\documentclass{article}      % Specifies the document class
\usepackage{stmaryrd}	%gestion des parall¸les 
\usepackage{amssymb} % pour les inferieurs
\usepackage{multicol} % pour gerer plusieurs colonnes
\usepackage{yhmath} % permet de gˇrer les arcs
\usepackage{makeidx}
\usepackage[T1]{fontenc}
\usepackage[LY1]{fontenc}
\usepackage{txfonts}
\usepackage{pxfonts}
\usepackage{textcomp}
\usepackage{txfonts}
\usepackage{wasysym}
\usepackage[left=0.5in, right=0.5in, top=0.5in, bottom=0.5in, textwidth=2in]{geometry} % The preamble begins here.
\title{LATEX Example document.tex}  % Declares the document's title.
\author{produced by  "iMathGeo"  \& "Softwares" generator under \copyright }      % Declares the author's name.
\date{Sunday on June 12, 2011 at 09:01AM}      % Deleting this command produces today's date.
\newcommand{\ip}[2]{(#1, #2)}
                             % Defines \ip{arg1}{arg2} to mean
                             % (arg1, arg2).
\def\euro{\mbox{\raisebox{.25ex}{{\it =}}\hspace{-.5em}{\sf C}}}

%\newcommand{\ip}[2]{\langle #1 | #2\rangle}
                             % This is an alternative definition of
                             % \ip that is commented out.

\newif\ifpdf
\ifx\pdfoutput\undefined
\pdffalse % we are not running PDFLaTeX
\else
\pdfoutput=1 % we are running PDFLaTeX
\pdftrue
\fi

\ifpdf
\usepackage[pdftex]{graphicx}
\else
\usepackage{graphicx}
\fi

\ifpdf
\DeclareGraphicsExtensions{.pdf, .jpg}
\else
\DeclareGraphicsExtensions{.eps, .jpg}
\fi
%! iTeXMac(mark): ADDED

\begin{document}             % End of preamble and beginning of text.
\maketitle                   % Produces the title.
\fontencoding{T1}
\fontfamily{Times New Roman}
\fontseries{m}
\fontsize{12}{15}
  \selectfont
\title{ typographical news}
\newline
$\alpha  , \beta  , \chi  , \delta  , \eta  , \gamma  , \kappa  , \iota  , \omega  , \sigma  , \theta  , \tau  , \xi  , \pi , \psi  , \rho  , \mu  , \nu  , \varpi  , \lambda  , \phi  , \varphi  , \epsilon  , o  , \upsilon  , \vartheta  , \zeta $
\newline
$A  , B  , X  , \Delta  , H  , \Gamma  , K  , I  , \Omega  , \Sigma  , \Theta  , T  , \Xi  , \pi , \Psi  , P  , M  , N  , \Lambda  , \Phi  , E  , O  , Y  , Z $
\newline
$C \in \left( AB \right]$
\newline
$C \in \left[ AB \right)$
\newline
$i \in \left\llbracket 1 ; 2 \right\rrbracket$
\newline
$A \not\in \left[ AB \right)$
\newline
$A \not\subset B$
\newline
$A \not\subseteq B$
\newline
$A \supset B$
\newline
$A \supseteq B$
\newline
$A \not\supset B$
\newline
$A \not\supseteq B$
\newline
$A \ni B$
\newline
$A \not\ni B$
\newline
$\left( AB \right) \not\parallel \left( CD \right)$
\newline
$\left( AB \right) \not\perp \left( CD \right)$
