Thesis Notes - WikispacesNotes.pdfThesis Notes 9 messages Mani Thu, ... {This is first chapter}...

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usman chaudry <[email protected]>

Thesis Notes9 messages

Mani <[email protected]> Thu, Aug 9, 2012 at 12:59 AMTo: usman chaudry <[email protected]>

Personal Agents:ECAI2012DocSymposiumChair

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Organizational Agents:

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Sub-Organizational Agent (RuleML-2012)

Sub-Organizational Agent (RuleML Structure)


UNBThesis2.tex

\documentclass[12pt]{unbthesis}

%\usepackage[left=4cm, right=2.5cm, top=2.5cm, bottom=2.5cm]{geometry}

\usepackage{graphicx}

\usepackage{subfig}

\usepackage[subfigure]{tocloft} % no number for Vita in ToC

\usepackage{fancyhdr}

\usepackage[english]{babel}

\usepackage{footmisc}

\usepackage{algorithmic}

\usepackage{listings}

\usepackage{fancyvrb}

\title{Type Title of Thesis here}

\author{Name of Candidate}

\predegree{Previous Degrees (i.e. Degree, University, Year)\\

Bachelor of Arts, UNB, 1999}

\degree{Name of Degree}

\gau{your GAU}

\supervisor{name1,degree department/field\\ & name2, degree

department/field}

\examboard{name1, degree, department/field,

Chair\\ & name2, degree, department}

\externalexam{name, degree,

department/field, institution}

\date{Month, Year of submission to Graduate School}

\copyrightyear{Year of graduation}

\setlength\parindent{0pt}

\newtheorem{theorem}{Theorem}[section]

\newtheorem{definition}{Definition}[section]

\newtheorem{lemma}{Lemma}[section]

\newtheorem{notation}{Notation}[section]

\begin{document}

\unbtitlepage

\setcounter{secnumdepth}{3} \setcounter{tocdepth}{3}


\pagenumbering{roman} \setcounter{page}{1}

\include{dedication}

\include{abstract}

\include{acknowledgments}

%%-----------Table of Contents------------------

\renewcommand{\contentsname}{Table of Contents}

\tableofcontents{}

\addcontentsline{toc}{chapter}{Table of Contents}

%%------------List of Tables----------------------

\listoftables{}

\addcontentsline{toc}{chapter}{List of Tables}

%%------------List of Figures----------------------

\listoffigures{}

\addcontentsline{toc}{chapter}{List of Figures}

\include{abbreviations}

%%-------------change single space to double space--------

\doublespacing \pagenumbering{arabic} \setcounter{page}{1}

\include{chapter1}

\include{chapter2}

\include{chapter3}

\include{chapter4}

\include{chapter5}

%\include{bibliography}

% changes default name Bibliography to References

%\renewcommand{\bibname}{References}

\bibliographystyle{amsplain}

\bibliography{mybibliography}

\addcontentsline{toc}{chapter}{Bibliography}

\include{appendices2}

\include{glossary}

\include{vita}

\end{document}


%%-----------Chapters start-------------------------------------

%%-----------Chapter 1------------------------------------------

\chapter{This is first chapter}

%\setcounter{secnumdepth}{3} \pagenumbering{arabic}

%\setcounter{page}{1} \pagestyle{myheadings}

%\markboth{}{}\markright{} \rhead{\thepage} \setcounter{page}{1}

%\pagestyle{myheadings} \pagenumbering{arabic} \rhead{\thepage}

%\setcounter{page}{1}

\section{ A section}

\subsection{A subsection}

This is a subsection. This is a subsection. This is a subsection.

This is a subsection. This is a subsection. This is a subsection.

This is a subsection. This is \hfill a subsection.


