On the Margin Stability of Interval Matrices · On the Margin Stability of Interval Matrices by...

63
On the Margin Stability of Interval Matrices by Muhammad Yousuf A Thesis Presented to the FACULTY OF THE COLLEGE OF GRADUATE STUDIES KING FAHD UNIVERSITY OF PETROLEUM & MINERALS DHAHRAN, SAUDI ARABIA In Partial Fulfillment of the Requirements for the Degree of MASTER OF SCIENCE In MATHEMATICAL SCIENCES December, 1996

Transcript of On the Margin Stability of Interval Matrices · On the Margin Stability of Interval Matrices by...

Page 1: On the Margin Stability of Interval Matrices · On the Margin Stability of Interval Matrices by Muhammad Yousuf A Thesis Presented to the FACULTY OF THE COLLEGE OF GRADUATE STUDIES

On the Margin Stability of Interval Matrices

by

Muhammad Yousuf

A Thesis Presented to the

FACULTY OF THE COLLEGE OF GRADUATE STUDIES

KING FAHD UNIVERSITY OF PETROLEUM & MINERALS

DHAHRAN, SAUDI ARABIA

In Partial Fulfillment of the Requirements for the Degree of

MASTER OF SCIENCE

In

MATHEMATICAL SCIENCES

December, 1996

Page 2: On the Margin Stability of Interval Matrices · On the Margin Stability of Interval Matrices by Muhammad Yousuf A Thesis Presented to the FACULTY OF THE COLLEGE OF GRADUATE STUDIES
Page 3: On the Margin Stability of Interval Matrices · On the Margin Stability of Interval Matrices by Muhammad Yousuf A Thesis Presented to the FACULTY OF THE COLLEGE OF GRADUATE STUDIES
Page 4: On the Margin Stability of Interval Matrices · On the Margin Stability of Interval Matrices by Muhammad Yousuf A Thesis Presented to the FACULTY OF THE COLLEGE OF GRADUATE STUDIES
Page 5: On the Margin Stability of Interval Matrices · On the Margin Stability of Interval Matrices by Muhammad Yousuf A Thesis Presented to the FACULTY OF THE COLLEGE OF GRADUATE STUDIES
Page 6: On the Margin Stability of Interval Matrices · On the Margin Stability of Interval Matrices by Muhammad Yousuf A Thesis Presented to the FACULTY OF THE COLLEGE OF GRADUATE STUDIES
Page 7: On the Margin Stability of Interval Matrices · On the Margin Stability of Interval Matrices by Muhammad Yousuf A Thesis Presented to the FACULTY OF THE COLLEGE OF GRADUATE STUDIES
Page 8: On the Margin Stability of Interval Matrices · On the Margin Stability of Interval Matrices by Muhammad Yousuf A Thesis Presented to the FACULTY OF THE COLLEGE OF GRADUATE STUDIES
Page 9: On the Margin Stability of Interval Matrices · On the Margin Stability of Interval Matrices by Muhammad Yousuf A Thesis Presented to the FACULTY OF THE COLLEGE OF GRADUATE STUDIES
Page 10: On the Margin Stability of Interval Matrices · On the Margin Stability of Interval Matrices by Muhammad Yousuf A Thesis Presented to the FACULTY OF THE COLLEGE OF GRADUATE STUDIES
Page 11: On the Margin Stability of Interval Matrices · On the Margin Stability of Interval Matrices by Muhammad Yousuf A Thesis Presented to the FACULTY OF THE COLLEGE OF GRADUATE STUDIES
Page 12: On the Margin Stability of Interval Matrices · On the Margin Stability of Interval Matrices by Muhammad Yousuf A Thesis Presented to the FACULTY OF THE COLLEGE OF GRADUATE STUDIES
Page 13: On the Margin Stability of Interval Matrices · On the Margin Stability of Interval Matrices by Muhammad Yousuf A Thesis Presented to the FACULTY OF THE COLLEGE OF GRADUATE STUDIES
Page 14: On the Margin Stability of Interval Matrices · On the Margin Stability of Interval Matrices by Muhammad Yousuf A Thesis Presented to the FACULTY OF THE COLLEGE OF GRADUATE STUDIES
Page 15: On the Margin Stability of Interval Matrices · On the Margin Stability of Interval Matrices by Muhammad Yousuf A Thesis Presented to the FACULTY OF THE COLLEGE OF GRADUATE STUDIES
Page 16: On the Margin Stability of Interval Matrices · On the Margin Stability of Interval Matrices by Muhammad Yousuf A Thesis Presented to the FACULTY OF THE COLLEGE OF GRADUATE STUDIES
Page 17: On the Margin Stability of Interval Matrices · On the Margin Stability of Interval Matrices by Muhammad Yousuf A Thesis Presented to the FACULTY OF THE COLLEGE OF GRADUATE STUDIES
Page 18: On the Margin Stability of Interval Matrices · On the Margin Stability of Interval Matrices by Muhammad Yousuf A Thesis Presented to the FACULTY OF THE COLLEGE OF GRADUATE STUDIES