\newline
$a \not> b$
\newline
$a \not< b$
\newline
$a \not\ge b$
\newline
$a \not\le b$
\newline
$ ~\mathbb{Z} \slash 2~\mathbb{Z}^{\star}$
\newline
$\mathbb{Z} \slash 2~\mathbb{Z}~\left[ X \right]$
\newline
$ ~\mathbb{Z} \slash 2~\mathbb{Z}^{\star}~\left[ X \right]$
\newline
$\left( f \ast g \right)~\left( x \right) = \int_{-\infty}^{+\infty}f(x - t ) . g(t) . dt$
\newline
$\left( f \ast g \right)~\left( x \right) = \displaystyle {\sum_{m=-\infty}^{+\infty}}f(n - m ) . g(m) = \displaystyle {\sum_{m=-\infty}^{+\infty}}f(m) . g(n - m )$
\newline
$\left( f \ast \left( g + h \right) \right)~\left( x \right) \substack{def \\ = }~\int_{-\infty}^{+\infty}f(x - t ) . \left( g(t) + h(t) \right) . dt$
\newline
$\| \overrightarrow{ AB } \| + \| \overrightarrow{ BC } \| \leqslant \| \overrightarrow{ AC } \|$
\newline
$\pi_ (x) , \pi_ _{x}$
\newline
$e(x) , e_{x}$
\newline
$cos^{2}~x + sin^{2}~x = 1$
\newline
$log^{2}~x$
\newline
$x \in \Im~and~y \in \Re$
\newline
$\partial , \hbar , \lambdabar$
\newline
$\left\{ a\ \wedge\ b \right\} \Rightarrow C$
\newline
$\left\{ a~and~b \right\} \Rightarrow C$
\newline
$\left\{ a\ \vee \ b \right\} \Rightarrow C$
\newline
$\left\{ a~or~b \right\} \Rightarrow C$
\newline
$\left\{ a\ xor\ b \right\} \Rightarrow C$
\newline
$  \Leftrightarrow x + 2 = 0 \Leftrightarrow x = -2$
\newline
$\left( A \cup B \right) \cap C$
\newline
$\left( d' \right) \parallel \left( d \right)~and~\left( d'' \right) \parallel \left( d \right) \Rightarrow \left( d'' \right) \parallel \left( d \right)$
\newline
$\left( d' \right) \perp \left( d \right)$
\newline
$\exists\ \left( x ; y \right) \in \mathbb{N} \times \mathbb{N} $
\newline
$\nexists\ x  \left| toto \right.$
\newline
$\forall\ \epsilon  > 0  ; \exists\ \eta  > 0 ~tel~que~si~\left| x - x0  \right| < \eta  \Rightarrow \left| f(x) - f(x0)  \right| < \epsilon $
\newline
$P(\omega  \in \Omega  \left| x(\omega ) \leqslant \frac{3}{2} \right.) = \int_{-\infty}^{\frac{3}{2}}e^{-t^{2}}dt$
\newline
$A \subset B \cup C \cap D$
\newline
$A \subseteq B$
\newline
$P(A \cup B) = P(A) + P(B) - P(A \cap B) $
\newline
$x \equiv 1\ mod\ 2$
\newline
$f \sim g + h$
\newline
$f + f_{x} + f(x)$
\newline
$f + f_{x}^{2} + f(x)$
\newline
$\int_{\mathbb{R}}^{\ }fdx$
\newline
$\int_{x \in \mathbb{H} \cup \mathbb{C}}^{\ }\psi (x ; t)dx$
\newline
$\int_{\mathbb{H} \cup \mathbb{C}}^{\ }\psi (x ; t)dx$
\newline
$\frac{1}{\sqrt{ 2 \pi }}~\int_{x \in \left[ 1 ; 2 \right] \cap \left[ -\frac{1}{2} ; +\infty \right[}^{\ }\psi (x ; t)~\sqrt[3]{2}dx$
\newline
$\frac{1}{\sqrt{ 2 \pi }}~\int_{\ }^{x \in \left[ 1 ; 2 \right]}\psi (x ; t)~\sqrt[3]{2}dt$
\newline
$\displaystyle {\sum_{n \in \mathbb{N} \cap \left[ 1 ; 2 \right]}}\frac{1}{n^{2}}$
