%%					%%
%%	 TJM sample file		%%
%%					%%

\documentclass{article}

\usepackage{amsmath,amssymb}	% to deal with mathematics

\usepackage{graphicx}		  % to deal with graphicals

\usepackage{tjm}%%% This is it!

%%% Theorem Definitions %%%
\newtheorem{thm}{Theorem}
\newtheorem{lem}{Lemma}
\newtheorem{prop}{Proposition}
\newtheorem{cor}{Corollary}
\newtheorem{defn}{Definition}
\newtheorem{rem}{Remark}
\newtheorem{cla}{Claim}
%\italiclist{Claim}
%%% substitute original commands %%
\newcommand{\GF}{\mathbb{F}}
\newcommand{\GL}{\mathbb{L}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



\title[Sample File    %%% This option is for the running head %%%
]{Sample \LaTeX\ Source File}

\author{Author1 Name and Author2 Name}

\affils{Sophia University and Chuo University}

\com{(Communicated by X. Communicator)}

\date{Received June 3, 1998; revised July 22, 1998}
\subjclass{22E27}

%\renewcommand{\keywordsname}{Key words}% when changing the name "Key words"
\keywords{aaaa, bbb, ccc, ddd}


\authorname{Author1 Name}
\address{Department of Mathematics,\\
Sophia University,\\
Kioicho, Chiyoda-ku, Tokyo, 102-8554 Japan.}
\email{author1@sophia.ac.jp}

\authorname{Author2 Name}
\address{Department of Mathematics, Faculty of Science and Engineering,\\
Chuo University,\\
Kasuga, Bunkyo-ku, Tokyo, 112-8551 Japan.}
\email{author2@chuo.ac.jp}


%%%%%%    TEXT START    %%%%%%

\begin{document}

\maketitle

\begin{abstract}
This paper will illustrate how to use the tjm.sty file with your \LaTeX\ source file.
\end{abstract}

\section{Introduction}

\subsection{Case 1.}
When you do not need equation numbers, you can write
\[ E_z(a)\geq \int_0^1\hat\omega_t(a)dt . \]

\subsection{Case 2.}
When you need equation numbers, you can write
\begin{equation}
E_z(a)=\int_0^1\hat\omega_t(a)dt .
\end{equation}

\subsection{Case 3.}
When there are several equations,
\begin{align}
\begin{split}
\frac{d\theta}{dh}&=\frac{1}{(1+h)\tan \gamma} ,\\
\frac{du}{dh}&=-\frac{2}{(1+h)^2}-\frac{B \left(1+\lambda^2
\right)u e^{-h/\varepsilon}}{\varepsilon E^{*} \sin\gamma},\\
\frac{du}{dh}&\leq \Bigl\{\frac{1}{(1+h)}-\frac{1}{u(1+h)^2}
\Bigr\}\frac{1}{\tan \gamma}+\frac{B\lambda
e^{-h/\varepsilon}}{\varepsilon \sin \gamma}.
\end{split}
\end{align}

\section{Theorems}
Theorem, Proposition, Definition, Lemma etc.\ are written in
small capitals.

\begin{thm}
This might be followed by a series of equations
\begin{align*}
P_x  ( X \in A \,|\, \tau > \tau_y )
& \ge 
P_x  ( X \in A , \tau > \tau_y >s) /
P_x  ( \tau > \tau_y ) \\
& = 
E_x
g( 
{ P_{ X(s) } ( \tau > \tau_y ) \over  P_x ( \tau > \tau_y ) }  
, ( \tau_y \wedge \tau)> s , X \in A ) \,.
\end{align*}  
\end{thm}

\begin{lem}\label{basic lemma}
Let $ x > 0 $ and $ \theta >0.$
\begin{enumerate}
 \item[$(a)$] If $ X $ is in Class {\rm I}, then
\[
\lim_{ t \to \infty }
t^{3/2}( e^{- \theta X(t) } , \tau >t) =
{c_1 \over \sqrt{2\pi \phi''(\alpha)  } }
\,  U(x)
\int_0^\infty e^{-\theta z} U(z) dz\, .
\]
\item[$(b)$] If $ X $ is in Class {\rm III}$,$ then
\[
\lim_{ t \to \infty }
t^{3/2}( e^{- \theta X(t) } , \tau >t) =
{c_1 r \over \sqrt{2\pi \phi''(\alpha)  } }
\,  U(x)  \sum_{ j \in  r {\bf N} }
e^{-\theta  ( j+ l(x) )  } U( j) \,.
\]
\end{enumerate}
Here $ c_1 = \exp\{ \int_0^\infty ( e^{-t} -1) t^{-1}
( X_t =0 ) dt \} $
and $ l(x)= x-rk  $ if $ \,  r(k-1) < x \le rk ,\: k \in {\bf N}.$
In addition,
we can replace $ \tau, X, U(x) $ by their duals.
\end{lem}

\section{Tables}
Tables should be produced in the following way:
\begin{table}[htbp]
\begin{center}
\setlength{\tabcolsep}{10pt}
\footnotesize
\begin{tabular}{|c|c|c|} \hline
First & Second & Third \\ \hline
11 & 22 & 33 \\   \hline
111 & 222 & 333  \\  \hline
\end{tabular}
\end{center}
\caption{(captions like this are optional)}
\end{table}

\section{Pictures}
Pictures should be in EPS format. Here is an example.
\begin{figure}[h]
\begin{center}
\includegraphics[scale=.6]{tjm.eps}
\caption{(captions like this are optional)}
\end{center}
\end{figure}

\section{Text}

You must use the \lq\lq return" command (not \verb|\\|) to start a new paragraph, in order to produce the correct indentation.

Paragraphs should be separated by blank lines.

References \cite{c}, \cite{h}, and \cite{zs} below are samples of three different types.

\begin{ack}
Your acknowledgments go here if necessary.
\end{ack}

\begin{thebibliography}{9}

\bibitem{c}
\textsc{S.~C.~Coutinho},
\textit{A Primer of Algebraic D-Modules},
LMS Student Texts 33,
Cambridge Univ. Press,
1995.

\bibitem{h}
\textsc{A.~Haefliger},
Local theory of meromorphic connections in dimension one (Fuchs theory),
\textit{Algebraic D-modules},
eds. A.~Borel et al,
Perspectives in Math. 2,
Academic Press,
1987,
129--149.

\bibitem{zs}
\textsc{V.~E.~Zakharov, A.~B.~Shabat},
Integration  of non-linear equations of mathematical physics by the inverse scattering method II,  
Funct. Anal. Appl.
\textbf{13} (1979), 
166--174.

\end{thebibliography}

\end{document}