-Phase BIB Designs

M. Shamsuddin

Department of Statistics, King Abdulaziz University Saudi Arabia

Abstract

The multi-stage multi-phase BIB designs are the chain of BIB factorial designs produced at each of its different stages

of fractional factorials. It is very interesting and important that it meets the scarcity of development of different types

of BIB designs providing individual factorial treatment ss’s equivalent to BIB’s adjusted treatment ss for each. A chain

example is given to illustrate procedure in details.


257


A Fuzzy Goal Programming Approach to

Multi-Objective Transportation Problems

M. A. Yaghoobi

Department of Statistics, Faculty of Mathematics and Computer,

Shahid Bahonar University of Kerman, Kerman, Iran

[email protected]

Abstract

Transportation problem is one of the most widely used operations research tools and has been a decision making aid

in almost all manufacturing industries and service organizations. This paper focuses on multi-objective transportation

problems (MOTPs). To deal with MOTPs, a new approach based on fuzzy goal programming is suggested. In fact, the

proposed approach considers each objective function as a fuzzy goal. Then a solution to MOTP obtains using a method

developed in [4,5] interactively. The performance of the proposed approach is evaluated by comparing its result with that of

some existing methods in [1,2,3]. Indeed, the proposed approach can be implemented easily during the interactive procedure

and its solution is better than some of the other methods presented in [1].

References[1] W. F. Abd El-Wahed, S. M. Lee, Interactive fuzzy goal programming for multi-objective transportation problems, Omega 34 (2006)

158-166.

[2] W. F. Abd El-Wahed, A multi-objective transportation problem under fuzziness, Fuzzy Sets and Systems 117 (2001) 27-33.

[3] A. K. Bit, M. P. Biswal, S. S. Alam, Fuzzy programming approach to multicriteria decision making transportation problem, FuzzySets and Systems 50 (1992) 35-41.

[4] M. A. Yaghoobi, D. F. Jones, M. Tamiz, Weighted additive models for solving fuzzy goal programming problems, Asia-Pacific Journalof Operational Research 25 (2008) 715-733.

[5] M. A. Yaghoobi, M. Tamiz, A method for solving fuzzy goal programming problems based on MINMAX approach, European Journal

of Operational Research 177 (2007) 1580-1590.

2000 Mathematics Subject Classification. 90C08, 90C29, 90C70Key words and phrases. Multi-objective transportation problem, fuzzy goal programming, interactive approach**This paper has been partially supported by the Research Group of Dynamical Systems, Shahid Bahonar University of Kerman,Iran

258


A model to create orthogonal Graeco Latin square

experimental designs

Mahdi Bashiri 1, Ehsan Korani 2

1 Department of Industrial engineering, Shahed University,

Tehran, Iran, P. O. Box 18155/159

[email protected]

2 Department of Industrial engineering, Shahed University,

Tehran, Iran, P. O. Box 18155/159

[email protected]

Abstract

Graeco Latin square designs and Latin square designs are using as experimental designs including more blocks. A Latin

square arrangement is an arrangement of n symbols in n rows and n columns, such that every symbol occurs once in each row

and each column. When two Latin squares of same order are superimposed on one another, in the resultant array if every

ordered pair of symbols occurs exactly once, then the two Latin squares are said to be orthogonal or Graeco Latin square.

Creating a Graeco Latin square arrangement is time consuming. However, it has good usage in scope of blocking design

in DOE. It helps the SSE (Sum of Squares Error) of design to be pure because of disarticulation of block factors’ effects

from the error effects. This paper proposes a model to arrange the position of pair words of Latin and Graeco. A heuristic

approach to set the Graeco Latin Square design and a proposed Linear Assignment Model are two proposed methods to

develop mentioned experimental designs. To solve the proposed linear model for any rank of square, we used Lingo software

to program the problem. And finally some numerical examples were used to show the applicability of proposed methods.

2000 Mathematics Subject Classification. 62Kxx, 90BxxKey words and phrases. Design of experiments, Blocking design, Nuisance factor, Graeco Latin Square, Linear Programming(LP), Assignment, Mutually Orthogonal Latin Square.

259


Distributions of order statistics from a bivariate

selection elliptical distribution as mixtures of univariate

selection elliptical distributions

Mahdi Salehi1, Ahad Jamalizadeh 2

1 Shahid Bahonar University, Department of Statistics,

Kerman, Iran

[email protected]

2 Shahid Bahonar University, Department of Statistics,

Kerman, Iran

[email protected]

Abstract

We consider here a univariate selection elliptical distribution, and focus on normal and t ones. In the normal case we

derive its moment generating function as well as the first and second moments. Next, we show that the distributions of order

statistics from a bivariate selection elliptical distribution are mixtures of these univariate selection elliptical distributions;

hence, using the established properties of the univariate selection elliptical distribution, we derive the moment generating

functions of order statistics, and also present expressions for means and variances of these order statistics, where they exist.

References[1] Reinaldo B. Arellano-Valle, Marcia D. Branco and Marc G. Genton (2006). A unified view on skewed distributions arising from

selections, Canadian Journal of Statistics, 34, 1-21.

[2] Reinaldo B. Arellano-Valle and Marc G. Genton (2009). An invariance property of quadratic forms in random vectors with a selection

distribution, with application to sample variogram and covariogram estimators, Annals of the Institute of Statistical Mathematics,

(In Press).

2000 Mathematics Subject Classification. 62H05, 62H10, 62E10, 62E15Key words and phrases. Elliptical distribution; Multivariate selection elliptical distribution; Order statistics; Mixture distribution

260


Total Ordering Cones in Rn and Optimality Condition

for Set-Valued Optimization Problems

Mahide Kucuk*, Mustafa Soyertem**, Yalcın Kucuk***

Anadolu University, Yunus Emre Campus,

Department of Mathematics, Eskisehir, Turkey

*[email protected]

**[email protected]

***[email protected]

Abstract

In this work, existence of a total ordering cone that consists a cone with a compact base is shown, the representation

of a convex, pointed, total ordering cone in Rn is given and it is shown that any total ordering cone in Rn is isomorphic to

the cone Rnlex. Then optimality conditions are given by using total ordering cone to scalarize the set-valued optimization

problem.

References[1] E. Hernndez, L. Rodrguez-Marn, Nonconvex scalarization in set optimization with set-valued maps, Journal of Mathematical Analysis

and Applications, 325(2007), 1-18.

[2] J. Jahn, Scalarization in vector optimization, Math. Program., 29(1984), 203-218.

[3] J. Jahn, Vector Optimization, Springer, Heidelberg, 2004.

[4] M. Ehrgott, Multicriteria Optimization, Springer, Berlin, 2005.

2000 Mathematics Subject Classification.80M50, 49J53Key words and phrases. total ordering cone, scalarization, set valued optimization

261


Repairable 2-Consecutive-2-Out-Of-n:F System

Mahmoud Boushaba

Laboratory of mathematical modeling and simulation, University of

Constantine Route d’An-El-Bey Constantine, Algeria

[email protected]

Abstract

In this paper, a repairable 2-consecutive-2-out-of-n: F system is studied. Assume that the working time and the repair

time of each component are both exponentially distrubuted, and each component after repair is as good as new. By using

the notion of generalized transition probability, we derive the state transition probability of the system. we obtain the

exact formulas of the system reliability.

2000 Mathematics Subject Classification. 90B25, 60K20Key words and phrases. 2-consecutive-2-out-of-n: F system; generalized transition probability; exponential distribution; repairablesystem.

262


Prey- Predator system and Lotka-Volterra model

Mahmoud Maheri1, Somayyeh Gholizadeh2

1 Azad University- Miyaneh Branch

[email protected]

2 Azad University- Miyaneh Branch

s [email protected]

Abstract

Lotka -Volterra equation are a pair of first order nonlinear differential equations that are used for analyzing the biological

and dynamical systems. This paper gives an improvement for prey-predator system in N species case with an overview

for the nonlinear dynamical system and the result of simulations, by solving of Lotka-Volterra equation analytically and

numerically by using rung kutta method.

2000 Mathematics Subject Classification.Key words and phrases. dynamical system, prey-predator system, Lotka-Volterra equation

263


Fixed Point Theorems With Contractive Conditions

Involving Product On Cone Metric Spaces

Mahpeyker Ozturk*, Metin Basarır**

*Sakarya Univ. Department of Math. 54100 Sakarya Turkey

[email protected]

**Sakarya Univ. Department of Math. 54100 Sakarya Turkey

[email protected]

Abstract

In this paper, we generalized the consequence of fixed point theorem with contractive conditions involving products, of

Pachpatte and investigated properties P and Q, which defined by Rhoades and Jeong on cone metric spaces.

References[1] Abbas, M., Rhoades, B.E., Fixed and Periodic Point Results in Cone Metric Spaces, Applies Math. Letters, 22(4),(2009), 511-515.

[2] Fisher, B., Common Fixed Points and Constant Mappings on Metric Spaces, Math. Sem. Notes (Univ Kobe), 1978.

[3] Huang, L.-G.,Zhang,X., Cone Metric Spaces and Fixed Point Theorems of Contractive mappings, J.Math. Anal. Appl., 332,(2007),1468-1476.

[4] Ilic, D., Rakocevic, V., Common Fixed Points for Maps on Cone Metric Space, J.Math. Anal. Appl., 341,(2008), 876-882.

[5] Jeong, G. S., Rhoades, B.E., Maps For Which F(T)=F(T?), Fixed Point Theory and Aplications, 6, (2004), 71-105.

[6] Pachpatte, B.G., Some Common Fixed Point theorems for mappings in metric spaces, Chung Yuan J. ,9, (1980), 14-16.

2000 Mathematics Subject Classification.47H10Key words and phrases.Fixed Point, Cone Metric Space.

264


A Simple algorithm for inverse general pentadiagonal

matrix with LU method

Majid Erfaniyan*, Seyed Masih Ayat**

*Department of Mathematics, Zabol University, Zabol, Iran

[email protected]

**Department of Mathematics, Zabol University, Zabol, Iran

Abstract

In this paper, we compute determinant of matrix A by Sogabe’s and Zhao’s algorithms. Then employing the Doolittle

and Court factorization matrix A is factorized into uptriangular and downtriangular matrix. The inverse of matrix A is

obtained by suitable algorithm. This method is more efficient than the others as such as illustrated.

References[1] T. Sogabe,A fast numerical algorithm for the determinant of the pentadiagonal matrix, Appl. Math. Comput. 196(2008),835–841.

[2] T. Sogabe,On a two-term recurrence for the determinant of a general matrix, Appl. Math. Comput. 187(2007),785–788.

[3] X.L. Zhao and T.Z. Huang, On the inverse of a general pentadiagonal matrix, Appl. Math. Comput. 202(2008),639–646.


265


Identification of all DEA Efficient Facets

Majid Zohrehbandian

Department of Mathematics, Islamic Azad University-Karaj Branch,

P.O.Box 31485-313, Karaj, Iran.

[email protected]

Abstract

The ability of identifying efficient frontier prior to the DEA calculation is of extreme importance to an effective and

efficient DEA computation. We introduce a new computational framework which is based on enumerating the extreme

points of a convex polytope specified by some linear constraints. The number of extreme points of the proposed model is

about equal to the number of efficient facets of the production possibility set (PPS). Access to efficient frontier of PPS

permits a complete analysis in a second phase for the corresponding model either oriented or orientation-free.

References[1] Ali A.I. Streamlined computation for data envelopment analysis. European Journal of Operational Research 64 (1993) 61-67.

[2] Ali A.I., Lerme C.S., Seiford L.M. Components of efficiency evaluation in data envelopment analysis. European Journal of Opera-tional Research 80 (1995) 462-473.

[3] Barr R.S., Durchholz M.L. Parallel and hierarchical decomposition approaches for solving large-scale data envelopment analysismodels. Annals of Operations Research 73 (1997) 339-372.

[4] Dula J.H. Computations in DEA. Pesquisa Operacional 22 (2002) 165-182.

[5] Dula J.H., Helgason R.V., Venugopal N. An Algorithm for Identifying the Frame of a Pointed Finite Conical Hull. INFORMSJournal on Computing 10 (1998) 323-330.

[6] Dula J.H., Thrall R.M. A computational framework for accelerating DEA. Journal of Productivity Analysis 16 (2001) 63-78.

[7] Jahanshahloo G.R., Shirzadi A. and Mirdehghan S.M., Finding strong defining hyperplanes of PPS using multiplier form. EuropeanJournal of Operational Research 194 (2009) 933-938.

[8] Olesen O.B., Petersen N.C. Indicators of ill-conditioned data sets and model misspecification in data envelopment analysis: Anextended facet approach. Management Science 42 (1996) 205-219.

[9] Olesen O.B., Petersen N.C. Identification and use of efficient faces and facets in DEA. Journal of Productivity Analysis 20 (2003)323-360.

[10] Yu G., Wei Q., Brockett P., Zhou L. Construction of all DEA efficient surfaces of the production possibility set under generalized

data envelopment analysis model. European Journal of Operational Research 95 (1996) 491-510.

2000 Mathematics Subject Classification. 90C05, 90B50Key words and phrases.Data Envelopment Analysis, Efficient Frontier, Vertex Enumeration.This research was supported by Islamic Azad University-Karaj Branch

266


On a class of divergent sequences

Malisa R. Zizovic, Dragan Djurcic, Ljubisa D.R. Kocinac

Technical Faculty in Cacak, University of Kragujevac, Serbia

[email protected]

Technical Faculty in Cacak, University of Kragujevac, Serbia

[email protected]

Faculty of Sciences and Mathematics, University of Nis, Serbia

[email protected]

Abstract

A sequence x = (xn)n∈N of positive real numbers belongs to the class ARVs if for each λ > 1 there are n0 ∈ N and

c(λ) > 1 such that for each n ≥ n0 it holds x[λn] ≥ c(λ) · xn. We present some results on this class of sequences and its

relationships with translationally regularly varying and translationally rapidly varying sequences.

2000 Mathematics Subject Classification. 26A12, 40A05, 54A20, 91A44Key words and phrases. Regular variation, rapidly varying sequence, quotient speed, selection principles, game theory.

267


Quasi-Permutation Representations of the Borel and

Maximal Parabolic Subgroups of G2(2n)

Maryam Ghorbany

Department of Mathematics, Iran University of Science

and Technology, Emam, Behshahr, Mazandaran, Iran

[email protected]

Abstract

By a quasi-permutation matrix we mean a square matrix over the complex field C with non-negative integral trace.Thus

every permutation matrix over C is a quasi-permutation matrix. For a finite group G the minimal degree of a faithful

representation of G by quasi-permutation matrices over the complex numbers is denoted by c(G) , and r(G) denotes the

minimal degree of a faithful rational valued complex character of G. In this paper c(G) and r(G) are calculated for the

Borel and maximal parabolic subgroups of G2(2n).

References[1] H. Behravesh , Quasi-permutation representations of p-groups of class 2 , J.London Math. Soc. (2)55 , 251-26 (1997).

[2] M.R. Darafsheh and M.Ghorbany, Quasi-permutation representations of the groups SU(3, q2) and PSU(3, q2), Southest AsianBulletin of Mathemetics (2002)26 ,395-406.

[3] H. Enomoto, The characters of G2(2n), Japan. J. Math. Vol. 12, No. 2, (1986), 326-377.

[4] W.J. Wong , Linear groups analogous to permutation groups , J. Austral. Math. Soc (Sec. A) 3 (1963), 180-184 .

2000 Mathematics Subject Classification.20C15Key words and phrases.Character table, Quasi-permutation representation, Schurindex

268


P-Adic Study in Linear 2-Normed Spaces

Mehmet Acıkgoz

University of Gaziantep, Faculty of Science and Arts,

Department of Mathematics, 27310 Gaziantep, Turkey

[email protected]

Abstract

We shall study p-adic analysis in linear 2-normed spaces and give some results in this sense.

References[1] Bachman, G., Introduction to p-adic numbers and valuation theory, Academic press, 1964.

[2] Bachman, G., Narici, L., Functional Analysis, Academic Press, New York and London.

[3] Baker, A. J., An introduction to p-adic numbers and p-adic analysis, URL: http:// www.maths.gla.ac.uk/˜ajb.

[4] Cho, Y., Lin, P., Kim, S.S., Misiak, A., Theory of 2-Inner Product Spaces, Nova Science Publishers, 2001.

[5] Dragovich, B., p-adic approach to the genetic code and genome, Institute of Physics, Belgrade, Serbia, TAG, 20-24 Oct 2008,Annecy.

[6] Freese, R., Cho, Y., Geometry of Linear 2-Normed Spaces, Nova Science Publishers, 2001.

[7] Gouvea, F. Q., P-adic Numbers: An introductory survey. Berlin: Springer-Verlag.

[8] Gouvea, F. Q., P-adic: An introduction, universitext, Springer-Verlag, 1993.

[9] Gahler, S., Linear 2-normerte Raume, Math.Nachr, 28 (1965), 1-45.

[10] Hensel, K., Theorie der Algebraischen Zahlen, Teubuer, Leipzing, 1908.

[11] Katok, S., Real and p-adic analysis course notes for math 497C Mass program, Fall 2000 Revised, The Pennsylvania state university,University Park, PA 16802, U.S.A. November 2001.

[12] Koblitz, N., P-adic Numbers, p-adic analysis, and zeta-Functions, 2nd ed. New York: Springer-Verlag, 1984.

[13] Kurt, M., Introduction to p-adic numbers and their functions, 2nd ed. Cambridge, England: Cambridge University Press, 1981.

[14] Lewandowska, Z., Generalized 2-normed spaces, Stuspskie Prace Matematyczno-Fizyczne 1(2001),33-40.

[15] Lewandowska, Z., Linear operators on generalized 2-normed spaces, Bull. Math. Soc. Sci. Math. Roumanie (N.S.) 42(90)(1999),no.4,353-368.

[16] Lewandowska, Z., On 2-normed sets, Glasnik Mat. Ser.III 38(58) (2003), no.1, 99-110.

[17] Mahler, K., Introduction to P-adic numbers and their functions, 2nd ed. Cambridge, England: Cambridge University Press, 1981.

[18] Robert, A. M., A course in p-adic analysis, Graduate texts in mathematics, vol. 198, (2000).

[19] Vladimirov, V. S., Volovich, I. V., Zelenov, E. I., p-adic analysis and mathematical physics, World scientific, Singapore, 1994.

[20] White, A., 2-Banach spaces, Math Nachr.42(1969), 43-60.

2000 Mathematics Subject Classification.46A15, 41A65, 11B68, 11S80.Key words and phrases.2-normed spaces, p-adic numbers, p-adic norm, p-adic 2-norm.

269


The Effect Of Multiple Intelligence Approach In Project

Based Learning To Mathematics Learning Achievement

Mesut Tabuk , Ahmet Sukru Ozdemir


Abstract

The purpose of this research is to determine effects of multiple intelligence approach in project based learning applied

in mathematics lesson on the students’ mathematics achievements. This experimental research that was conducted related

to this aim was designed in the model of pretest-posttest with control group. The experimental study was conducted at

two different schools in the Fatih district of Istanbul in the spring semester of 2006-2007 education years. The participants

of the study are totally 144 students of 6th classes of these schools. In each school, three classes are randomly chosen

as two experiment groups and one control group. While students in experimental groups learn mathematics with project

based learning, control group students learn mathematics with traditional method. In the project application, in the first

experiment groups the project topics are assigned according to intelligences which the students get the maximum points

in multiple intelligence quiz. In the second experiment groups, the project topics are assigned according to intelligences

which the students get the minimum points in multiple intelligence quiz. The data in the research were gathered through

mathematics achievement test and multiple intelligence quiz. The data were analyzed descriptively and then the findings

were determined and evaluated based on the research questions by the help of some statistical programs. At the end of the

study, it was found that there is no statistically important effect of multiple intelligence approach in project based learning

applied in mathematics lesson on the students’ mathematics achievements.

2000 Mathematics Subject Classification. 97C40Key words and phrases. Project Based Learning, Multiple Intelligence Approach, Attitude towards Mathematics, Mathematics

270


A unified approach to generalized continuities

Milan Matejdes

Department of Mathematics Faculty of Applied Informatics

Tomas Bata University in Zlın Nad Stranemi 4511, 760 05 Zlın, Czech Republic

[email protected]

Abstract

Contribution deals with a concept which covers many known types of continuities. Method is based on stating ap-

propriate system E of subsets on domain. The first motivation for introducing comes from definition of quasi continuity.

Namely, a mapping f : X → Y is E-continuous at x, if for any open sets V and U such that x ∈ U and f(x) ∈ V , there is

a set E ∈ E, such that E ⊂ U ∩ f−1(V ). The next, stronger variant, is generalization of continuity. A function f is dense

E-continuous at x, if for any open set V containing f(x), there is an open set U 3 x, such that for any open set H ⊂ U ,

there is a set E ∈ E such that E ⊂ H ∩ f−1(V ). When E is system of all non-empty open sets, it is equivalent to the

notion of quasi continuity or (dense variant) α-continuity. Using different systems E, we are able to describe many types of

continuities. Approach is used in function as well as multifunction setting.


271


On analysis of nonlinear dynamic system of separation

Mimoun Zelmat

Laboratory of Applied Automation University of Boumerds 35000 Algeria,

[email protected]

Abstract

This paper proposes an approach to quantitately and systematically search for analysis process of separation which is

highly nonlinear. Since the separation process unrolls inside a block of separation, used in hydrocarbon field, it is necessarily

that the model takes in the account the dimension of the separator and the physical properties of the composites to be

separated. This paper deals with the problem of finding a moderately complex model of the separator that may capture

the key dynamical properties of the physical plant.

2000 Mathematics Subject Classification.Key words and phrases. nonlinear dynamic system, modelling, process of separation

272


A SystemC QoS router design with virtual channels

reservation in a wormhole-switched NoC

Mohamed Horchani

EE Laboratory, Faculty of Sciences, 5000 Monastir, Tunisia

[email protected]

Abstract

Abstract-The current levels of integration make it possible to assemble on the same chip a complete numerical system.

The systems on chip or SoCs become increasingly complex; the forecasts promise in the next years the integration of

electronic systems of 4 billion transistors for frequencies close to 10 GHz. A powerful and economic solution consists

in benefitting from an infrastructure of pre-established configurable communication, namely NoC for Network on Chip.

The components communicate then between them by exchanging packages through interconnected network, providing a

reusable communication-structure. The recourse to NoC is essential for the great dimension circuits, as well from the

technological point of view, as from the functional point of view (facilitated connection of the IPs components and thus

of their re-use). The control of the NoC characteristics is a major asset because the consumption and the performance

of SoC will be dominated more and more by the communication resources. This paper presents the design of an on-chip

network router with Quality-of- Service (QoS) support. The router uses virtual channel architecture with a priority-based

scheduler to differentiate between multiple connections with various QoS requirements sharing the same physical channel.

The architecture that we propose in this work is composed mainly of five ports. In addition, inside a router we find two

under-routers. A SystemC based methodology is used to achieve an RTL simulation of the design.


273


Determination of Residual Stress by Artificial Neural

Network in Hsla-100 Steel Weldments

Mohammad Heidari

Islamic Azad University, Aligudarz Branch, Aligudarz, Iran, P.O.Box 159

[email protected]

Abstract

The residual stress fields near the weld bead in HSLA-100 steel weldments were examined in detail by means of neural

network. Many different specimens that were subjected to different conditions were studied. At first, the residual stress by

x- ray diffraction is calculated. Then a neural network is created. The input of this network is heat input, preheat, and

yield strength, temperature of age and measurement direction. Residual stresses were determined without any calculating or

experiment on the surface by using this network under any condition of problem. However, accurate predictions of residual

stress could not be obtained without a large number of time and money by experimentally method. An application of the

back-propagation neural net work using short term measuring data is presented in this paper. In this study experimental

and numerical methods are combined to determination of the residual stress. Some advantage of this numerical method

is saving in time and money. The Artificial Neural Network (ANN) is superior to existing experimental techniques. In

this study, the neural networks have been employed as a general approximation tool for estimation of the residual stresses

in welding of steel. For this purpose used of three functions such as newelm, newff and newcf and by using of MATLAB

software, the network is created. The Levenberg-Marquardt algorithm is chosen to perform the training of the networks. A

number of samples are analyzed with ANN for parameters of residual stress and the results are compared with experimental

method. Back Propagation Neural network (BPN) is used to approximation of residual stress. Resultant low relative error

value of the test indicates the usability of the BPN in this area. The results show that, estimation by newelm function is

better than newff and newcf functions because it has less error than another function. Also specimens which are subjected

to different welding heat input have similar distributions of residual stress on the surface, but the magnitudes of stresses

are different. Higher welding heat input generates smaller stress.

2000 Mathematics Subject Classification.Key words and phrases. Residual Stress, Welding, HSLA100, Artificial Neural Networks.

274


A survey on Mathematics’ role on Customer

Relationship Management (CRM) to Improve

Customer Satisfaction and Production Increase

Mohammad Reza Noruzi1, Narges Sariolghalam2

1 Executive Master Business Administration, MA Islamic Azad University,

Bonab, Iran

[email protected]

2 Applied Mathematics, Faculty member Payam e Noor University of

Maragheh,Iran

Abstract

Emergence of new products in chaotic markets and development of small and medium enterprises, (SME’s) in national

and international era has caused companies, factories and in general whole enterprises in private and also governmental

and non-governmental organizations by different challenges which all have gone to bring new customers and also to keep

previous ones who are accounted for their revenue. For this a new aspect of management science and mathematics as a

basic and mother science shines to keep enterprise’s efficiency in the current economical recession. The aim of this paper

is analyzing the role of problem solving strategies in mathematics with Customer Relationship Management, CRM. This

paper will be studying the logical relation between them.

2000 Mathematics Subject Classification. 92-xxKey words and phrases. Mathematics Problem solving strategies, Customer Relationship Management, Proficiency, Customer,SME

275


Generalized Bi-Quasi-Variational Inequalities for

Quasi-Pseudo-Monotone Type II Operators on

Compact Sets

Mohammad Showkat Rahim Chowdhury

Dept. of Mathematics Lahore University of Management Sciences (LUMS)

Lahore-54792 Pakistan

[email protected]

Abstract

In this paper, the authors prove some existence results of solutions for a new class of generalized bi-quasi-variational

inequalities (GBQVI) for quasi-pseudo-monotone type II and strongly quasi-pseudo-monotone type II operators defined on

compact sets in locally convex Hausdorff topological vector spaces. In obtaining these results on GBQVI for quasi-pseudo-

monotone type II and strongly quasi-pseudo-monotone type II operators, we shall use Chowdhury and Tan’s generalized

version in [M. S. R. Chowdhury and K.-K. Tan, Generalization of Ky Fan’s minimax inequality with applications to

generalized variational inequalities for pseudo-monotone operators and fixed point theorems, J. Math. Anal. Appl. 204

(1996), 910–929] of Ky Fan’s minimax inequality in [K. Fan, A minimax inequality and applications, in “Inequalities, III”

(O. Shisha, Ed.), pp.103-113, Academic Press, San Diego, 1972] as the main tool.

References[1] M. S. R. Chowdhury and K.-K. Tan, Generalization of Ky Fan’s minimax inequality with applications to generalized variational

inequalities for pseudo-monotone operators and fixed point theorems, J. Math. Anal. Appl. 204 (1996), 910–929.

[2] K. Fan, A minimax inequality and applications, in ”Inequalities, III” (O. Shisha, Ed.), pp.103-113, Academic Press, San Diego,

1972.

2000 Mathematics Subject Classification. 47, 46, 54, 90Key words and phrases. Generalized bi-quasi-variational inequalities, quasi-pseudomonotone type II operators, strongly quasi-pseudo-monotone type II operators, locally convex Hausdorff topological vector spaces.

276


Stability Analysis of Infectious Disease with Media

Coverage and Poverty

Mohammed Al Jaffreh* and Rajinder Sharma**

*Department of Information Technology,

Shinas College of Technology, Oman.

[email protected]

**Department of Information Technology(Mathematics Section),

Shinas College of Technology, Oman.

Abstract

In this paper, the effect of poverty along with media coverage on the stability of dynamics of infectious disease has been

checked. The incorporation of the factor, poverty along with media coverage makes our model more closer to the real life

situations. Using stability theory, the analysis of the model has been made by finding out all the equilibrium points of the

system. The stability analysis has also been done for parameters involved in the model.

2000 Mathematics Subject Classification.Key words and phrases.Poverty; equilibrium points; media coverage; stability.

277


Modelling The Interaction Between Crude Oil Price

And Other Commodities Price

Mohd Tahir Ismail*, Zetty Ain Kamaruzzaman**

*School of Mathematical Sciences, Universiti Sains Malaysia,

11800 USM, Penang, Malaysia

[email protected]

**School of Mathematical Sciences, Universiti Sains Malaysia,

11800 USM, Penang, Malaysia

[email protected]

Abstract

Crude oil price issues have gained much attention worldwide lately. This is due to the shortage of crude oil production,

which increases the price tremendously. The fact that an increase in crude oil price will then increase the disposal income

of oil exporting countries together with the demand for some commodities have outburst the primary idea of doing this

research. In this paper, we study the nonlinear interactions between crude oil price changes on five commodities namely

lamb, olive oil, rubber, tea, wheat and zinc by using a two regimes multivariate Markov switching vector autoregressive

(MS-VAR) model with regime shifts in both the mean and the variance. The empirical results show that all the series are

not cointegrated but the MS-VAR model with two regimes manage to detect common regime shifts behaviour in all the

series. The estimated MS-VAR model reveals that when the crude oil price fall the price of the five commodities also moving

downward and when the crude oil price gain the price of the five commodities will increase. In addition, the MS-VAR model

fitted the data better than the linear vector autoregressive model (VAR).

2000 Mathematics Subject Classification. 37M10, 91B82, 91B84.Key words and phrases.Markov switching vector autoregressive model, crude oil price, nonlinearity.

278


A new system of implicit variational-like inclusion

problems involving (H(., .), η)-monotone operators

Mohsen Alimohammady, Mehdi Roohi


m.alimohammadygmail.com

University of Mazandaran, Babolsar 47416-1468, Iran

[email protected]

Abstract

In this paper, we introduce a new concept of (H(., .), η)-monotone operator. The generalized resolvent operator as-

sociated with this type of monotone operators is defined and Lipschitz continuity of it is established. By using Lipschitz

continuity of generalized resolvent operator a new system of implicit variational-like inclusion problems is solved. Finally,

some algorithms and their convergence theorems are considered.

References[1] S. Adly, Perturbed algorithm for sensitivity analysis for a general class of variational inclusions, J. Math. Anal. Appl. 201(1996),

609–630.

[2] Y. P. Fang and N. J. Huang, H-monotone operators and system of variational inclusions, Comm. Appl. Nonlinear Anal. 11(1)(2004),93–101.

[3] Y. P. Fang, N. J. Huang and H. B. Thompson, A new system of variational inclusions with (H, η)-monotone operators in Hilbertspaces, Comput. Math. Apll. 49(2–3)(2005), 365–374.

[4] J. W. Peng, System of generalized set-valued quasi-variational-like inequalities, Bull. Austral. Math. Soc. 68(2003), 501–515.

[5] J. W. Peng and D. L. Zhu, A new system of generalized mixed quasi-variational inclusions with (H, η)-monotone operators, J.Math. Anal. Appl. 327(2007), 175–187.

[6] R.-U. Verma, A-monotonicity and applications to nonlinear variational inclusion problems, J. Appl. Math. Stoch. Anal.2004(2)(2004), 193–195.

[7] R.-U. Verma, Approximation solvability of a class of nonlinear set-valued variational inclusions involving (A, η)-monotone map-pings, J. Math. Anal. Appl. 337(2008), 969–975.

2000 Mathematics Subject Classification. 47H05, 47J20, 49J40Key words and phrases. monotone operator, resolvent operator, implicit variational inclusion

279


Some Characterizations of Multi-Criteria Shortest Path

in A Multi-Valued Network

Moncef Abbas

USTHB, Faculty of Mathematics, Laid3 BP 32, Bab-Ezzouar, 16111, Algiers Algeria

moncef [email protected]

Abstract

The problem of shortest path is considered as one of combinatorial optimization problems the most important and moststudied ([1], [2]). Mono-criteria variant of this problem is considered as practically solved ([3]). But the case of multi-criteria variant is NP-complete ([4], [5]). The algorithms for solving the problem of multi-criteria shortest path is basedessentially on the use of algorithms of the classical problem or slightly modified versions ([6], [7], [8]). In several problems inthe routing network, conflicting objectives must be considered. Paths problems in networks are usually multi-dimensionalnature and in many cases the explicit consideration of multiple objectives is adequate. Objectives related to cost, distance,time, environmental impact, ...etc. are appropriate to select the best compromise solution ([9]). Our contribution is focusedon two research problems of shortest paths in the multi-objectives context. We establish some results, particularly in thecharacterization of the existence of non-dominated solutions. We also give the mathematical formulation of multi-objectiveproblems as well as the resolution algorithms.