%%----------Chapter 2------------------------------------------

\chapter{This is second chapter}

\section{Example citation}

%%---------------example citation---------------------

Start writing from here. Here is a citation~\cite{Knuth92}

\section{Example Tables}

\subsection{A table with border} another paragraph and more text

and more and more and more and more and more text


%%------------------example table--------------------

\begin{table}[!h]

\caption{Example table}

\begin{center}

\begin{tabular}{| l || r | r | r | c |}

\hline

Name&Exam1&Exam2&Exam3&Grade\\

\hline\hline

John&19& 28&33&C \\

\hline

Smith&49& 35&60&B \\

\hline

Peter&76& 38&59&A \\

\hline

\end{tabular}

\end{center}

\end{table}

\subsection{A table without border}

Here is another example table without border. some symbols with

label can be refereed later on.

\begin{table}[!h]

\caption{Variable-sized Symbols}

\begin{center}

\begin{tabular}{l l l l l l}

$\sum$ \label{p1}&$\backslash$sum &$\bigcap$ \label{p2}&$\backslash$bigcap &$\bigodot$ &$\backslash$bigodot \\

$\prod$ &$\backslash$prod &$\bigcup$ &$\backslash$bigcup &$\bigotimes$ &$\backslash$bigotimes\\

$\coprod$ &$\backslash$coprod &$\bigsqcup$ &$\backslash$bigsqcup &$\bigoplus$ &$\backslash$bigoplus \\

$\int$ &$\backslash$int &$\bigvee$ &$\backslash$bigvee &$\biguplus$ &$\backslash$biguplus\\

$\oint$ &$\backslash$oint &$\bigwedge$ &$\backslash$bigwedge

\end{tabular}

\end{center}

\end{table}

\section{Example List}

\subsection{Example dotted list}

%%-----------------example dotted list--------------------


\smallskip

\textbf{Some special characters in TeX:}

\begin{itemize}

\item Accents

\item Braces

\item Dollar signs

\end{itemize}

\subsection{Example numbered list}

%%----------------example numbered list---------------------

\smallskip


\begin{enumerate}

\item Accents

\item Braces

\item Dollar signs

\end{enumerate}

\section{Math Example}

\subsection{Inline math mode}

%%-------------------example math equation----------

Mathematical material to be typeset inline must be surrounded by a

single dollar sign. For example: $a2 + b2 = c2$.

\subsection{Displayed math}

This is a displayed math example without numbering.

\[

\lim_{x \to a}f(x)

\]

\[

\left|\sum_{i=1}n a_ib_i\right| \le \left(\sum_{i=1}n

a_i2\right){1/2} \left(\sum_{i=1}n b_i2\right){1/2}

\]

This is a math equation with numbering.

\begin{equation}

(a+b)3 = (a+b)2(a+b)

\end{equation}

%%-----------------example aligned equation------------------

This is multiline equation example.

\begin{align}

(a+b)3 &= (a+b)2(a+b)\\

&=(a2+2ab+b2)(a+b)\\

&=(a3+2a2b+ab2) + (a2b+2ab2+b3)\\

&=a3+3a2b+3ab2+b3

\end{align}

%%--------------example matrix-------------------------------

This is a matrix


\[

\begin{matrix}

a+b & uv & x-y & 5\\

a+b+c & u+v &x+y & 10

\end{matrix}

\]

%%------------example cases----------------------------------

This is a case

\[

f(x)=

\begin{cases}

-x{2}, &\text{if $x<0$;}\\

\alpha+x, &\text{if $0 \leq x \leq 1$;}\\

x{2}, &\text{otherwise.}

\end{cases}

\]

%%-----------example theorem, definition, notation and lemma-----------

\subsection{math theorem, definition, notation and lemma}

\begin{theorem} A polynomial $p(z)$ of degree $n$ over $C$ has $n$ roots.

\end{theorem}

\begin{lemma} A polynomial $p(z)$ of degree $n>0$ over $C$ has at least

one root.

\end{lemma}

\begin{definition}

Let $D_{i}$, $i \in I$, be complete distributive

lattices satisfying condition~\textup{(J)}. Their

$\Pi{*}$ product is defined as follows:

\[

\Pi{*} ( D_{i} \mid i \in I ) =

\Pi ( D_{i}{-} \mid i \in I ) + 1;

\]

that is, $\Pi{*} ( D_{i} \mid i \in I )$ is

$\Pi ( D_{i}{-} \mid i \in I )$ with a new unit element.

\end{definition}

\begin{theorem}

If a lexicographic bottleneck problem can be solved in $O(f(m))$

time, then the type-1 lexicographic balanced optimization problem

can be solved in $O(mf(m))$ time.