\newline
$\displaystyle {\sum_{n \in \mathbb{N}}}\frac{1}{n^{2}}$
\newline
$\displaystyle {\prod_{n \in \mathbb{N}}}\frac{1}{n^{2}}$
\newline
$\displaystyle\lim_{x \to +\infty}\frac{\sin\left( x \right)}{x}$
\newline
$\displaystyle\lim_{x \rightarrow +\infty}\frac{\sin\left( x \right)}{x}$
\newline
$\displaystyle\lim_{x \rightarrow +\infty}x$
\newline
$\displaystyle\lim_{\substack{x \rightarrow 0 \\x < 0}}\frac{\sin\left( x \right)}{x}$
\newline
$\displaystyle\lim_{x \rightarrow 0^{\  + \ }}\frac{\sin\left( x \right)}{x}$
\newline
$\displaystyle\lim_{x \to 0^{\  + \ }}\frac{\sin\left( x \right)}{x}$
\newline
$\begin{pmatrix}
   1 & \cdots & \cdots & \cdots & N \\
 \vdots & \vdots & \  & \  & \vdots \\
 \vdots & \  & \vdots & \  & \vdots \\
 \vdots & \  & \  & \vdots & \vdots \\
 N & \cdots & \cdots & \cdots & N   
\end{pmatrix}$
\newline
$\begin{pmatrix}
   a_{11} & \cdots & \cdots & \cdots & a_{n1} \\
 \vdots & \vdots & \  & \  & \vdots \\
 \vdots & \  & \vdots & \  & \vdots \\
 \vdots & \  & \  & \vdots & \vdots \\
 a_{1~n} & \cdots & \cdots & \cdots & a_{nn}   
\end{pmatrix}$
\newline
$\left\{ 2^{d}~\log\left( 2 \right) \right\} = \left\{ \displaystyle {\sum_{n=1}^{d}}\frac{2^{d - n }}{n} \right\} + \displaystyle {\sum_{n=d + 1}^{+\infty}}\frac{2^{d - n }}{n}$
\newline
$\displaystyle {\sum_{k=0}^{+\infty}}\left( -1 \right)^{k}~u_{k} = \displaystyle {\sum_{k=0}^{m - 1 }}\left( -1 \right)^{k}~u_{k} + \displaystyle {\sum_{k=0}^{\infty}}\left( -1 \right)^{k}~\Delta ^{k}~u_{n}$
\newline
$\Delta ^{1}~u_{n} = u_{n + 1} - u_{n} $
\newline
$\Delta ^{2}~u_{n} = \Delta ^{1}~u_{n + 1} - \Delta ^{1}~u_{n}  = u_{n + 2} - 2~u_{n + 1}  + u_{n}$
\newline
$\Delta ^{3}~u_{n} = \Delta ^{2}~u_{n + 2} - \Delta ^{2}~u_{n + 1}  = u_{n + 3} - 3~u_{n + 2}  + 3~u_{n + 1} - u_{n} $
\newline
$\displaystyle {\sum_{k=1}^{\infty}}\left( 1 + \frac{1}{2} + \cdot \cdot \cdot  + \frac{1}{k} \right)~k^{-2} = \frac{17 \pi^{4}}{360}$
\newline
$\left( a + b \right)^{n} = \displaystyle {\sum_{k=0}^{n}}C_{n}^{k}~a^{k}~b^{n - k }$
\newline
$\left( a + b \right)^{n} = \displaystyle {\sum_{k=0}^{n}}C_{n}^{k}~a^{k}~b^{n - k }$
\newline
$A_{n}^{k}$
\newline
$m\cdot ~\overrightarrow{ a_{x} } = \overrightarrow{ P_{x} } + \overrightarrow{ F_{ski} } + \overrightarrow{ F_{air} }$
\newline
$a_{x} = g\cdot ~\sin\left( \alpha  \right) - \frac{F_{ski}}{m}  - \frac{F_{air}}{m} $
\newline
$\overline{ z } = 2 - 3 i $
\newline
$E = h~\nu $
\newline
$P = \frac{h}{\lambda }$
\newline
$E = \frac{p^{2}}{2}~m + V(r)$
\newline
$E = h~\nu $
\newline
$P = \frac{h}{\lambda }$
\newline
$E = \frac{p^{2}}{2}~m + V(r)$
\newline
$\overrightarrow{ p }$
\newline