References[1] Dijksta, E. W. A note on two problems in connexion with graphs. Numerische, Mathematik, 1 p.269-271, 1959

[2] Pallottino, S. et Scutell, M.G. Shortest path algorithms in transportation models: classical and innovative aspects. In Equilibriumand Advanced Transportation Modelling, kluwer, p. 245-281, 1998.

[3] Lacomme, P., Prins, C et Sevaux, M. Algorithmes de graphes. Editions Eyrolles. 2003.

[4] Vincke, P. Problme multicitre. Cahiers du Centre d’Etudes de Recherche Oprationnelle, 16, p.425-439, 1974.

[5] Martins, E.Q.V. On multicriteria shortest path problem. European Journal of Operational Research, 16: 236-245, 1984.

[6] Boussedjra, M. Contribution la rsolution du problme du plus court chemin multiobjectif par algorithmes volutionnistes: applicationaux systmes de transport intermodal. Thse de Doctorat, Spcialit Automatique et informatique. Universit de Technologie de Belfort-Montbliard, UTBM, 2005.

[7] Climaco, J.C.N and Martins, E.Q.V. On the determination of the nondominated path in a multiobjective network problem.Methodsin Operations Research, 40 p.255-258, 1981.

[8] Ehrgott, M and Gandibleux, X. Asurvey and annotated bibliography of multicriteria combinatorial optimization. OR Spectrum22.p.425-460,2002.

[9] Gandibleux. X, Beugnies.F, Randriamasy.S. Martins’ algorithms revisited for multi-objective shortest path problem with a MaxMin

cost function. 4OR: Quaterly journal of Operational Research, 4(1): 47-59, 2006.

2000 Mathematics Subject Classification. 90B50, 90C27, 65K05, 52B05Key words and phrases. multi-criteria shortest path problem, combinatorial optimization, mathematical programming.

280


Asymptotic behaviour of a dynamic problem of linear

elasticity with Tresca boundary conditions

Mourad Dilmi

Department of Mathematics, M’sila University, 28000, M’sila, Algeria

[email protected]

Abstract

We consider a problem associated to the linear elastic body in dynamic regime in a three dimensional thin domain Ωε.

We first establish an existence result for weak solutions of this problem. Then we study the asymptotic analysis when one

dimension of the domain tends to zero . A specific weak Reynolds equation, the limit of Tresca boundary conditions are

obtained. The uniqueness result for the limit problem is also proved.

References[1] G. Duvant, J.L. Lions, Les inequations en mecanique et en physique, Dunod Paris (1972).

[2] M. Boukrouche, R. El mir, Asymptotic analysis of non-Newtonian fluid in a thin domain with Tresca law. Nonlineat analysis,Theory Methods anad applicatios. 59 (2004), 85-105.

[3] G. Bayada, M. Boukrouche, On a free boundary problem for Reynolds equation derived from the Stokes system with Tresca boundaryconditions. J. Math. Anal. Appl. 382 (2003), 212-231.

[4] M. Boukrouche, G. ÃLukaszewicz, Asymptotic analysis of solutions of a thin film lubrication problem with nonlinear boundaryconditions, Int. J. Eng. Sci. 41 (2003) 521–537.

[5] M. Dilmi et H. Benseridi, Probleme de Contact sans frottement –Dirichlet pour les equations de Laplace et de Lame dans un

polygone. Anal. Univ. Oradea, Fasc. Mathematica, Tom XIV (2007), 221-236.

2000 Mathematics Subject Classification.35R35; 78M35; 35B65.Key words and phrases.Free boundary problems; Tresca law; Elasticity system; Asymptotic approach; Reynolds equation.

281


Generalized potentials in weighted variable exponent

Lebesgue spaces on homogeneous spaces

Mubariz G. Hajibayov, Stefan G. Samko

Institute of Mathematics and Mechanics of NAS of Azerbaijan

9, F.Agaev str. AZ1141 Baku, Azerbaijan

[email protected]

Department of Mathematics, University of Algarve

Campus de Gambelas

8005-139 Faro,Portugal

Abstract

In the sequel (X, %, µ) always stands for a bounded quasimetric space with quasidistance % and Borel regular measureµ. We denote d = diam X. The measure µ is supposed to satisfy the growth condition

µ (B (x, r)) < KrN

.

A function Φ : X × [0,∞) → [0, +∞) is said to be an N-function, if

1. for every x ∈ X the function Φ (x, t) is convex, nondecreasing and continuous in t ∈ [0,∞),

2. Φ (x, 0) = 0, Φ (x, t) > 0 for every t > 0,

3. Φ (x, t) is a µ-measurable function of x for every t ≥ 0.

Let Φ be an N-function and w a weight. The weighted Orlicz-Musielak space LΦ(X, w) is defined as the set of all real-valuedµ-measurable functions f on X such that

∫

X

Φ

(x,

w(x)f(x)

λ

)dµ(x) < ∞

for some λ > 0. We equip it with the norm

‖f‖Φ,w = inf

λ > 0 :

∫

X

Φ

(x,

w(x)f(x)

λ

)dµ(x) ≤ 1

.

In particular, Φ(x, t) = tp(x), where 1 ≤ p(x) < ∞, is an N-function and the corresponding space is the variable exponent

Lebesgue space Lp(·)(X, w). Everywhere in the sequel, when dealing with the space Lp(·)(X, w), we suppose that

1 < p− ≤ p(x) ≤ p+ < +∞, (0.1)

|p(x)− p(y) ≤ A

ln 1%(x,y)

, %(x, y) <1

2(0.2)

and denotew

ν= [%(x, x0)]

ν, x0 ∈ X.

The function a : [0, d] → [0,∞) is assumed to satisfy the assumptions1) a(r) is continuous, almost increasing, positive for r > 0 and a(0) = 0,

2)d∫0

a(r)r dr < ∞. We denote

A(r) =

r∫

0

a(t)

tdt.

The lower dimension of X is defined by

dim(X) = supt>1

ln

(lim inf

r→0inf

x∈X

µB(x,rt)µB(x,r)

)

ln t.

It is clear that dim(X) = N in the cases where X has constant dimension N , that is, c1rN ≤ µB(x, r) ≤ c2rN . In general,if X has the property that

0 < dim(X) < ∞,

then X satisfies the growth condition with every 0 < N < dim(X).

282


Theorem Let (X, %, µ) be quasimetric space with doubling measure and positive finite lower dimension dim(X), andlet p fulfill assumptions (0.1)-(0.2) and

0 ≤ ν <dim(X)

p′(x0).

Suppose that there exists a β ∈(

0,dim(X)

p+

)such that

a(r)

rβis almost decreasing. Then the operator

Iaf (x) : =

∫

X

a (% (x, y))

[% (x, y)]Nf(y)dµ(y)

is bounded from the space Lp(·) (X, wν) into the weighted Orlicz-Musielak space LΦ(X, wν1 ), where ν1 = νp(x0) and the

N-function Φ is defined by its inverse (for every fixed x ∈ X)

Φ−1

(x, r) =

r∫

0

A(

t− 1

N

)t− 1

p′(x) dt.

2000 Mathematics Subject Classification. 43A85, 46E30, 47B38Key words and phrases. Weighted estimates, generalized potential, variable exponent, variable Lebesgue space, Musielak-Orliczspace

283


Fixed Points of Mappings Satisfying a New Condition

in Cone Metric Spaces

Muhib Abuloha, Duran Turkoglu

Department of Mathematics, Institute of Science and Technology

Gazi University, 06500, Ankara-Turkey

[email protected]

Department of Mathematics, Faculty of Science and Arts

Gazi University, 06500, Ankara-Turkey

[email protected]

Abstract

In this paper we proved some fixed points of mappings satisfying a new condition in cone metric spaces, where some of

the main results of iri [4] are recovered.

References

[1] D. Ili., V. Rako.evi., Common Fixed Points for Maps on Cone Metric Space. J. Math. Anal. Appl. (2007), doi:10.1016/j.jmaa.

2007.10.065.

[2] D. Turkoglu, M. Abuloha, Cone Metric Spaces and Fixed Point Theorems in Diametrically Contractive Mappings. Acta

Mathematica Sinica, English Series (to appear).

[3] R. Raja, S. M. Vaezpour, Some Extensions of Banach‘s Contraction Principle in Complete Cone Metric Spaces. Fixed Point

Theory and Applications, Vol. 2008, doi: 10.1155/2008/768294.

[4] Lj. B. .iri., Fixed Points of Mappings Satisfying a New Condition, Proc. Nat. Acad. Sci. India Sect. A Phys. Sci. no. 3,73 (2003).

[5] L.G. Huang, X. Zhang, Cone Metric Spaces and Fixed Point Theorems of Contractive Mappings. J. Math. Anal. Appl., 332,

1468-1476, 2007.

[6] M. Abbas, G. Jungck, Common Fixed Point Results for Non Commuting Mappings Without Continuity in Cone Metric Spaces.

J. Math. Anal. Appl. (2007), doi: 10.10161/j.Jmaa. 2007.09.070.

[7] Pasquale Vetro, Common Fixed Points in Cone Metric Spaces. Rendi Conti Del Matematico Di Palermo. Serie II, Tomo LVI,

464-468,2007.

[8] Sh. Rezapour, R. Hamlbarani, Some Notes on the Paper ”Cone Metric Spaces and Fixed Point Theorems of Contractive

Mappings”. J. Math. Anal. Appl. (2008),doi10.1016

[9] D. Ili., V. Rako.evi., Quasi-Contraction on Cone Metric space. Applied Mathematics Letters (2008),

doi:10.1016/j.aml.2008.08/011.

[10] M. Abbas, B.E.Rhoades, Fixed and Periodic Point Results in Cone metric Spaces. Applied Mathematics Letters (2008),

doi:10.1016/j.aml.2008.07/001.

[11] D. Wardowski, Endpoint and Fixed Points of set-valued Contractions in Cone Metric Spaces, Nonlinear Analysis (2008),

doi:10.1016/j.na.2008.10.089.

[12] K. Deimling, Nonlinear Functional Analysis, Springer-Verlage, 1985.

[13] Sh. Rezapour, Best Approximations in Cone Metric Spaces, Mathematica Moravica, Vol.11 (2007), 85-88.

[14] Cristina Di Bari, Pasquale Vetro, .-Pairs and Common Fixed Points in Cone Metric Spaces, Rendiconti del Circolo Matematico

di Palermo, 57,doi: 10.1007/s 12215-008-0020-9, 2008.

2000 Mathematics Subject Classification.Key words and phrases. Fixed point, cone metric space, minihedral cone, strongly minihedral cone, cone metrically convex

284


Using the Algebra of Hypergraph for Reconstruction

Phylogenetic Trees

Mulia Astuti Msc1, Dr.Irawati2, Dr.Intan Muchtadi-Alamsyah3,

Dr.Ahmad Muchlis4, Achirul Akbar S.Si dan Muliana5, A. Halim MSi6

1 Department of Mathematics Faculty of Mathematics and Natural Sciences

Universitas Bengkulu, Jl. Raya Kandang Limun Bengkulu

Mulia [email protected]

2, 3, 4, 5, 6 Algebra Research Group, Faculty of Mathematics and Natural Sciences,

Institut Teknologi Bandung (ITB), Jl.Ganesha no.10 Bandung 40132

2 [email protected] 3 [email protected], 4 [email protected]

Abstract

In this paper, we will construct phylogenetic trees by using the algebra of hypergraph through Neighbor Joining

Algorithm. Directed hypergraph can represent metabolic networks M(X,), where X is the set of metabolites and is the set

of chemistry reactions. Metabolic network datas are obtained from citric-acid cycle of microorganism of 3 classes, which are

4 Archea, 11 Bacteria and 1 Eukaryote. Moreover, the result will be compared to the phylogenetic tree based on nucleotide

sequences of 16s rRNA Gene of the same microorganisms.

2000 Mathematics Subject Classification.Key words and phrases. phylogenetic tree, algebra of hypergraph, Neighbor Joining Algorithm, metabolic networks, citric-acidcycle, nucleotide sequence of 16s rRNA Gene

285


Some Applications of Determinant in Undergraduate

Statistics Courses

Munir Mahmood

Department of Mathematics & Natural Sciences Gulf University for

Science & Technology Hawally

32093 P.O. Box: 7207 Kuwait

Abstract

This paper explains some concepts of statistics and probability courses via the approach of determinant. It demonstratesthe concept of independence of Navidi (2008) along with its implication on the basic properties of probability. The definitionof conditional probability leads to Bayes’s rule and the determinant form of it yields that they are equivalent. Thepresentation of the proof via determinant approach is simple, interesting and it derives the strength from Venn diagramsof the relevant events.

An alternative formula of pairwise independence is presented when dealing with three events. This is different fromDevore (2004). Applications of determinant help provide a new approach to revisit the contingency tables. Finally, theconcept of correlation is explained by utilyzing the notion of determinant. Throughout the paper, examples are presentedto point out the usefulness of the various determinant formulas.

The aim of this paper is provide insights that determinants are extremely useful as they create pedagogical value to

one’s learning.


286


Implementation of New Algorithm for Steepest Descent

Method

Mustafa bin Mamat*, Aw Siew Yee**, Ismail bin Mohd***

*Department of Mathematics University of Malaysia

Terengganu Mengabang Telipot, 21030 K.Terengganu

[email protected]

**Department of Mathematics University of Malaysia


siewyee [email protected]

***Department of Mathematics University of Malaysia


[email protected]

Abstract

Exact line searches along each steepest descent direction converge very slowly. Barzilai and Borwein suggested two

stepsizes that ensures superlinear convergence and performs quite well. Barzilai-Borwein method is not monotone, thus it is

not easy to be generalized for general nonlinear functions. A new stepsize enables fast convergence and possesses monotone

property is proposed by Yuan. The new stepsize is modified to obtain modified new steepest descent method, which is for

convex quadratic problems only is proposed by Yuan. The new steepest descent method uses the new stepsize after every

m exact line search iterations. An algorithm for m=2 is proposed in this paper. We use quadratic functions to test the

performance of our algorithm.

2000 Mathematics Subject Classification.Key words and phrases.steepest descent, line search, unconstrained optimization, convergence, monotone

287


On Some Generalized Sequence Spaces Of Fuzzy

Numbers Defined By A Sequence Of Orlicz Functions

Mustafa Kayıkcı, Selma Altundag, Metin Basarır

Duzce MYO, Duzce Univ. 81010, Duzce,Turkey

[email protected]

Sakarya Univ. Department of Math. 54100 Sakarya Turkey

[email protected]

Sakarya Univ. Department of Math. 54100 Sakarya Turkey

[email protected]

Abstract

The purpose of the paper is to introduce the concepts of almost λ-statistical convergence and strongly almost λ-

convergence of sequences fuzzy numbers. We establish some connections between these concepts. It is also shown that if

a sequence of fuzzy numbers is strongly almost λ-convergent with respect to a sequence of Orlicz funtions then it is almost

λ-statistical convergent.

References[1] L. A. Zadeh, Fuzzy sets, Inform. Control, 8 (1965), 338-353.

[2] M. Matloka, Sequences of fuzzy numbers, BUSEFAL 28, (1986), 28-37.

[3] S. Aytar, S. Pehlivan, Statistically monotonic and statistically bounded sequences of fuzzy numbers, Inform. Sci., 176 (6) (2006),734-744.

[4] M. Basarır, M. Mursaleen, Some sequence spaces of fuzzy numbers generated by infinite matrices, J. Fuzzy Math., 11 (3) (2003),757-764.

[5] H. Fast, Sur la convergence statistique, Colloq. Math., 2 (1951), 241-244.

[6] B. C. Tripathy, Matrix transformations between some classes of sequences, J. Math. Anal. Appl., 206 (2) (1997), 448-450.

[7] J. Lindenstrauss, L. Tzafriri, On Orlicz sequence spaces, Isr. J. Math., 10 (1971), 379-390.

[8] S. D. Parashar, B. Choudhary, Sequence spaces defined by Orlicz functions, Indian J. Pure Appl. Math., 25 (4) (1994), 419-428.

[9] B.C. Tripathy, A. J. Dutta, On fuzzy real-valued double sequence space 2lpF , Math. Comput. Modelling, 46 (9-10) (2007), 1294-1299.

[10] P. Diamond, P. Kloeden, Metric spaces of fuzzy sets, Fuzzy Sets and Systems, 35 (2) (1990), 241-249.

[11] V. Lakshmikantham, R. N. Mohapatra, Theory of Fuzzy Diffeential Equations and Inclusions, Taylor and Francis, New York, 2003.

[12] J. Lindenstrauss, L. Tzafriri, On Orlicz sequence spaces, Isr. J. Math., 10 (1971), 379-390.

[13] L. Leindler, Uber de la Vale Pounsische Summierbarkeit allgemeiner Orthogonalreihen, Acta Math. Acad. Sci. Hung., 16 (1965),375-378.

[14] G. G. Lorentz, A contribution to the theory of divergent sequences, Acta Math., 80 (1948), 167-190.

2000 Mathematics Subject Classification.40A05,40D25Key words and phrases. Fuzzy numbers, Orlicz function, de la Vallee-Poussin means, statistical convergence.

288


Hybrid Broyden Method For Unconstrained

Optimization

Mustafa Mamat,*, Ismail Mohd,**, Leong Wah June***

*Department of Mathematics, Faculty of Science and Technology,

University Malaysia Terengganu, 21030 Kuala Terengganu, Terengganu, Malaysia.

[email protected]

**Department of Mathematics, Faculty of Science and Technology,

University Malaysia Terengganu, 21030 Kuala Terengganu, Terengganu, Malaysia.

[email protected]

***Department of Mathematics, Faculty of Science,

University Putra Malaysia, 43400 UPM, Serdang, Selangor, Malaysia.

[email protected]

Abstract

In this article we consider a hybrid search direction of Broyden method and steepest descent method. In particular, we

try to analyze the performance and discuss thoroughly on the convergence of this hybrid method. We also provide some

numerical results to show that the algorithm is comparable to the Broyden algorithm.

2000 Mathematics Subject Classification.Key words and phrases.Broyden method, superlinearly convergent, hybrid search direction, Hessian approximation.

289


Discretization Methods for Nonconvex Differential

Inclusions

Mustapha Yarou

[email protected]

Abstract

In the present paper we consider the Cauchy problem for first order differential inclusion of the form

x(t) ∈ F (x(t)) + f(t, x(t)), x(0) = x0 (1.1)

where F is a given set-valued map with nonconvex values and f is a Caratheodory function. The nonconvexity of the values

of F do not permit the use of classical technique to obtain the existence of solution to this problem. One way to overcome

this fact is to suppose F upper semicontinuous cyclically monotone, ie. the values of F are contained in the subdifferential

of a proper convex lower semicontinuous function. The first result is du to [4] when f ≡ 0 and [1] for the problem (1.1) in

the finite dimensional setting. An extension of this results is obtained by [21] under the assumption that F (x) is contained

in the subdifferential of a Clarke regular function. A different class of function has been used in [3] to solve the same

problem, namely the authors take F (x) in the proximal subdifferential of a locally Lipschitz uniformly regular function

and proved that any convex lower semicontinuous function is uniformly regular. The present paper is a continuation of the

above results. We prove that, for locally Lipschitz functions, the class of convex functions, the class of lower-C2 functions

and the class of uniformly regular functions are strictly contained within the class of regular functions and we present

existence results to problem (1.1) in in the finite and infinite dimensional setting with weaker and more natural conditions.

An application to a controlled nonlinear diffusion inclusion is given.

References[1] F. Ancona, G. Colombo, Existence of solutions for a class of nonconvex differential Inclusions, Rend. Sem. Mat. Univ. Padova, Vol.

83, (1990).

[2] H. Benabdellah, C. Castaing and A. Salvadori, Compactness and Discretization Methods for differential Inclusions and EvolutionProblems, Atti. Sem. Mat. Univ. Modena, XLV, 9-51, (1997).

[3] M. Bounkhel, Existence Results of Nonconvex Differential Inclusions, Portugaliae Mathematica, Vol. 59 (2002), No. 3, pp. 283-310.

[4] A. Bressan, A. Cellina, G. Colombo, Upper semicontinuous differential Inclusions without convexity, Proc. Amer. Math. Soc., 106,771-775, (1989).

[5] M. Yarou, Discretization Methods for Nonconvex Differential Inclusions, EJQTDE, n 12, 1-10, 2009.

2000 Mathematics Subject Classification: 34A60, 49J52.Key words and phrases. Clarke regularity, Caratheodory perturbation, subdifferential, multifunction.

290


On the non-commuting graph of the simple groups

N. Ahanjideh1, A. Iranmanesh2

1Department of Mathematics, Shahrekord University, Shahrekord, Iran

neda−[email protected]

2Department of Mathematics, Tarbiat Modares University


[email protected]

Abstract

Given an arbitrary non-abelian group G and arbitrary finite group H, denote by Γ(G) the non-commuting graph of

G and denote by GK(H) the prime graph of H. In 2006, A. Abdollahi, S. Akbari and H. R. Maimani put forward the

following conjecture [1]:

AAM’s Conjecture: If S is a non-abelian finite simple group and H is a group such that Γ(H) ∼= Γ(S), then H ∼= S.

Even thought this conjecture is known to hold for finite simple groups with disconnected prime graph [2, 3], it is still unknown

for simple groups with connected prime graph. In this paper, we show that if Γ(H) ∼= Γ(S), then GK(H) = GK(S).

References[1] A. Abdollahi, S. Akbari and H. R. Maimani, Non-commuting graph of a group, J. Algebra, 298 (2006) 468-492.

[2] M.R. Darafsheh, Groups with the same non-commuting graph, Discrete applied mathematics, 157 (2009) 833-837.

[3] A. Iranmanesh and A. Jafarzadeh, Characterization of finite groups by their commuting graph, Acta Mathematica Academiae

Paedagogicae Nyiregyhaziensis, 23 (2007) 7-13.

2000 Mathematics Subject Classification. 20D06, 20D20, 20E28Key words and phrases. Simple group of Lie type, non-commuting graph, maximal independent set.

291


Mixed Problems for systems of First Order PDE

N.A. Aliev1, O.H. Asadova2

1 Baku State University, 23, Z. Khalilov str., AZ1148, Baku, Azerbaijan

[email protected]

2 Baku State University, 23, Z. Khalilov str., AZ1148, Baku, Azerbaijan

[email protected]

Abstract

In this talk, we will study the following mixed problem.

A∂u(x, t)

∂t+ B

∂u(x, t)

∂x+ Cu(x, t) = f(x, t) x ∈ (0, 1), t > 0 (1)

αu(0, t) + βu(1, t) = 0 t ≥ 0 (2)

Au(x, 0) = Aϕ(x), x ∈ [0, 1] (3)

where A, B, C are real m×n matrices, f(x, t) is a m×k matrix whose entries are functions upon the variables x, t, ϕ(x)is a n× k matrix whose entries are functions upon the variable x and u(x, t) is a n× k matrix whose entries are unknownfunctions upon the variables x, t . Finally, α and β are n× k real matrices which satisfy the condition

rankB = rank(α, β) (4)

where (α, β) is the m× 2n real matrix which we obtain it by putting the matrix β next to the matrix α .

References[1] H. Begehr, Systems of First Order Partial Differential Equations, A Hypercomplex Approach, Partial Differential and Integral

Equations, Kluver Academic Publishers, 1999,155-175


292


Properties of γtr-vertex critical graphs

N. Jafari Rad

Department of Mathematics, Shahrood University of Technology

University Blvd., Shahrood, Iran

[email protected]

Abstract

A graph G with no isolated vertex is total restrained domination vertex critical if for any vertex v of G that is not

adjacent to a vertex of degree one, the total restrained domination number of G − v is less than the total restrained

domination number of G. In this talk, we study properties of γtr-critical graphs.

2000 Mathematics Subject Classification. 05c69Key words and phrases. Total restrained domination; Matching; Critical

293


Variational analysis of a frictionless contact problem for

viscoplastic materials with internal state variables

N. Lebri

Department of Mathematics, Faculty of Sciences

University of Farhat Abbas, Setif, 19000, Algeria

Abstract

The subject of this work is the study of a value problem describing the quasistatic evolution of semilinear retetype

viscoplastic models with internal state variables, and we suppose the problem of Tresca s Friction Law at the presence of

recal forces. The existence and uniqueness of the solution is proved using results of evolutionary variational inequalities

and a fixed point theorem..

2000 Mathematics Subject Classification. 74M15, 74S05, 65M60Key words and phrases. viscoplasticity, Trasca s law, variational inequality, fixed point.

294


Non-Uniqueness of Solution of Tticomis Problem for

Degenerating Multidimensional Mixed

Hyperbolic-Parabolic Equations

N. Orshubekov

Al-Farabi Kazakh National University, Department of Mechanics and

Mathematics, Almaty, Kazakhstan

[email protected]

Abstract

Let D- final area of Euclidean space Em+1 of the points (x1, ..., xm, t) , limited in half-space t > 0 by cones K0 : |x| =2

2+p t2+p2 , K1 : |x| = 1− 2

2+p t2+p2 , 0 ≤ t ≤ ( 2+p

4 )2

2+p and at t < 0 - cylindrical surface Γ = (x, t) : |x| = 1 and a plane

t = t0 < 0 , where |x| - vector-length and p = const > 0. Let’s designate through D+, D− the parts of domain D lying

respectively in half-paces t > 0 and t < 0. And parts of the cones K0, K1 limiting areas D+, well denote through S0 andS1, accordingly. Let Γ = (x, t) : t = 0, |x| = 1 . Consider following mixed modeling hyperbolic- parabolic equation inarea :

0 =

tp∆xu− utt +∑m

i=1 ai(x, t)uxi+ b(x, t)ut + c(x, t)u, t > 0,

∆xu− ut, t < 0(1)

where ∆x is the Laplace operator on variable x1, x2, ..., xm, m > qeq2. Following a technique from [1] as multidimen-sional analogue of a problem of Trikomi we will consider the following problem Problem T: To find a solution of equation(1) in the area Dε when t 6= 0 on the class C(D \ Γ0) ∩ C1(D) ∩ C2(D+ ∪D−) satisfying boundary conditions:

u|S0 = 0 , u|Γ = 0.

For smooth coefficients of the equation (1) examples are constructed, which show, that the problem T has innumerable

solutions.

References[1] A.M. Nahushev, The Problems with offset for the equations in partial derivatives., Moscow, Nauka. 2006-287.

2000 Mathematics Subject Classification. 35Q99Key words and phrases. degenerating hyperbolic-parabolic equation, the problem of Tricomi, non-uniqueness of solution.

295


Bayesian Methods For The Occurrence Of REM Among

Apnea Patients

N.Z., Mohd Saata1, K. Ibrahim2, A. A., Jemain3,S.H. AlMashoor4

1 Dept of Biomedical Science, Faculty of Allied Health Science,

Universiti Kebangsaan Malaysia, Kuala Lumpur, MALAYSIA

[email protected]

2 School of Mathematical Sciences, Faculty of Science and Technology,

Universiti Kebangsaan Malaysia, Bangi, Selangor, MALAYSIA

[email protected]

3 School of Mathematical Sciences, Faculty of Science and Technology,

Universiti Kebangsaan Malaysia, Bangi, Selangor, MALAYSIA

[email protected]

4 Faculty of Medicine, Universiti Teknologi MARA, Shah Alam, Selangor, MALAYSIA

shassan [email protected]

Abstract

Studies on apnea patients are often carried out based on data obtained from the sleep study. Sleep stages that occurred

during sleep is light sleep, deep sleep and Rapid Eye Movement (REM). The proportion of REM during sleep is difference

according to gender, age group and Body Mass Index(BMI). Most apnea events occurred during REM sleep stages. Data on

apnea subjects is quite scarce since high cost is required for conducting the study. Bayesian method is particularly suitable

for analyzing limited data as it allows for updating of information by combining the current information with the prior

belief. In this paper we demonstrate the use of Bayesian methods to rank the occurrence of REM for 22 apnea patients,

based on the posterior mean of the rate of occurrence of REM. From the comparison of results using three different prior

distributions for the underlying rate of occurrence of REM, that is improper, gamma and log-normal priors, the ranking of

patients in terms of severity of apnea are the same, regardless of the choice for the prior distributions, but the model fitting

is found to be slightly better when based on gamma prior. Based on the sample, it is found that the most frequent case of

REM experiences two episodes of REM for every two minutes.

References[1] T. Young , M. Palta , J. Dempsey , J. Skatrud , S. Weber ,S. Badr . The Occurrence of sleep disordered breathing among middle-aged

adults. N Engl J. Med. 328(1993) 1230-35.

[2] American Academy of Sleep Medicine. Sleep related breathing disorders in adults: recommendations for syndrome definition andmeasurement techniques in clinical research. Sleep 22 (1999) 667-89.

[3] S.F. Quan , B. V.Howard,C. Iber ,J.P. Kiley ,F.J. Nieto , G.T. O’Connor, D.M. Rapoport, S. Redline , J. Robbins , J.M. Samet ,P.W.Wahl PW. The Sleep Heart Health Study: design,rationale, and methods. Sleep 20 (1997) 1077- 85.

[4] D. Clayton , J. Kaldor . Empirical Bayes estimates of age standardized relative risks for use in disease mapping. Biometrics 43 (1987) 671-81.

[5] D.J. Spiegelhalter, N.G. Best , B.P. Carlin, A. Van der Linde . Bayesian measures of model complexity and fit. J.R.Soc .B 64 (2002583-640.

[6] L.J . Findley, S.C. Wilhoit, P.M .Suratt Apnea duration and hypoxemia during REM sleep in patients with obstructive sleep apnea.44 Chest (1985) 432-436

2000 Mathematics Subject Classification.Key words and phrases. apnea, REM, gamma prior, log-normal prior, improper prior.

296


Fully Spectral Methods for the Solution of High Order

Differential Equations

N. Vaissmoradi*, A. Malek**, S. H. Momeni-Masuleh***

*Department of Applied Mathematics, Tarbiat Modares University,

P.O. Box 14115-175, Tehran, Iran.

[email protected]


P.O. Box 14115-175, Tehran, Iran.

[email protected]

***Department of Mathematics, Shahed University, Tehran,

P. O. Box: 18151-159, Iran.

[email protected]

Abstract

In the recent years spectral methods are used for solving stiff and non-stiff partial differential equations and ordinary

differential equations. Various types of spectral methods for steady and unsteady problems are proposed to solve stiff and

non-stiff partial differential equations efficiently. In this article some schemes for solving stiff partial differential equations

are derived. There are twofold: first method is based on Chebyshev polynomials for solving high-order boundary value

problems. Second methods are based on Fourier-Galerkin and collocation spectral methods in space and Runge-Kutta,

exponential time differencing, Taylor expansion and contour integral in time for solving stiff PDEs. Numerical results show

the efficiency of proposed schemes.

2000 Mathematics Subject Classification. 65M70, 35Q53, 74H15, 65L10.Key words and phrases. Spectral methods, Exponential time differencing, KdV and KS equations.

297


Prime submodules of multiplication modules and

Cohen-Macaulay property

N. Zamani

Department of Mathematics, University of Mohaghegh Ardabili, Iran,

[email protected]

Abstract

Let R be a multiplication commutative ring with nonzero identity and M be a unitary multiplication R-module. A

characterization of certain prime submodules of M will be presented. Also we show that if R is Noetherian and M is finitely

generated, then M is Cohen-Macaulay R-module. As a consequence any multiplication Noetherian ring is Cohen-Macaulay.

2000 Mathematics Subject Classification. 13C14, 13E05Key words and phrases. Sprime submodule, multiplication rings and modules, Cohen-Macaulay rings and modules.

298


Decomposition of Additive Processes

Nadia-Mirela Stoian

Dept. of Mathematical Analysis and Probability, Transilvania University of Brasov

nadia [email protected]

Abstract

The main purpose of this paper is to prove that every additive process is the sum of three independent parts, i. e. the

deterministic part, the discontinuous part and the continuous part.

References[1] Bertoin J., Levy Processes, Cambridge Univ. Pres, Cambridge, 1996.

[2] Kiyosi I., Stochastic Processes, Denmark Univ. Aarhus, 2000.

[3] Kunita H., Stochastic Flows and Stochastic Differential Equations, Cambridge Univ. Press, Cambridge,1990.

[4] Orman V. G. Lectures on Stochastic Approximation Methods and Related Topics, Preprint, ”Gerhard Mercator” University, Duis-burg, Germany, 2001.

[5] Orman V. G. Handbook of Limit Theorems and Stochastic Approximation, ”Transilvania” University Press, Brasov, 2003.