\end{theorem}

\begin{theorem}The lexicographic bottleneck problem can be

solved in polynomial time if and only if LBaOP1 can be solved in

polynomial time.

\end{theorem}

\begin{notation}

If $i \in I$ and $d \in D_{i}{-}$, then

\[

\langle \dots, 0, \dots, \overset{i}{d}, \dots, 0,

\dots \rangle

\]

is the element of $\Pi{*} ( D_{i} \mid i \in I )$ whose

$i$th component is $d$ and all the other components

are $0$.

\end{notation}

%%---------------------------example proof---------------------

\subsection{math proof}

\begin{proof}[math theorem proof]

Let the length of every Hamiltonian path in $G$ be $\alpha .$ For

any edge $e=(i,j)\in E(G),$ let $w(e)=c_{ij}.$ Let $H$ be an

arbitrary Hamiltonian cycle in $G$ with

$E(H)=\{e_{1},e_{2},...,e_{n}\}$. For any $i\in \{1,\ldots ,n\},$

$C(H-e_{i})=\alpha .$ Hence $w(e_{i})=\alpha/(n-1)$ for $i=1,\ldots

,n.$ Since $H$ is arbitrary and $G$ is strongly Hamiltonian,

$w(e)=\alpha /(n-1)$ for all $e\in E(G).$

\end{proof}

\section{Graphics example}

\subsection{UNB logo}

%%--------------------example figure-------------------


The ideal graphics format for inclusion in a LaTex document is

"encapsulated postscript" or eps. Here is an example figure.

\begin{figure}[!hbp]

\begin{center}

\includegraphics{unblogo}

\caption{UNB logo}

\end{center}

\end{figure}


%%--------------------Chapter 3------------------------

\chapter{This is third chapter}

\section{A section}

%%--------------------example citation-----------------

Start writing from here~\cite{ConcreteMath}

\subsection{A subsection}

some text with footnote\footnote{A first}. more

text\footnote{second} and more.

%%-----------------text superscript, subscript--------------------

A sentence with superscript.\textsuperscript{superscript}. A

sentence with subscript.$_{\mbox{\footnotesize{subscript}}}$

%%-----------------printing verbatim--------------------------------


\subsection{Printing Verbatim}

\begin{verbatim}

THIS TEXT WILL BE DIRECTLY PRINTED AS IF TYPED ON A TYPEWRITER, WITH

ALL LINE BREAKS AND SPACES, without any LaTex command

being executed.

public class BasicsDemo{

public static void main(String[] args){

int sum = 0;

for (int current = 1; current <= 10; current++){

sum += current;

}

System.out.println("Sum = " + sum);

}

}

\end{verbatim}

\begin{Verbatim}[frame=single, xrightmargin=2pc]



int sum = 0;


sum += current;

}



}

}

\end{Verbatim}

%%---------------program code-------------------------------------

\section{A section}

\subsection{Pretty-printing program code}

\singlespacing

\begin{algorithmic}

\IF {$i\leq0$} \STATE $i\gets1$ \ELSE \IF {$i\geq0$} \STATE

$i\gets0$ \ENDIF \ENDIF

\end{algorithmic}

\subsubsection{Example Java code}

The following is an code example:

\begin{lstlisting}[language=Java]



int sum = 0;


sum += current;

}


}

}

\end{lstlisting}

\doublespacing



%%----------------Bibliography--------------------------------

\begin{thebibliography}{99}

\addcontentsline{toc}{chapter}{Bibliography}

\bibitem{k1} R.J. Drofnats, \emph{Proof of the Riemann

Hypothesis}, preprint, available at

\texttt{http://www.drofnats.com/riemann.ps}.

\bibitem{k2} P. Erd\H os, \emph{A selection of problems and

results in combinatorics}, Recent trends in combinatorics

(Matrahaza, 1995), Cambridge Univ. Press, Cambridge, 2001, pp. 1--6.

\bibitem{k3}

R.L. Graham, D.E. Knuth, and O. Patashnik, \emph{Concrete

mathematics}, Addison-Wesley, Reading, MA, 1989.

\bibitem{Knuth92} D.E. Knuth, \emph{Two notes on notation}, Amer.