Page 19: On the Margin Stability of Interval Matrices · On the Margin Stability of Interval Matrices by Muhammad Yousuf A Thesis Presented to the FACULTY OF THE COLLEGE OF GRADUATE STUDIES
Page 20: On the Margin Stability of Interval Matrices · On the Margin Stability of Interval Matrices by Muhammad Yousuf A Thesis Presented to the FACULTY OF THE COLLEGE OF GRADUATE STUDIES
Page 21: On the Margin Stability of Interval Matrices · On the Margin Stability of Interval Matrices by Muhammad Yousuf A Thesis Presented to the FACULTY OF THE COLLEGE OF GRADUATE STUDIES
Page 22: On the Margin Stability of Interval Matrices · On the Margin Stability of Interval Matrices by Muhammad Yousuf A Thesis Presented to the FACULTY OF THE COLLEGE OF GRADUATE STUDIES
Page 23: On the Margin Stability of Interval Matrices · On the Margin Stability of Interval Matrices by Muhammad Yousuf A Thesis Presented to the FACULTY OF THE COLLEGE OF GRADUATE STUDIES
Page 24: On the Margin Stability of Interval Matrices · On the Margin Stability of Interval Matrices by Muhammad Yousuf A Thesis Presented to the FACULTY OF THE COLLEGE OF GRADUATE STUDIES
Page 25: On the Margin Stability of Interval Matrices · On the Margin Stability of Interval Matrices by Muhammad Yousuf A Thesis Presented to the FACULTY OF THE COLLEGE OF GRADUATE STUDIES
Page 26: On the Margin Stability of Interval Matrices · On the Margin Stability of Interval Matrices by Muhammad Yousuf A Thesis Presented to the FACULTY OF THE COLLEGE OF GRADUATE STUDIES
Page 27: On the Margin Stability of Interval Matrices · On the Margin Stability of Interval Matrices by Muhammad Yousuf A Thesis Presented to the FACULTY OF THE COLLEGE OF GRADUATE STUDIES
Page 28: On the Margin Stability of Interval Matrices · On the Margin Stability of Interval Matrices by Muhammad Yousuf A Thesis Presented to the FACULTY OF THE COLLEGE OF GRADUATE STUDIES
Page 29: On the Margin Stability of Interval Matrices · On the Margin Stability of Interval Matrices by Muhammad Yousuf A Thesis Presented to the FACULTY OF THE COLLEGE OF GRADUATE STUDIES
Page 30: On the Margin Stability of Interval Matrices · On the Margin Stability of Interval Matrices by Muhammad Yousuf A Thesis Presented to the FACULTY OF THE COLLEGE OF GRADUATE STUDIES
Page 31: On the Margin Stability of Interval Matrices · On the Margin Stability of Interval Matrices by Muhammad Yousuf A Thesis Presented to the FACULTY OF THE COLLEGE OF GRADUATE STUDIES
Page 32: On the Margin Stability of Interval Matrices · On the Margin Stability of Interval Matrices by Muhammad Yousuf A Thesis Presented to the FACULTY OF THE COLLEGE OF GRADUATE STUDIES
Page 33: On the Margin Stability of Interval Matrices · On the Margin Stability of Interval Matrices by Muhammad Yousuf A Thesis Presented to the FACULTY OF THE COLLEGE OF GRADUATE STUDIES
Page 34: On the Margin Stability of Interval Matrices · On the Margin Stability of Interval Matrices by Muhammad Yousuf A Thesis Presented to the FACULTY OF THE COLLEGE OF GRADUATE STUDIES
Page 35: On the Margin Stability of Interval Matrices · On the Margin Stability of Interval Matrices by Muhammad Yousuf A Thesis Presented to the FACULTY OF THE COLLEGE OF GRADUATE STUDIES
Page 36: On the Margin Stability of Interval Matrices · On the Margin Stability of Interval Matrices by Muhammad Yousuf A Thesis Presented to the FACULTY OF THE COLLEGE OF GRADUATE STUDIES
Page 37: On the Margin Stability of Interval Matrices · On the Margin Stability of Interval Matrices by Muhammad Yousuf A Thesis Presented to the FACULTY OF THE COLLEGE OF GRADUATE STUDIES
Page 38: On the Margin Stability of Interval Matrices · On the Margin Stability of Interval Matrices by Muhammad Yousuf A Thesis Presented to the FACULTY OF THE COLLEGE OF GRADUATE STUDIES
Page 39: On the Margin Stability of Interval Matrices · On the Margin Stability of Interval Matrices by Muhammad Yousuf A Thesis Presented to the FACULTY OF THE COLLEGE OF GRADUATE STUDIES
Page 40: On the Margin Stability of Interval Matrices · On the Margin Stability of Interval Matrices by Muhammad Yousuf A Thesis Presented to the FACULTY OF THE COLLEGE OF GRADUATE STUDIES