2000 Mathematics Subject Classification. 62P10Key words and phrases. additive process, decomposition, stochastic continuity

299


Linear And Nonlinear Models Of Heredity For Blood

Groups And Rhesus Factor

Nasir Ganikhodjaev*, Jamal I. Daoud**, Makhsuma Usmanovaa***

*Faculty of Science,IIUM, 25200, Kuantan, Malaysia

[email protected]

**Faculty of Engineering ,IIUM , 50728, Kuala Lumpur, Malaysia

[email protected]

***Institute of Mathematics and Information Technology, 100125, Tashkent, Uzbekistan

[email protected]

Abstract

We consider linear and nonlinear stochastic models for transmission of blood types and Rhesus factor from parents

to their offspring and investigate long run behavior of these models. In this paper we will consider an application of the

theory of Markov chains and the theory of nonlinear transformations in medicine. It is well known that the gene which

determines blood group in humans has three different alleles, A, B, O and that there are four groups of blood ,A, B, AB,

and O. The aim is to investigate the transmission of blood groups from parents to their offspring. For simplicity, we will

consider only positive Rhesus factors, since the portion of the population with negative Rhesus is around 1%. It is well

known that the blood groups of parents do not determine unambiguously their offsprings blood group. To describe this

transmission, we have rather extensive statistics for blood groups of parents and their offspring. In connection with these

statistics, we construct the following two Markov chains. The first Markov chain describes the transmission from a father

to his sons; the second Markov chain describes the transmission from a mother to her daughters.

References[1] Bernstein S N (1924) Solution of a mathematical problem connected with the theory of heredity, Ann.Sci. de l’Ukraine,1:83- 114.

[2] Bird, G W G , Wingham J, Watkins W et al (1978) Inherited mosaicism within the ABO blood group system. J.Immunogenet.5:215-219.

[3] Ganikhodjaev N N (1999). An application of the theory of Gibbs distributions to Mathematical Genetics, Doklady Mathematics,61(3): 13-16.

[4] Hummel K, Badet J, Bauermeister W, et al (1977) Inheritance of cis-AB in three generations(family Lam.) Vox Sang.33:290-298.

[5] Jenks R D (1969) Quadratic Differential Systems for Interactive Population Models, J. Diff. Eqs. 5 : 497-514.

[6] Kesten H (1970) Quadratic transformations: a model for population growth .I, II, Adv. Appl. Prob., 2: 1-82, 179-228.

[7] Lyubich Yu I (1971). Basic concepts and theorems of the evolution genetics of free populations , Russian Math. Surveys, 26 (5):51-116.

[8] Reed M L (1997). Algebraic structure of genetic inheritance, Bulletin of AMS, 34(2): 107-130.

[9] Seyfried H , Walewska I, Werbinska B (1964) Unusual inheritance of ABO group in a family with weak B antigens. Vox Sang9:268-277.

[10] Yamaguchi H , Okubo Y, Hazama F (1965) An A2B3 phenotype blood showing atypical mode of inheritance. Proc. Jpn. Acad.41:316-320.

[11] Yamaguchi H , Okubo Y, Hazama F (1966) Another Japanese A2B3 blood-group family with propositus having O-group father.Proc. Jpn. Acad. 42:517-520.

[12] Yamaguchi H, Okubo Y, Tanaka M (1971) Cis AB bloods found in Japanese families. Jap. J Hum Genet 15: 198-215.

[13] Yoshida A , Yamaguchi H , Okubo Y (1980) Genetic mechanism of cis-AB inheritance. II. Cases associated with structural mutationof blood group glycosyltransferase. Am.J.Hum.Genet.32:645-650.

2000 Mathematics Subject Classification. 62P10Key words and phrases. Markov Chain; Quadratic Stochastic Operator; Blood type; Rhesus factor; Heredity.**This research was supported by Research Center IIUM

300


Equivalent of elliptic integrals

Necat Tasdelen

Fecriebcioglu Sokak No: 18/A 1-Levent, Istanbul, Turkey

[email protected]

Abstract

The finite elliptic similar integrals of second kind are well known as

L = a

∫ 1

0(1 + (

b

a)2(

kr

(1− kr))(2r−2)

r )12 dk.

Those integrals cannot be solvable by any classical method. In this paper, we prove that the above equation can be replacedby

L = a.(1 + (b

a)s)1s .

As known, on the positive Cartesian, all astroids are expressed by:

(x

a)r

+ (y

b)r

= 1,

where a, b, and r are any positive constant real numbers. Using this equivalency and when (r = 2) the perimeter of an

ellipse is estimated at full-range with a maximum error % = −0, 000002432. Full-range is (1 < ba < ∞).

2000 Mathematics Subject Classification. 14Q05,14Q99,44A45Key words and phrases. integrals-equivalent-arc length

301


Numerical Solutions Of Hyperbolic Equations With

The Nonlocal Integral Condition

Necmettin Aggez

Department of Mathematics, Fatih University, 34500 Istanbul, Turkey.

[email protected]

Abstract

In present paper joint with Prof. Dr. A. Ashyralyev, the mixed boundary value problem for the multi-dimensionalhyperbolic equation

∂2u(t,x)∂t2

−m∑

r=1(ar(x)uxr )xr = f(t, x),

x = (x1, . . . , xm) ∈ Ω, 0 < t < 1,

u(0, x) =1∫0α (ρ) u(ρ, x)dρ + ϕ(x), x ∈ Ω,

ut(0, x) = ψ(x), x ∈ Ω,

u(t, x) = 0, x ∈ S, 0 ≤ r ≤ m

(0.1)

is considered. Here Ω is the unit open cube in the m-dimensional Euclidean space Rm x = (x1, · · ·, xm) : 0 < xj < 1, 1 ≤ j ≤ mwith boundary S, Ω = Ω∪ S, ar(x) (x ∈ Ω), ϕ(x), ψ(x) (x ∈ Ω) and f(t, x) (t ∈ (0, 1), x ∈ Ω) are given smooth functionsand ar(x) ≥ a > 0 .

A numerical method is proposed for solving multidimentional hyperbolic partial differential equations with nonlocal

integral condition. The first and second orders of occuracy stable difference schemes are presented. The stability of these

difference schemes are established. The method is illustrated by numerical examples.

References[1] A. Ashyralyev, and N. Aggez, A Note on the Difference Schemes of the Nonlocal Boundary Value Problems for Hyperbolic Equations,

Numer. Funct. Anal. Optimization, 25 (2004) 1-24.

[2] A. Ashyralyev, O. Yildirim,On Multipoint Nonlocal Boundary Value Problems for Hyperbolic Differential and Difference Equations,

Taiwanese Journal of Mathematics, 13 (2009) 365-369.

2000 Mathematics Subject Classification. 65J10, 65N12Key words and phrases.Hyperbolic equation, Nonlocal integral condition, Difference scheme, Stability.

302


Hilbert transforms and related topics associated with

the Dunkl-Hermite functions

Nejib Ben Salem, Taha Samaali

Nejib Ben Salem, University Tunis El Manar

Faculty of Sciences of Tunis

Department of Mathematics,2092 Tunis, Tunisia

[email protected]

Abstract

We consider expansions of functions in Lp(R, |x|2kdx), 1 ≤ p < +∞ with respect to Dunkl-Hermite functions in the

rank-one setting. We actually define the heat-diffusion and Poisson integrals in the one-dimensional Dunkl setting and study

their properties. Next, we define and deal with Hilbert transforms and conjugate Poisson integrals in the same setting. The

formers occur to be Calderon-Zygmund operators and hence their mapping properties follow from general results.

References[1] De Jeu M. F. E., The Dunkl transform. Invent. Math. 113, no. 1. (1993), 147-162.

[2] Dunkl C. F., Hankel transforms associated to finite reflections groups. Hypergeometric functions on domains of positivity, Jackpolynomials and applications (Tampa, FL, 1991). Contemp. Math. Amer. Math. Soc. Providence, R. I. 138, (1992), 123-138.

[3] El Garna A., The left-definite spectral theory for the Dunkl-Hermite differential-difference equation. J. Math. Anal. Appl. 298, no.2. (2004), 463-486.

[4] Gosselin J., Stempak K., Conjugate expansions for Hermite functions, Illinois J. Math. 38, no. 2. (1994), no. 2, 177-197.

[5] Journe J. L., Calderon-Zygmund operators, pseudo-differential operators and the Cauchy integral of Calderon. Lecture Notes inMathematics. Springer-Verlag, Berlin. (1983).

[6] Nowak A., Stempak K., Riesz transforms for the Dunkl harmonic oscillator. To appear in Math. Zeit.

[7] Rosenblum M., Generalized Hermite polynomials and the Bose-like oscillator calculus. Oper. Theory Adv. Appl. 73. Birkhauser,Basel, (1994), 369-396.

[8] Rosler M., Generalized Hermite polynomials and the heat equation for Dunkl operators. Comm. Math. Phys. 192, no. 3. (1998),519-542.

[9] Rosler M., Positivity of Dunkl’s intertwining operator. Duke Math. J. 98, no. 3. (1999), 445-463.

[10] Stein E. M., Topics in Harmonic Analysis Related to the Littlewood-Paley Theory. Annals of Mathematics Studies, PrincetonUniversity Press, (1970).

[11] Stempak K. , Torrea J. L., Poisson integrals and Riesz transforms for Hermite function expansions with weights. J. Funct. Anal.202, no. 2. (2003), 443-472.

[12] Thangavelu S., Lectures on Hermite and Laguerre Expansions. Mathematical Notes. Princeton University Press, (1993).

2000 Mathematics Subject Classification. 33C52, 43A32, 33C80, 22E30Key words and phrases. Dunkl operator, Paley–Wiener theorem, generalized translations

303


Effect of a Deformable Free Surface on the Marangoni

Convection in a Horizontal Porous Layer Permeated by

a Fluid Layer in the Presence of Internal Heat

Generation

Nor Fadzillah Mohd Mokhtar1, Norihan Md Arifin1,

Roslinda Nazar2, Fudziah Ismail1, Ioan Pop3

1Department of Mathematics, Faculty of Science,

Universiti Putra Malaysia, 43400 UPM, Serdang, Selangor


2School of Mathematical Sciences, Faculty of Science and Technology,

National University of Malaysia, 43600 UKM

[email protected]

3Faculty of Mathematics, University of Cluj, R-3400 Cluj, CP 253, Romania

[email protected]

Abstract

The onset of Marangoni convection in a two-layer system comprising an incompressible fluid-saturated porous layer

over which lies a layer of the same fluid in the presence of internal heat generation is investigated theoretically. The

upper free surface is assumed to be deformable and the lower boundary is conducting to temperature perturbation. The

Beavers-Joseph condition is employed at the interface and the Forchheimer-extended-Darcy equation is used to describe the

flow regime in the porous medium. The linear stability theory and the normal mode analysis are applied and the resulting

eigenvalue problems are solved exactly. We found that an increase of the surface deflection effect that is Crispation number,

Cr; destabilize the system. However an increase of the Bond number and the decrease of the Darcy number will help to

slow the process of destabilizing.

References[1] Nield, D.A. and Bejan, A.,Convection in Porous Media (3rd edition), Springer, New York, 2006.

[2] K.Vafai (Ed.), Handbook of Porous Media, second ed., Taylor & Francis, Boca Rotan, FL, 2005.

[3] I. Pop and D.B Ingham, Convective Heat Transfer:Mathematical and Computational Modelling of Viscous Fluids and Porous MediaPergamon Press. Oxford, 2001.

[4] Gasser, R. D. and Kazimi, M. S. Onset of Convection in a Porous Medium with Internal Heat Generation. Fast Reactor SafetyDivision, Department of Applied Science, Brookhaven National Laboratory, Upto, New York. Journal of Heat Transfer ; 1976; 76:49, 54.

[5] Ming-I Char and Ko-Ta Chiang. Stability Analysis of Benar-Marangoni Convection in Fluids with Internal Heat Generation., J.Phys. D: Appl. Phys., 1994; 27:748 , 755.

[6] Wilson.S.K. The Effect of Uniform Internal Heat Generation on the Onset of Steady Marangoni Convection in a Horizontal LayerFluid, Acta Mechanica., 1997; 124:63 ,78.

[7] Nield.D.A, Onset of Convection in a Fluid Layer overlying a layer of Porous medium. J. Fluid Mech., 1977; 81:513 , 522.

[8] Straughn.B., Surface-Tension-Driven convection in a fuid overlying a porous layer. Computational Physics., 2001; 170:320 ,337.

[9] Shivakumara I. S., Suma S.P and Chavaraddi K.B., Onset of surface-tension-driven convection in Superposed Layers of Fluid and

Saturated Porous Medium, Arch.Mech., 2006;55:327 ,348.

2000 Mathematics Subject Classification.primary:76S05 secondaries:26C10Key words and phrases.Marangoni Convection, Heat Generation, Porous Medium**This research was supported by Ministry of Higher Education Malaysia in the form of scholarship (SLAI)

304


Generalized Flat Eeg with Depth Orientation and

Regression

Noraini Ismail1, Tahir Ahmad2, Arminora Idris3, Siti Rahmah Awang4

Fuzzy Modeling Group (FMG), Department of Mathematics, Faculty Of Science,

University Teknologi Malaysia 81310 Skudai, Johor, Malaysia

Pediatrics Unit, Hospital Besar Kuala Lumpur,

1 [email protected], 2 tahir [email protected],

3 [email protected], 4 [email protected]

Abstract

A study is carried out to model tracks followed by clusters of electrons during the sporadic burst of the brainstorm

epilepsy The challenges faced were to choose the right model for the event as well as to maximize the accuracy of the real

time data taken. The growth of cosmic structure, including a detailed formation of galaxies with super massive black holes

in their centers provides a great model for this brainstorm epileptic event. General relativity explains that the fundamental

force of gravitation can be described as a curved spacetime caused by the presence of matter and energy. Excellent data

from Generalized EEG signals, with six flat cubic surfaces represent mass and energies of clusters of electrons from an

epileptic patient were converted into clusters of three dimensional space and time. When fed into Einstein Field Equation,

these masses and energies curved the spacetime which represents the movements or tracks of these electrons in a given time.

The domains of these tracks were the first to be identified. Strength of each EEG signals as well as the locations of each

domain relative to each other were weighted and later were regressed to estimate the best location that represents point

of embarkation of these electrons for each second during an epilepsy attack. Correlation analysis identified outliers which

might come from other epileptic foci burst. These represent much smaller bursts of electrons that occur simultaneously.

Illustrations for these tracks are plotted in three dimensional spaces as time progresses.

2000 Mathematics Subject Classification. 93A30, 83C05, 92C55Key words and phrases. Tracks, electrons clusters, generalized EEG, curved spacetime, domains.

305


Generalized characteristic polynomials of a square

matrix

Nosratollah Shajareh-Poursalavati

Department of Mathematics and Mahani Mathematical Research Center,

Shahid Bahonar University of Kerman, Kerman, I.R.Iran

[email protected]

Abstract

Let n be a positive integer number and G be a subgroup of the full symmetric group on n letters. Assume that F

be a favorite field and c be a function from G to F . We refer the generalized matrix function afforded by G and c, dGc ,

which is a generalization of the concept of ordinary determinant of n by n matrices. By using dGc , we refer and determine

the generalized characteristic polynomials of n by n matrices over a favorite filed F afforded by some permutation groups,

which is a generalization of the concept of ordinary characteristic polynomial.

References[1] M.R. Darafsheh, K. Mallahi, M.R. Pournaki, A Note on Cayley-Hamilton Theorem for Generalized Matrix Function, Pure Math.

Appl. 11 (2000) 553-557.

[2] R. Grone, R. Merris, W. Watkins, Cones in the group algebra related to Schur’s determinantal inequality, Rockey Mtn. J. Math. 18(1988) 137-146.

[3] G. James, A. Kerber, The Representation Theory of the Symmetric Group, Addision-Wesley, Reading, MA., 1981.

[4] R. Merris, Multilinear Algebra, Gordon and Breach Science Publishers, 1997.

[5] N. Shajareh-Poursalavati, Some properties of the generalized matrix functions, Rev. Bull. Cal. Math. Soc. 14, (2006), 3540.

[6] J. Turner,, Generalized Matrix Functions and the Graph Isomorphism Problem, SIAM J. Appl. Math. 16, 520-526.

2000 Mathematics Subject Classification. 15A69Key words and phrases. Generalized matrix function, Generalized characteristic polynomial.

306


A Quasistatic contact problem with slip dependent

friction for linear elastic materials

Nouiri Brahim, Benabderrahmane Benyattou


University of Batna, Algeria

[email protected],


University of Laghouat, Algeria

[email protected]

Abstract

We consider a mathematical model describing the contact with friction between a deformable body and a foundation.

We use a linear elastic constitutive law. The contact takes into account the effects of friction, which are modelled with

the slip dependent friction law. We derive a variational formulation of the problem and establish the existence of a weak

solution under a smallness assumption of the friction coefficient. The proof is based on arguments of compactness, lower

semicontinuity and time discretization

2000 Mathematics Subject Classification. 35J85, 49J40, 47J20, 58E35Key words and phrases. linear elasticity; slip dependent friction; variational inequality; weak solution; time discretization method.

307


New method for constructing exact solutions to

nonlinear PDEs

Nouredine Benhamidouche1, Arioua Yacine2

1 Laboratory for Pure and Applied Mathematics, University of M’sila.

[email protected]

2 Laboratory for Pure and Applied Mathematics, University of M’sila.

[email protected]

Abstract

We propose in this paper a new approach to construct exact solutions of nonlinear PDEs. The method used is called

”the travelling profiles method”. The travelling profiles method enables us to obtain many exact solutions to large classes

of nonlinear PDEs.

References[1] F.Cariello, M.Tabor, Physica D,53 (1991), 59.

[2] Ibragimov, N. H.(Editor), CRC Handbook of Lie group Analysis of Diferential Equations, Vol 1 Symmetries, Exact solutions andConservation Laws, CRS Press , Boca Raton, 1994.

[3] L.Huibin, W.Kelin, J. Phys. Math. Gen, 23, 3923, 1990.

[4] R.Hirota, J.Math.Phys, 14, 810, 1973.

[5] V.A. Galaktionov, Posashkov, New exact solutions of parabolic equation with quadratic non-linearities, USSR. Compt. Math. Match.Phys, Vol 29, N 2 pp112-119, 1989.

[6] V.A. Galaktionov, V. A. Posashkov, S. A. Svirshchevskii, S. R., Generalized separation of variables for diferential equations withpolynomial right-hand sides, Dif. Uravneniya, 31(2), 253, 1995.

[7] M.Otwinowski, al, Phys.Lett.A, 128 (1988), 483.

[8] Polyanin. A.D, Zaitsev. V. F, Handbook of Nonlinear Partial Equation, Chapman&Hall/CRC, Boca Raton, 2004.

2000 Mathematics Subject Classification. 35K55, 35B35, 35K65.Key words and phrases. Nonlinear PDE - exact solutions - travelling profiles method.

308


A Tabu Search Algorithm to Find the Pareto Solutions

of Dual Response Systems in Quality Engineering

O. Koksoy1, C. H. Aladag2

1 Department of Mathematical Sciences, The State University of New York,

Binghamton, New York 13902-6000, U.S.A.,

[email protected]

2 Department of Statistics, Hacettepe University, Beytepe, Ankara, Turkey

[email protected]

Abstract

This paper presents a tabu search metaheuristic algorithm for finding the Pareto optimal solutions of the dual response

system problems in industrial applications. First we convert the problem into a scalar one by using a weighted linear sum

of objectives and then optimize the combined objective function of the mean and the standard deviation of a given quality

characteristic. The proposed formulation does not require any constraints on the secondary response (i.e., the process

standard deviation). Unlike the other multi-objective alternatives, tabu approach does not set any specific assumptions on

the behavior or the preference structure of the decision maker. A further advantage of tabu search is its simplicity and

we show that the entire process only occupies a few lines of codes and generates string of solutions in speedy manner.

This makes the search simpler and also computationally attractive than the other heuristic algorithms. The procedure is

illustrated with an example.

References[1] Box, G.E.P., Draper, N.R. (1987). Empirical Model Building and Response Surfaces, John Wiley & Sons, New York.

[2] Caserta, M., Uribe, A.M. (2009). ”Tabu Search-Based Metaheuristic Algorithm for Software System Reliability Problem”, Computers& Operations Research, 36, 811-822.

[3] Chao, I-M. (2002). ”A Tabu Search Method for the Truck and Trailer Routing Problem”, Computers & Operations Research, 29,33-51.

[4] Copeland, K.A.F., Nelson, P.R. (1996). ”Dual Response Optimization via Direct Function Minimization”, Journal of Quality Tech-nology, 28, 331-336.

[5] Del Castillo, E., Montgomery, D.C. (1993). ”A Non-Linear Programming Solution to the Dual Response Problem”, Journal of QualityTechnology, 25, 199-204.

[6] Glover, F. (1986). ”Future paths for Integer Programming and Links to Artificial Intelligence”, Computers and Operations Research,13, 533-549.

[7] Gungor, Z., Unler, A. (2008), ”K-Harmonic Means Data Clustering with Tabu-Search Method”, Applied Mathematical Modelling,32, 1115-1125.

[8] Hansen, P. (1986). ”The Steepest Ascent Mildest Descent Heuristic for Combinatorial Programming”, Paper Presented at Congresson Numerical Methods in Combinatorial Optimization, Capri, Italy.

[9] Khuri, A.I. (1996). ”Multiresponse surface methodology”, Handbook of Statistics, Vol. 13, S. Ghosh and C.R. Rao eds., ElsevierScience, 377-406.

[10] Kim, K., Lin, D.K. (1998). ”Dual Response Surface Optimization: A Fuzzy Modeling Approach”, Journal of Quality Technology,30, 1-10.

[11] Koksoy, O., Doganaksoy, N. (2003). ”Joint Optimization of Mean and Standard Deviation in Response Surface Experimentation”,Journal of Quality Technology, 35, 239-252.

[12] Taguchi, G. (1986). Introduction to Quality Engineering: Designing Quality into Products and Processes, Kraus InternationalPublications, White Plains, NY.

[13] Taguchi, G., Wu, Y. (1985). ”Introduction to Off-Line Quality Control”, Central Japan Quality Control Association, Nagaya, Japan.

[14] Vilcot, G., Billaut, J-C. (2008). ”A Tabu Search and A Genetic Algorithm for Solving a Bicriteria General Job Shop SchedulingProblem, European Journal of Operational Research, 190, 398-411.

[15] Vining, G.G., Myers, R.H. (1990), Combining Taguchi and Response Surface Philosophies: A Dual Response Approach, Journal ofQuality Technology, 22, 38-45.

2000 Mathematics Subject Classification. 62P30, 62K25, 62K20, 65K10Key words and phrases. Robust Design, Quality Engineering, Response Surface Methodology

309


Numerical Approximation of Dirichlet Problem in

Bounded Domains and Applications

Oana Rachieru

Transilvania University of Brasov, Department of Mathematical Analysis and

Probability, Brasov, Romania

[email protected]

Abstract

We consider numerical approximation of Dirichlet problem for the Laplace equation in a domain D ∈ Rd, that is wewill consider the problem of finding a C2 function

u = u(z) ∈ C2(D) ∩ C

0(D) such that

∆u = 0 , in D

u = 0 , on ∂D

Using probabilistic methods we can give explicit reprezentation of solution of Dirichlet problem u(z) = Ezf(BτD) , where

Bt is a Brownian motion starting at B0 = z, Ez denotes the expectation of function in BτD, and τD = inft ≥ 0, Bt /∈ D

is the exit time of Brownian motion from D. We give a Mathematical implementation of function u(z) for different choicesof f and domain D (half-plane, unit disc, rectangle, triangle) and we apply it to obtain some numerical results.

References[1] R.F. Bass, Probabilistic Techniques in Analysis, Speringer, New York (1995).

[2] R. Durrett, Brownian motion and Martingales in Analysis, Wadsworth, Belmont, CA (1984).

[3] R. J. Elliott, Stochastic Calculus and Applications, Los Angeles, CA (1982).

[4] I.Karatzs, S.E. Shreve, Brownian Motion and Stochastic Calculus, Second Edition, Springer-Verlag, New York (1991).

[5] L.B. Korolov, Y.G. Sinai, Theory of Probability and Random Processes, Springer, (2007)

[6] B. Oksendal, Stochastic differential equations: An introduction with applications, sixth edition, Springer (2003).

[7] M. N. PASCU, Brownian Motion and Applications, Brasov, Transilvania University of Brasov Printing House, (2006).

2000 Mathematics Subject Classification.Key words and phrases. Brownian motions, Laplace equation, Dirichlet problem, stochastic approximation

310


A note on the multipoint nonlocal boundary value

problems for elliptic-parabolic equations

Okan Gercek

Vocational School, Fatih University


[email protected]

Abstract

In present paper joint with Prof. A. Ashyralyev, we are interested in studying the stable difference schemes for thenumerical solution of the multipoint nonlocal boundary value problem

−utt −n∑

r=1(ar(x)uxr )xr = g(t, x), 0 < t < 1, x ∈ Ω,

ut +n∑

r=1(ar(x)uxr )xr = f(t, x),−1 < t < 0, x ∈ Ω,

u(t, x) = 0, x ∈ S, −1 ≤ t ≤ 1; u(−1, x) =n∑

r=1αru(µr, x) + ϕ(x),

n∑r=1

|αr| ≤ 1, 0 ≤ µ1 < µ2 < ... < µn ≤ 1,

u(0+, x) = u(0−, x), ut(0+, x) = ut(0−, x), x ∈ Ω

(0.1)

for multidimensional elliptic-parabolic equations. Here Ω be the unit open cube in the n-dimensional Euclidean space Rn

(0 < xk < 1, 1 ≤ k ≤ n) with boundary S, Ω = Ω ∪ S. The first and second orders of accuracy difference schemes are

presented. The coercive stability and almost coercive stability of these difference schemes are obtained. The method is

illustrated by numerical examples.

References[1] P.E. Sobolevskii, On difference methods for the approximate solution of differential equations, Izhat. Voronezh. Gosud. Univ. Press

(1975).(Russian)

[2] A. Ashyralyev, H. Soltanov, On elliptic-parabolic equations in a Hilbert space, Proceeding of the IMM and CS of Turkmenistan 4(1995) 101-104.(Russian)

[3] A. Ashyralyev, O. Gercek, Nonlocal boundary value problems for elliptic-parabolic differential and difference equations, DiscreteDynamics in Nature and Society 2008 (2008) 1-16.

2000 Mathematics Subject Classification. 65N: 65M: 65J: 35M: 49K:Key words and phrases. nonlocal boundary value problems; difference schemes; elliptic-parabolic equation; coercive stability

311


Spectral properties of one class of sign-symmetric

matrices

Olga Y. Kushel

Department of mechanics and mathematics

Belorussian State University, Nezavisimosti sq.

4, 220050, Minsk, Belarus

[email protected]

Abstract

A matrix A of a linear operator A : Rn → Rn is called J –sign-symmetric, if there exists such a subset J ⊆ 1, . . . , n,that the inequality aij ≤ 0 follows from the inclusions i ∈ J , j ∈ J c and j ∈ J , i ∈ J c for any two numbers i, j, and oneof the inclusions i ∈ J , j ∈ J c or j ∈ J , i ∈ J c follows from the strict inequality aij < 0 (here J c = 1, . . . , n \ J ).This definition is a generalization of the well-known definition of positive matrices, which are widely used in economics,mechanics, biology and other branches of science.

Let A be a J –sign-symmetric matrix, and let J be a subset of 1, . . . , n in the definition of J –sign-symmetricity.

Let its second compound matrix A(2) also be a J –sign-symmetric matrix. Let J be a subset of 1, . . . , C2n in the

definition of J –sign-symmetricity for the matrix A(2). Let us construct the set W (J , J ) ⊆ (1, . . . , n × 1, . . . , n)by the following way: (i, j) ∈ W (J , J ) if and only if one of the following two cases takes place:

(a) both the numbers i, j belong either to the set J , or to the set J c, besides, if i < j, then the number of the pair

(i, j) in the lexicographic numeration belongs to the set J , and if i > j, then the number of the pair (j, i) belongs to the

set J c = 1, . . . , C2n \ J ;

(b) one of the numbers i, j belongs to the set J , the other belongs to the set J c, besides, if i < j, then the number of

the pair (i, j) belongs to the set J c, and if i > j, then the number of the pair (j, i) belongs to the set J .

Such a set is not uniquely defined, but there is a finite number of different ways of its constructing. The set W (J , J )

is called transitive if the inclusion (i, k) ∈ W (J , J ) follows from the inclusions (i, j) ∈ W (J , J ) and (j, k) ∈ W (J , J ) forany indices i, j, k ∈ 1, . . . , n.Theorem 0.1 Let the matrix A of a non-zero linear operator A be J –sign-symmetric together with its second compound

matrix A(2). Then the operator A has a positive eigenvalue λ1 = ρ(A). More than that, if λ1 is a simple eigenvalue,then one of the following two cases takes place:

(1) If at least one of the possible sets W (J , J ) is transitive, then the second in modulus eigenvalue λ2 of the operatorA is nonnegative and different in modulus from the first eigenvalue λ1.

(2) If all the possible sets W (J , J ) are not transitive, there there is an odd number k of eigenvalues on the spectral

circle |λ| = ρ(A). All of them are simple and coincide with kth roots of (ρ(A))k.

2000 Mathematics Subject Classification. primary 15A48, secondaries 15A18, 15A75Key words and phrases. Totally positive matrices, Sign-symmetric matrices, Eigenvalues, Gantmacher–Krein theorem

312


The Development of Mathematics Problem Solving

Attitude Scale (MPSAS)

Orhan Canakcı, Ahmet Sukru Ozdemir

Marmara University, Deparment of Primary Mathematics Education

[email protected]

Marmara University, Deparment of Primary Mathematics Education

[email protected]

Abstract

Lack of scale measuring students’ attitudes of mathematics problem solving (at grades 6, 7 and 8) has been observed in

the relevant literature. The present research, which was motivated to remedy such deficiency, aims to develop a likert-type

attitude scale (Mathematics Problem Solving Attitude Scale-MPSAS). A draft of the scale which contained 77 items was

composed based on both review of the extant literature and the opinions of experts on this area of research. The draft scale

was tested on a group of 638 students at 6th, 7th and 8th grades. As a result of factor analysis, 58 items were omitted,

and the remaining 19 items have been divided into two dimensions called ”Enjoyment” and ”Teaching”. Two dimensions

accounted for 43Various techniques were used to ensure the content and construct validity of the scale. Test-retest and split-

half test techniques were used to test the reliability. The Pearson correlation coefficient revealed by test-retest technique

was 0.89. Cronbach alpha coefficient calculated to ensure the internal consistency was 0,848 for MPSAS, 0,869 and 0,777

for the sub scales MPSAS-E (Enjoyment) and MPSAS-T (Teaching) respectively. The research has produced a valid and

reliable likert-type attitude scale as a research instrument.

2000 Mathematics Subject Classification. 97C40Key words and phrases. Mathematics Education, Mathematics Problem Solving, Problem Solving Attitude, Attitude Scale, ScaleDevelopment

313


Global geometries in space kinematics

Osman Gursoy, Muhsin Incesu

Maltepe University, Department of Mathematics

Faculty of Science and Letters, Istanbul, Turkey

[email protected]

Abstract

The geometry of path trajectory ruled surfaces generated by the oriented lines fixed in a moving rigid body is important

in the study of rational design problem of spatial mechanism. An x-closed trajectory ruled surface (x-c.t.s.) is characterized

by two real integral invariants, the pitch and the angle of pitch . Using the integral invariants, the closed trajectory surfaces

have been studied in many papers [1],[2]. In this study, based on [3] introducing a relationship between the dual integral

invariant, and the dual area vector, Vx, of the spherical image of an x-c.t.s., new results on the feature of the trajectory

surfaces are investigated. And also, since the dual angle of pitch, defined in [4], of an x-c.t.s. is a useful apparate in the

study of line geometry, we use the dual representations of the trajectory surfaces with their dual angle of pitches.

Therefore, besides the results on the real angle of pitches, that some of them given [3] many other results on the pitches

of closed trajectory ruled surfaces are obtained. And some relationships between the other invariants are given. Also, using

the some method, the area of projections of spherical closed images of the trajectory surfaces are studied.

It is hoped that the findings will contribute to the geometry of trajectory surfaces, so the rational design of spatial

mechanisms.

References[1] A. Yang, Y. Kirson and B. Roth, On a Kinematics Theory For Ruled Sur- face, Proceedings of Fourth World Congress on the Theory

of Machines and Mechanisms, Newcastle Upon Tyne, 1975 pp. 737-742.

[2] H. H. Hacısalihoglu, On the Pitch of a Closed Ruled Surface, Mech. Mach. Theory (1972) 7 291-305 .

[3] O. Gursoy and A. Kuc.uk, On the Invariants of Trajectory Surfaces, Mech- anisms and Machine Theory (Submitted), 1996.