Math. Monthly \textbf{99} (1992), 403--422.

\bibitem{Drofnats} R.J. Drofnats, \emph{Proof of the Riemann

Hypothesis}, preprint, available at

\texttt{http://www.drofnats.com/riemann.ps}.

\bibitem{Erdos01} P. Erd\H os, \emph{A selection of problems and

results in combinatorics}, Recent trends in combinatorics

(Matrahaza, 1995), Cambridge Univ. Press, Cambridge, 2001, pp. 1--6.

\bibitem{ConcreteMath}

R.L. Graham, D.E. Knuth, and O. Patashnik, \emph{Concrete

mathematics}, Addison-Wesley, Reading, MA, 1989.

\end{thebibliography}



%%---------------Appendices--------------------------------

\appendix

\chapter{this is Appendix A}

\section{this is section1}

Start writing here.

\begin{equation}

(a+b)3 = (a+b)2(a+b)

\end{equation}

\section{this is section2}

\begin{equation}

(a+b)3 = (a+b)2(a+b)

\end{equation}

\chapter{this is Appendix B}

\section{this is section1} Start writing here.

\begin{equation}

(a+b)3 = (a+b)2(a+b)

\end{equation}

\subsection{this is subsection}

\begin{equation}

(a+b)3 = (a+b)2(a+b)

\end{equation}

Mani <[email protected]> Thu, Aug 9, 2012 at 3:29 PMTo: usman chaudry <[email protected]>

%%----------Chapter 2------------------------------------------

\chapter{This is second chapter}

\section{Example citation}

%%---------------example citation---------------------

Start writing from here. Here is a citation~\cite{Knuth92}

\section{Example Tables}

\subsection{A table with border} another paragraph and more text

and more and more and more and more and more text

%%------------------example table--------------------


[Quoted text hidden]

\smallskip


\begin{itemize}

\item Accents

\item Braces

\item Dollar signs

\end{itemize}

\subsection{Example numbered list}

%%----------------example numbered list---------------------

\smallskip


\begin{enumerate}

\item Accents

\item Braces

\item Dollar signs

\end{enumerate}

\section{Math Example}

\subsection{Inline math mode}

%%-------------------example math equation----------


Mathematical material to be typeset inline must be surrounded by a

single dollar sign. For example: $a2 + b2 = c2$.

\subsection{Displayed math}

This is a displayed math example without numbering.

\[

\lim_{x \to a}f(x)

\]

\[

\left|\sum_{i=1}n a_ib_i\right| \le \left(\sum_{i=1}n

a_i2\right){1/2} \left(\sum_{i=1}n b_i2\right){1/2}

\]

This is a math equation with numbering.

\begin{equation}

(a+b)3 = (a+b)2(a+b)

\end{equation}

%%-----------------example aligned equation------------------

This is multiline equation example.

\begin{align}

(a+b)3 &= (a+b)2(a+b)\\


&=(a2+2ab+b2)(a+b)\\

&=(a3+2a2b+ab2) + (a2b+2ab2+b3)\\

&=a3+3a2b+3ab2+b3

\end{align}

%%--------------example matrix-------------------------------

This is a matrix

\[

\begin{matrix}

a+b & uv & x-y & 5\\

a+b+c & u+v &x+y & 10

\end{matrix}

\]

%%------------example cases----------------------------------

This is a case

\[

f(x)=

\begin{cases}

-x{2}, &\text{if $x<0$;}\\

\alpha+x, &\text{if $0 \leq x \leq 1$;}\\

x{2}, &\text{otherwise.}

\end{cases}

\]

%%-----------example theorem, definition, notation and lemma-----------

\subsection{math theorem, definition, notation and lemma}

\begin{theorem} A polynomial $p(z)$ of degree $n$ over $C$ has $n$ roots.

\end{theorem}

\begin{lemma} A polynomial $p(z)$ of degree $n>0$ over $C$ has at least

one root.

\end{lemma}

\begin{definition}

Let $D_{i}$, $i \in I$, be complete distributive

lattices satisfying condition~\textup{(J)}. Their

$\Pi{*}$ product is defined as follows:

\[

\Pi{*} ( D_{i} \mid i \in I ) =

\Pi ( D_{i}{-} \mid i \in I ) + 1;

\]

that is, $\Pi{*} ( D_{i} \mid i \in I )$ is

$\Pi ( D_{i}{-} \mid i \in I )$ with a new unit element.