$\widehat{ \sigma  } = \sqrt{ \frac{1}{n - 1 }~\displaystyle {\sum_{i=1}^{n}}\left( x - \overline{ X }  \right)^{2} }$
\newline
$\wideparen{ AB }$
\newline
$f : \substack{\mathbb{R} \rightarrow \mathbb{R} \\x \mapsto 2~x + 3}$
\newline
$f : \substack{\mathbb{R} \rightarrow \mathbb{R} \\x \mapsto f(x)}$
\newline
$C(n ; k) = C_{n}^{k} = nC_{k} = \begin{pmatrix}
   n \\
 k   
\end{pmatrix} = \frac{n!}{k!~\left( n - k  \right)!}$
\newline
$\operatorname{erf}\left( z \right) = \frac{2}{\sqrt{ \pi }}~\displaystyle {\sum_{n=0}^{+\infty}}\left( -1 \right)^{n}~\frac{z^{2~n + 1}}{n!~\left( 2~n + 1 \right)}$
\newline
$\displaystyle {\bigcup_{i=1}^{N}}f$
\newline
$\displaystyle {\bigcap_{i=1}^{N}}f$
\newline
$\int_{1}^{N}fdi$
\newline
$\displaystyle {\iint\limits_{i=1}^{N}}f$
\newline
$\displaystyle {\iiint\limits_{i=1}^{N}}f$
\newline
$\displaystyle {\int\limits_{i=1}^{N}}f$
\newline
$\displaystyle {\iint\limits_{\Omega }}f$
\newline
$\displaystyle {\iiint\limits_{i=1}^{N}}f$
\newline
$\displaystyle {\oint\limits_{i=1}^{N}}f$
\newline
$\displaystyle {\oiint\limits_{i=1}^{N}}f$
\newline
$\displaystyle {\oiiint\limits_{i=1}^{N}}f$
\newline
$\displaystyle {\oiiint\limits_{\Omega }}f$
\newline
$\displaystyle {\bigoplus_{i=1}^{N}}f$
\newline
$\displaystyle {\bigotimes_{i=1}^{N}}f$
\newline
$\displaystyle {\bigodot_{i=1}^{N}}f$
\newline
$\displaystyle {\sum_{i=1}^{N}}f$
\newline
$\left\{ \substack{x + y = 2 \\2~x + 3~y = 32} \right.$
\newline
$\left. \substack{x + y = 2 \\2~x + 3~y = 32} \right\} \Leftrightarrow x \in \left\{ -26 ; 28 \right\}$
\newline
$\left\{ \substack{x + y = 2 \\2~x + 3~y = 32} \right. \Leftrightarrow x \in \left\{ -26 ; 28 \right\}$
\newline
$\left\{ \substack{x + y = 2 \\2~x + 3~y = 32} \right. \Leftrightarrow x \in \left\{ -26 ; 28 \right\}$
\newline
$\left\{ \substack{x + y = 2 \\2~x + 3~y = 32} \right. \Leftrightarrow x \in \left\{ -26 ; 28 \right\}$
\newline
$\left\{ \substack{x + y = 2 \\2~x + 3~y = 32} \right\} \Leftrightarrow x \in \left\{ -26 ; 28 \right\}$
\newline
$\left| x \right| = \left\{ \substack{x~si~x \geqslant 0 \\-x~si~x < 0} \right.$
\newline
$f(x) = \left\{ \substack{\substack{x~si~x \in \left] -\infty ; -1 \right] \\-2~x~si~x \in \left] 1 ; 2 \right]} \\-2~x + \frac{1}{2}~si~x \in \left] 2 ; +\infty \right[} \right.$
\newline
$a \oplus b$
\newline
$a \otimes b$
\newline
$a \odot b$
\newline
$a \oplus b$
\newline
$\overrightarrow{ z } \wedge \left( \overrightarrow{ a } \wedge \overrightarrow{ b } \right)$
\newline
$\overrightarrow{ z } . \left( \overrightarrow{ a } \wedge \overrightarrow{ b } \right)$
\newline
$\overrightarrow{ a } . \overrightarrow{ b }$
\newline
$\overrightarrow{ a } . \overrightarrow{ b }$