[4] O. Gursoy, The Dual Angle of Pitch of a Closed Ruled Surface, Mech.Mach. Theory (1990) 25 131-140.

2000 Mathematics Subject Classification. 53C99Key words and phrases. Global invariants, Line surfaces.

314


Local Group-Groupoids

Osman Mucuk, H.Yesim Ay, Berrin Bagrıyanık

Department of Mathematics, Erciyes University, Kayseri 38039 Turkey

[email protected]

Abstract

The theory of covering groupoids plays an important role in the applications of groupoids (cf. [1], [5]).There are two important results about group-groupoids given in [2].One is that if X is a topological group whose underlying space has a universal cover, then the category TGCov/X of

topological group covers of X is equivalent to the category GpGpdCov/π1X of group-groupoid covers of π1X.The other is that if G is a group-groupoid, then the category the category GpGdCov/G of covering morphisms over G

is equivalent to the category GpGdAct(G) of group-groupoid actions of G on groups is equivalent to equivalent.In this paper we introduce the notion of a local group-groupoid as a local group object in the category of gorupoids

and prove local group-groupoid version of these results.For the first result we prove that if L is a local topological group, whose underlying topology has a universal cover,

then the category LTGCov/L of local topological covers of L and the category LGGdCov/π1(L) of local group-groupoidcovers of π1(L) are equivalent.

For the second result we prove that if G is a local group-groupoid, then the category LGpGdCov/G of local group-groupoid covers is equivalent to the category LGpGdAct(G) of local group-groupoid actions of G on local groups.

References[1] Brown, R., Topology and groupoids, BookSurge LLC, U.K 2006.

[2] Brown, R. and Mucuk, O., Covering groups of non-connected topological groups revisited, Math. Proc. Camb. Phill. Soc. 115 (1994)97-110.

[3] Chevalley, C., Theory of Lie groups, Princeton University Press, 1946.

[4] Douady L. and Lazard, M., Espaces fibres en algebres de Lie et en groupes, Invent. Math. 1 (1966) 133-151.

[5] Higgins, P.J., Groups with multiple operators, Proc. London Math. Soc. (3) 6 (1956) 366-416.

[6] Mucuk, O., Covering groups of non-connected topological groups and the monodromy groupoid of a topological groupoid, PhDThesis, University of Wales, 1993.

[7] Taylor, R.L., Covering groups of non-connected topological groups, Proc. Amer. Math. Soc., 5 (1954) 753-768.

2000 Mathematics Subject Classification. 20L05, 57M10, 22AXX, 22A22Key words and phrases. Fundamental groupoid, local topological group, local group-groupoid

315


Quasilinearity of the classical sets of sequences of fuzzy

numbers and some related results

Ozer Talo, Feyzi Basar

Anatolian High School, Sehirgosteren, 44170-Malatya, Turkiye

[email protected]

Fatih Universitesi, Fen-Edebiyat Fakultesi, Matematik Bolumu,

Buyukcekmece Kampusu 34500-Istanbul, Turkiye

[email protected]

Abstract

In the present study, we prove that the classical sets `∞(F ), c(F ), c0(F ) and `p(F ) of sequences of fuzzy numbers are

normed quasilinear spaces and the β−, α−duals of the set `1(F ) is the set `∞(F ). Besides this, we show that `∞(F ) and

c(F ) are normed quasialgebras and an operator defined by an infinite matrix belonging to the class (`∞(F ) : `∞(F )) is

bounded and quasilinear. Finally, as an application, we characterize the class (`1(F ) : `p(F )) of infinite matrices of fuzzy

numbers and establish the perfectness of the spaces `∞(F ) and `1(F ).

2000 Mathematics Subject Classification. 46S40, 03E72, 46A45, 40A05Key words and phrases. Classical sets of sequences of fuzzy numbers, quasilinear space, β−dual, α−dual, matrix transformations.

316


A note on hyperbolic equations with nonlocal boundary

and Dirichlet-Neumann conditions

Ozgur Yıldırım

Department of Mathematics, Uludag University

16500 Gorukle, Bursa, Turkey

[email protected]

Abstract

In present paper joint with Prof. Allaberen Ashyralyev, the nonlocal boundary value problem

∂2u(t,x)∂t2

−m∑

r=1(ar(x)uxr )xr + σu = f(t, x),

x = (x1, . . . , xm) ∈ Ω, 0 < t < 1,

u(0, x) =n∑

j=1αju(λj , x) + ϕ(x),

ut(0, x) =n∑

k=1βkut(λk, x) + ψ(x), x ∈ Ω,

x ∈ Ω; u(t, x) = 0, x ∈ S1,∂u(t,x)

∂n = 0, 0 ≤ t ≤ 1, x ∈ S2,

(0.1)

for the multidimensional hyperbolic equation is considered.Here Ω be the unit open cube in the m-dimensional Euclideanspace Rm x = (x1, · · ·, xm) :

0 < xj < 1, 1 ≤ j ≤ m with boundary S = S1⋃

S2, Ω = Ω ∪ S.

The first and second order of accuracy difference schemes for the numerical solution of hyperbolic equations with nonlocal

boundary and Dirichlet-Neumann conditions are presented. The stability estimates for the solutions of the difference schemes

are obtained. A procedure of modified Gauss elimination method is used for solving these difference schemes in the case of

one dimensional hyperbolic equation.

References[1] A. Ashyralyev, N. Aggez, A note on the difference schemes of the nonlocal boundary value problems for hyperbolic equations,

Numerical Functional Analysis and Optimization 25(5-6) (2004) 1-24.

[2] A. Ashyralyev, O. Yildirim, On multipoint nonlocal boundary value problems for hyperbolic differential and difference equations,Taiwanese Journal of Mathematics 13 (2009).

2000 Mathematics Subject Classification. 65N12: 65M12: 65J10Key words and phrases. hyperbolic equation, nonlocal boundary value problems, difference schemes, stability

317


On The Asymptotic Behaviour Of The Negative Part

Of the Second Order Differential Operator

Ozlem Baksi

Department of Mathematics, Faculty of Arts and Science,

Yıldız Technical University Davutpas.a, Istanbul,Turkey

[email protected]

Abstract

In this work we find the asymptotic formula for the negative eigenvalues of Sturm-Liouville operator with unboundedoperator coefficient which has singularity in the space H1 = L2(H; [0, ∞)) where H is a separable Hilbert space.

2000 Mathematics Subject Classification. 34B24Key words and phrases. Hilbert space, self-adjoint operator, kernel operator, completely continuous operator.

318


Solving linear programming using Newton method and

Goldstein conditions

P. Khosravi*, H. Navidi**, A. Malek***

*Department of Applied Mathematics, Shahed University, Tehran, Iran

email:parvin [email protected]

**Department of Applied Mathematics, Shahed University, Tehran, Iran


***Department of Applied Mathematics, Shahed University, Tehran, Iran

[email protected]

Abstract

The aim of this paper is to find an exact least 2-norm solution to the dual linear programming problem and to generate

an exact solution to the primal programming problem. The Newton method is proposed for solving linear programs with

very large numbers of constraints and variables. We use Goldstein conditions in order to find a suitable step-size in each

iteration. The proposed method is based on the apparently overlooked fact that the dual of an exterior penalty formulation

of a linear program provides an exact least 2-norm solution to the dual of the linear program. Solving the dual yields an

exact least 2-norm solution to the dual and the exact least 2-norm solution to dual problem can be used to generate an exact

primal solution. A simple prototype of the method is given in eleven lines of MATLAB code. Encouraging computational

results are presented.

2000 Mathematics Subject Classification.90C05, 90C06, 90C20Key words and phrases.Newton method, Goldstein conditions, penalty function, least 2-norm solution.

319


Recent Trends in Fixed Point Theorems and

Applications

P. P. Murthy

Department of Pure and Applied Mathematics

Guru Ghasidas Vishwavidyalaya ( A Central University)

Bilaspur (C.G.), India

[email protected]

Abstract

In this talk, I will start form the results of fixed point theory and applications after the remarkable fixed point theorem

due to Banach(Surles operations dans les ensembles abstraits et leur applications anx equations integrables, Fund. Math.

3(1922), 131 - 181 ) , Kannan(Some results on fixed points, Bull. Cal. Mth. Soc. 60(1968), 71 - 76 ), Edelstein( An

extension of Banach’s contraction principle, Proc. Amer. Math. Soc. 12(1961), 7 - 10) , Boyd and Wong’s( On

non-linear contractins, Proc. Amer. Math. Soc. 20(1969), 458 - 464), Ciric’s( Generalized contractions and fixed point

theorems, Publ. Inst. Math. 12(26)(1971), 19 - 26), Das and Naik’s( Common Fixed Point theorems for commuting

maps on a metric space, Proc. Amer. Math. Soc. 77(1979), 369 - 373) Fixed Point Theorems many types of results

appeared in the literature of Fixed Point Theory and Applications. In this talk, I would like to discuss some TOOLS and

their importance for obtaining fixed points . Some applications also discussed in the field of Dynamic Problems, Integral

Equations, etc. Very recently the concept of Cone Metric Space introduced by Haung and Zhang(Cone metric spaces

and fixed point theorems of contractive mappings, J. Math.Anal. Appl. 332(2007), 1468 - 1476 ) and proved some

common fixed point theorems in this space. We shall discuss in detail about this space and few results in this line by

generalizing some results of metric fixed point theorems.


320


Application of stochastic differential equations models

for solving ship roll motion

P. Nabati1, R. Farnoosh2

1 Islamic Azad University, Salmas Branch, Iran.

[email protected]

2 Iran University of Science and Technology, Department of Mathematics,

Tehran, Iran

[email protected]

Abstract

Stochastic differential equation (SDE) models play a relevant role in many application areas including environmental

modeling, biological and engineering modeling. This paper is intended to provide a second order SDE model excited by

random sea waves for ship roll motion.The mathematical (SDE) model for the responses of a ship to the random sea waves

will be presented and then this model will be solved analytically and numerically. Numerical examples are performed by

using the Euler-Maruyama method in order to show the accuracy of the present work.

References[1] Nicolau, J., Modeling financial time series through second-order stochastic differential equations, Statistics and probability letters,

2008.

[2] Shidfar, A., AND Nabati, P., Numerical Study for solving heave and pitch equations of a ship, Kuwait Journal of Science andEngineering, 2007.

[3] Carletti, M., Numerical Simulation of Stochastic ordinary Differential equations in biomathemathical modeling, Mathematics andComputers in Simulation, 2004.

[4] Journee, J. M. J. Massie, W. W. Offshore Hydromechanics. Delft University of Technology, Delft, The Netherlands, 2001.

[5] Oksendal, B., Stochastic Differential Equations, Fifth edition, Springer, 1998.

[6] Kloeden, P. E., AND Platen, E., Numerical Solution of stochastic differential equations, Springer, Berlin, 1995.

2000 Mathematics Subject Classification. 65C30Key words and phrases. stochastic differential equations, ship roll motion, Brownain motion, Euler- Maruyama method.

321


Torsion Graph of Modules

P. Malakooti Rad1, SH. Ghalandarzadeh2, S. Shirinkam3

1,3Department of Mathematics, Ph.D. student, K. N. Toosi

University of Technology P. O. Box 16315− 1618, Tehran, Iran

[email protected]

2Department of Mathematics, Faculty of Science, K. N. Toosi


Abstract

Let R be a commutative ring and M be an R-module. the concept of zero-divisor graph of a commutative ring was

introduced by I. Beck in 1988. He let all elements of the ring be vertices of the graph and was interested mainly in colorings.

In this talk, we give a generalization of the concept of zero-divisor graph in a commutative ring with identity to torsion-

graph in a module. We associate to M a graph denoted by Γ(M) called torsion graph of M whose vertices are non-zero

torsion elements of M and two different elements x, y ∈ T (M)−0 are adjacent if and only if [x : M ][y : M ]M = 0. The

residual of Rx by M , denoted by [x : M ], is a set of elements r ∈ R such that rM ⊆ Rx for x ∈ M . The annihilator of an

R-module M denoted by AnnR(M) is [0 : M ]. Let T (M) be a set of element of M such that Ann(m) 6= 0. It is clear that

if R be an integral domain T (M) is a submodue of M and is called torsion submodule of M . We investigate the interplay

between module-theoretic properties of M and the graph-theoretic properties of Γ(M). An R-module M is a multiplication

module if for every R-submodule K of M there is an ideal I of R such that K = IM . Among the other result, we prove that

Γ(M) is finite if and only if either M is finite or M is a torsion free R-module and Γ(M) is connected and diam(Γ(M)) ≤ 3

for faithful R-module M , and that if M be a multiplication R-module. then there is a vertex of Γ(M) which is adjacent to

every other vertex if and only if either M = M1⊕M2 is a faithful R-module, where M1, M2 are two submodules of M such

that M1 has only two elements, M2 is finitely generated with T (M) = (x, 0), (0, m2)|x ∈ M1, m2 ∈ M2, or T (M) = IM ,

where I is an annihilator ideal of R. Also if M be a multiplication R-module, then Γ(M) and Γ(S−1M) are isomorphic as

graph where S = R− Z(M).

References[1] D.F. Anderson, R. Levyb, J. Shapirob Zero-divisor graphs, von Neumann regular rings, and Boolean algebras, J. Pure Appl. Algebra

180 (2003) 221-241

[2] D.F. Anderson, P.S. Livingston, The zero-divisor graph of a commutative ring, J. Algebra 217 (1999) 434-447.

2000 Mathematics Subject Classification. 13A99, 05C99, 13C99Key words and phrases. MTorsion graphs, Multiplication modules

322


Existence Of Fixed Point In C-Contraction

Parvin Azhdari

Department of Statistics, Islamic Azad University

North Tehran Branch, Tehran, Iran

par [email protected]

Abstract

Kramosil and Michalek introduced the notion of fuzzy metric space which is similar to generalized Menger space. ThenGeorge and Veeramani imposed some stronger conditions on fuzzy metric space in order to obtain a Hausdorff topology.Many authors have extended fixed point theorem to different type of contraction in both probabilistic and fuzzy metricspace. Mihet also showed fixed point theorem for fuzzy contractive mappings by using point convergence. In this paperwe use the concept of point convergence for showing the existence of fixed point for B-contractions and C-contractionsmapping. We notice that the condition of point convergency is weaker than convergency.Definition 1: A B-contraction on a probabilistic space (X, F) is a sel fmapping f of X for which Ff(p)f(q)(kt) Fpq(t) 8p,q 2 X, 8t ¿ 0, k 2 (0, 1). A mapping f : X ! X is called a C-contraction if there exists k 2 (0, 1) such that for all Fxy(t) ¿ 1- t ) Ff(x)f(y)(kt) ¿ 1 - kt 8x, y 2 X , t ¿ 0. Definition 3: Let (X,M, T) be a fuzzy metric space. A sequence xn in X is saidto be point convergent to x 2 X if there exists t ¿ 0 such that limn!1M(xn, x, t) = 1Theorem 1: [1]: Let (X,M, T) be George and Veeramani fuzzy metric space and sup 0 a ¡1 T(a, a) = 1 and A : X ! X be aB-contraction. Suppose that for some x 2 X the sequence of An(x) has a p-convergent subsequence. Then A has a uniquefixed point. Theorem 2 [1]: Let (X,M, T) be a George and Veermani fuzzy metric space and A : X ! X be a C-contractionand sup 0 a¡1T(a, a) = 1. Suppose that for some x 2 X the sequence of An(x) has a p-convergent subsequence. Then A hasa unique fixed point. Existence of fixed point when the subsequence satisfied in p-convergency condition can extended togeneralized C-contraction.Theorem [2]: Let (X,M, T) be a George and Veermani fuzzy metric space and A : X ! X be a generalized C-contractionand sup 0 a¡1T(a, a) = 1. Suppose that for some x 2 X the sequence An(x) has a p-convergent subsequence. Then, A hasa fixed point.

References

[1] R. Farnoosh, A. Aghajani, P. Azhdari, Contraction theorems in fuzzy metric space, Chaos, Solitons and Fractals, In press (2008).

[2] P. Azhdari, R. Farnoosh, Fixed point theorems for the generalized C-contraction, Applied Mathematical Science, In press (2009).

2000 Mathematics Subject Classification.Key words and phrases.B-contraction, C- contraction, fixed point, fuzzy metric space.

323


Numerical Solutions of nonlinear Volterra-Fredholm

integro differential-difference equations

Parviz Darania, Karim Ivaz

Department of Mathematics and Computer Science, University of Tabriz,Tabriz-Iran

Center of Industrial Mathematics, University of Tabriz, Tabriz-Iran

[email protected]

Department of Mathematics and Computer Science, University of Tabriz,Tabriz-Iran

Center of Industrial Mathematics, University of Tabriz, Tabriz-Iran

[email protected]

Abstract

In this paper, by using the theories and methods of mathematics analysis and computer algebra, a new reliable algorithmfor solving high-order nonlinear VolterraFredholm integro differential-difference equation

R∑

r=0

m∑

j=0

prj(x)y(j)

(αrjx + βrj) = f(x) + λ1

∫ x

a

K1(x, t, y(t))dt + λ2

∫ b

a

K2(x, t, y(t))dt,

with the mixed conditions

m−1∑

j=0

[aijy(j)

(a) + bijy(j)

(b) + cijy(j)

(c)] = µi, i = 0, 1, ..., m− 1, a ≤ c ≤ b,

will establish, where f(x), K1(x, t, y(t)), K2(x, t, y(t)), prj(x), r = 0, 1, ..., R and j = 0, 1, 2, ..., m are functions that

have suitable derivatives on an interval a ≤ x, t ≤ b, and a, b, λ1, λ2 and αrj , βrj , µi (i = 0, 1, 2, ..., m − 1) are

constants. The results of the examples indicated that this method is simple and effective, and could provide an accuracy

approximate solution or exact solution of the high-order nonlinear Volterra - Fredholm integro-differential equation. This

would be useful for solving integro-differential equation, integral equations and ordinary differential equation. Results of

approximate solution to test problems are demonstrated.

References[1] P. Darania and K. Ivaz, Numerical solution of nonlinear Volterra-Fredholm integro-differential equations, Computers and Mathe-

matics with Applications, 56 (2008) 2197-2209.

[2] A. M. Wazwaz, A new method for solving singular value problems in the second-order ordinary differential equations, Appl. Math.Comput., 128 (2001), 268-281.

[3] S. Yalcinbas and M. Sezer, The approximate solution of high-order linear Volterra-Fredholm integro-differential equations in termsof Taylor polynomials, Applied Math. Comput., 112 (2000), 291-308.

2000 Mathematics Subject Classification. 47G20Key words and phrases. Taylor polynomials and series, Volterra and Fredholm integral equation, Integro-differential equations

324


Neural Networks in the Analysis of Nucleotide Genomic

Signals

Paul Dan Cristea

C.M. Romanian Academy, Director, BioMedical Eng. Center,

Univ. “Politehnica” of Bucharest, Romania

[email protected]

Abstract

Converting nucleotide sequences to digital signals [1] allows to apply signal processing methods for the analysis ofgenomic data. The method reveals surprising regularities in the distribution of nucleotides, pairs of nucleotides and smallgroups of nucleotides along a chromosome, in both prokaryotes and eukaryotes. These features of nucleotide sequenceswould be difficult to find by using only symbolic genomic sequences and standard statistical and pattern matching methods[2].

The mapping we have used in our work [1, 3] is a one-to-one unbiased representation of nucleotide equivalence classes,which attaches quadrantal complex numbers to adenine, cytosine, guanine and thymine nucleotides:

a = 1 + j, c = −1− j, g = −1 + j, t = 1− j (1)

While conserving the information in the initial symbolic sequence, this mapping introduces no artefacts related to specificassumptions on the types of interaction that characterize the nucleotides. Two simple signatures can be used to syntheticallydescribe the statistics along a nucleotide sequence:• the nucleotide imbalance:

Nc = 3(nG − nC) + (nA − nT ), (2)

where nA, nC , nG and nT are the numbers of adenine, cytosine, guanine and thymine nucleotides in the sequence, from thefirst to the current entry, and• the nucleotide pair imbalance:

Pu = n+ − n−, (3)

where n+ is the number of positive pairs (A → G, G → C, C → T, T → A), and n− the number of negative pairs(A → T, T → C, C → G, G → A).

The genomic signal approach reveals large scale features of DNA sequences that are maintained over distances of106 − 108 base pairs, including both coding and non-coding regions [4, 5]. The methodology is also adequate for the studyof pathogen variability and the identification of multiple drug resistance, important for fast diagnoses and prompt socio-medical decisions in contamination with pathogens such as Human immunodeficiency virus (HIV ) [6], Avian influenzavirus (H5N1) [7] and Mycobacterium tuberculosis (MT) [8, 9, 10]. Some of the main features resulting from the analysis ofthe nucleotide sequences are [1, 3, 5]: (1) A remarkable good linearity of the nucleotide pair imbalance Pu. The root meansquare error per nucleotide of the linear fitting to Pu is typically very small (e.g., 0.0045 for MT), while the ratio of thelinear per irregular variation is quite large (14.5 for MT), which corresponds to a smooth strait line at large scale. (2) Anapproximately piece-wise linear nucleotide imbalance Nc, for prokaryotes. (3) The extremes of Nc correspond to the originand the terminus of genome replication. Re-orienting all exons in a sequence along the same positive direction reveals some’hidden’ features of a DNA sequence [11]: (1) A (perfect) invariance of the nucleotide pair imbalance Pu, is invariant, asthe direct (n+) and inverse (n−) numbers of pairs are conserved when reversing and complementing a segment of a DNAdouble helix. (2) An approximately linear shape of Nc after re-orientation, suggesting a highly regular ancestral genomicstructure, from which the current nucleotide longitudinal structures have evolved under evolutionary pressure. The longrange regularities show that, from the structural point of view, a genome resembles less to a ”plain text”, which simplyexpresses a semantics in accordance to certain grammar rules, but more to a ”poem”, which also obeys additional rulesof symmetry, giving it ”rhythm” and ”rhyme”. The correlations and regularities in the genomic signals can be used topredict nucleotides based on knowledge about the nucleotides preceding them in the sequence in a way similar to time seriesprediction. The efficiency of the nucleotide prediction can be improved by using a two step procedure comprising a PCAstage, which retains only the high variance components of the input signal, and an ANN, which performs the predictionbased on these components. For signals satisfying some mild statistical regularities, the PCA stage performs an approximateDFT, passing from the time (space) domain to the frequency domain. The ANN implements the inverse DFT, generatingthe estimate of the next sample of the sequence in the time (space) domain using the Fourier coefficients. The predictionmodel shows a quite good efficiency, which is the effect of the multilevel regularities in the structure of genomic sequences.

References[1] P.D. Cristea, Chapter 1, ”Representation and analysis of DNA sequences”, in Genomic Signal Processing and Statistics, E. Daugherty,

I. Shmulevich, J. Chen and Z.J. Wang, Eds., EURASIP Book Series on Signal Processing and Communications, Hindawi Publ. Corp.,p. 15-65, 2005

[2] S.F. Altschul, T.L., Madden, et. al., ”Gapped BLAST and PSI-BLST: a new generation of protein database search programs,” Nucl.Acids Res. 25, p. 3389-3402, 1997, http://www.ncbi.nlm.nih.gov/blast/.

2000 Mathematics Subject Classification. 92D20, 92B20, 62H25Key words and phrases. Nucleotide Genomic Signals, Sequence Prediction, Neural Networks

325


[3] P.D. Cristea, ”Conversion of Nitrogenous Base Sequences into Genomic Signals”, Journal of Cellular and Molecular Medicine, 6(2),p.279-303, 2002.

[4] E. Chargaff, ”Structure and function of nucleic acids as cell constituents”, Fed. Proc., 10, p. 654-659, 1951.

[5] P.D. Cristea, ”Large Scale Features in DNA Genomic Signals”, Signal Processing, Special Issue on Genomic Signal Processing,ELSEVIER, 83, pp. 871-888, 2003.

[6] P.D. Cristea, D. Otelea, R.Tuduce, ”Genomic Signal analysis of HIV variability”, SPIE - BIOS 2005, Proc. of SPIE, 6, (14), p.362-372, 2005.

[7] P. D. Cristea, ”Genomic Signal Analysis of Pathogen Variability”, Progress in Biomedical Optics and Imaging, Proc. of SPIE, vol.6088, pp. P1-P12, 2006.

[8] S.T. Cole, R. Brosch, J. Parkhill, et al., ”Deciphering the biology of Mycobacterium tuberculosis from the complete genome sequence”,Nature, 393 (6685), p. 537-544, 1998.

[9] P.F. Barnes, D.L. Lakey, and W.J. Burman, ”Tuberculosis in patients with HIV infection”, Infect. Dis. Clin. North Am., 16, p.107-126, 2002.

[10] P. D. Cristea, ”Genomic Signal Analysis of Mycobacterium tuberculosis”, Progress in Biomedical Optics and Imaging, Proc. of SPIE,vol. 6447, p. C-1 - C8, 2007 .

[11] P.D. Cristea, Genomic Signals of Re-Oriented ORFs, EURASIP - Journal on Applied Signal Processing, Special Issue on GenomicSignal Processing, 2004 (1), p. 132-137, 2004.

326


Effect Of Feedback Mechanism Over Ad Hoc Network

For Audio & Video Communications

Pejman Panahi

Iranian Academic Center For Education, Culture and Research- Urmia Branch

[email protected]

Abstract

An Ad hoc Network provides quick and easy networking under circumstances that require temporary network services

or when cabling is hard to deploy. It can be adopted as a solution for coverage in rural areas, disasters and military

applications. Ad hoc Networks can be used to extend the range of wireless service coverage. Providing quality of service in

ad hoc networks is an extremely challenging task, due to several factors like the unrestricted mobility of nodes, dynamically

varying network topology, and other ones. There are two approaches to audio and video transmission: single stream and

multi stream. The former transmits a single transport stream of interleaved audio and video, while the latter treats the two

media as separate transport streams. In this paper, we describe a novel scheme for audio and video transport over wireless

ad hoc networks. The main idea of this work is based on selecting special nodes of transferring path as proxy nodes. In each

of every transmitting routes only one node will select as audio & video proxy nodes based on an agreement between sender

and receiver or network traffic status. The duty of these nodes is to receiving and recognizing audio and video streams,

buffering of favorite streams and if possible managing errors locally. Choosing these nodes and employing them at network

add to increasing network life time will result in reduced end to end delay between sender and receiver.

2000 Mathematics Subject Classification. 68-xx(68-06)Key words and phrases. Multimedia Streaming, Ad Hoc Network, Proxy Nodes, Feedback Mechanism, Quality Of Service.

327


A Graph Coloring Approach To Airline Crew

Scheduling Problem

Pınar Dundar, Hande Tuncel, Onur Kılıncceker

Ege University, Department of Mathematics, Izmir , Turkey

[email protected]

Izmir University of Economics , Department of Mathematics, Izmir , Turkey

[email protected]

Mugla University, Department of Computer Engineering , Mugla, Turkey

[email protected]

Abstract

The airline crew scheduling problem is well-known as one of the most difficult combinatorial problem. Crew scheduling

for airlines requires an optimally scheduled coverage of flights with regard to given timetables. In this paper, in order to

construct daily feasible flight sequence for an employee, we proposed an approach with graph coloring. Same colors determine

daily feasible schedule which can be task with same crew. After daily composition of pairings with graph coloring approach,

we modeled problem as crew assignment problem. So, we assembled pairings into monthly work schedules and assigned

to individual crew member. While solving this problem, we used some data which belongs to a domestic airline company

called Izair.

References[1] B. Gopalakrishnan, E. L. Johnson, Airline Crew Scheduling: State-of-the-Art , Annals of Operations Research 140 (2005), 305-337.

[2] C. Barnharth, A.M. Cohn, E.L. Johnson, D. Klabjan, G.L. Nemhauser, P.H. Vance Handbook of transportation science: Airlinecrew scheduling, Kluwer Sci. Publ. (2003) 517-560.

[3] F.M. Zeghal, M. Minoux, Modeling and solving a Crew Assignment Problem in air transportation , European Journal of OperationalResearch 175 (2006) 187-209.

[4] J.L. Gross, J. Yellen, Graph theory and its applications, CRC Press (1999).

[5] M. Gamache, A. Hertz, J. E. Ouellet,A graph coloring model for a feasibility problem in monthly crew scheduling with preferentialbidding, Kluwer Sci. Publ. Computers and Operations Research 34 (2007) 2384 - 2395.

[6] N. Christofides, Graph theory: An algorithmic approach, Academic Press Inc.(1975).

2000 Mathematics Subject Classification. 68R10, 05C15, 90C27, 90C35, 90B35Key words and phrases. Graph Coloring , Crew Assignment.

328


On The Galerkin Method For Non-Linear Evolution

Equation

Polina Vinogradova

Far Eastern State Transport University, department of natural sciences

680021, Khabarovsk, Serisheva 47, Russia

[email protected]

Abstract

Let H1 be a Hilbert space densely and compactly embedded in a Hilbert space H. In the space H we consider theCauchy problem

u′(t) + A(t)u(t) + K(u(t)) = h(t), u(0) = 0. (0.1)

We assume that the operators A(t) and K(·) have the following properties.1) A(t) is self-adjoint operator in H with domain D(A(t)) = H1. A(t) is positive definite operator.2) The operator A(t) is strongly continuously differentiable on [0, T ]. There is a constant β ≥ 0 such that (A′(t)v, v)H ≤β(A(0)v, v)H .3) The non-linear operator K(·) is subordinate to operator A(0) with order 0 ≤ τ < 1, i.e. D(K(·)) ⊃ D(A(0)) and forany v ∈ H1 the inequality ‖K(v)‖ ≤ ‖A(0)v‖τ ϕ(‖v‖2) holds, where ϕ(ξ) is a continuous positive function on [0,∞). Theoperator K(t) is compact.4)There is given a positively definite self-adjoint operator B which is similar to A(0), i.e., D(B) = D(A(0)).5) The operators A(t) and B satisfy the inequality(A(t)v, Bv)H ≥ m‖A(0)v‖‖Bv‖, where a constant m > 0 is independent of the choice v ∈ H1 and t.

By e1, e2, . . . , en, . . . we denote a complete orthonormalized system of eigenvectors of B with the corresponding eigen-values λ1, λ2, . . . , λn, . . . , so that 0 < λ1 ≤ λ2 ≤ . . . ≤ λn . . . and λn → ∞ as n → ∞. Let Pn be the orthogonalprojection in H onto the linear span Hn of the elements e1, e2, . . . , en. In Hn we consider the problem:

u′n(t) + PnA(t)un(t) + PnK(un(t)) = Pnh(t), un(0) = 0. (0.2)

Let h(t) ∈ L2(0, T ; H). It was proved, that problems (1) and (2) have at least one solution at each n and that from thesequence un(t) it is possible to select the subsequence, which converges to the solution of problem (1) in strong norm.

2000 Mathematics Subject Classification. 12H20Key words and phrases. Cauchy problem; Operator equation; Galerkin method; Hilbert space; Orthogonal projection

329


Characterization Properties Of Some Classes Of

P -Valent Meromorphic Functions Involving Certain

Convolution Structure

Poonam Sharma

Department of Mathematics and Astronomy University of Lucknow, U.P., India

[email protected]

Abstract

In this paper we investigate various characterization properties of some classes of p-valent meromorphic functions which

satisfy certain subordinate condition under several different relationship that involve a convolution structure. Our study

certainly unify several previously obtained results.

References[1] M. K. Aouf, Certain subclasses of meromorphically multivalent functions associated with generalized hypergeometric func-

tions,Computers and Mathematics with Applications, 55 (2008), 494-509.

[2] M. K. Aouf and A. O. Mostafa, Certain subclasses of p-valent meromorphic functions involving certain operator, J. Inequal. Pureand Appl. Math., 9(2) (2008), Art. 45, 8pp.

[3] E. Aqlan, J.M. Jahangiri and S.R. Kulkarni, Certain Integral operators applied to meromorphic p-valent functions, J. of Nat.Geom., 24 (2003), 111-120.

[4] P. Eenigenburg, S.S. Miller, P.T. Mocanu and M.O. Reade, On a Briot-Bouquet Differential subordination, Rev. Roumania Math.Pures Appl., 29(1984), 567–573.

[5] Jin-Lin Liu, A linear operator and its applications on meromorphic p-valent functions, Bulletin of the Institute of mathematicsacademia Sinica,, 31, 1 March 2003.

[6] Jin-Lin Liu and H. M. Srivastava, A linear operator and associated families of meromorphically multivalent functions, Journal ofmathematical analysis and applications, 259 (2001), 566–581.

[7] Poonam Sharma and Deepali Chowdhary, Inclusion relations involving certain classes of p-valent meromorphic functions with positivecoefficients based on a linear operator, Advances in theoretical and Applied Mathematics, 2 (1) (2007) 15–30.