Page 41: On the Margin Stability of Interval Matrices · On the Margin Stability of Interval Matrices by Muhammad Yousuf A Thesis Presented to the FACULTY OF THE COLLEGE OF GRADUATE STUDIES
Page 42: On the Margin Stability of Interval Matrices · On the Margin Stability of Interval Matrices by Muhammad Yousuf A Thesis Presented to the FACULTY OF THE COLLEGE OF GRADUATE STUDIES
Page 43: On the Margin Stability of Interval Matrices · On the Margin Stability of Interval Matrices by Muhammad Yousuf A Thesis Presented to the FACULTY OF THE COLLEGE OF GRADUATE STUDIES
Page 44: On the Margin Stability of Interval Matrices · On the Margin Stability of Interval Matrices by Muhammad Yousuf A Thesis Presented to the FACULTY OF THE COLLEGE OF GRADUATE STUDIES
Page 45: On the Margin Stability of Interval Matrices · On the Margin Stability of Interval Matrices by Muhammad Yousuf A Thesis Presented to the FACULTY OF THE COLLEGE OF GRADUATE STUDIES
Page 46: On the Margin Stability of Interval Matrices · On the Margin Stability of Interval Matrices by Muhammad Yousuf A Thesis Presented to the FACULTY OF THE COLLEGE OF GRADUATE STUDIES
Page 47: On the Margin Stability of Interval Matrices · On the Margin Stability of Interval Matrices by Muhammad Yousuf A Thesis Presented to the FACULTY OF THE COLLEGE OF GRADUATE STUDIES
Page 48: On the Margin Stability of Interval Matrices · On the Margin Stability of Interval Matrices by Muhammad Yousuf A Thesis Presented to the FACULTY OF THE COLLEGE OF GRADUATE STUDIES
Page 49: On the Margin Stability of Interval Matrices · On the Margin Stability of Interval Matrices by Muhammad Yousuf A Thesis Presented to the FACULTY OF THE COLLEGE OF GRADUATE STUDIES
Page 50: On the Margin Stability of Interval Matrices · On the Margin Stability of Interval Matrices by Muhammad Yousuf A Thesis Presented to the FACULTY OF THE COLLEGE OF GRADUATE STUDIES
Page 51: On the Margin Stability of Interval Matrices · On the Margin Stability of Interval Matrices by Muhammad Yousuf A Thesis Presented to the FACULTY OF THE COLLEGE OF GRADUATE STUDIES
Page 52: On the Margin Stability of Interval Matrices · On the Margin Stability of Interval Matrices by Muhammad Yousuf A Thesis Presented to the FACULTY OF THE COLLEGE OF GRADUATE STUDIES
Page 53: On the Margin Stability of Interval Matrices · On the Margin Stability of Interval Matrices by Muhammad Yousuf A Thesis Presented to the FACULTY OF THE COLLEGE OF GRADUATE STUDIES
Page 54: On the Margin Stability of Interval Matrices · On the Margin Stability of Interval Matrices by Muhammad Yousuf A Thesis Presented to the FACULTY OF THE COLLEGE OF GRADUATE STUDIES
Page 55: On the Margin Stability of Interval Matrices · On the Margin Stability of Interval Matrices by Muhammad Yousuf A Thesis Presented to the FACULTY OF THE COLLEGE OF GRADUATE STUDIES
Page 56: On the Margin Stability of Interval Matrices · On the Margin Stability of Interval Matrices by Muhammad Yousuf A Thesis Presented to the FACULTY OF THE COLLEGE OF GRADUATE STUDIES
Page 57: On the Margin Stability of Interval Matrices · On the Margin Stability of Interval Matrices by Muhammad Yousuf A Thesis Presented to the FACULTY OF THE COLLEGE OF GRADUATE STUDIES
Page 58: On the Margin Stability of Interval Matrices · On the Margin Stability of Interval Matrices by Muhammad Yousuf A Thesis Presented to the FACULTY OF THE COLLEGE OF GRADUATE STUDIES
Page 59: On the Margin Stability of Interval Matrices · On the Margin Stability of Interval Matrices by Muhammad Yousuf A Thesis Presented to the FACULTY OF THE COLLEGE OF GRADUATE STUDIES
Page 60: On the Margin Stability of Interval Matrices · On the Margin Stability of Interval Matrices by Muhammad Yousuf A Thesis Presented to the FACULTY OF THE COLLEGE OF GRADUATE STUDIES
Page 61: On the Margin Stability of Interval Matrices · On the Margin Stability of Interval Matrices by Muhammad Yousuf A Thesis Presented to the FACULTY OF THE COLLEGE OF GRADUATE STUDIES
Page 62: On the Margin Stability of Interval Matrices · On the Margin Stability of Interval Matrices by Muhammad Yousuf A Thesis Presented to the FACULTY OF THE COLLEGE OF GRADUATE STUDIES
Page 63: On the Margin Stability of Interval Matrices · On the Margin Stability of Interval Matrices by Muhammad Yousuf A Thesis Presented to the FACULTY OF THE COLLEGE OF GRADUATE STUDIES