\newline
$\overrightarrow{ a } . \left( \overrightarrow{ b } + \overrightarrow{ c } \right) = \overrightarrow{ a } . \overrightarrow{ b } + \overrightarrow{ a } . \overrightarrow{ c }$
\newline
$\left\{ \substack{x \equiv 2\ mod\ 3 \\x \equiv 5\ mod\ 7} \right.$
\newline
$\left( f \circ g \right)~\left( x \right) = f(g(x))$
\newline
$\left( f \circ g \right)~'(x) = f'(g(x)) \times g'(x)$
\newline
$\left( f \times g \right)~' = f' \times g + g' \times f$
\newline
$\left( f \times g \right)~'(x) = f'(x) \times g(x) + g'(x) \times f(x)$
\newline
$\left( \frac{f}{g} \right)^{'} = \frac{f' \times g - g' \times f }{g^{2}}$
\newline
$\sigma\left( X \right)$
\newline
\title{ Physic}
\newline
$\langle a \left| b \right. \rangle$
\newline
$\langle a \left| \  \right.$
\newline
$ \  \left| b \right. \rangle$
\newline
$H_{2}~SO_{4}$
\newline
$SO_{4}^{2 - \  }$
\newline
$\ _{92}^{238}~U$
\newline
$CH_{4} + 2~O_{2} \rightarrow CO_{2} + 2~H_{2}~O$
\newline
$ \frac{\widehat{ \overrightarrow{ p } }^{2}}{2~m}~\left| \Psi (t) + V(\widehat{ \overrightarrow{ r } } , t) \right|~\Psi (t) \rangle$
\newline
$ \  \left| tyo \right. \rangle$
\newline
$f(p_{i} , q_{i} , t)$
\newline
\textit{  is given by}
\newline
$\frac{df}{dt} = \left\{ f , H \right\} + \frac{\partial~f}{\partial~t}$
\newline
$\left\{ f ; g \right\} = \displaystyle {\sum_{i=1}^{N}}\left( \frac{\partial~f}{\partial~q_{i}} \frac{\partial~g}{\partial~p_{i}} - \frac{\partial~f}{\partial~p_{i}} \frac{\partial~g}{\partial~q_{i}}  \right)$
\newline
$\left[ A ; BC \right] = \left[ A ; B \right]~C + B~\left[ A ; C \right]$
\newline
$\frac{d}{ds}~BC = \frac{dA}{ds}~C + B~\frac{dC}{ds}$
\newline
$grad~T = \frac{\partial~T}{\partial~x}$
\newline
$\nabla~T(x) = T'(x) = \frac{dT}{dx}~\left( x \right)$
\newline
$f : \mathbb{R}^{2} \mapsto \mathbb{R}$
\newline
$grad~f = \nabla~f$
\newline
$\frac{\partial^2}{\partial t^2 }\left( f \right)$
\newline
$\frac{ \partial}{\partial t }\left( f \right)$
\newline
$\frac{\partial^2}{\partial t\partial u }\left( f \right)$
\newline
$\frac{\partial^2 f}{\partial t\partial u }$
\newline
$E = \hbar~\nu $
\newline
$ \widehat{ H } \left| \Psi  \right. \rangle =  i \hbar \frac{d}{dt} \left| \Psi  \right. \rangle$
\newline
$J^{2} = j \left( j + 1 \right) \hbar^{2} with : j = 0 , 1 , 2 , 3 , 4 ,  ... $
\newline
$J_{z} = m \hbar$
\newline
$\Delta ~x~\Delta ~p \geqslant \frac{1}{2} \hbar$
\newline
\textit{  Gradient et vari\'{e}t\'{e} riemanniene}
\newline
   D\'{e}veloppement limit\'{e}
\newline
   Soit une application:
\newline
   avec ( n  In  {2;3} for example) 
\newline
   est monotone (resp. strictement monotone), alors f est convexe (resp. strictement convexe). 