[8] S. Sivaprasad kumar, V. Ravichandran and H. C. Taneja, Meromorphic functions with positive coefficients defined using convolution,J. Inequal. Pure and Appl. Math., 6 (2) (2005) 58.

[9] B. A. Uralegaddi and C. Somanatha, Certain classes of Meromorphic Multivalent functions, Tamkang Journal of Mathematics, 23

(1992) 223–231.

2000 Mathematics Subject Classification.30C45, 30C55.Key words and phrases.p-valent meromorphic starlike(convex) functions, convolution, calculus operators, subordination.

330


The Initial Flow Past an Impulsively Started Oscillating

Circular Cylinder

Qasem Al-Mdallal

Department Mathematical Sciences Mathematical Sciences, U.A.E. University,

Al-Ain, P.O. Box: 17555, U.A.E

[email protected]

Abstract

The initial flow past an oscillating circular cylinder is investigated numerically for different values of an oscillating

frequency at a fixed Reynolds number R = 200. The numerical simulations are conducted at displacement amplitude-to-

cylinder radius ratios of A = 0.6. Results show the development of the physical properties of the flow at early stages at

different values of unsteady loading on the cylinder, which is characterized by the ratio of excitation frequency f , to Karman

shedding frequency f0 . Previously computed results are compared to current visualizations and agreement is found to be

excellent.


331


On Covering of Products of T - generalized State

Machines

R. Ameri, M. Sadeghi



[email protected]

Abstract

We introduce the concepts of T -generalized state machines, and coverings of products of them. Also some of algebraic

properties of them are investigated. Some products such as direct sum and sum of T -generalized state machines are

introduced. An interesting distributive property of cascade product over the sum of T -generalized state machines concern

to covering of T -generalized state machines is established.

2000 Mathematics Subject Classification.Key words and phrases. T-generalized state machine; Covering; Cascade product; Wreath product; Sum of two T -generalizedstate machines;Direct sum*The first author partially has been supported by the Fuzzy Systems and Its Applications Center of Excellence, Shahid BahonarUniversity of Kerman, Iran.

332


Bayesian Test for Homogeneity Hypothesis

R. Farnoosh1 , A. Hajrajabi2

1 Islamic Azad University, South Tehran Branch, Tehran, Iran

[email protected]

2 Iran University of Science and Technology,

Department of Mathematics, Tehran, Iran

[email protected]

Abstract

Population which consist of several subpopulation with different properties is called heterogeneous. Hence homogeneity

means not mixing population distribution. Modified likelihood ratio test and EM test which are based penalized likelihood

function are usually used for testing homogeneity under the mixture models. In this paper we will show that efficiency

of these tests is influenced by the shape of the chosen penalty function, Hence none of these tests is generally optimal.

Parameters of poisson mixture models and parameter of determinative shape of the penalty function are estimated by a

bayesian approch and homogeneity test is implemented by using the criteria of the optimal model choice.

References[1] Chen, J. Penalized Likelihood Ratio Test for Finite Mixture Models with Multinomial Observations. Canadian Journal of Statistics,

26, (1998). 583-599.

[2] Chen, J. and Li, P. Homogeneity Test in Normal Mixture Models. The EM Approach. Techinical Report. University of BritishColumbia. (2008).

[3] Dempster, A. P., Laird, N. M., and Rubin, D. B. Maximum Likelihood from Incomplete Data Via EM Algorithm. Journal of theRoyal Statistical Society, 39, (1997), 1-38.

[4] Marin, J. M., Mengersen, K., and Robert, C. Bayesian modelling and inference on mixtures of distribution. In Rao, C. And Dey, D.,editors, Handbook of statistics, Volume 25. Springer-Verlag, New York.

[5] Richardson, S. and Green, P. J. On Bayesian Analysis of Mixtures with an Unknown Number of Components. Journal of the RoyalStatistical Society, 59, (1997). 731-792.

2000 Mathematics Subject Classification. 46NxxKey words and phrases. Mixture model, Homogeneity test, EM algorithm, Metropolis-Hasting sampling

333


On Application Mathematical Procedures for Data

Envelopment Analysis to Resource Allocation Strategy

of Police Organization

R. Poursaberi

Payame Noor University(PNU),Iran

Abstract

In this paper our aims to build the measurement model of efficiency analysis and allocate efficiency of police organization

by taking twenty city police bureaus in Iran as an example for the empirical study.This study applies Data Envelopment

Analysis (DEA) to reinforce the single-index evaluation method of police organization performance currently, and the

Frontier software is used to obtain the efficiency value of each decision making units.

References[1] B. M. Richman and R. M. Farmer, Management and Organizations, Random House Press, New York, 1975, p.364

[2] P. Agrell and B. M. West, A caveat on the measurement of productive eciency, Interna- tional Journal of Production Economics,Vol. 69 (2001), pp.1-14.

[3] L. Navaei and R. porsaberi, On application of hypothesis testing for steganography systems,Journal of Advances in computer scienceand engineering, Vol. 2 (2008). no.3. pp. 221-234.

[4] S. P. Robbins, Organizational Behavior, Concept, Controversies and Application, 71st edition, Prentice-Hall, Inc., New Jersey, 1996.

2000 Mathematics Subject Classification.65M15Key words and phrases. Data Envelopment Analysis (DEA), Frontier software,efficiency.

334


Generalized Humbert Matrix Polynomials

Raed S. Batahan

Mathematics Department, Faculty of Science,

Hadhramout University of Science and Technology

[email protected]

Abstract

In the present paper, we introduce and study the generalized Humbert matrix polynomials for a matrix that satisfies

an appropriate spectral property. We have presented, by means of the generalized hypergeometric matrix function, some

hypergeometric matrix representations of the generalized Humbert matrix polynomials. In addition to establishing struc-

tures of generating matrix functions, expansions of the generalized Humbert matrix polynomials in series of Hermite and

Laguerre matrix polynomials are obtained. The Gegenbauer matrix polynomials are here a particular case of the generalized

Humbert matrix polynomials.

References[1] R. S. Batahan, A new extension of Hermite matrix polynomials and its applications. Linear Algebra & its Applications, 419 (2006)

82 - 92.

[2] R. S. Batahan, Generalized Gegenbauer Matrix Polynomials, Series Expansion and Some Properties, In: Linear Algebra ResearchAdvances, Editor: Gerald D. Ling, Nova Science Publishers, Inc.,(2007), 291-305.

[3] R. S. Batahan, On Humbert matrix polynomials, Proceeding of the Third International Conference on Research and Education,ICREM3, 10 - 12 April 2007, Kuala Lumpur, Malaysia, (2007) 92-96.

[4] J. Sastre, E. Defez and L. Jdar, Laguerre matrix polynomial series expansion: Theory and computer applications. Math. Comput.Modelling, 44, (2006) 1025-1043.

2000 Mathematics Subject Classification.Key words and phrases. Gamma and Beta matrix function, Hermite, Laguerre, Gegenbauer and Humbert matrix polynomials

335


Contra-Gamma-Continuous Mappings in Topological

Spaces

Raja Mohammad Latif,Muhammad Razaq

Department of Mathematics and Statistics

King Fahd University of Petroleum and Minerals

Dhahran 31261 Saudi Arabia

[email protected]

Department of Computer Science

Raja Sarfraz Khan Study Center Allama Iqbal Open University

Bhaun Chowk, Chakwal, Pakistan

[email protected]

Abstract

The notion of semi-convergence of filters was introduced by Latif (1999) who investigated some characterizations related

to semi-open continuous functions. In the spirit of Latif (1999) , Min (2002) used the idea of semi-convergence of filters

to introduce a new class of sets, called γ − open sets, and the notions of γ − closure, γ − interior and γ − continuity

and investigated some properties. In this paper, we apply the notion of γ − open sets in topological spaces to present and

study certain properties and characterizations of contra − γ − continuity as a new generalization of contra − continuity

[Dontchev, 1996] .

References[1] J. Dontchev, Contra− continuous functions and strongly S − closed spaces, Internat. J. Math. Sci., 19 (1996) , 303− 310.

[2] Raja M. Latif, Semi-convergence of Filters and Nets; Mathematical Journal of Okayama University, Vol. 41(1999), 103 − 109.

[3] Won K. Min, γ − sets and γ − continuous functions, Int. J. Math. Math. Sci., 31 (2002) , no. 3, 177− 181.

2000 Mathematics Subject Classification.54A05, 54C08Key words and phrases. Topological Space, γ − open set, γ − closed set, contra− γ − closed, γ − compact, strongly S − closed,contra− γ − continuity

336


Potential Flow On Two Identical Tubes

Rajai S. Alassar

King Fahd University of Petroleum & Minerals

Department of Mathematics and Statistics

[email protected]

Abstract

An exact solution of the transient problem of potential flow past two identical circular cylinders is obtained. The two

cylinders may be located at any distance from each other with the flow being perpendicular to the center-to-center line.

The stream function formulation is used. The pressure distribution around the surfaces of the two cylinders is calculated

and the effect of the center-to-center distance is studied. The exact solution is verified against that of the flow past a single

cylinder by considering the limiting case when the center-to-center distance between the two cylinders increases indefinitely.

Error bounds on the series solution show that the error decays exponentially.

2000 Mathematics Subject Classification. 76B99, 76A02, 30B99Key words and phrases. Cylinders, Inviscid Flow, Stream Function, Bipolar Coordinates.

337


The most accurate approximation for numerical

solution of stochastic differential equation with Poisson

white noise by Skew-Normal distribution

Ramzan Rezaeyan, Rahman Farnoosh

Department of mathematics, Faculty of Basic sciences,

Islamic Azad University, sciences and research branch, Tehran, Iran.

[email protected]

Department of Applied Mathematics, University of Science and Technology,

Narmak, Tehran, 16844, Iran.

[email protected]

Abstract

In this paper the stochastic differential equation (SDE) with Poissonian white noise (PWN) is considered. The parameter

of Poisson distribution plays an important role in numerical solution for SDE with PWN. If this parameter be almost large,

then we show that using the Skew-Normal distribution (SND) to approximate Poisson distribution is better than Normal

distribution. We show, the accuracy of the present work, some example are considered.

2000 Mathematics Subject Classification. 60H10Key words and phrases. Stochastic Dierential Equation, Skew - Normal distribution, approximation, Poissonian white noise,Gaussian white noise, Euler method.

338


Spline Solution of Fourth-Order Obstacle

Boundary-Value Problems

Reza Jalilian

Department of Mathematics, Ilam University, PO Box 69315-516, Ilam, Iran

[email protected]

Abstract

We use quintic spline function to develop numerical method for approximation to the solution of a system of fourth-order boundary-value problems associated with obstacle, unilateral and contact problems. The convergence analysis of themethod has been discussed. Numerical examples are presented to illustrate the applications of method, and to compare thecomputed results with other known methods. We shown that the given approximations are better than collocation, finitedifference and spline methods.

References[1] J. Rashidinia, R. Mohammadi, R. Jalilian, M. Ghasemi Convergence of cubic-spline approach to the solution of a system of boundary-

value problems,Appl. Math. Comput. 192(2007)319-331

[2] R.A. Usmani , The use of quartic splines in the numerical solution of a fourth-order boundary value problem,J.Comput. Appl. Math.

44 (1992) 187-199.

2000 Mathematics Subject Classification. 65L10Key words and phrases. Quintic spline, Boundary formula, Convergence, Obstacle problems.*This research was supported by Ilam University.

339


Existence Of Positive Solutions For A Discrete

Boundary Value Problem

Rodica Luca-Tudorache

Department of Mathematics, Gh. Asachi Technical University,

11 Blvd. Carol I, Iasi 700506, Romania

[email protected]

Abstract

We study the existence and nonexistence of positive solutions of the discrete system with second-order differences

(S)

∆2un−1 + bnf(vn) = 0, n = 1, N − 1

∆2vn−1 + cng(un) = 0, n = 1, N − 1, (N ≥ 2),

with m + 1-point boundary conditions

(BC)

βu0 − γ∆u0 = 0, uN −m−2∑

i=1

aiuξi= b,

βv0 − γ∆v0 = 0, vN −m−2∑

i=1

aivξi= b, m ≥ 3,

where ∆ is the forward difference operator with stepsize 1, ∆un = un+1 − un. The arguments for existence of solutions

are based upon the Schauder fixed point theorem and some auxiliary results from [1] and [2].

References[1] W.T. Li, H.R. Sun, Positive solutions for second-order m-point boundary value problems on times scales, Acta Math. Sin., Engl.

Ser. 22, No.6 (2006), 1797-1804.

[2] R. Luca, Positive solutions for m + 1-point discrete boundary value problems, Libertas Math., in press.

2000 Mathematics Subject Classification. 39A10Key words and phrases. difference equations, multi-point boundary value problem, positive solution, fixed point theorem.

340


Classification of exceptional train algebras of rank 3 and

type (4, 2): step 1

Roseli Arbach , Luis Antonio Fernandes de Oliveira



[email protected]



[email protected]

Abstract

Let F be a field with char(F ) 6= 2, A a commutative F -algebra, not necessarily associative and ω : A → F a nonzerohomomorphism. If there exists γ ∈ F such that, for all x in A, x3 − (1 + γ)ω(x)x2 + γω(x)2x = 0, then the pair(A, ω) is called a (commutative) train algebra of rank 3. When we consider 2γ 6= 1, there is an idempotent e ∈ A andrelative to this element, A has a Peirce decomposition A = Fe ⊕ Ue ⊕ Ve, where Ue = u ∈ Ker(w)N : 2eu = u andVe = v ∈ Ker(w) : ev = γv. The type of A is the ordered pair of integers (1+r, s), where r = dim(Ue) and s = dim(Ve).

If A = Fe⊕ Ue ⊕ Ve is a train algebra of rank 3 and dimension 6, the possible types of A are (5, 1), (4, 2), (3, 3), (2,

4) and (1, 5). The train algebras of rank 3 and types (n, 1), (3, n - 2), (2, n - 1) and (1, n) had already been classified and

so, in order to complete the classification of the train algebras of rank 3 and dimension 6, we have to analyse such algebras

of type (4, 2). Here we begin this classification.

References[1] ARBACH, R., Sobre os P-subespacos em uma train algebra de posto 3, Ph.D. thesis, Instituto de Matematica e Estatıstica da

Universidade de Sao Paulo, 1997.

[2] ARBACH, R., FERNANDES, L. A. O. Subclasses of a train algebra of rank 3, Rev. Mat. Estat., Sao Paulo, v.25, n.1, p.23-29,jan.-mar.2007

[3] COSTA, R., Principal train algebras of rank 3 and dimension ≤ 5, Proceedings of the Edinburgh Mathematical Society 33 61-70(1990).

[4] COSTA, R., On train algebras of rank 3, Linear Algebra and its Applications 148 1-12 (1991).

[5] REED, M.L., Algebraic Structure Of Genetic Inheritance, Bulletin (New Series) of the American Mathematical Society v. 34, n.2, p. 107-130, April 1997

[6] WORZ, A., Algebras in Genetics, Lecture Notes in Biomathematics 36, Berlin-Heidelberg-New York (1980).

2000 Mathematics Subject Classification. 17D99Key words and phrases. t-equation and t-algebra, type of a t-algebra, exceptional t-algebras*This research was supported by by FUNDUNESP, Proc.:00296/09 - DFP

341


Large probability models of access control security

system architecture

Roushanak Lotfikar , Bagher Arayesh

Islamic Azad University, branch Ilam, Ilam, Iran

[email protected]

Islamic Azad University, branch Ilam, Ilam, Iran

[email protected]

Abstract

This paper presents probability models of access control security system architecture . Access control is the process of

screening objects : for example people ,baggage ,entering a secured area in order to detect and prevent entry by threats such

as unauthorized personal firearms , Explosives . A security system architecture consist of Device technologies, as well as

operational policies and procedures for utilizing the technologies . The probability models are developed based on type 1(a

false alarm is given) and type 2 ( a threat is not detected) errors . The concept of controlled sampling in which objects may

take Different paths through the system , is introduced .New architectures consisting of Multiple devices and Controlled

Sampling are Proposed and analyzed. The Results of this research show that for specific threats levels , Multiple device

system can be identified which out perform single device systems for certain error probability measures.

References[1] Doyan L., Stochastic modeling of facility systems for analytical solution.comp and Eng ,5(2000)127-138.

[2] Davis CF. and Wormington TD., Measures of effectiveness for physical security assessment. IEEE carnahan conference on securityTechnology, Kentuucky, pp:177-185(2002).

[3] Payeron F. Doyon LR. and Hanse J., Computer analysis of security system. IEEE carnahan conference on security Technology ,Zurich, Switzerland ,pp:23-29(1983).

[4] Christer, AH.Modeling the quality of automatic quality checks. Jopnl Res Soc,45(2004).

2000 Mathematics Subject Classification. 94A15, 68U35Key words and phrases. probability models , security system ,statistical threats.

342


On the fuzzy minimal spaces

S. A. Mohammadzadeh, Mehdi Roohi


[email protected]

University of Mazandaran, Babolsar 47416-1468, Iran

[email protected]

Abstract

At the present paper, the concept of fuzzy minimal spaces is introduced and some basic properties of them is considered.

Further, several types of fuzzy continuity are defined and some characterization of them are investigated. Moreover, to

support our results many examples are constructed.

References[1] M. Alimohammady, S. Jafari and M. Roohi, Fuzzy minimal connected sets Bull. Kerala Math. Assoc. 5(1)(2008), 1–15.

[2] M. Alimohammady and M. Roohi, Fuzzy minimal structure and fuzzy minimal vector spaces, Chaos, Solitons & Fractals27(3)(2006), 599–605.

[3] C. L. Chang, Fuzzy topological spaces, J. Math. Anal. Appl. 24(1968), 182–190.

[4] R. Lowen, Fuzzy topological spaces and fuzzy compactness, J. Math. Anal. Appl. 56(1976), 621–633.

[5] H. Maki, J Umehara and T. Noiri, Every topological space is pre T 12, Mem. Fac. Sci. Kochi Univ. Ser A. Math. 17(1996), 33–42.

[6] A. P. Sostak, On a fuzzy topological structure, Suppl. Rend. Circ. Matem. Palermo Ser. II, 11(1985), 89–103.

[7] L. A. Zadeh, Fuzzy sets, Inf. control, 8(1965), 338–353.

2000 Mathematics Subject Classification. Primary 54A40, Secondary 03E72, 54A05Key words and phrases. Fuzzy set, fuzzy topology, fuzzy minimal space, fuzzy minimal continuity, fuzzy compactness

343


Fisher Information of a Single Qubit System

S. Abdel-Khalek


Sohag University, 82524 Sohag, Egypt

[email protected]

Abstract

In this paper, we study the interaction between a single trapped ion with a laser field. The concept of quantum Fisher

information (QFI) in terms of the atomic density operator is introduced. This quantity is used as a best estimation of

entanglement compared with classical Fisher information (CFI) and von Neumann entropy of a single qubit system. We

demonstrate connections between these measures. The results show the important roles played by the fluctuations of the

laser phase and initial state setting in the evolution of the quantum and classical Fisher information

2000 Mathematics Subject Classification. 65L99, 34A45Key words and phrases. Trapped ion, Carrier side band excitation, quantum Fisher information, classical Fisher information.

344


Path Planning Algorithm for Mobile Robot Based on

Multilayered Cellular Automata

S. Behmanesh*, H.S.Javadi** ,H.Erfani***

*Islamic Azad University, Computer Engineering, Qazvin, Iran

[email protected]

**Shahed University, Mathematics and Computer Science, Tehran, Iran

[email protected]

***Science and Research University,Computer Engineering,Tehran,Iran

[email protected]

Abstract

In the present work, it is described Motion Planner for mobile moving on terrains. we describe the architecture base on

the paradigm of Cellular Automata. It can be applied to Euclidean workspace. We have studied an algorithm based on a

Euclidean distance from goal and the score of each cell. We have Multilayered Cellular automata, these properties impart

us having more than one mobile robot and different goals. Also Attraction layer is separated from Obstacle’s layer. These

characteristics plus giving score to each cell enable our algorithm to find a way for continuing. In the first practice, the

algorithm calculates the cells scores and by learning in each iteration it cause the algorithm comes more efficient in next

practices.

References[1] Marchese F. M., ”A Path - Planner for Generic- Shaped Non-Holonomic Mobile Robots ”, Proc. of European conf. on Mobile Robots

(ECMR 2003), Sept 2003.

[2] Marchese F. M., ”A Path-Planner for Mobile Robots of Generic-Shaped with Multilayered Cellular Automata”, Springer-Verlag,pp. 178-189, 2002.

[3] Wolfram S., ”Statistical Mechanics of Cellular Automata”, Review of Modern Physics, 55, PP.601-644, 1983.

[4] Meybodi M.R., Beygi H., Taherkhani M., ”Cellular Learning Automata”, Proc. of 6th Annual CSI Computer Conference, pp.153-156,20-22Feb 2001.

[5] Tsoularis A., Kambhampati C., Warwick K., ”Path Planning of Robots in Noisy Workspaces using Learning Automata”, proc. ofInternational symposium on intelligent Control, August 1993.

[6] Marchese F. M., ”The Architecture of a Reactive Path-Planner for Mobile Robots Based on Cellular Automata”, Springer-Verlag,pp. 182-185, 2005.

[7] Marchese F. M., ”A Directional Diffusion Algorithm on Cellular Automata for Robot Path-Planning”, Future Generation Computer

System 18, pp. 983-994, 2002.

2000 Mathematics Subject Classification. 37B15 Cellular AutomataKey words and phrases.Cellular Automata, Learning , Robot path-planning

345


Frictionless contact problem on nonlinear elasticity

S. Boutechebak*, N. Lebri**

*Department of Mathematics, Faculty of Sciences


**Department of Mathematics, Faculty of Sciences


Abstract

The subject of this work is the study of the contact problem with out friction between an elastic nonlinear body and a

rigid foundation.Under suitable conditions, we extend the results given in [6] and [11] to our problem. For that, we present

first associated variational problem as well as the study of existence and uniqueness of its solution. Secondly, we deal with

some properties of this solution and its dependence with a given parameter. Finally, we shall introduce a penalized problem

of the mechanical problem.

2000 Mathematics Subject Classification.74M15, 74S05, 65M60.Key words and phrases.Elastic body, Contact without friction, Operator strongly monotone, Penalized problem.

346


Experimental Approach of Flux Estimation in Real

Time for Induction Motors Drives

S. Grouni1, A. Aibech 2, R. Ibtiouen3, M. Kidouche 4, O. Touhami 5

1 High school Polytechnic, ENP, Algiers, Algeria

Physics Department, Faculty. Sciences, University of Boumerdes, Algeria

[email protected]

2 Physics Department, Faculty. Sciences, University of Boumerdes, Algeria

[email protected]


4 Physics Department, Faculty. Sciences, University of Boumerdes, Algeria


Abstract

This paper deals with an experimental approach of flux estimation in real time for induction motors drives. Based on

the real currents stator, voltages and rotor speed measurements, the rotor fluxes are estimated using different methods.

The reduced order model of induction motor is used to offer many advantages for real time identification parameters of the

induction machine. The major contributions of this work are: first, avoid the use sensors of direct rotor flux to increase

the installation cost and degrade the mechanical robustness. Second, by reducing the order of the induction machine

model, the implementation of the proposed real time estimation flux has a good dynamic behavior and therefore is well

suited for high performance applications. Third, the estimation of rotor and stator flux can be performed even at variable

regime flux and at low loads. Further, the estimation algorithm involves no derivative terms. Finally, we show that the

proposed experimental scheme is not sensitive to disturbances parametric errors and it is robust against load variations.

The experimental results and the estimated values of fluxes are compared and shown in real time application.

References[1] J. Holtz, ”Sensorless control of Induction Machines- with or without Signal Injection?” Overview Paper, IEEE Trans. on Ind. Elect.,

Vol. 53, No.1, Feb. 2006, pp. 7-30.

[2] K. Wang, J. Chiasson, M. Bodson, L. M. Tolbert, ”An Online Rotor Time Constant Estimator for the Induction Machine,” IEEETrans. Contr. Syst. Technol., vol.15, No.2, pp. 339-347, March 2007.

[3] R. Krishnan ”Electric Motor Drives, Modeling, Analysis and control ” 2001, Prentice Hall.

[4] J.Holtz, J. Quan, ”Sensorless control of induction motor drives” Proceedings of IEEE, Vol.( 90), No.8, Aug. 2002,pp1359-1394.

[5] SH. Jeon, KK. Oh, JY. Choi, ”Flux observer with on line tuning of stator and rotor resistance for induction motors” IEEE Trans.Ind. Electron. Vol. 49, No.3, 2002, pp. 653-664.

2000 Mathematics Subject Classification.Key words and phrases. Induction Machine, Field Oriented Control, Flux Estimation, Real Time Application.

347


Heat Conduction Equation At Micro And Nano Scale:

Approximation Methods

S. H. Momeni-Masuleh

Department of Mathematics, Shahed University, Tehran,

P. O. Box: 18151-159, Iran.

[email protected]

Abstract

In the classical theory of diffusion, Fourier law of heat conduction, it is assumed that the heat flux vector and temperature

gradient across a material volume occur at the same instant of time. It has shown that if the scale in one direction is at

the microscale (of order 0.1 µm), then the heat flux and temperature gradient occur in this direction at different times.

In the so-called non-Fourier heat conduction equation a second-order derivative of temperature with respect to time and a

third-order mixed derivative of temperature with respect to space and time will appear. Among the frameworks to study the

non-Fourier heat conduction equation, the dual-phase-lag framework is employed. In this talk, some numerical approaches

for solving the heat conduction equation in various domains are presented.

2000 Mathematics Subject Classification.35K05, 65M70, 65M06, 74K35Key words and phrases.eat conduction equation; Spectral methods, Finite difference methods; Thin film.

348


Fixed Point Of Mappings In Fuzzy 2-Metric Spaces

S. Jahedi, K. Jahedi

Mathematics Department, College of Basic Sciences,

Shiraz University of Technology

P.o.Box 7155-313, Shiraz, Iran

[email protected]

Department of mathematics, Islamic Azad University

Shiraz Branch, Shiraz, Iran

[email protected]

Abstract

Fixed point theory has important applications in approximation theory, game theory, mathematical economics, potential

theory, etc. A number of fixed point theorems have been obtained by various authors in fuzzy metric spaces [1,2,3,4,5]. The

aim of this paper is to dene the notion of different types of a pair of compatible self maps (f, g) in a fuzzy 2-metric space

and prove some common fixed point theorem for them.

References

[1] M. Grabiec, Fixed points in fuzzy metric spaces, Fuzzy sets and systems, 27 (1989) 385-389.

[2] V. Gregori, A. Sapena, On fixed point theorem in fuzzy metric space, Fuzzy sets and systems, 125 (2002) 245-252.

[3] S. N. Mishra, N. Mishra, S. L. Singh, Common fixed point of compatible maps in fuzzy metric space, Fuzzy sets and systems,

115 (2000) 471-45.

[4] V. Pant, R. P. Pant, Fixed points in fuzzy metric space for noncompatible maps, Soochow J. of mathematics, vol.33, 4 (2007)

647-655.

[5] B. Singh, S. Jian, Semi-compatibility, compatibility and fixed point theorems in fuzzy metric space, J. of the Chungcheong

mathematical society, Vol.18, No.1, April 2005.

2000 Mathematics Subject Classification. 47H10, 54H25.Key words and phrases. fuzzy 2-metric space, compatible map, common fixed point.

349


Armijo Rule and Strong Wolfe line search in

Generalized Newton Method

S. Ketabchi*, M. Parandegan** and H. Navidi***

*Department of Mathematics, The University of Guilan, Rasht, Iran

[email protected]

**Department of Mathematics, The University of Guilan, Rasht, Iran

[email protected]

***Department of Applied Mathematics, Shahed University,


[email protected]

Abstract

The line search method is one of the two fundamental strategies to solve unconstrained optimization problem that havebeen developed up to now. The second strategy is trust region method. In the line search method, the success of thealgorithm not only depends on well-chosen search direction but also well-chosen step length.

In this paper we compare the Armijo step size regulation and Strong Wolfe conditions in generalized Newton algorithm

to minimizing a piecewise quadratic convex function. This function arises from dual exterior penalty problem for the

problem of finding normal solution of the system of linear equalities. Numerical experience for systems which are selected

in NETLIB indicates the behavior of the two inexact line searches differs markedly.

2000 Mathematics Subject Classification.90C06, 90C20Key words and phrases.piecewise quadratic programs, generalized Newton method, Armijo rule, Strong Wolfe inexact line search,alternative method

350


Hash Function Based on Chaos

S.M. Hashemiparast*, H. Fallahgoul**

*Department of Mathematics, Faculty of Science, K. N. Toosi University of Technology,

P.O. Box 16765− 165, Tehran, Iran

[email protected]

** Department of Mathematics, Faculty of Science, K. N. Toosi University of Technology,

P.O. Box 16765− 165, Tehran, Iran

[email protected]

Abstract

Data encryption has an important role in communication security, hash function in a kind of encryption of data and the

famous hash functions like SHA, MD4, MD5, WHIRPOOL need a great deal of computations even for the small messages.

There are some other methods based on chaos which are in fact the art of security achievement by encoding the messages to

make them non-readable, the chaos based encryptions are widely extended since last ten years, because of chose relations

between chaos and cryptography and chaotic systems having some properties such as sensitivity to the initial conditions,

and control parameters, and randomized behavior which can be connected with some conventional properties of good ciphers

such as confusion/diffusion, secures the communications[1]. The algorithms are mostly constituted on a linear or nonlinear

mapping [2, 3,] as the random encryptions are performed in this algorithms, the algorithms posses a high level of security.

In this paper we introduce a one-sided hash function algorithm is constructed on exponential scores with a changeable

parameter say p. A section of this function is given, in each run block ciphers encryption procedure produces the parameter

p then the value of hash function is obtained by randomized setting of the first few sequences of iterations. Statistical

analysis and computer simulation indicates a good performance of Hash function and is reliable with high potential.

References[1] Di Xiao, Xiaofeng Liao, Shaojiang Deng. One-way hash function construction based on the chaotic map with changeable parameter,

Chaos, Soliton and Fractals, 24, 65-71, (2005).

[2] A. Meneze, P. Van Orschot and S. Vanstone. Handbook of Applied Cryptography, CRC Press, (1996).

[3] Linhua Zhang, Xiaofeng Lio and Xuebing Wang, An image encryption approach based on chaoticmaps, Soliton and Fractals, 24,

759-765, (2005).

2000 Mathematics Subject Classification.68XXKey words and phrases.Hash Function, Data encryption

351


Different convergences in approximation of evolution

equations

S. Piskarev

Lomonosov Moscow State University, Moscow, Russia

[email protected]

Abstract

Consider the semilinear equation in Banach space Eα

u′(t) = Au(t) + f(u(t)), t ≥ 0,

u(0) = u0 ∈ Eα,(0.1)

where f(·) : Eα ⊆ E → E, 0 ≤ α < 1, is assumed to be continuous, bounded and continuously Frechet differentiablefunction. The problem (0.1) in the neighborhood of the hyperbolic equilibrium can be written in the form

v′(t) = Au∗v(t) + Fu∗ (v(t)), v(0) = v

0, t ≥ 0, (0.2)

where Au∗ = A+f ′(u∗), Fu∗ (v(t)) = f(v(t)+u∗)−f(u∗)−f ′(u∗)v(t). We consider approximation of (0.2) by the followingscheme

Vn(t + τn)− Vn(t)

τn

= Au∗n,nVn(t + τn) + Fu∗n,n(Vn(t)), t = kτn,

with initial data Vn(0) = v0n. The solution of such problem is given by formula

Vn(t + τn) = (In − τnAu∗n,n)−1

Vn(t) + τn(In − τnAu∗n,n)−1

Fu∗n,n(Vn(t)) =

= (In − τnAu∗n,n)−k

Vn(0) + τnΣkj=0(In − τnAu∗n,n)

−(k−j+1)Fu∗n,n(Vn(jτn)), t = kτn,

where Vn(0) = v0n. We consider different kind of consistency of generators under which one can get convergence of solutions

in the vicinity of hyperbolic stationary point.

2000 Mathematics Subject Classification. 65J, 65M, 65N, 35J, 35KKey words and phrases. Abstract differential equations, theory of shadowing, abstract parabolic problem, analytic C0-semigroups,Banach spaces, hyperbolic equilibrium point, semidiscretization, discretization in space, fractional powers of operators, compactconvergence of resolvents*Research was supported by grants of Russian Foundation for Basic Research 07-01-00269, 07-01-92104

352


Using Fractional Factorial Design And Its Application

To Study Of Effective Factors On Amount Of Chest

Drainage By Gomco Suction Pumps After Cardiac

Surgery

S. S. Moghadam1, R. Heidari2, M.Ahadpour3

1 Department Of Industrial Engineering, Shahed University, Tehran, Iran

[email protected]

2 Department Of Industrial Engineering, Shahed University, Tehran, Iran

[email protected]

3 Rajayee Cardiac Hospital, Tehran, Iran

[email protected]

Abstract

Because of the nature Cardiac surgery, the bleeding during and after surgery are inevitable. Chest drainage is the

removal of excess fluid, air, blood, pus, or other secretions from the chest cavity and space surrounding the lung(s). the

accumulated drainage is very dangerous and can stop the heart beat. The amount of chest drainage is depends on some

body factors. These factors, their relation to each other and CD, the amount of their effects are important for experts.