\end{definition}


\begin{theorem}

If a lexicographic bottleneck problem can be solved in $O(f(m))$

time, then the type-1 lexicographic balanced optimization problem

can be solved in $O(mf(m))$ time.

\end{theorem}

\begin{theorem}The lexicographic bottleneck problem can be

solved in polynomial time if and only if LBaOP1 can be solved in

polynomial time.

\end{theorem}

\begin{notation}

If $i \in I$ and $d \in D_{i}{-}$, then

\[

\langle \dots, 0, \dots, \overset{i}{d}, \dots, 0,

\dots \rangle

\]

is the element of $\Pi{*} ( D_{i} \mid i \in I )$ whose

$i$th component is $d$ and all the other components

are $0$.

\end{notation}

%%---------------------------example proof---------------------

\subsection{math proof}

\begin{proof}[math theorem proof]

Let the length of every Hamiltonian path in $G$ be $\alpha .$ For

any edge $e=(i,j)\in E(G),$ let $w(e)=c_{ij}.$ Let $H$ be an

arbitrary Hamiltonian cycle in $G$ with

$E(H)=\{e_{1},e_{2},...,e_{n}\}$. For any $i\in \{1,\ldots ,n\},$

$C(H-e_{i})=\alpha .$ Hence $w(e_{i})=\alpha/(n-1)$ for $i=1,\ldots

,n.$ Since $H$ is arbitrary and $G$ is strongly Hamiltonian,

$w(e)=\alpha /(n-1)$ for all $e\in E(G).$

\end{proof}

\section{Graphics example}

\subsection{UNB logo}

%%--------------------example figure-------------------

The ideal graphics format for inclusion in a LaTex document is

"encapsulated postscript" or eps. Here is an example figure.

\begin{figure}[!hbp]

\begin{center}


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\includegraphics{unblogo}

\caption{UNB logo}

\end{center}

\end{figure}

Mani <[email protected]>To: usman chaudry <[email protected]>

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You are here: Resources » LaTeX Guide » Symbols

LaTeX:Symbols

LaTeX

About - LaTeX on AoPS - Downloads - Basics - Math - Examples - Pictures - Layout - Symbols - Commands - Packages - Help

This article will provide a short list of commonly used LaTeX symbols.

Contents [hide]

1 Operators

2 Relations

3 Greek Letters

4 Headline text

5 Arrows

6 Dots

7 Accents

8 Others

9 Command Symbols

10 European Language Symbols

11 Bracketing Symbols

12 Multi-Size Symbols

13 Examples

14 See Also

Operators

SymbolCommand SymbolCommandSymbolCommand

\pm \mp \times\div \cdot \ast\star \dagger \ddagger

\amalg \cap \cup\uplus \sqcap \sqcup\vee \wedge \oplus\ominus \otimes \circ\bullet \diamond \lhd\rhd \unlhd \unrhd

\oslash \odot \bigcirc

\triangleleft \Diamond \bigtriangleup\bigtriangledown \Box \triangleright

\setminus \wr


\sqrt{x}

Relations


\le \ge \neq

\sim \ll \gg\doteq \simeq \subset\supset \approx \asymp\subseteq \supseteq \cong\smile \sqsubset \sqsupset\equiv \frown \sqsubseteq\sqsupseteq \propto \bowtie\in \ni \prec

\succ \vdash \dashv\preceq \succeq \models

\perp \parallel \|

\mid

Negations of many of these relations can be formed by just putting \not before the symbol, or by slipping an n between the \ and the word. Here

are a few examples, plus a few other negations; it works for many of the others as well.


\nmid \nleq \ngeq

\nsim \ncong \nparallel

\not< \not> \not=

\not\le \not\ge \not\sim

\not\approx \not\cong \not\equiv

\not\parallel \nless \ngtr

\lneq \gneq \lnsim

\lneqq \gneqq

To use other relations not listed here, such as =, >, and <, in LaTeX, you may just use the symbols on your keyboard.