\newline
   C'est-\`{a}-dire, en utilisant la caract\'{e}risation par les cordes :
\newline
\title{ Relations vectorielles}
\newline
$M(x ; y ; z) \in \left( ABC \right) \Leftrightarrow x + 3~y - 5~z  + 5 = 0$
\newline
$\begin{pmatrix}
   x1 \\
 y1 \\
 z1   
\end{pmatrix} \wedge \begin{pmatrix}
   x2 \\
 y2 \\
 z2   
\end{pmatrix} = \begin{pmatrix}
   \left( -y1 \right)~z2 - y2~z1  \\
 -(\left( \left( x1~z2 - x2~z1  \right) \right)) \\
 x1~y2 - x2~y1    
\end{pmatrix}$
\newline
$\overrightarrow{ n } = \overrightarrow{ AB } \wedge \overrightarrow{ AC } = \left( -2 ; -6 ; 10 \right)$
\newline
$\overrightarrow{ n1 } = -1 \slash 2~\overrightarrow{ n }$
\newline
$\overrightarrow{ grad }~f = \overrightarrow{ \nabla }~f$
\newline
$\frac{ \partial}{\partial t }\left( \nabla~f \right) = \nabla~\frac{ \partial f}{\partial t }$
\newline
$div(\overrightarrow{ grad }~f) = \Delta ~f$
\newline
$\overrightarrow{ grad }~\left( div~f \right) = \overrightarrow{ rot }~\left( \overrightarrow{ rot }~f \right) + \overrightarrow{ \Delta  }~\overrightarrow{ f }$
\newline
\textit{  Changement of Base }
\newline
$\overrightarrow{ \nabla }~S . \overrightarrow{ dOM } = \left( y~\overrightarrow{ i } + x~\overrightarrow{ j } \right) . \left( dx~\overrightarrow{ i } + dy~\overrightarrow{ j } \right) = \left( \frac{(null)(xy)}{\partial~x}~\overrightarrow{ i } + \frac{(null)(xy)}{\partial~y}~\overrightarrow{ j } \right) . \left( dx~\overrightarrow{ i } + dy~\overrightarrow{ j } \right)$
\newline
$\overline{ 12345 }^{two} = 11000000111001$
\newline
$N_{p} = \left\{ \substack{p - 1~si~p  \equiv +1~\left( mod 4 \right) \\p + 1~si~p \equiv -1~\left( mod 4 \right)} \right.$
\newline
$2 \equiv +1$
\newline
$t = 0 , 1 ,  ...  , p - 1  , \infty$
\newline
$-1 = i^{2}$
\newline
$\displaystyle {\prod_{p}}\frac{p}{N_{p}} = \displaystyle {\prod_{p}}\left( 1 - \frac{a_{p}}{p}  \right)^{-1}$
\newline
$  = \left( \displaystyle {\prod_{\left( p \equiv 1 \left( 4 \right) \right)}}\left( 1 - \frac{1}{p}  \right)^{-1} \right) . \left( \displaystyle {\prod_{\left( p \equiv -1~\left( 4 \right) \right)}}\left( 1 - \frac{1}{p}  \right)^{-1} \right)$
\newline
$  = \left( \displaystyle {\prod_{\left( p \equiv 1 \left( 4 \right) \right)}}1 + \frac{1}{p} + \frac{1}{p^{2}} + \frac{1}{p^{3}} + \cdot \cdot \cdot  \right) . \left( \displaystyle {\prod_{\left( p \equiv -1~\left( 4 \right) \right)}}1 - \frac{1}{p}  + \frac{1}{p^{2}} - \frac{1}{p^{3}}  + \cdot \cdot \cdot  \right)$
\newline
$  = 1 - \frac{1}{3}  + \frac{1}{5} - \frac{1}{7}  + \frac{1}{9} - \frac{1}{11}  + \cdot \cdot \cdot \cdot $
\newline
$  = \frac{\pi}{4}$
\newline

\end{document}               % End of document.