The DOE methods (Design Of Experiment) can solve these problem. Factorial designs are most efficient methods for

experiments involve in the study of the effects of two or more factors. In this paper, we consider fractional factorial design

for an amount of Chest Drainage with Gomco suction pumps after Cardiac Surgery which is a medical pump device that

help doctors to exit patient’s chest drainage with negative pressure. The objective of this problem is examining factors of

the human body that suppose to influence the amount of Chest Drainage ”CD”. There is one response variable for this

problem: amount of chest drainage. The fractional factorial design is applied for this problem and then with the normal

probably plot we determine the significant factors that influence the chest drainage and finally we analysis the main effect

and the relationship between factors and response variable and interaction between factors.

References[1] Montgomery. D.C, (2005), Design and Analysis of Experiments, 6th ed. Wiley.

[2] Boyle, C., Shin, W., (1996). An interactive multiple-response simulation optimization method. IIE Transaction 28, 453-462

[3] Castro M. , Baccan N., Application of factorial design in optimization of preconcentration procedure for copper determination insoft drink by flame atomic absorption spectrometry, Journal of Talanta, 65 (2005), 1264-1269 Bernstein S N (1924) Solution of amathematical problem connected with the theory of heredity, Ann.Sci. de l’Ukraine,1:83- 114.

2000 Mathematics Subject Classification. 62K15 , 94C30, 62B15Key words and phrases. Factorial design, application of design of experiment, Statistical Analysis, health care

353


Improving Energy Relaxation of Hopfield Network

With Augmented Lagrange Multipliers

S. Sathasivam

School of Mathematical Sciences, Universiti Sains Malaysia, Penang, Malaysia

[email protected]

Abstract

The convergence property for energy relaxation of Little-Hopfield neural network using the Augmented Lagrange Mul-

tipliers is shown to be better than using Hebbian learning. This paper proposes a new method, called the Augmented

Lagrange Hopfield method, to improve method of doing logic programming in neural network. In this paper, it has been

proven by computer simulations that the new approach provides good solutions.

2000 Mathematics Subject Classification.Key words and phrases. Little-Hopfield neural networks, Augmented Lagrange Multiplier, logic programming

354


Weakly Continuous modules

S. Shirinkam1,SH. Ghalandarzadeh2,P. Malakooti Rad3

1,3Department of Mathematics, Ph.D. student, K. N. Toosi


[email protected]

2Department of Mathematics, Faculty of Science, K. N. Toosi


Abstract

Let R be a commutative ring with identity and M be an unitary R-module. In this article we investigate the conceptof weakly continuous modules as a natural generalization of weakly continuous rings. M is called weakly continuous ifthe annihilator of each element of M is essential in a summand of R, and M satisfies the C2-condition. Also M is calledF -semiregular if for every x ∈ M , there exists a decomposition M = A ⊕ B such that A is projective, A ≤ Rx andRx ∩ B ≤ F . If M is a module, the following conditions are equivalent for m ∈ M : (1) Ann(m) ⊆ess eR for somee2 = e ∈ R.(2) mR = P ⊕ S where P is projective and S is singular submodule.

M is called ACS module if the above conditions are satisfied for every element m ∈ M . We investigate some equivalentconditions of weakly continuous multiplication modules. An R-module M is a multiplication module if for every submoduleK of M there is an ideal I of R such that K = IM . A submodule N of M is idempotent if (N : M)N = N . Let thefollowing statements:

(1) M is semiregular and J(M) = Z(M).

(2) M is Z(M)− semiregular.

(3) If T is a finitely generated multiplication submodule of M , then T = γ(M) ⊕ S where γ2 = γ and S is a singularsubmodule.

(4) M is a ACS-module and every multiplication projective submodule is a summand.

(5) M is a ACS-module which is also a C2-module.

we prove that (1) =⇒ (2) =⇒ (3) =⇒ (4) =⇒ (5) for projective multiplication faithful modules. Also (5) =⇒ (1) is hold, if

M be a faithful multiplication module in which every cyclic submodule is idempotent.

References[1] W. K. Nicholson, M. F. Yousif, Weakly Continuous and C2-Rings, Comm. Alg. 29(6) (2001) 24292446.

[2] W. K. Nicholson, M. F. Yousif, Quasi-Frobenius Rings, Cambridge University Press (2003).

2000 Mathematics Subject Classification. 13C10, 13C99Key words and phrases. Weakly Continuous Module, Semiregular Submodule

355


New Algorithms Based On The Interior Point Method

For Convex Quadratic Programming

S. Tahmasebzadeh1, H. Navidi2, A. Malek3

1 Department of Applied Mathematics,Tehran, Iran

[email protected]

2 Department of Applied Mathematics,Tehran, Iran

[email protected]

3 Department of Applied Mathematics, Tarbiat Modares University, Tehran, Iran

[email protected]

Abstract

This paper presents three new algorithms for solving convex quadratic programming problems subject to the linear

constraints. These algorithms are based on the general theory of Karmarkar interior points techniques. The first one uses

the Karmarkar idea and linearization of the objective function. The second and third algorithms are modification of the

first algorithm using the Schrijver and Malek-Naseri approaches respectively. These three new schemes are tested against

the algorithm of Kebbiche-Keraghel-Yassine (KKY). It is shown that these three new algorithms are more efficient and

converge to the correct optimal solution, while the KKY algorithm does not converge in some cases. Numerical results are

given to illustrate the performance of the new algorithms.

2000 Mathematics Subject Classification. 90C20, 90C25, 90C51Key words and phrases. Convex quadratic programming, Karmarkar’s algorithm, Schrijver’s algorithm, Malek-Naseri’s algorithm.

356


Cech Homology Groups of Sostak Fuzzy Topological

Spaces

Sadi Bayramov, Cigdem Gunduz (Aras)

1Department of Mathematics, Kafkas University, Kars, 36100-Turkey,

[email protected]

2Department of Mathematics, Kocaeli University, Kocaeli, 41380-Turkey

[email protected]

Abstract

By using the covering of Sostak fuzzy topological spaces, inverse system of simplicial complexes is constituted. Cech

homology groups are defined via of the inverse system. It is proved that Cech homology groups are a functor. Later, axioms

of homology theory are checked for this homology groups. To prove homotopic invariant of homology groups, we give new

homotopy relation in the category of Sostak fuzzy topological spaces.

2000 Mathematics Subject Classification. 54A40, 55U10, 55U40Key words and phrases. Sostak fuzzy topological space; simplicial complexes, homology theory, homotopy relation

357


Convergence To Common Fixed Points For

Asymptotically Nonexpansive Mappings By A Modified

Iteration Process

Safeer Hussain Khan, Mujahid Abbas

Department of Mathematics and Physics, Qatar University

Doha 2713, Qatar


Department of Mathematics, Lahore University of Management Sciences

54792- Lahore, Pakistan

[email protected]

Abstract

We modify an iteration scheme of Agarwal et al to the case of two asymptotically nonexpansive mappings and prove

some weak and strong convergence theoerems. We will also point out that this scheme cannot be used for three mappings

in its existing form. We have to impose an extra condition to get convergence. We will mention the condition and give an

example to show that there exist two nonexpansive mappings satisfying that condition.

2000 Mathematics Subject Classification.47H05, 49M05.Key words and phrases. Asypmtotically nonexpansive mappings, Kadec-Klee property, weak convergence, strong convergence,iteration process.

358


A modified nonlinear conjugate gradient algorithm for

unconstrained optimization

Saman Babaie-Kafaki, Reza Ghanbari, Nezam Mahdavi-Amiri

Sharif University of Technology, Department of Mathematical Sciences,

P.O.Box 11155-9415, Azadi street, Tehran, Iran.

[email protected], [email protected],

[email protected]

Abstract

Conjugate gradient (CG) algorithms have played special roles in solving large scale nonlinear optimization problems

with smooth objective functions f : Rn → R. Search directions in the CG algorithms are generated by the sequence

d1 = −∇f(x1) and dk = −∇f(xk) + βkdk−1, for k ≥ 2. By introducing different conjugacy conditions, researchers

proposed different formulas for βk. The related CG algorithms may have quite different behaviors for general functions.

Recently, Dai and Liao [1] proposed some new formulas for βk based on the standard secant equation. On the basis of the

idea proposed by Dai and Liao, researchers made some efforts to obtain new formulas for βk [2, 4, 5]. Here, we first make

a modification on the secant equation proposed by Zhang and Xu [3], and then, using our modified secant equation and

Dai-Liao’s approach, we propose a new conjugacy condition and obtain a new formula for βk. It can be shown that under

some proper conditions our CG algorithm is globally convergent for general functions. Numerical results showed that our

algorithm is competitive and sometimes preferable to some recently proposed CG algorithms.

References[1] Y.H. Dai and L.Z. Liao, New conjugacy conditions and related nonlinear conjugate gradient methods, Appl. Math. Optim. 43 (2001)

87-101.

[2] H. Yabe and M. Takano, Global convergence properties of nonlinear conjugate gradient methods with modified secant condition,Comput. Optim. Appl. 28 (2004) 203-225.

[3] J.Z. Zhang and C.X. Xu, Properties and numerical performance of quasi-Newton methods with modified quasi-Newton equation, J.Comp. Appl. Math. 137 (2001) 269-278.

[4] W. Zhou and L. Zhang, A nonlinear conjugate gradient method based on the MBFGS secant condition, Optim. Meth. Soft. 21(5)(2006) 707-714.

[5] G. Li, C. Tang and Z. Wei, New conjugacy condition and related new conjugate gradient methods for unconstrained optimization,

J. Comput. Appl. Math. 202(2) (2007) 523-539.

2000 Mathematics Subject Classification.90C30, 65K05Key words and phrases.Unconstrained optimization, Nonlinear conjugate gradient algorithm, Secant equation.**This research was supported by Research Council of Sharif University of Technology.

359


Claims Validation System Fuzzy Approach

Sanjeev Kumar 1, Pooja Pathak2

1 Dept. of Mathematics, Dr. B. R. Ambedkar University, IBS, Khandhari,

Agra 282002, India

[email protected]

2 GLA Institute of technology and Management, Dept. of Applied Sciences

Mathura, India

[email protected]

Abstract

The markets are dynamically changing with changing consumer behavior. End users in all sectors, be it product or

service find themselves empowered with wide range of options available to them. And therefore in today’s world nothing

exists like monopoly. Insurance today is not what it used to be decade ago. It has evolved now, where consumers are more

concerned about the quality, customer handling, transparent and easy process and proactive value added customer service.

Insurance claim settlement process tops the priority list of all policy holders. From insurance company perspective, it is one

of the most tedious business processes which directly impacts profit margins, policy holder satisfaction and business growth

in turn. In order to reduce turnaround time of claim settlements besides settling the claim, claims needs to be verified

and validated. Till now it is ensured by human adjusters and this process makes claim settlement vulnerable to subjective

judgment and the use of discretion while finalizing a claim. Trends show adjusters get biased to claimants and settle claims

in their favor and impact monetary gains of insurers, to counter this growing trend and limiting cost on human expertise,

companies are in need of reliable expert systems that can help them in validating or authenticating processed claims. This

work presents a model (of Claims Validation System) which is designed by using fuzzy mathematics and expert system.

This model will provide indicative result on the authenticity of claim in process and the result from this system will also

help Auditors during settlement process. The methodology is also supported with the help of an example.

References[1] Bellman, R. and Giertz, M. (1973), On the analytic formalism of the theory of fuzzy sets,Information Sciences, Vol. 5, pp. 149-56.

[2] Bezdek, J.C. (1981), Pattern Recognition with Fuzzy Objective Function Algorithms, Plenum Press,New York, NY.

[3] Brockett, P.L., Xia, X. and Derrig, R. (1995), Using Kohonens self organizing feature map to uncover automobile bodily injuryclaims fraud, paper presented at Special Actuarial Seminar. Automobile Insurers Bureau. Boston, MA, 25 January.

[4] Brockett, P.L., Xia, X. and Derrig, R. (1998), Using Kohonens self organizing feature map to uncover automobile bodily injuryclaims fraud, The Journal of Risk and Insurance, Vol. 65 No. 2, pp. 245-74.

[5] Brockett, P.L., Derrig, R., Golden, L., Levine, A. and Alpert, M. (2002), Fraud classification using principal component analysis ofRIDITs, The Journal of Risk and Insurance, Vol. 69 No. 3,pp. 341-71.

[6] Crocker, K.J. and Tennyson, S. (2002), Insurance fraud and optimal claims settlement strategies, Journal of Law and Economics,Vol. 45 No. 2, pp. 469-507

[7] Deshmukh, A. and Lakshminarayana, T. (1998), A rule-based fuzzy reasoning system for assessing the risk of management fraud,International Journal of Intelligent Systems in Accounting, Finance & Management, Vol. 4, pp. 231-41.

[8] Derrig, R. and Ostaszewski, K. (1995), Fuzzy techniques of pattern recognition in risk and claim classification, The Journal of Riskand Insurance, Vol. 62 No. 3, pp. 447-82

[9] Fanning, K.M. and Cogger, K.O. (1998), Neural network detection of management fraud using published financial data, InternationalJournal of Intelligent Systems in Accounting, Finance & Management, Vol. 7 No. 1, pp. 21-41.

[10] Jagdish Pathak(2005) A fuzzy-based algorithm for auditors to detect elements of fraud in settled insurance claims, ManagerialAuditing Journal Vol. 20 No. 6, 2005 pp. 632-644

[11] Ross, T.J. (1997), Fuzzy Logic With Engineering Applications, McGraw-Hill, Singapore.

[12] Zadeh, L.A. (1965), Fuzzy sets, Information and Control, Vol. 8, pp. 338-53.

[13] Zyl, S.V. (2003), Canadian P/C insurers in intensive care?, National Underwriter, Vol. 107 No. 22,pp. 30-1.

2000 Mathematics Subject Classification. 03B52.Key words and phrases. Fuzzy logic, Insurance, Inference system, Claim validation, MATLAB.

360


An algorithm for solving the fractional Burgers

equations

Selin Sarıaydın1, Ahmet Yıldırım2

1,2Department of Mathematics, Science Faculty,

Ege University, 35100 Bornova-Izmir, Turkey

[email protected]

Abstract

In this paper, a scheme is developed to study numerical solution of the space- and time fractional Burgers equations with

initial conditions by the homotopy perturbation method (HPM). The fractional derivatives are considered in the Caputo

sense. The solutions are given in the form of series with easily computable terms. Numerical solutions are calculated for

the fractional Burgers equation to show the nature of solution as the fractional derivative parameter is changed.

2000 Mathematics Subject Classification.35C10Key words and phrases. Caputo sense, Fractional calculus, Time- and space- fractional Burgers equation, Homotopy perturbationmethod.

361


On Generalized Paranormed Statistically Convergent

Sequence Spaces Defined By Orlicz Function

Selma Altundag, Metin Basarır

Sakarya Univ. Department of Math. 54100 Sakarya, Turkey

[email protected]

Sakarya Univ. Department of Math. 54100 Sakarya, Turkey

basarı[email protected]

Abstract

In this paper, we define generalized paranormed sequence spaces −c(σ, M, p, q, s), −c0(σ, M, p, q, s), m(σ, M, p, q, s)

and m0(σ, M, p, q, s) defined over a seminormed sequence space (X, q).We establish some inclusion relations between these

spaces under some conditions.

References[1] G. G. Lorentz, A contribution to the theory of divergent sequences, Acta Math., 80 (1948), 167-190.

[2] I. J. Maddox, Spaces of strongly summable sequences, Quart. J. Math., 18 (1967), 345-355.

[3] P. Schaefer, Infinite matrices and invariant means, Proc. Amer. Math. Soc., 36 (1972), 104-110.

[4] Mursaleen, Invariant means and some matrix transformations, Tamkang J. Math., 10 (1979),183-188.

[5] H. Fast, Sur la convergence statistique, Colloq. Math., 2 (1951), 241-244.

[6] E. Savas, Strongly almost convergent sequences defined by Orlicz functions, Comm. Appl. Analy. 4 (4) (2000), 453-458.

[7] J. Lindenstrauss and L. Tzafriri, On Orlicz sequence spaces, Israel Jour. Math., 10 (1971), 379-390.

[8] I. J. Maddox, Paranormed sequence spaces generated by infinite matrices, Proc. Camb. Phil. Soc., 64 (1968), 335-340.

[9] I. J. Maddox, Statistical convergence in locally convex spaces, Math. Proc. Camb. Phil. Soc., 104 (1988), 141-145.

[10] B. C. Tripathy and M. Sen, On generalized statistically convergent sequence spaces, Indian J. Pure Appl. Math., 32:11 (2001),1689-1694.

[11] B. C. Tripathy, On generalized difference paranormed statistically convergent sequences, Indian J. Pure Appl. Math., 35:5 (2004),655-663.

[12] I. J. Maddox, Sequence spaces defined y a modulus, Math. Proc. Cambridge Philos. Soc., 100 (1986), 161-166.

[13] S. D. Parashar, B. Choudhary, Sequence spaces defined by Orlicz functions, Indian J. Pure Appl. Math., 25 (4) (1994), 419-428.

[14] M. A. Krasnoselskii, Y. B. Rutitsky, Convex Function and Orlicz Spaces, Noordhoff, Groningen, 1961.

[15] H. Nakano, Modular sequence spaces, Proc. Japan Acad., 27 (1951), 508-512.

[16] P. K. Kampthan and M. Gupta, Sequence spaces and Series, Marcel Dekkar, 1980.

2000 Mathematics Subject Classification. 40A05,46A45Key words and phrases. Seminorm, paranorm, statistical convergence, invariant means.

362


General Weyl-Heisenberg Frames

Shahram Banaei, Vahid Aghapouramin

Department of Mathematics, Islamic Azad University of Bonab

Laleh, Bonab, Iran

sh [email protected],vah [email protected]

Abstract

Every function f ∈ L2(R) can be written as an infinite linear combination of translates and modulates versions of the

fixed function g ∈ L2(R)as Weyl-Heisenberg (W-H)frames (EmbTnag)m,n∈Z = (e2πimb(0)g(0 − na))m,n∈Z . For a sharp

signal f we needed many coefficients of W-H frames to reconstruction f as a superposition of translation and modulation.

Now in the present paper we introduce the general W-H frame as the translates, dilation and modulates versions of the

fixed function g ∈ L2(R). We find sufficient condition for (EmbDkcTnag)m,k,n∈Z to be a frame for L2(R).

References[1] P.G. Casazza, The art of frame theory, Taiwanese J. of Math. 4 (2000), 129-201.

[2] O. Christensen, An Introduction to Frames and Riesz Bases, Birkhauser, 2002.

2000 Mathematics Subject Classification.Key words and phrases. Frame, Frame sequence, Averaging frame, W-H frame.

363


Necessary conditions for singular controls in systems

with nonlocal boundary conditions

Sharifov Ya. A., Mamedova M.B.

Baku State University

Department Applied Mathematics and Cybernetics

AZ1148, Z.Khalilov 23, Baku, Azerbaijan

[email protected]

Abstract

Let it be required to minimize the functional:

J(u) = ϕ(x(t0), x(t2)) (0.1)

on the restrictions:x = f(x, u, t), t ∈ T = [t0, t1], (0.2)

Ax(t0) +

∫

T

h(t)x(t)dt + Bx(t1) = c, (0.3)

u(t) ∈ V ∈ Rr, t ∈ T (0.4)

The given functions ϕ ∈ R1, f ∈ Rnare supposed to be continuous by the collection of arguments and have continuoussecond derivatives with respect to x and x, y; c ∈ Rn×1; A, B, h(t) ∈ Rn×n are given matrices, V ∈ Rris an open set.

Firs constructive sufficient conditions for existence and uniqueness of the solution for boundary problem (2)-(3) arefound.

The formula of second order increment of functional (1) is calculated. The necessary condition of optimality for singular

controls in classic sense is obtained in optimal control problem (1)-(4) on the basis of control variation.

2000 Mathematics Subject Classification. primary: 49J15; secondaries: 49K15, 34B10Key words and phrases. optimal control, boundary value problem, necessary condition of optimality

364


Why Magnetic Monopoles Are Not Seen?

Siamak Khademi

Department of Physics, 6th Km of Tabriz Road, Zanjan University, Zanjan-Iran

[email protected]

Abstract

Dual symmetry of Maxwell’s equations predicts the existence of magnetic monopoles which are not detected until

now. As an important consequence of this prediction, the quantization of electric charge is obtained by P.A.M. Dirac. In

this paper I show the uncertainty in the phase space quantum mechanics could be the responsible of the non-visibility of

magnetic monopoles.

2000 Mathematics Subject Classification. 81V10Key words and phrases. Magnetic Monopoles, Uncertainty, Phase Space Quantum Mechanics, Charge Quantization

365


Modelling The Effect Of Vaccination Policy On

Epidemics With Time Delay

Sumit Kumar Banerjee

Department of Mathematics & Statistics Caledonian College Of Engineering

[email protected] , dr [email protected]

Abstract

The spread of communicable diseases depends on rate of transmission or contact rate , removal rate , mode of transmis-sion , latent and incubation period , age - specific susceptibility and immunity of individuals to the disease . The immunityto the specific disease in the individuals can be artificially developed with the help of vaccination . It is understood thatthe vaccination leads to complete protection and vaccinated individuals are immune but this is not true and in generalvaccination only leads to partial protection . The role of latent period in the dynamics of communicable diseases is alsoan important factor and should be considered in the epidemic models . Further , while studying age-structured epidemicmodels, maturation period should also be considered in the model, because in the case of several infectious diseases thepopulations of certain Age - groups are immune from diseases for some finite period and after that they become susceptible.

In view of the above , therefore , in this paper a delay epidemic model has been studied to investigate the effect of age

- based vaccination policy on the dynamics of a communicable disease incorporating latent period and maturation delay .

For the model , the disease- free and endemic equilibrium points have been obtained and their local and global stability

analysis have been carried out.

2000 Mathematics Subject Classification.Key words and phrases. Incubation period, Immunity, Maturation delay, Global Stability

366


Algebraic Method Applied To Solving Inversion

Problem Of Single Layered Rigid Pavements

T. Akhlaghi

Islamic Azad University-Salmas Branch, Jomhori Islami Boulevard,

PO Box 58815-386, Salmas, Iran

touhid [email protected]

Abstract

Surface waves can be used to determine the mechanical and physical properties of the materials of a layered structuresuch as soil sites and highway pavements. The elastic properties and thicknesses of the component materials are derivedfrom measurements of the frequency and the phase velocity of vibrations generated along the surface of the ground. Thephase velocity is not constant, but varies with the frequency, enabling an experimental dispersion curve of the system to beplotted. The experimental dispersion data is then used to back calculate the unknown parameters of the system throughan inversion process by employing one of the available inverse methods.

For many years, the numerical inverse procedure has been extensively used for determination of the layers moduli andthicknesses of a layered structure. However, this technique is complex, time consuming and requires experienced personand engineering judgment. Ideally, the inverse should be obtained by means of a true mathematical inverse. The frequencyequation for the system is expanded as a polynomial, and is solved for the unknown parameters of the system. In thisresearch a direct symbolic solution for determination of the thickness of a free plate model, using ”Mathematica” computersoftware, has been developed. It is used to calculate the thickness of the uniform free plate corresponding with pairs ofthe values of phase velocity and frequency as data. The wave propagation in elastic plates is analogous to propagation inlayered spaces and therefore the free plate system can be used to model the surface layer of a single layered rigid pavementstructure. Single layered rigid pavements are extensively and increasingly used in highways and airport runways. Thecharacteristic equation of the system which corresponds with surface waves can be represented by power series. By makingpower series, the equation is expanded symbolically in terms of the layer thickness parameter. Inverse series performsreversion of the series, which gives a series for the inverse of the function. The normal expression now is a polynomialrepresenting the thickness of the surface layer in terms of the velocities of waves in the surface layer and of the measuredvalues of the frequency and the corresponding phase velocity. The frequency and the phase velocity are obtained from theresults of the measurements made in the field on the ground surface of the structure.

In order to evaluate the effectiveness and reliability of the proposed technique, the application of the method to anumber of published set of data obtained in the field has been investigated and assessed. The comparison between theexperimental results and the developed algebraic solutions show very good agreement, indicating that the proposed methodcan be used as an economic and effective technique to determine the thickness of the rigid pavements surface layer.

2000 Mathematics Subject Classification. 86A22, 65Z05Key words and phrases. Algebraic solution, inversion problem

367


Trapezoidal Fuzzy Data In Possibility Linear Regression

Analysis

T. Razzaghnia

Department of Statistics, Islamic Azad University, Roudehen Branch, Tehran, Iran

t [email protected]

Abstract

Fuzzy linear regression was proposed by Tanaka et al. [3] in 1982. Many different fuzzy regression approaches havebeen proposed by different researchers since then [1],[2] and also this subject has drawn much attention from more and

more people concerned.and more people concerned. A fuzzy number A is a convex normalized fuzzy subset of the real lineR with an upper semi-continuous membership function of bounded support.

Definition: A symmetric fuzzy numberA, denoted by A = (α, c)L is defined as A = L((x− α)/c),c > 0,Where α and

c are the center and spread of A and L(x) is a shape function of fuzzy numbers. A fuzzy regression analysis results in the

following regression model: ˆY = A0Xi0 + A1Xi1 + . . . + ApXip = AXi i = 1, 2, . . . , n.In this paper, we aim to extended the constraints of Tanaka’s [3] model. Applied coefficients of the fuzzy regression

by them is the symmetric triangular fuzzy numbers, while we try to replace it by more general asymmetric trapezoidalone. Possibility of two asymmetric trapezoidal fuzzy numbers is explained by possibility distribution. Two different modelsis presented and a numerical example is given in order to compare the proposed models with previous one. Error valuesshows advantage of the presented models with respect to constraints of Tanaka’s model. For the possibility distributionwith asymmetric trapezoidal fuzzy numbers, we prove the following theorem.

Theorem: IfA = (a(1), a(2), a(2), a(3)) and B = (b(1), b(2), b(2), b(3)) ,then

POS(A = B) =

L( a(2)−b(2)

[a(2)−a(1)]+[b(3)−b(2)]) a(2) ≥ b(2)

L( a(2)−b(2)

[a(3)−a(2)]+[b(2)−b(1)]) a(2) ≤ b(2)

L( a(2)−b(2)

[a(2)−a(1)]+[b(2)−b(1)]o.w

References[1] T. Razzaghnia, E. Pasha, A New Mathematical programming approach in fuzzy linear regression models, J.Sci.I.A.U, vol.18, No.70/2

(2009) 50-59.

[2] T. Razzaghnia , E. Pasha, T. Allahviranloo, Fuzzy linear regression models with fuzzy entropy, Applied Mathematical Sciences, Vol1, No. 35, (2007)1715-1724.

[3] H. Tanaka, S. Uejima and K. Asia, ”Linear regression analysis with fuzzy model” IEEE Transactions on Systems, Man, and Cyber-netics. Vol. 12(1982 ) 903-907.

2000 Mathematics Subject Classification. 90C70Key words and phrases. Trapezoidal fuzzy numbers, Fuzzy linear regression, Possibility distribution, Mathematical programming

368


The k-ε Model in Turbulence

Tanfer Tanrıverdi

Harran University, Faculty of Arts and Sciences,

Department of Mathematics, Sanlurfa 63300, Turkey

[email protected]

Abstract

We prove analytically the existence of self-similar solutions for the k-ε model arising in the evolution of turbulent bursts

by employing a topological shooting technique where α > β with different conditions.

2000 Mathematics Subject Classification.76F60Key words and phrases. k-ε modeling*The author was supported by the Scientific and Technological Research Council of Turkey (TUBITAK).**He is also thankful to the Oxford Center for Nonlinear PDE, and to the Mathematical Institute of the University of Oxford,for the hospitality they offered him during his visit.

369


Trapezoidal approximation based on middle of maxima

and middle of support

Tayebeh Hajjari

Firuz Kuh Branch of Islamic Azad University,

Department of Mathematics, Firuz Kuh, Iran

[email protected]

Abstract

In many fuzzy logic applications, the calculations strongly depend on the fuzzy number membership functions. Less

regular membership functions lead to calculations that are more complicated. A natural need is to approximate fuzzy num-

bers with the simpler shapes which are easy to handle and have natural interpretations. Since one can easily propose many

other approximation methods, a natural question arises: how to construct a good approximation operator? Defuzzification

methods have been widely studied for some years and were applied to fuzzy expert system. The major idea behind these

methods was to obtain a typical value from a given fuzzy set according to some specified characters. In other words, each

defuzzification method provides a correspondence from the set of all fuzzy sets into the set of real numbers. Obviously, in

defuzzification methods that replace a fuzzy set by a single number, we generally loose too much important information.

The aforementioned explanation shows that the trapezoidal approximation of a fuzzy number is meaningful topic. Since

trapezoidal approximation could be also performed in many ways, there are a number of criteria such as translation invari-

ance, scale invariance, identity which the approximation operator should or just can possess. In this paper, we introduce a

trapezoidal approximation of an arbitrary fuzzy number, which preserves its the middle of maxima and middle of support.

The operator is called trapezoidal approximation based on middle of maxima and middle of support. In case that the middle

of maxima and middle of support are identical the trapezoidal approximation is symmetric. We then discuss properties

of the approximation strategy including translation invariance, scale invariance and identity. The advantage is that the

presented method is simpler than other methods computationally. The method is illustrated by some numerical examples.

References[1] S. Abbasbandy and B. Asady, The nearest trapezoidal fuzzy number to a fuzzy quantity, Appl. Math. Comput. 156 (2004) 381-386.

[2] S. Abbasbandy and T. Hajjari, A new approach for ranking of trapezoidal fuzzy numbers, Comput. Math. Appl., 57 (2009) 413-419.

[3] A. Ban, Approximation of fuzzy numbers by trapezoidal fuzzy numbers preserving the expected interval, Fuzzy Sets Syst. 159 (2008)755-756.

[4] C.T. Yeh, On improving trapezoidal and triangular approximations of fuzzy numbers, Internat. J. Approx. Reason. 48 (2008) 297-313.

2000 Mathematics Subject Classification. 93C42Key words and phrases. Approximation, Core, Fuzzy number, Trapezoidal fuzzy number, Support*The author is most grateful to Prof. S. Abbasbandy for his valuable comments and suggestions.

370


Frobenius Q-Groups and 2-Transitive Frobenius

Q-Groups

Temha Erkoc1 , Erhan Guzel2

1 Istanbul University, Faculty of Science, Department of Mathematics, Istanbul, Turkey

[email protected]

2 Istanbul University, Faculty of Science, Department of Mathematics, Istanbul, Turkey

[email protected]

Abstract

A finite group whose complex characters are rationally-valued is called a Q-group. For example, all of the symmetric

groups and finite elemantary abelian 2-groups are Q-groups. The property of being a Q-group is characterized by saying

that the generators of every cyclic subgroup are conjugate. Depending upon the group, by using this characterization, it

may be easier to say that the group is a Q-group or not. Kletzing’s lecture notes present a detailed investigation into the

structure of Q-groups. In group theory, general classification of Q-groups has not been able to be done up to now, but some

special Q- groups have been classified. In this study, we find the structure of Frobenius Q-groups with a new proof and all

2-transitive Frobenius Q-groups.

References[1] M.R. Darafsheh, H. Sharifi, Frobenius Q-Groups, Arch. Math. 83, 102-105, (2004)

[2] D. Kletzing, Structure and Representations of -groups, Springer -Verlag Berlin-Heidelberg New York Tokyo, 3-540-13865-X, (1984)

2000 Mathematics Subject Classification. 20C15Key words and phrases. Frobenius groups, rational groups.

371


Order Norm Completion of Cone Metric Spaces

Thabet Abdeljawad

Department of Mathematics and Computer Science

Cankaya University, 06530 Ankara, Turkey

[email protected]

Abstract

In this paper a completion theorem for cone metric spaces and a completion theorem for cone normed spaces are proved.

The completion spaces are constructed by means of an equivalence relation defined via an ordered cone norm on the Banach

space E whose cone is strongly minihedral and ordered closed. This order norm has to satisfy the generalized absolute

value property. In particular if E is a Dedekind complete Banach lattice then together with its absolute value norm they

satisfy the desired properties.

References[1] L-G Huang and X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl. 323 (2007),

1468–1476.