Exact sampling and counting for fixed-margin …EXACT SAMPLING AND COUNTING FOR FIXED-MARGIN MATRICES By Jeffrey W. Miller and Matthew T. Harrison∗ Brown University The uniform distribution

Exact sampling and counting for fixed-margin …EXACT SAMPLING AND COUNTING FOR FIXED-MARGIN MATRICES By Jeffrey W. Miller and Matthew T. Harrison∗ Brown University The uniform distribution

Dot Plots, Path Matrices, Score Matrices

Dot Plots, Path Matrices, Score Matrices

3. Matrices...3. Matrices • Introduction • Matrix • Types of Matrices • Operations on Matrices • Transpose of a Matrix • Symmetric and Skew Symmetric Matrices What are

3. Matrices...3. Matrices • Introduction • Matrix • Types of Matrices • Operations on Matrices • Transpose of a Matrix • Symmetric and Skew Symmetric Matrices What are

Matrices: §2.4 Elementary Matrices

Matrices: §2.4 Elementary Matrices

Statistics - Interval Estimationhomepage.ntu.edu.tw/~sschen/Teaching/Lecture9_IntervalEst... · 2019-12-15 · Interval Estimation Interval Estimator An interval estimator is a random

Statistics - Interval Estimationhomepage.ntu.edu.tw/~sschen/Teaching/Lecture9_IntervalEst... · 2019-12-15 · Interval Estimation Interval Estimator An interval estimator is a random

Matrices & Systems of Linear Equations. Special Matrices.

Matrices & Systems of Linear Equations. Special Matrices.