Greek Letters

Lowercase Letters

SymbolCommandSymbolCommandSymbolCommandSymbolCommand

\alpha \beta \gamma \delta\epsilon \varepsilon \zeta \eta\theta \vartheta \iota \kappa\lambda \mu \nu \xi\pi \varpi \rho \varrho

\sigma \varsigma \tau \upsilon\phi \varphi \chi \psi\omega

Capital Letters


\Gamma \Delta \Theta \Lambda\Xi \Pi \Sigma \Upsilon\Phi \Psi \Omega

Headline text

Arrows

SymbolCommand SymbolCommand

\gets \to\leftarrow \Leftarrow\rightarrow \Rightarrow\leftrightarrow \Leftrightarrow\mapsto \hookleftarrow\leftharpoonup \leftharpoondown\rightleftharpoons \longleftarrow\Longleftarrow \longrightarrow\Longrightarrow \longleftrightarrow

\Longleftrightarrow \longmapsto\hookrightarrow \rightharpoonup\rightharpoondown \leadsto\uparrow \Uparrow

\downarrow \Downarrow

\updownarrow \Updownarrow

\nearrow \searrow

\swarrow \nwarrow

Dots


\ldots 2 \vdots \cdots 2 \ddots

(The '2's after \ldots and \cdots are only present to make the distinction between the two clear.)

Accents

SymbolCommandSymbolCommandSymbolCommand


\hat{x} \check{x} \dot{x}

\breve{x} \acute{x} \ddot{x}\grave{x} \tilde{x} \mathring{x}\bar{x} \vec{x}

When applying accents to i and j, you can use \imath and \jmath to keep the dots from interfering with the accents:


\vec{\jmath} \tilde{\imath}

\tilde and \hat have wide versions that allow you to accent an expression:


\widehat{3+x} \widetilde{abc}

Others

SymbolCommandSymbolCommand SymbolCommand

\infty \triangle \angle\aleph \hbar \imath\jmath \ell \wp

\Re \Im \mho\prime \emptyset \nabla\surd \partial \top

\bot \vdash \dashv\forall \exists \neg\flat \natural \sharp

\backslash \Box \Diamond

\clubsuit \diamondsuit \heartsuit\spadesuit \Join \blacksquare

\S \P \copyright

\pounds

Command Symbols

Some symbols are used in commands so they need to be treated in a special way.


$$ \$ \& \% \#

\_ \{ \} \backslash

European Language Symbols


{\oe} {\ae} {\aa} {\o}{\OE} {\AE} {\AA} {\O}

{\l} {\ss} !{\L} {\SS} ?`

Bracketing Symbols

In mathematics, sometimes we need to enclose expressions in brackets or braces or parentheses. Some of these work just as you'd imagine in

LaTeX; type ( and ) for parentheses, [ and ] for brackets, and | and | for absolute value. However, other symbols have special commands:


\{ \} \|

\backslash \lfloor \rfloor

\lceil \rceil \langle

\rangle

You might notice that if you use any of these to typeset an expression that is vertically large, like

(\frac{a}{x} )2

the parentheses don't come out the right size:

If we put \left and \right before the relevant parentheses, we get a prettier expression:

\left(\frac{a}{x} \right)2

gives

\left and \right can also be used to resize the following symbols:

SymbolCommandSymbolCommand SymbolCommand

\uparrow \downarrow \updownarrow

\Uparrow \Downarrow \Updownarrow

Multi-Size Symbols

Some symbols render differently in inline math mode and in display mode Display mode occurs when you use \[...\] or $$...$$, or environments like

\begin{equation}...\end{equation}, \begin{align}...\end{align}. Read more in the commands section of the guide about how symbols which take

arguments above and below the symbols, such as a summation symbol, behave in the two modes.


In each of the following, the two images show the symbol in display mode, then in inline mode.


\sum \int \oint

\prod \coprod \bigcap

\bigcup \bigsqcup \bigvee

\bigwedge \bigodot \bigotimes

\bigoplus \biguplus

Examples

x^y is the same as x^{y}, producing .

x_y is the same as x_{y}, producing .

However, x^10 is not the same as x^{10}. The former produces instead of .

See Also

Next: Commands

Previous: Layout

Category: LaTeX

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