[2] Sh. Rezapour and R. Hamlbarani, Some notes on the paper ”Cone metric spaces and fixed point theorems of contractive mappings”J.Math. Anal. Appl. 345, 2 (2008) 719-724.

2000 Mathematics Subject Classification.Key words and phrases. Cone metric space, cone norm space, strongly minihedral,cone isometry, absolute value preoperty

372


Stability, bifurcations and non-linear eigenvalue

problems in physics

Todor L. Boyadjiev

Faculty of Mathematics and Informatics

Sofia University “St. Kl. Ohridski”, Sofia, Bulgaria

[email protected]

Bogoliubov Laboratory of Theoretical Physics

Joint Institute for Nuclear Research, Dubna, Russia

[email protected]

Abstract

A major number of physics problems related to the study of the stability of solutions of differential equations can be

interpreted as nonlinear eigenvalue problems. In this study we offer an effective numerical method for solving such problems.

This method is based on the continuous analog of Newton’s method. The linearized equations occurring at every iteration

are solved using a spline-collocation scheme. Concrete examples of applying the method to various physical problems are

demonstrated.

2000 Mathematics Subject Classification. primary: 65L07, 65L15; secondaries: 65Z05Key words and phrases. Stability, bifurcations, Newton method, Josephson junctions*This research was partially supported by grant No 39/2009, Sofia University Scientific foundation, Bulgaria

373


The properties of fuzzy submodules of a R-module and

their radicals

V. Aghapouramin

1 Islamic Azad University of Bonab, Department of Mathematics, Bonab, Iran

vah [email protected]

Abstract

In this paper we show that properties of fuzzy submodule of a Rmodule and their radicals(R is a commutative ring

with identity)connected with fuzzy quotient modules and radical of a fuzzy submodules, characterization of notherian and

artinian modules in terms of the set of values of fuzzy submodules.

References[1] W.j.Liu, fuzzy in variant subgroups and fuzzy ideals, fuzzy sets and systems , 8(1982),133-139.

[2] A.rosen feld,fuzzy groups.j.math.anal.appl.35(1971).512-51.

2000 Mathematics Subject Classification.Key words and phrases. fuzzy submodules,commutative ring ,notherian and artinian modules.

374


Analytical Solution Of The Heat Conduction Equation

In One-Dimensional Spherical Coordinates At

Nanoscale

V. Mohammadi-Fakhar*, S. H. Momeni-Masuleh**

*Department of Mathematics, Shahed University, Tehran,

P. O. Box 18151-159, Iran.

[email protected]


P. O. Box 18151-159, Iran.

[email protected]

Abstract

Heat conduction equation at microscale has been widely applied to thermal analysis of thin metal films. The microscopic

heat flux equation developed from physical and mathematical reasoning is different from the traditional heat equation. Here

a second-order derivative of temperature with respect to time and a third-order mixed derivative of temperature with respect

to space and time will appear in the heat equation. An approximate analytical solution to the non-Fourier heat conduction

equation in one-dimensional spherical coordinates based on the dual-phase-lag framework is obtained by employing the

Adomian decomposition method (ADM). The application of ADM to partial differential equations, when the exact solution

is not reached or existed, demands the use of truncated series. The major reduction in computational effort associated with

the ADM is the main factor behind their popularity while other numerical methods require extensive computation. The

ADM does not discretize variables and gives an analytical solution in the form of truncated series. If there are nonlinear

factors in an equation, ADM gives the analytical solution without any need for linearization. In this presentation, the

reliability and efficiency of the solution were verified using the ADM.

2000 Mathematics Subject Classification. 65M99, 35K05, 35C10, 74K35.Key words and phrases.Adomian decomposition; heat conduction equation; nanoscale; spherical coordinates.

375


On the symmetry of Hamiltonian systems

V.G. Gupta*, P. Sharma**

*Department of Mathematics, University of Rajasthan,302004 Jaipur, India

[email protected]

**Department of Mathematics, University of Rajasthan, 302004 Jaipur, India

[email protected]

Abstract

In this paper, we use the formalism of Hamiltonian system on symplectic manifold due to Reeb[2] given in Abraham

and Marsden[6] and Arnold[7] to derive the equation of motion for (1) A particle on a line in a plane with a spring force

and (2) A free particle in n-space. The time flows for both the problems mentioned above are also determined and proved

that the determined flow is a Hamiltonian flow, i.e., the symmetry of a Hamiltonian system. A non-Hamiltonian flow is

also considered and it is shown that by changing the symplectic form and the phase space of the system we can convert it

into a Hamiltonian flow. The translation and rotational symmetry related to linear and angular momentum respectively

for the motion of a free particle in n-space is also considered, which is useful in reducing the phase space of a mechanical

system.

References[1] E. Cartan, Lecons sur les Invariants integraux. Hermann, Paris (1922).

[2] G. Reeb, Varietes symplectiques, Varietes Presque-Complexes et systemes dynamiques. C.R. Acad. Sci. Paris (1952) 235 : 776-778.

[3] G.F. Simmons, Differential Equations with Applications and Historical Notes, Second Edition, McGraw Hill, Inc., New York (1991).

[4] J. E. Marsden, and T. S. Ratiu, Introduction to Mechanics and Symmetry, Second Edition, Springer-Verlag, New York (1999).

[5] M. Artin, Algebra, Prentice Hall, Upper Saddle River, New Jersey (1991).

[6] R. Abraham, and J. Marsden, Foundations of Mechanics, Second Edition, Addison-Wesley, Reading, MA (1978).

[7] V.I. Arnold, Mathematical Methods of Classical Mechanics, Second Edition, Springer-Verlag, New York (1989).

2000 Mathematics Subject Classification. 37N05, 63D05Key words and phrases. Hamiltonian System, Symplectic manifold, Lie-Group Action, Hamiltonian Flow.

376


Solving Singular Initial Value Problems of

Emden-Fowler and Lane-Emden Type

V.G. Gupta*, P. Sharma**

*Department of Mathematics, University of Rajasthan,302004 Jaipur, India

[email protected]

**Department of Mathematics, University of Rajasthan, 302004 Jaipur, India

[email protected]

Abstract

In this paper, Singular initial value problems are investigated by using Taylor series method. The solutions are con-

structed in the form of a convergent series. The method is applied to Emden-Fowler and Lane-Emden equations.

References[1] S. Chandrasekhar, Introduction to the study of stellar structure, Dover, New York, (1967).

[2] H.T. Davis, Introduction to Nonlinear Differential and Integral equations, Dover, New York, (1962).

[3] N.T. Shawagfeh, Nonperturbative approximate solution for Lane-Emden equation, J. Math.Phys.,34 : (1993) 4364-4369.

[4] G. Adomian, Nonlinear stochastic operator equation, Academic Press, San Diego, CA (1968).

[5] A.M. Wazwaz, A new algorithm for solving differential equations of Lane-Emden type. Applied Math. Comput., 118 : (2001) 287-310.

[6] R.D. Russell, L.F. Shampine, Numerical method for singular boundary value problem, SIAM J.Numer. Anal., 12: (1975) 13-36.

[7] ] M.M. Chawla, C.P. Katti, A finite-difference method for a class of singular boundary-value problem, IMA. J. Numer. Anal., 4(1984) 457-466.

[8] M.M. Chawla, S. Mckee, G. Shaw, Order method for singular two point boundary value problem,BIT., 26 (1986) 318-326.

[9] S.R.K. Iyengar, P. Jain, Spline difference method for singular two-point Boundary-value problems, Numer. Math., 50 : (1987)363-376.

[10] R.K. Jain, P. Jain, Finite difference for a class of singular two-point boundary-value problems,Int. J. Comput. Math., 27 (1989)113-120.

[11] S.M. El-sayed, Multi-integral method for nonlinear boundary-value problems: A fourth order method for a singular two pointboundary value problem, Int. J. Comput. Math., 71 (1999) 259-265.

[12] Y.Q. Hasan, L.M. Zhu, Solving singular initial value problems in the second-order ordinary differential equations, J. of AppliedSciences, 7(17): (2007) 2505-2508.

[13] V.S. Erturk, Differential Transformation method for solving differential equations of Lane-Emden type, Mathematical and comp.Appl., 12(3): (2007) 135-139.

[14] M.S.H. Chowdhury, I. Hashim, Solutions of Emden-Fowler equations by homotopy-perturbation method, Nonlinear Analysis: RealWorld Applications 10 (2009) 104-115.

[15] A.M. Wazwaz, Adomian decomposition method for a reliable treatment of the Emden-Fowler equation, Appl. Math. Comput. 166

(2005) 638-651.

2000 Mathematics Subject Classification.34B15, 34B16Key words and phrases.Taylor series method, Emden-Fowler equation, Lane-Emden equation*This presentation was supported by DST, INDIA

377


Some Spectral Propersties Of Linear Operators In Umd

Spaces And Applications

Veli B. Shakhmurov

Okan University

Department of Electronics Engineering and Communication,

Akfirat, Tuzla 34959 Istanbul, Turkey

[email protected]

Abstract

In this paper the general spectral properties of linear operators in Banach spaces are studied. We find sufficientconditions on structure of Banach spaces and resolvent properties that guarantee completeness of roots elements of Schattenclass operators. It is generalizes the well known result for linear operators in Hilbert spaces (see [1], Theorem XI. 6.29 ).The main result is:

Theorem1. Let the following conditions hold:(1) E is a Banach space with base satisfying the Parsewall condition and A is an operator in σp (E), p ∈ (1,∞) ;(2) γ1, γ2, ..., γs is non overlapping, differentiable arcs in the complex plane starting at the origin. Suppose that each

of the s regions into which the plans is divided by these arcs is contained in an angular sector of opening less then πp ;

(3) m > 0 is an integer so that the resolvent of A satisfies the inequality

‖R (λ, A)‖ = O(|λ|−m

)(0.1)

as λ → 0 along any of the arcs γi. Then the subspace spA contains the subspace AmE.In applications the nonloca BVPs for the degenerate abstract equation of second order with variable coefficients

(L + λ) u = a (x) u[2]

(x) + B (x) u[1]

(x) + Aλ (x) u (x) = f (x) , x ∈ (0, 1) (0.2)

Lku =

mk∑

i=0

αkiu

[i](0) + βkiu

(i)(1) +

Nk∑

j=1

δkju[i]

(xkj)

= 0, k = 1, 2, (0.3)

is studied, where u[i] =(xγ d

dt

)iu (x) , Aλ = A + λ, A = A (x) , B = B (x) are linear operators in a Banach space E,

a = a (x) is a complex valued function, αki, βki, δkj are complex numbers, xkj ∈ (0, 1) and λ is a spectral parameter.The principal part of the appropriate differential operator Q is not self-adjoint. The discreetness of spectrum and

completeness of root elements of this operator is obtained.Let I = I (E (A) , E) denote the embedding operator from E (A) to E and sj (I (E (A) , E)) denote the approximation

numbers of the operator I. Let C be a set of complex numbers and

Sϕ = ξ; ξ ∈ C, |arg ξ| ≤ ϕ ,0 ≤ ϕ < π. (0.4)

Theorem 2. Let the following conditions be satisfied:(1) E is an UMD space with base;

(2) A is an R-positive in E with ϕ ∈ [0 π) , A (x) A−1 (x) ∈ C ([0, 1] ; L (E)) , x ∈ (0, 1) and BA

(12−µ

)∈ L∞ (0, 1; B (E))

for 0 < µ < 12 ,

∣∣αkmk

∣∣ +∣∣βkmk

∣∣ > 0;

(3) −a ∈ S (ϕ1) ∩C/R−, a 6= 0, η (x) 6= 0, 0 ≤ ϕ1 < π, λ ∈ S (ϕ2) , ϕ1 + ϕ2 < ϕ, 0 ≤ γ < 1− 1p ;

(4)

sj (I (E (A) , E)) ∼ j− 1

ν , j = 1, 2, ...,∞, ν > 0. (0.5)

Then;(a)

sj

((Q + λ)

−1(Lp (0, 1; E))

)∼ j

− 22ν+1 (0.6)

(b) the system of root functions of differential operator Q is complete in Lp (0, 1; E) .

References[1] Dunford N., Schwartz J. T., Linear operators. Parts 2. Spectral theory, Interscience, New York, 1963.

2000 Mathematics Subject Classification. 34G10, 34B10, 35J25Key words and phrases. Uniformly convex Banach spaces; Abstract functions; Schatten class of operators; Completeness of rootelements; Separable boundary value problems; Differential-operator equations

378


The Metallic Means Family (MMF)

Vera W. de Spinadel

Laboratory of Mathematics & Design Faculty of Architecture,

Design and Urban Planning University of Buenos Aires

Buenos Aires, Argentina

[email protected]

Abstract

The main purpose of this presentation is to introduce a new family of quadratic irrational numbers. This family wasintroduced by the author in 1997 as the Metallic Means Family (MMF). Its more prominent member is the well knownGolden Mean . Among its relatives, let us mention the Silver Mean, the Bronze Mean, the Copper Mean, the Nickel Mean,etc. They are a family because, aside from carrying the name of a metal, they enjoy common mathematical properties. Forexample, they are subdivided into two subfamilies:

a) the subfamily of the positive irrational numbers that have a purely periodic continued fraction expansionsb) the subfamily which members have a periodic continued fraction expansion.The members of the first subfamily are fundamental in the actual research on the stability of micro- and macro-physical

systems, going from the DNA internal structure to the astronomical galaxies. The main results of this new research are:1) The members of the MMF intervene in the determination of the quasiperiodical behavior of non linear dynamical

systems, being therefore an invaluable key in the search of universal ways on the roads to chaos.2) The numerical sequences based on the members of the MMF satisfy many additive properties and simultaneously

are geometric sequences, having been in consequence chosen as basis of different systems of proportions, particularly theGolden Mean and the Silver Mean.

2000 Mathematics Subject Classification. 26C10, 11J70, 11A51, 40A15Key words and phrases. continued fraction expansions, Metallic Means, Golden Mean, Silver Mean

379


Rao-blackwellized Estimates for the Multivariate

Bayesian Inference

Vilda Purutcuoglu1, Ernst Wit2

1 Middle East Technical University, Department of Statistics, Ankara, Turkey

[email protected]

2 University of Groningen, Institute of Mathematics and Computing Science,

Groningen, The Netherlands

[email protected]

Abstract

In Bayesian inference the summary statistics of the parameter estimates are generally chosen as the mean and stan-dard deviation of the posterior distribution after the burn-in period. If we know the conditional distribution of eachparameter cj (j = 1, . . . , r) given other parameters ck (k 6= j), the mean of the estimates can be improved via Rao-blackwellization estimator which is the conditional probability of cj averaged over the conditional probability of ck’s via

E(cj) = 1n

∑nk=1 E(cj |Θ(k)

−j ). Here Θ(k) denotes the r-dimensional parameter vector Θ = (c1, . . . , cr) at the kth iteration

after the burn-in period, thereby Θ(k)−j states all the components of Θ(k) except for cj . Finally n represents the number

of samples chosen from the conditional posterior distribution of the parameter after burn-in. From empirical results, it isshown that due to the consequence of the Rao-blackwell theorem, the given equation above typically gives better estimatethan the mean of the posterior distribution of cj in terms of accuracy.

In Rao-blackwellization where the direct computation of Θ component is not possible, whereas the full conditionaldistribution of cj is known, the sampler for cj can be generated via Gibbs sampling from the MCMC outputs (Gelfandand Smith, 1990; Boys et al., 2000). On the other hand if the conditional distribution of Θ is unknown, hereby Gibbs isnot applicable, an ε-neighbourhood of Θ is defined in such a way that a sufficiently small sphere with radius ε can cover nsamples of cj (Tanner and Wong, 1987). Although this idea works for small set of variables, it is difficult to find such anε-radial sphere for high dimensional multivariate estimation unless we reduce the dimension of Θ.

For calculating a Rao-blackwellized estimate for the model parameters in which the Gibbs and ε-neighbourhood tech-niques cannot be plausible, we propose an alternative solution in such a way that the unknown normalizing constant of thetransition probability from the full conditional distribution of parameters is calculated by numerical integration. By usingthe available MCMC results, we approximate a specific normalizing constant for each cj considering the possible interval ofΘ without reducing any dimension. Then these findings are combined with the computations of the conditional distributionof Θ which are updated by either Gibbs or Metropolis-Hasting algorithms.

To evaluate the performance of our approach, we implement it to estimate the Rao-blackwellized estimates of modelparameters of a large biological network where the known methods cannot be utilized.

References[1] R. J. Boys and D. A. Henderson and D. J. Wilkinson, Detecting homogeneous segments in DNA sequences by using hidden markov

models, Applied Statistics. 49, Vol. 2 (2000) 269-285.

[2] A. E. Gelfand and A. F. M. Smith, Sampling-based approaches to calculating marginal densities, Journal of the American StatisticalAssociation. 85, Vol. 410 (1990) 398-409.

[3] M. A. Tanner and W. H. Wong, The calculation of posterior distributions by data augmentation, Journal of the American StatisticalAssociation. 82, Vol. 398 (1990) 528-540.

2000 Mathematics Subject Classification. 60J70, 35K57Key words and phrases. Rao-blackwellization, Bayesian inference, Multivariate diffusion approximation

380


The Guelph Expansion:

A Special Mathematical Formulation for Polynomial

Expansion

Wajdi M. Ratemi1, Hussein Abdullah2

1 Alfateh University, Nuclear Engineering Department,

P.O.Box 91821, Tripoli, Libya

wm [email protected]

2 University Of Guelph, Engineering Systems And Computing,

Guelph, Ontario, Canada N1G 2W1

[email protected]

Abstract

Special mathematical formulation is introduced for polynomial expansion, Ratemi (1996), Ratemi and Eshabo(1998).

n∐

i=1

(ω + λi) =

n∑

k=0

ωn−k

∑

T=[ nk

]

λ...k...λ

Such polynomial expansion helped in developing a new compact polynomial formula for the characteristic equation of anuclear reactor model with n- groups of delayed neutrons which is known as the inhour equation, Hetrick (1971), Duderstadtand Hamilton(1976), and Lewins (1978). The coefficients of the new form of the inhour equation (the polynomial form)can be impeded in an algebraic solution for the solution of the point reactor kinetic model, Ratemi (2001). An AnalyticalExponential Mode (AEM) method has been developed by Aboanber(2003) which is based on the developed formulationof the polynomial expansion and its application to the inhour equation for the solution of the point reactor model whichincludes delayed neutron groups as well as photo-delayed neutron groups associated with beryllium, and heavy water insome types of nuclear reactors. Such new polynomial expansion ( The Guelph expansion) with the new introduced Tripoliindexing (T) has already an application to the solution of nuclear reactor models and helped in getting solutions whichoverrided system stiffness with better accuracy as well as the advantage of using larger numerical sampling time, Aboanber(2003). It is suggested in this paper for researchers to consider such polynomial expansion for other application in otherdisciplines.

2000 Mathematics Subject Classification. 12-06Key words and phrases. Guelph Expansion, Tripoli Index, Polynomial Expansion, Inhour Equation, Point Reactor Kinetics

381


On The Solvability Of Abel-Poisson Integral Equation

In Downward Continuation For Gravity Field Modeling

Y. Allahtavakoli1, A. Safari2

1 National Iranian Oil Company (NIOC), Exploration Directorate

y [email protected]

2 Department of Surveying and Geomatics Engineering, University of Tehran

Abstract

The problem of downward continuation of the gravity field from the Earth’s surface to the reference ellipsoid arises from

the fact that the solution to the boundary value problem for geoid determination without applying Stokes formula is sought

in terms of the disturbing potential on the ellipsoid but the gravity observations are only available on the Earth’s surface.

Downward continuation is achieved via Abel-Poisson integral and its derivatives. Before solving downward continuation

problem it should be checked the solvability of the problem. The solvability of the problem is guarantied if Picard condition

is satisfied. The topic of this paper is the study of solvability of downward continuation problem via Picard condition.

References[1] Grafarend, E. W. (2001). ”The spherical horizontal and spherical vertical boundary value problem-vertical deflections and geoidal

undulations- the completed Meissl diagram.” Journal of Geodesy, Vol. 75, PP. 363-390.

[2] Griffel, D. H. (1988). Applied Functional Analysis. Ellis Horwood Limited Publishers.

[3] Hadamard, J. (1902). Sur les Problems aux derives particles et leur signification physique. Princeton University Bulletin, Vol. 13,PP. 49-52.

[4] Hansen, P.C. (1996). Rank-Deficient and Discrete Ill-posed problems. PhD Dissertation. Department of mathematical modelingbuilding 305, technical university of Denmark, Dk-2800 Lyngby, Denmark.

[5] Kirsch, A. (1996). ”An introduction to the mathematical theory of inverse problems.” Applied Mathematical Sciences, Vol. 120,Springer-Verlag, New York.

[6] Moritz, H. (1966a). Linear Solutions of the geodetic boundary-value problem. Rep. 79, Department of geodetic science and surveying,the Ohio state university, Columbus, USA. Bernstein S N (1924) Solution of a mathematical problem connected with the theory ofheredity, Ann.Sci. de l’Ukraine,1:83- 114.

2000 Mathematics Subject Classification. 45Q05Key words and phrases. Boundary Value Problem, Abel-Poisson Iintegral, Inverse Problem, Picard Condition

382


Non linear boundary value problem: Faedo-Galerkin

methode of the non linear boundary value problem

Y. Boukhatem, B. Benyattou, R. Abita

Department of Mathematics, Faculty of Sciences, University of Batna

Batna (05000), Algeria

[email protected]

Dept. of Inf., Faculty of Sciences, University of Laghouat

Laghouat (03000), Algeria

[email protected]

Dept. of Inf., Faculty of Sciences, University of Laghouat

Laghouat (03000), Algeria

[email protected]

Abstract

In this note, we consider a nonlinear boundary value problem. The use of Faedo-Galerkin techniques and a compactness

result, while passing to the limit, we prove the existence of the variational solution of the considered problem. A new result

is given by showing the uniqueness of the solution basing on the hypotheses which are weaker than those considered by ([6]

: J.L. Lions, Quelques methodes de resolution des problemes aux limites non lineaires, Paris, Dunod, (1969)), for a similar

problem. We will finish by studying the regularity of the gotten solution.

2000 Mathematics Subject Classification. 37L65, 47J35Key words and phrases. Compacity, Faedo-Galerkin, Gronwall, Cauchy Schwartz inequality, Holder inequality, variational problem

383


The Average Chebyshev Distance In A Grid

Y. Tavakoli*, H. Haj Seyyed Javadi** and Sa. Adabi***

*Computer Engineering Department, IAU,

Science and Research Unit, Tehran, Iran

[email protected]


P.O. Box: 18151-159, Iran

[email protected]

***Computer Engineering Department, IAU,

Northern Tehran Unit, Tehran, Iran

[email protected]

Abstract

Chebyshev distance has been an interesting topic in mathematics so far; for both theoretical attractions and practical

applications which spread from warehouse logistics to the game of chess in plane geometry. Through the presented study

we will examine and discover certain enumerative properties of a grid which is associated with Chebyshev distance, and

then we will calculate the mean value of the distance between two randomly chosen points. While mentioned mean value

plays an important role in further probabilistic methods, this study will also develop our structural knowledge of those

grids which are associated with Chebyshev distance.

2000 Mathematics Subject Classification. 05A15, 60C05.Key words and phrases. Finite Combinatorial Enumeration, Mean Value, Chebyshev Distance.

384


Symmetry classes of tensors associated with Young

subgroups

Y. Zamani* , M. Shahryari**

*Faculty of Sciences, Sahand University of Technology, Tabriz, Iran.

[email protected]

**Department of Pure Mathematics, Faculty of Mathematical Sciences,

University of Tabriz, Tabriz, Iran.

[email protected]

Abstract

Let V be an n-dimensional complex inner product space and G be a subgroup of the full symmetric group Sm. LetV ⊗m denote the tensor product of m copies of V and for any σ ∈ G, define the permutation operator

Pσ : V⊗m → V

⊗m

byPσ(v1 ⊗ v2 ⊗ · · · ⊗ vm) = vσ−1(1) ⊗ vσ−1(2) ⊗ · · · ⊗ vσ−1(m).

Suppose χ is a complex irreducible character of G and define the symmetrizer

T (χ, G) =χ(1)

|G|∑

σ∈G

χ(σ)Pσ.

The symmetry class of tensors associated with G and χ is the image of T (χ, G) and it is denoted by Vχ(G). So

Vχ(G) = T (χ, G)(V⊗m

).

The aim of this paper is to study symmetry classes of tensors associated with Young subgroups of the symmetric group.

We will discuss the dimension as well as ∗-bases of these types of symmetry classes.

References[1] H. F. da Cruz, J. A. Dias da Silva, Equality of immanantal decomposable tensors (II), Linear Alg. and Appl. 395 (2005) 95-119.

[2] M. Isaacs, Character theory of finite groups, Academic Press, 1976.

[3] R. Merris, Multilinear algebra, Gordon and Breach Science Publisher, 1997.

[4] B. Sagan, The Symmetric Group: Representation, Combinatorial Algorithms and Symmetric Functions, Wadsworth and Brook/Cole math. series, 1991.

[5] M. Shahryari, On the orthogonal bases of symmetry classes, Journal of Alg. 220 (1999), 327-332.

[6] Y. Zamani, On the special basis of a certain full symmetryclass of tensors, pure Mathematics and Appl. 18 (2007) 357-363.

2000 Mathematics Subject Classification. Primary: 15A69 Secondary: 20C15Key words and phrases.Symmetry classes of tensors, Young subgroup, Irreducible characters

385


Necessary conditions of second order optimality for

systems with three-point boundary conditions

Yagub A. Sharifov, Shamo I. Djabrailov

Baku State University, Department Applied Mathematics and Cybernetics

AZ1148, Z.Khalilov 23, Baku, Azerbaijan

[email protected]

Abstract

In this report the object of investigation is an optimal control problem in systems of nonlinear first order ordinarydifferential equations with three-point boundary conditions:

x = f(x, u, t), x(t) ∈ Rn

, t ∈ T = [t0, t1], (1)

Ax(t0) + Bx(t1) + Dx(t2) = c, t1 ∈ (t0, t2), (2)

Here f ∈ Rn is continuous by collection of variables together with its partial derivatives with respect to x and u up tothe second order inclusive, A, B, D ∈ Rn×n, c ∈ Rn×1 are constant matrices. It is supposed that control action satisfyrestriction u(t) ∈ V, t ∈ T, where V is a convex compact set from Rr.

The goal of optimal control problem is optimization of the functional:

J(u) = ϕ(x(t0), x(t2)) (3)

defined on the solutions of boundary problem (1)-(2) at admissible controls where it is supposed that function ϕ(x, y) iscontinuous by x and y up to the second order inclusive. The formula of the second order increment of functional (3) iscalculated.

On the basis of control variations there are obtained new necessary conditions of optimality for quasi-singular controls

for systems which are described by a set of differential equations with three-point boundary conditions

2000 Mathematics Subject Classification. 49J15,49K15, 34B10Key words and phrases. optimal control, boundary value problem, necessary condition of optimality

386


On D12 Modules

Yahya Talebi, Ali Reza Moniri

Department of Mathematics, Faculty of Basic Science,


[email protected]

Department of Mathematics, Faculty of Basic Science,


[email protected]

Abstract

In this paper we introduce Rad-D12 modules as a generalization of D12 modules. We also investigate some properties

of Rad-⊕-supplemented modules relative to Rad-D12 modules. Necessary and sufficient conditions for a module to be

Rad-D12 are obtained.

References[1] F. W. Anderson, K. R. Fuller, Rings and Categories of Modules, Graduate Texts in Mathematics., vol. 13, Springer-Verlag, New

York, (1992).

[2] K. R. Goodearl, Ring Theory,Nonsingular rings and modules, New York and Basel, (1976).

[3] A. T. Khaled, Cofinitely δ-supplemented and cofinitely δ-semiperfect modules, International Journal of Algebra, Vol. 1, 12 (2007)601-613.

[4] S. H. Mohammed, B. J.Muller, Continous and Discrete Modules, London Math.Soc., LN 147, Cambridge Univ. Press, (1990).

[5] R. Tribak, A. Idelhadj, On some properties of ⊕-supplemented modules, International Journal of Mathematics and MathematicalSciences, no. 69 (2003) 43734387.

[6] R. Wisbauer, Foundations of Module and Ring Theory, Gordon and Breach, Reading,(1991).

[7] H.Zoschinger, Komplementierte Moduln uber Dedekindringen, J. Algebra 29 (1974) 4256 (German).

[8] Y. Zhou, Generalizations of perfect, semiperfect, and semiregular rings, Alg. Coll. 7 (3) (2000) 305-318.

2000 Mathematics Subject Classification. 16D10, 16D70Key words and phrases. Small submodule, Rad-⊕-supplemented , Rad-D12 module

387


FPGA Implementation of Vedic Signed Multiplier

Yajnesh Padiyar1, Mahalinga V. Mandi2, Ramesh S.3, Dileep D.4

1 Dr. Ambedkar Inst. of Tech., Dep. of Electr. & Comm., Bangalore, India

[email protected]


[email protected]


rameshs [email protected]

4 R&D Services, MindTree Ltd, Bangalore, India

[email protected]

Abstract

Vedic mathematics is the name given to the ancient Indian system of mathematics. To be precise, a unique techniqueof calculations based on simple rules and principles with which any mathematical problems related to arithmetic, algebra,geometry or trigonometry can be solved. The system was rediscovered in the early twentieth century from ancient Indiansculptures (Vedas). The system is based on 16 Vedic sutras or aphorisms [1], which are actually Vedic mathematical for-mulae describing natural ways of solving a whole range of mathematical problems. The Vedic mathematics approach istotally different and considered very close to the way a human mind works. A large amount of work has so far been donein understanding various methodologies (sutras). The need for high speed processing has been increasing as a result ofexpanding signal processing and computer applications. Higher throughput arithmetic operations are important to achievethe desired performance in many real time signal and image processing applications. One of the important arithmeticoperations in such applications is to perform a large number of mathematical calculations in a very less time. Since inperforming mathematical calculations especially multiplication, a computer spends a considerable amount of its processingtime, an improvement in the speed of a math coprocessor for performing multiplication will increase the overall speedof the computer. There are several multiplier algorithms that can be implemented such as: Array, Booth, Carry save,modified Booth algorithms and Wallace tree. The most significant aspect of the multiplier architecture of ancient IndianVedic mathematics is that it is based on vertical and crosswise structure of ancient Indian Vedic mathematics as in [1] and [7].

In this paper a signed binary multiplication algorithm is presented based on ancient Indian Vedic mathematics. The

signed multiplication algorithm is realized using verilog coding, simulated with Modelsim and implemented on Xilinx

Spartan2 XC2S100-PQ208 Field Programmable Gate Array (FPGA). The paper explains 8X8 multiplication of signed

binary numbers, its realization and implementation, which can be extended to a NXN signed binary numbers. The system

works satisfactorily under ideal condition and is tested for multiplying various combinations of signed and unsigned 8 bit

binary numbers. From the synthesis report of both the proposed algorithm and the booth algorithm [8] it is observed

that the maximum combinational path delay was found to be 47.706 ns which are found to be less than Modified Booth’s

algorithm that requires 67.961ns implemented on the same device. Not only the time required for the multiplication is less

but also the hardware utilization is also found to be less by 2% which is very significant in case of VLSI design. The signed

multiplier algorithm discussed in this paper can be substituted in [2] – [7] in case if it is really required to use signed and

unsigned numbers.

References[1] Jagadguru Swami Sri Bharati Krisna Tirthaji Maharaja, Vedic Mathematics: Sixteen Simple Mathematical Formulae from the Veda.

Publisher Motilal Banarsidass, Delhi (1965).

[2] Purushottam D. Chidgupkar, Mangesh T. Karad, “The Implementation of Vedic Algorithms in Digital Signal Processing”, GlobalJ. of Engg. Educ., Vol.8, No.2, (2004) 153-158.

[3] Himanshu Thapliyal, Hamid R. Arabnia, “A Time-Area- Power Efficient Multiplier and Square Architecture Based On AncientIndian Vedic Mathematics”. Book title ESA/VLSI ,Publisher CSREA Press(2004) 434-439.

[4] Kumaravel, S. Marimuthu, R., “VLSI Implementation of RSA Encryption System Using Ancient Indian Vedic Mathematics”,Proceedings of IEEE Conference on Computational Intelligence and Multimedia Applications, (2007) 126 – 128.

[5] Harpreet Singh Dhillon and Abhijit Mitra, “A Reduced-Bit Multiplication Algorithm for Digital Arithmetic”, International Journalof Computational and Mathematical Sciences, (2008) 64-68.

2000 Mathematics Subject Classification. 00Key words and phrases. Vedic mathematics; FPGA; Signed binary multiplication

388


[6] Himanshu Thapliyal, Hamid R. Arabnia, “High Speed Efficient N Bit By N Bit Division Algorithm And Architecture Based OnAncient Indian Vedic Mathematics”. Book title ESA/VLSI ,Publisher CSREA Press(2004) 413-416.