CROP MARKS MARGIN MARGIN Fra MARGIN … CROP MARKS MARGIN MARGIN CROP MARKS MARGIN MARGIN CROP MARKS MARGIN MARGIN CROP MARKS MARGIN Fraud Barometer 2018 | 5 The national picture nd

CROP MARKS MARGIN MARGIN Fra MARGIN … CROP MARKS MARGIN MARGIN CROP MARKS MARGIN MARGIN CROP MARKS MARGIN MARGIN CROP MARKS MARGIN Fraud Barometer 2018 | 5 The national picture nd

The Future of Defence · 0 MARGIN CROP MARKS MARGIN MARGIN CROP MARKS MARGIN MARGIN CROP MARKS MARGIN MARGIN CROP MARKS MARGIN The future of defence. Throughout this document, “we”,

The Future of Defence · 0 MARGIN CROP MARKS MARGIN MARGIN CROP MARKS MARGIN MARGIN CROP MARKS MARGIN MARGIN CROP MARKS MARGIN The future of defence. Throughout this document, “we”,

Ocean Drilling Program Initial Reports Volume 103...Figure 2. Bathymetry of the continental margin northwest of the Iberian Peninsula. Contours in meters; contour interval, 200 m.

Ocean Drilling Program Initial Reports Volume 103...Figure 2. Bathymetry of the continental margin northwest of the Iberian Peninsula. Contours in meters; contour interval, 200 m.

Matrices 4.1 Introduction to Matrices · Matrices 4.1 Introduction to Matrices Objectives: • Students will organize data into matrices • Students will solve equations using matrices

Matrices 4.1 Introduction to Matrices · Matrices 4.1 Introduction to Matrices Objectives: • Students will organize data into matrices • Students will solve equations using matrices

Matrices & Determinants Chapter: 1 Matrices & Determinants.

Matrices & Determinants Chapter: 1 Matrices & Determinants.

CROP MARKS MARGIN The Wheely Big Cycle route map · MARGIN CROP MARKS MARGIN MARGIN CROP MARKS MARGIN MARGIN CROP MARKS MARGIN MARGIN CROP MARKS MARGIN. North Route South Route .

CROP MARKS MARGIN The Wheely Big Cycle route map · MARGIN CROP MARKS MARGIN MARGIN CROP MARKS MARGIN MARGIN CROP MARKS MARGIN MARGIN CROP MARKS MARGIN. North Route South Route .

FUZZY INTERVAL MATRICES, NEUTROSOPHIC INTERVAL MATRICES, by W.B.Vasantha Kandasamy, F.Smarandache

FUZZY INTERVAL MATRICES, NEUTROSOPHIC INTERVAL MATRICES, by W.B.Vasantha Kandasamy, F.Smarandache

Interval Linear Programming with generalized interval arithmetic › researchpaper › Interval-Linear... · 2016-09-09 · Interval Linear Programming with generalized interval arithmetic

Interval Linear Programming with generalized interval arithmetic › researchpaper › Interval-Linear... · 2016-09-09 · Interval Linear Programming with generalized interval arithmetic

FUZZY INTERVAL MATRICES,

FUZZY INTERVAL MATRICES,

FINANCIAL SECURITIES: MARGIN ACCOUNTS CIE 3M1. AGENDA OPENING A MARGIN ACCOUNT OPENING A MARGIN ACCOUNT MARGIN ACCOUNTS: A DEFINITION MARGIN ACCOUNTS:

FINANCIAL SECURITIES: MARGIN ACCOUNTS CIE 3M1. AGENDA OPENING A MARGIN ACCOUNT OPENING A MARGIN ACCOUNT MARGIN ACCOUNTS: A DEFINITION MARGIN ACCOUNTS:

KPMG Transport Tracker€¦ · MARGIN CROP MARKS MARGIN MARGIN CROP MARKS MARGIN MARGIN CROP MARKS MARGIN MARGIN CROP MARKS MARGIN. Market fundamentals . Share prices (end of October

KPMG Transport Tracker€¦ · MARGIN CROP MARKS MARGIN MARGIN CROP MARKS MARGIN MARGIN CROP MARKS MARGIN MARGIN CROP MARKS MARGIN. Market fundamentals . Share prices (end of October

Neutrosophic Super Matrices and Quasi Super Matrices

Neutrosophic Super Matrices and Quasi Super Matrices

MATRICES - · PDF filecrackiitjee.in MATRICES

MATRICES - · PDF filecrackiitjee.in MATRICES

MANUAL-Interval, Interval 120cm, Interval 140cm-ALL-vA

MANUAL-Interval, Interval 120cm, Interval 140cm-ALL-vA