[7] Shamim Akhter, “VHDL Implementation Of Fast NxN Multiplier Based On Vedic Mathematic”, IEEE Circuit Theory and Design,18th European Conference (2007) 472-475.

[8] Nazeih M Botros, “HDL Programming (VHDL and Verilog)”, publisher Dreamtech Press

389


On Generalized Weak Subdifferentiability of Vector

Valued Functions from Rn to Rm

Yalcın Kucuk, Ilknur Atasever, Mahide Kucuk

Anadolu University, Yunus Emre Campus,

Department of Mathematics, Eskisehir, Turkey

[email protected]

[email protected]

[email protected]

Abstract

In this work, by using special ordering cones (Rm+ , Rm

lex) on Rm and a special vectorial norm, it is shown that Lipschitz-

ness of a vector valued function from Rn to Rm implies generalized lower Lipschitzness of this function. Then by using this

notion necessary and sufficient conditions for generalized weak subdifferentiabilty of a vector valued function at a point are

given.

References[1] A.Y. Azimov, R.N. Gasimov, On weak conjugacy, weak subdifferentials and duality with zero gap in nonconvex optimization, Int.

J. of Appl. Math., 1 (1999), 171-192.

[2] A.Y. Azimov, R.N. Gasimov, Stability and duality of nonconvex problems via augmented Lagrangian, Cybernet. Systems Anal., 38(2002), 412-421.

[3] J. Jahn, Vector Optimization, Springer, Heidelberg, 2004.

[4] R.R. Phelps, Support cones in Banach spaces and their applications, Advences in Mathematics, 13 (1974), 1-19.

[5] R.T. Rockafellar, The Theory of Subgradients and Its Applications to Problems of Optimization-Convex and Nonconvex Functions,Heldermann, Berlin, 1981.

[6] R.T. Rockafellar, Proximal subgradients, marginal values, and augmented Lagrangians in nonconvex optimization, Math. Oper.Res., 6 (1981), 427-437.

[7] J. Zowe, Subdifferentiability of convex functions with values in an ordered vector space, Math. Scand., 34 (1974), 69-83.

2000 Mathematics Subject Classification.80M50, 26A24Key words and phrases.generalized weak subdifferential, generalized lower Lipschitz function, vector optimization

390


A new management approach to optimize the use of the

operating room

Yasmina Kerboua Ziari*, Djamel Chaabane*, Ahmed Benzaoui**

*LAID3, BP 32 El Alia University of Science and Technology

Houari Boumediene Algiers Algeria

ykerbouaz @yahoo.fr

** LTSE, BP 32 El Alia University of Science and Technology

Houari Boumediene Algiers Algeria

Abstract

The surgery is a highly strategic for hospitals because it is at the heart of medical and concentrated 10 to 15% of the

budget of the institution for its operation. It is therefore important for hospitals to assess the performance of organizational

strategies, programming and management procedure on the sector to improve service to patients and reduce operating costs.

Currently, health centres’ Algerian private or public, and especially surgical suffers from a lack of quality care and high cost

of interventions. One reason is the poor organization of the management of the logistics chain of various actors involved

in the care of the patient. The main objective of this work is to propose a provisional scheduling surgery to optimize the

management of operating units, and therefore reduce the waiting time for patients the report of the interventions surgery.

To carry out this delicate task, we undertook the following approach:

-Study the existing analysis of the different activities and tasks of the operating process to identify the strengths and

weaknesses of the existing as well as different management problems,

- Modelling of different management problems procedure process,

- Proposal of a new management approach to optimize the use of the operating room.

2000 Mathematics Subject Classification.90CxxKey words and phrases.Surgery, hospital management, optimization, modelling.

391


A note on Reidemeister torsion and period matrix of

Riemann surfaces

Yasar Sozen


34500 Istanbul, Turkey,

[email protected]

Abstract

We consider compact Riemann surfaces Σg with genus at least 2. We explain the relation between the Reidemeister

torsion of Σg and its period matrix.

References[1] J. Milnor, A duality theorem for Reidemeister Torsion, Ann. of Math. (1962) 137-147.

[2] J. Milnor, Whitehead torsion, Bull. Amer. Math. Soc. 72 (1966) 358-426.

[3] K. Reidemeister, Homotopieringe und Linsenraume, Abh. Math. Sem. Univ. Hamburg 11 (1935) 102-109.

[4] Y. Sozen, On Reidemeister torsion of a symplectic complex, Osaka J. Math. 45 (2008) 1-39.

[5] Y. Sozen, A note on Reidemeister torsion and period matrix of Riemann surfaces, Math. Slovaca (accepted)

[6] E. Witten, On quantum gauge theories in two dimensions, Comm. Math. Phys. 141 (1991) 153-209.

2000 Mathematics Subject Classification. 32G20, 57M99Key words and phrases.Reidemeister torsion, period matrix.

392


Numerical Solution Of A Non-Classical

Hyperbolic-Parabolic Problem

Yıldırım Ozdemir

Department of Mathematics, Duzce University, Duzce, 81620, Turkey

[email protected]

Abstract

This paper is a joint work with Prof. Allaberen Ashyralyev, Fatih University. Stable difference schemes of the first and

second orders of accuracy for solving multidimensional hyperbolic-parabolic partial differential equations with the nonlocal

boundary condition are presented. A procedure of modified Gauss elimination method is used for solving these difference

schemes in the case of a one-dimensional hyperbolic-parabolic partial differential equations. The method is illustrated by

numerical examples.

References[1] D. Bazarov, H. Soltanov, Some local and nonlocal boundary value problems for equations of mixed and mixed-composite types,

Ilim:Ashgabat (1995).(Russian)

[2] A. Ashyralyev, A. Yurtsever, A note on the second order of accuracy difference schemes for hyperbolic-parabolic equations, AppliedMathematics and Computation 165, no.3 (2005) 517-537.

[3] A. Ashyralyev, Y. Ozdemir, Stability of difference schemes for hyperbolic-parabolic equations, Computers and Mathematics withApplications 50, no.2 (2005) 1443-1476.

[4] A. Ashyralyev, Y. Ozdemir, On nonlocal boundary value problems for hyperbolic-parabolic equations, Taiwanese Journal of Mathe-matics 11 , no.13 (2007) 1077-1091.

[5] P. E. Sobolevskii, Difference methods for the approximate solution of differential equations, Izlad.Voronezh. Gosud. Univ., Voronezh(1975). (Russian)

2000 Mathematics Subject Classification.65N12, 65M12, 65J10.Key words and phrases.hyperbolic-parabolic equation, difference schemes, stability.

393


Smoothing the Global Mean Based on Functional

Principal Component Analysis

Y. Tandogdu1, Ovgu Cidar2

1 Department of Mathematics, Eastern Mediterranean Univ.

Magusa, North Cyprus

[email protected]

2 Department of Mathematics, Eastern Mediterranean Univ.


[email protected]

Abstract

There are many cases in almost all application fields where the estimation of population parameters is carried out usingsparse data. The data may be time or space ( τ) dependent. When such data comes from a set of n trajectories (subjects),the Functional Principal Component Analysis (FPCA) is used to process the data for estimation purposes. In this study,the estimation and smoothing of global mean is considered. Sparse functional data from many different trajectories areassumed to be independent realizations of a smooth random function with mean function E[X(t)] = µ(t) and covariancefunction Cov[X(s), X(t)] = C(s, t). Any subject can be expressed as Xi(t) = µ(t)+

∑k

ξikφk(t) . Here ξik are the functional

principal component scores. E(ξik) = 0, E[ξijξik] = 0 for j 6= k, E[ξ2ik] = λk. Also

∑k

λk < ∞, λ1 ≥ λ2 ≥ . . ..

Evidently in the functional representation of a trajectory, the global mean function µ(t) has a major role. Therefore,an accurate and robust estimation of µ(t) is essential. This estimation is based on the j th observation of the ith trajectoryrepresented by made at time Tij , j = 1, ..., Ni. Since the number of observations Ni made on each of the i subjects israndom, are assumed to be i.i.d. and independent random variables. Observations will inherently include some measurementerrors εij that are also assumed to be i.i.d. with E(εij) = 0 and constant variance σ2. The model representing the ithsubject based on observations can be written as

Yij = µ(Tij) +∞∑

k=1

ξikφk(Tij) + εij , Tij ∈ τ.

Local linear smoothers employing weighted least squares for the estimation of µ(t) is used. Estimated is carried out usingall available data from n subjects. The smooth estimator µ(t) is found by minimizing the smoother function with respectto related parameters.

This theory was applied to a data set on variable funds belonging to 12 banks from Turkey to estimate the smooth

mean. Daily changes were recorded as data values, and obtained smooth mean for the whole data as well as on daily bases

was found to be in close agreement with the corresponding true data averages.

References[1] F. Yao, H. G. Muller, J. L. Wang, Functional Data Analysis for Sparse Longitudinal Data. J of Amarican Statistical Association.

100,pp. 577-590, 2005

[2] H. G. Muller, Functional Modelling and Classification of Longitudinal Data. Scandinavian Journal of Statistics, 32, pp.223-240, 2005

2000 Mathematics Subject Classification. 62H11, 62H12, 62H25, 62P05, 91B28Key words and phrases. Smoothing, functional, sparse data, covariance**This research was supported by EMU

394


Sensitivities in Determining the Slope Parameter in

Functional Regression

Yucel Tandogdu

Department of Mathematics, Eastern Mediterranean Univ.


[email protected]

Abstract

In multivariate linear regression analysis the slope parameter is defined as β1 = Cov(X, Y )/var(X). Based on the factthat the predictors are uncorrelated the slope function in the functional case becomes

β(s, t) =

∞∑

k=1

∞∑

m=1

E[ζmξk]

E[ζ2m]

θm(s)φk(t)

The process involves the obtaining of an estimate C(s, t) for the cross-covariance C(s, t) = cov[X(s), y(t)]. This necessitatesthe smoothing of the raw cross-covariance . As a result an estimate for the cross covariance σkm = E[ζmξk] between the

kth predictor and mth response functions is obtained. Then the estimated slope function becomes.

β(s, t) =K∑

k=1

M∑

m=1

σkm

ρkm

θm(s)φk(t)

While in theory everything appears perfect, in the application to sparse and irregular data special care must be given to

the level of smoothing as well as the number of eigenfunctions to be included in the estimation process. Another sensitive

point is the computation of the canonical correlation . One has to show extreme care in selecting the canonical weighting

functions, so that the right choice can be made out of the many canonical correlations to be computed. The sensitivity

shown to the estimation of the slope function will certainly reflect in the prediction of the response trajectory Y in the

functional regression process.

References[1] F. Yao, H. G. Muller, J, L. Wang, Functional Linear Regression Analysis for Longitudinal Data. The Annals of Statistics, 33, (2005),

2873-2903.

[2] P. Hall, H. G. Muller, J. L. Wang, Properties of Principal Component Methods for Functional and Longitudinal Data Analysis, TheAnnals of Statistics, 34, (2006) 1493-1517.

[3] D. Senturk, H. G. M”uller, Covariate adjusted regression. Biometrika 92, (2005), 75-89

2000 Mathematics Subject Classification. 662H11, 62H12, 62H25Key words and phrases. smoothing, functional regression, sparse data, slope parameter**This research was supported by EMU

395


Kaplansky’s Construction And The Classes Of The

Weak Hopf Algebra In 2,3 Dimension

Z. Chebel*, A. Makhlouf**

*University of the Skikda, Laboratory of the physics,

the surface and the interface, Algeria,

zoheir [email protected]

**University Haute Alsace, Laboratory of Mathematics,

Informatics and Applications, Mulhouse, French.

[email protected]

Abstract

In this paper, we study the weak bialgebras and the weak Hopf algebras. These algebras form a class wider than the

bialgebras respectively the Hopf algebras. The corresponding algebraic varieties are considered. We give some constructions

and we establish this classification for isomorphism meadows the bialgebras and the weak Hopf algebras of dimension of n

3. We will determine then the stabilizer and the representative of these classes, the action being that of the linear group.

References[1] Irving Kaplansky. Bialgeras, Lecture note in mathematics, departement of mathematics, Univesity of Chicago

[2] A. N. Panov Ore Extensions of Hopf Algebras, Mathematical notes, vol.74, no.3, (2003), pp. 401-410.

2000 Mathematics Subject Classification.16W30Key words and phrases.bialgebras, Hopf algebras.

396


Quadrature Formula For Semi-Bounded Solution Of

Characteristic Singular Integral Equation Of Cauchy

Type

Z. K. Eshkuvvatov, N.M.A. Nik Long, M.Abdulkawi

Universiti Putra Malaysia (UPM), Department of Mathematics,

Serdang, Selangor, Malaysia


UPM, Institute for Mathematical research, Serdang, Selangor, Malaysia

Abstract

It is known that the solutions of characteristic singular integral equations (SIEs) are expressed in terms of singular

integrals of Cauchy type with wight functions of the form w(x) = (x − a)ν(b − x)µ , where −1 < ν, µ < 1. In this

paper new quadrature formulas are presented to approximate singular integrals of Cauchy type for half bounded solution of

characteristic SIEs on the interval [−1, 1]. Linear interpolation spline and modification discrete vortices method (MMDV)

are used to construct quadrature formula. Estimations of error are obtained in the classes of functions Hα([−1, 1]) and

C1([−1, 1]). Numerical experiments are presented to show the validity of the method presented.

References[1] Z. K. Eshkuvatov, N.M.A. Nik Long, M.Abdulkawi. Quadrature formula for approximating the singular integral of Cauchy type with

unbounded weight function on the edges. Submitted to the Journal of CAM.

[2] S. Belotserkovskii, I. Lifanov. Numerical methods in singular integral equations. Moscow: Nauka, 1985. (in Russian).

2000 Mathematics Subject Classification.65D32, 30C30, 65R20Key words and phrases.Singular integral, singular integral equations, quadrature formula, canonic partition, discrete vorticesmethod, approximation, spline

397


Some Results On Products Of Conjugacy Classes

Z. Mostaghim

Department of Mathematics,

Iran University of Science and Technology, Tehran,Iran

[email protected]

Abstract

Let G be a finite group , A and B be conjugacy classes of G .Then for some integer η(AB) > 0 , AB = ab|a, b ∈ Gis the union of η(AB) distinct conjugacy classes of G . In this note we study η(AA−1) for some classes of finite groups.

References[1] E.Adan-Bante, Conjugacy classes and finite p- groups , Arch.Math. 85 (2005)297-303.

[2] E.Adan-Bante, Products of characters and finite p-groups J.Algebra 277 (2004) 236-255.

2000 Mathematics Subject Classification.20D15.Key words and phrases.Conjugacy classes, Products , Nilpotent.

398


Pairwise Semiregular Properties on Generalized

Pairwise Regular-Lindelof Spaces

Zabidin Salleh, Adem Kılıcman

Department of Mathematics, Faculty of Science and Technology,

University Malaysia

Terengganu, 21030 Kuala Terengganu, Terengganu, Malaysia.

[email protected]

Department of Mathematics, Faculty of Science, University Putra Malaysia,

43400 UPM, Serdang, Selangor, Malaysia.

[email protected]

Abstract

In this paper we study pairwise semiregular properties of pairwise nearly regular-Lindelof, pairwise almost regular-

Lindelof and pairwise weakly regular-Lindelof spaces. We prove that pairwise almost regular-Lindelof and pairwise weakly

regular-Lindelof are pairwise semiregular properties. We also show that pairwise nearly regular-Lindelof satisfy the pairwise

semiregular invariant property.

2000 Mathematics Subject Classification. 54D20, 54E55Key words and phrases. Bitopological space, pairwise nearly regular-Lindelof, pairwise almost regular-Lindelof, pairwise weaklyregular-Lindelof, (i, j)-semiregular property, pairwise semiregular property

399


Efficient block method for solving directly third order

ordinary differential equations

Zanariah Abdul Majid*, Mohamed Suleiman**

*Mathematics Department,Faculty Science,Universiti Putra Malaysia,

43400 Serdang,Selangor Darul Ehsan,Malaysia

[email protected]

**Institute of Mathematical Research, Universiti Putra Malaysia,

43400 Serdang,Selangor Darul Ehsan,Malaysia

[email protected]

Abstract

In this research, a two point block direct implicit method is developed for solving directly the third order ordinarydifferential equations (ODEs) using variable step size. This method will estimate the solutions of initial value problems(IVPs) at two points simultaneously of the form

y′′′

= f(x, y, y′, y′′), y(a) = y0, y

′(a) = y

′0, y

′′(a) = y

′′0 , a ≤ x ≤ b (1)

Eq.(1) arises from many physical phenomena in a wide variety of applications especially in engineering such as the motion

of rocket or satellite, fluid dynamic, electric circuit and other area of application. A higher order ODEs can also be reduced

to a system of first order equations and then solved using any numerical methods. This approach is very well established

but it obviously will enlarge the system of first order ODEs. The approach for solving the higher order ODEs directly

has been suggested in (Suleiman, 1989) and (Omar, 1999). Block method for numerical solution had been introduced by

several researchers such as (Shampine & Watts, 1969) and (Rosser, 1976). A block method will computes simultaneously the

solution values at several distinct points on the x-axis in the block. There are many existing methods for solving the ODEs

as in (1) but those methods will only approximate the numerical solutions at one point sequentially. Therefore we need a

faster method that can give faster solution to the problem and yet manage to produce better accuracy.The current multistep

method for variable step (VS) or variable step and order (VSVO) technique for solving the higher order ODEs will involve

tedious computations of divided difference and the integration coefficients in the code. The idea of the code developed in

this research is to avoid those computations that can be very costly. Hence, the code will store all the coefficients of the

method. The propose block method in this paper is presented as in a simple form of Adams Moulton method. The method

is in a simple form but we intend for efficiency and economically. Numerical results show that the propose block method is

efficient than the existence block method in (Omar, 1999).

References[1] J.B. Rosser, Rungge Kutta For All Season, SIAM Rev. 9 (1976) 417-452.

[2] L.F. Shampine. & H.F.Watts, Block Implicit One-Step Methods,Math.Comp. 23 (1969) 731-740.

[3] M.B.Suleiman, Solving Higher Order ODEs Directly by the Direct Integration Method. Applied Mathematics and Computation 33(1989) 197-219.

[4] Z. Omar, Developing Parallel Block Methods For Solving Higher Order ODEs Directly, Ph.D. Thesis, University Putra Malaysia,

Malaysia (1999).

2000 Mathematics Subject Classification. primary:65L05 secondaries:65L06Key words and phrases.block method, higher order, direct method, ODEs*This research was supported by Institute of Mathematical Research, Universiti Putra Malaysia under RU Grant 05-01-07-0232RU

400


Three Point Block Backward Differentiation Formula

For Solving Stiff Ordinary Differential Equations

Zarina Bibi Ibrahim*, Mohamed Suleiman*, Khairil Iskandar Othman**

*Department of Mathematics Faculty of Science, Universiti Putra Malaysia,

43400 UPM, Serdang, Selangor, Malaysia

[email protected]

**Department of Mathematics Faculty of Information Technology and Science

Quantitative Universiti Technology MARA, 40450 Shah Alam, Selangor, Malaysia

[email protected]

Abstract

In this paper, a 3-point block method based on Backward Differentiation Formulas (BDF) which is called 3BBDF for

solving first order Ordinary Differential Equations (ODEs) using fixed step size is presented. This method will compute the

solutions of Initial Value Problems (IVPs) at three points simultaneously on the x-axis. The zero stability of the derived

3BBDF is also investigated. The efficiency of the 3BBDF is compared with the classical fixed step size BDF method.

Numerical results indicate that the resulting 3BBDF method outperform the BDF method in terms of execution times and

less number of steps taken to complete the integration in the given interval.

2000 Mathematics Subject Classification.Key words and phrases.Backward Differentiation Formulas, block, ordinary differential equations.

401


Processing of cyclic graphs with recursive neural

networks

Zeinab Rezaei

DIAU, Ardabil Branch, Ardabil, Iran

[email protected]

Abstract

Recursive neural networks are a powerful tool for processing structured data. They are filling the gap between connec-

tionism, which is usually related to poorly organized data, and a great variety of real-world problems such as document

processing, where the information is naturally incoded in the relationships among the basic entities. More precisely re-

cursive neural networks can deal only with directed ordered acyclic graphs (DOAGs), in which the children of any given

node are ordered. While this assumption is reasonable in some applications, it introduces unnecessary constraints in others.

Example of such applications is classification of HTML pages. In this paper, we explain a methodology, which allow us to

process any cyclic directed graph. The computational power of recursive neural networks is established.

2000 Mathematics Subject Classification.68T05Key words and phrases.Graph processing by neural networks, recursive neural networks, cyclic graphs.

402


A Note On The Solution Of The General Linear Matrix

Differential Equations

Zeyad Al-Zhour

Department of Mathematics, Faculty of Science and

Information Technology , Zarqa Private University (ZPU),

v P.O. Box 2000, Zarqa 1311, Jordan

[email protected] ; math [email protected]

Abstract

In this paper, we extend the use of connection between the Hadamard product and diagonal extraction (vector) operator

to produce a computationally -efficient solution of the general linear matrix differential equations. The analysis indicates

that the Hadamard structure method can achieve good efficient when the unknown matrices are diagonal. Several matrix

systems can be solved by the new approach as special cases.

2000 Mathematics Subject Classification.15A24; 15A69; 44A35Key words and phrases.Matrix Products, Coupled Matrix Differential Equations, Diagonal extraction operator.

403


Solving the Boundary Value Problem of the Wind

Turbine Blade Equation (Calculation of the Mode

Shape Functions)

Zine Labidine Mahri

Universite de Mentouri, Departement de Genie Climatique, Constantine, Alegria

[email protected]

Abstract

Rotor blades are the most flexible part of the wind turbine, and their modal behavior has a great influence on theoverall dynamics and energetic performance of the turbine. Consequently, the calculation of mode shapes and frequenciesof the blades is essential to predict the structural problem of the rotor such as blade fatigue (which is one of the majorconcerns of the designers) and to estimate the energetic performances of the turbine as well. This analysis can result in asubstantial saving of the system cost of energy. Recently more attention is given to modal analysis and many experimentaland numerical studies were carried out. The calculation of mode shapes is in fact a difficult task due to the complex natureof the blade movement. In this work, a numerical approach is used to solve the blade motion equation. The solution of thisfourth order differential equation is complicated by its special boundary conditions. This boundary problem is characterizedby two initial values (the displacement and the slope are nil, at the fixed end) and two final values (the shear force andthe bending moment must be zero at the free end). In order to start any numerical solution of the equation the boundaryproblem must be converted to an equivalent problem having four known initial values. For this task, an iterative algorithmwas developed to estimate the right initial-value problem that matches the specified boundary problem. This algorithmstarts from a first guess of the initial values, to allow the mode equation to be solved in order to obtain the final values (atthe free end of the blade). These initial values are then corrected by means of secant formula. This procedure is repeatedtill the calculated final values coincide with those specified by the original boundary problem. It has been verified thatthis algorithm converges when the predictor corrector method (Adam’s formula) is used to solve the equation, whereasconvergence is not achieved when the Runge-Kutta method is employed. A Fortran computer program was implementedto perform these computations. This modal analysis can be used to determine dynamic stresses and to estimate thereafterthe fatigue of the blades.

References[1] A. Baumgart, A mathematical model for wind turbine blade, Journal of sound and energy. Vol. 251(2002) 1-12.

[2] A. Bramwell, Helicopter dynamics, Edward Arnold. (1989).

[3] Z.L Mahri, Fatigue estimation of a rotating blade, Paper presented at the World renewable energy Congress, February, in Perth,Australia. (1999).

[4] F. Rasmunssen, M.H. Hansen, Present Status of Aeroelasticity of Wind Turbine, Wind Energy. Vol. 6 (2003) 213-228.

[5] R. Younsi,.Dynamic study of wind turbine blade with horizontal axis, Eurpean Journal of Mech A/solids. Vol. 20 (2001) 241-252.

2000 Mathematics Subject Classification.Key words and phrases. Wind Energy, Structural Dynamics, Aerodynamics, Numerical Analysis

404


Similarity Solution Of The Coagulation Equation In An

Electro-Rheological Colloidal Suspension

Zineb Mimouni, Jonathan A.D. Wattis

Department. of applied physics, University of Marrakesh,

Faculty of Sciences and Technology, 40000, Morocco

Mathematical School, University of Nottingham, UK

Abstract

Aggregation phenomena are met in a wide variety of physical, chemical and biological processes; for example the

formation of aerosols, micelles and vesicles, polymers, and even celestial bodies on astronomical scales. The irreversible

aggregation of colloidal particles is of interest, both from a fundamental point of view, and because of its industrial

applications. Electrorheological (ER) fuids are colloidal suspensions of conducting particles in an insulating fuid. The

particles acquire an electric dipole under the action of an external electric field. We present the analysis of a model for the

aggregation of colloidal particles which arises in an electrorheological system. Linear clusters grow upon the application

of an AC electric field. We consider coagulation kernels involving as negative powers of cluster sizes. We investigate the

reduction of the governing equations to a similarity solution in the large time limit. Comparison between the experimental

results and the theory shows a good agreement.

References[1] Z. Mimouni, R. Limage, Zamp, 60, 569-574, 2009

[2] Z. Mimouni, J.A.D. Wattis, Physica A, 388, 1067-1073, 2009

2000 Mathematics Subject Classification. 60G18Key words and phrases. Aggregation, similarity, electro-rheology.

405


On Additive Self-Dual Codes Over GF(4) And Their

Applications

Zlatko Varbanov

Department of Mathematics and Informatics, University of Veliko Tarnovo, Bulgaria

[email protected]

Abstract

After the publication [1], additive self-orthogonal codes over GF(4) under a trace inner product became of interestbecause of their correspondence to additive (or stabilizer) quantum error-correcting codes. Several papers were devotedto classifying or constructing additive self-dual codes over GF(4). It was shown [2] that certain vectors in some additiveself-dual codes over GF(4) hold generalized t-designs as well as classical t-designs with possibly repeated blocks. Also,every additive self-dual code over GF(4) can be uniquely represented as an undirected graph, and conversely. These factsmotivate the construction of additive self-dual codes over GF(4).

In this work we consider some constructive algorithms for additive self-dual codes over GF(4). We use these algorithmsto construct new codes. Also, we describe the relations between this class of codes and other combinatorial structures.

References[1] A. R. Calderbank, E. M. Rains, P. W. Shor, N. J. A. Sloane. Quantum error correction via codes over GF(4), IEEE Trans. Inform.

Theory. 44 (1998), 1369–1387.

[2] J.-L. Kim, V. Pless, Designs in Additive Codes over GF(4), Designs, Codes and Cryptography, Vol 30, (2003), 187–199

2000 Mathematics Subject Classification. primary: 94B05 secondaries: 05B05, 94B65, 68P30Key words and phrases. additive self-dual codes, block designs, quantum codes, constructive algorithms

406


8. ABOUT MALTEPE UNIVERSITY,ISTANBUL AND TURKEY

ABOUT MALTEPE UNIVERSITY

Maltepe University is the latest chain of the successful educational history of Marmara Education Institu-tions, which initiated its education with the motto ”From Kindergarten to University” in 1991. The University,which was founded by Istanbul Marmara Education Foundation (IMEV) in accordance with the law number4282, is subject to the terms pertaining to the Foundation and Higher Education Institution law number 2547,and it has the status of a legal entity. The University initiated its education in the buildings provided by theFoundation by admitting late-registered students in 1997. The Administrative Structure of the University wasset up in the historical pavilion at 39, Feyzullah Street. The University, which is made up of 9 faculties, 2vocational schools and 3 institutes, 2 vocational schools and 3 institutes, is currently rendering an invaluableservice with its scientific researches and publications. The University has brought together distinguished andexperienced academics to form its academic staff, and thanks to their efforts it has taken its place in theTurkish University system in high esteem.

ABOUT MALTEPE

Maltepe is a district in the suburbs of Istanbul, Turkey between Kadıkoy and Kartal. Its neighbors areKadıkoy to the west and Kartal to the east. The coast of Maltepe has been a retreat from the city sinceByzantine and Ottoman times, and right up until the 1970s was a rural area peppered with summer homes forwealthy Istanbul residents. Being on the suburban railway line Maltepe was a favorite spot for day-trippers orweekenders to visit the beach and many summer houses were built there. The sea-front is still pleasant to sit,drink tea and enjoy the views of the Princes Islands. The population grew rapidly from the 70’s onwards when,following the building of the Bosphorus Bridge, it became possible to commute from here to the European sideof the city. Buses along the E5 highway to the bridge, and minibuses to the ferry docks at Kadıkoy now carrylower-middle class commuters (the wealthier preferring to live in smarter areas nearer the city, in Kadıkoyitself). These people live either in quiet tree-lined streets of four- to six-storey apartment building with gardensaround them, or in modern housing complexes with tennis-courts, children’s playgrounds and security guardson the gate. The E5 highway cuts through Maltepe and north of the highway is the area of Basıbuyuk, atree-covered hill with a hospital on it (Istanbul’s tuberculosis isolation hospital) and also a large cemetery.Maltepe is also home to one of the largest Mosques in Istanbul. Below the Mosque there are a bookshop andsupermarket. The Mosque has been built according to the traditional standard shape of a Turkish Mosque(rounded shape with 4 minarets) but internally it is particularly impressive with a tall high dome, a largegallery and balcony where women may pray (which many do 5 times a day, it is now becoming more and morecommon to find women attending the Mosque to pray particularly on Fridays but more and more for all of thefive daily prayers especially amongst the young) The galleries have carved wood frames and there are severallarge tiled mosacs around the Mosque of various sights of importance to Islam and Muslims (for example theal-Aqsa Mosque in Jerusalem. The Mosque has become something of a central point for Maltepe as it bothcan be seen from a considerable distance and is a central stop for buses and minibuses taking commuters fromKadikoy to the outskirts of the city.

ABOUT ISTANBUL

The city which bridges two continents European side of Istanbul and Asian side of Istanbul, Istanbul whichwas known as capital of the capital cities, and created huge peace geographies with reigning to first Roma,and then Eastern Roman (Byzantium) Empire and continents, and was the capital city of Ottoman Empire, isgoing to be a modern future with preserving magnificence of history with proud. Variety in Istanbul is reallycharming the visitors. It is serving nice infinite nuances with its museums, churches, palaces, mosques, bazaar

407


places and natural beauties. When you lean against backside at the coast of the strait, you feel Istanbul as”center of the world” and understand why people select this extraordinary place centuries with watching thereflection of the red at sun set from the houses at the coast. It is the only city in the world to straddle two con-tinents, and the only one to have been a capital during two consecutive empires - Christian and Islamic. Oncecapital of the Ottoman Empire, Istanbul still remains the commercial, historical and cultural pulse of Turkey,and its beauty lies in its ability to embrace its contradictions. Ancient and modern, religious and secular, Asiaand Europe, mystical and earthly all co-exist here. Its variety is one of Istanbul’s greatest attractions: Theancient mosques, palaces, museums and bazaars reflect its diverse history.

ABOUT TURKEY

The Republic of Turkey, founded by Ataturk in 1923, has its roots in two historical sources deep in thedepths of the past. One of these resources inherited by modern Turkey is the successful and shining history ofthe Turks over a time frame of more than 4,000 years. The other is the fact that Turks have been settled inAnatolia since the 11th century. Ataturk coined the phrase ”The truest guide in life is science”.

General OutlineCapital City : AnkaraPopulation : 68,893,918 (July 2004 est.)The lands of Turkey are located at a point where the three continents making up the old world. Asia, Africa

and Europe are closest to each other, and straddle the point where Europe and Asia meet. Geographically,the country is located in the northern half of the hemisphere at a point that is about halfway between theequator and the north pole, at a longitude of 36 degrees N to 42 degrees N and a latitude of 26 degrees E to45 degrees E. Turkey is roughly rectangular in shape and is 1,660 kilometers wide. Because of its geographicallocation the mainland of Anatolia has always found favour throughout history, and is the birthplace of manygreat civilizations. It has also been prominent as a centre of commerce because of its land connections to threecontinents and the sea surrounding it on three sides.

AreaThe actual area of Turkey inclusive of its lakes, is 814,578 square kilometers, of which 790,200 are in Asia

and 24,378 are located in Europe.BoundariesThe land borders of Turkey are 2,573 kilometers in total, and coastlines (including islands) are another

8,333 kilometers, Turkey has two European and six Asian countries for neighbours along its land borders. Theland border to the northeast with the commonwealth of Independent States is 610 kilometers long; that withIran, 454 kilometers long, and that with Iraq 331 kilometers long. In the south is the 877 kilometer-long borderwith Syria. Turkey’s borders on the European continent consist of a 212-kilometre frontier with Greece and a269-kilometre border with Bulgaria.

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