\documentclass{jT}


\usepackage{amssymb,amsmath,latexsym,amsthm}%or any usual package
\usepackage[english]{babel}



\newtheorem{theorem}{Theorem}[section]
\newtheorem{lemma}{Lemma}[section]
\newtheorem{proposition}{Proposition}[section]
\newtheorem{corollary}{Corollary}[section]

\theoremstyle{definition}
\newtheorem*{definition}{Definition}
\newtheorem*{remark}{Remark}
\newtheorem*{example}{Example}

\numberwithin{equation}{section}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% you can of course create new environment such as conjecture,%
%notation,... and modify the way they are numbered            %
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\begin{document}


\title[Short title]{Full title}

%first author

\author[Pr\'enom1 {\sc Nom1}]{{\sc Pr\'enom1} NOM1}
\address{Pr\'enom1 {\sc Nom1}\\
Universit\'e Gauss\\
4, impasse de Diophante\\
00000 Mars Cedex, Espace}
\email{email address}
\urladdr{http://www.math.u-bordeaux.fr/A2X/}



% second author
\author[Pr\'enom2 {\sc Nom2}]{{\sc Pr\'enom2} NOM2}
\address{Pr\'enom2 {\sc Nom2}\\
Universit\'e Gauss\\
4, impasse de Diophante\\
00000 Mars Cedex, Espace}
\email{email address}


\maketitle


\begin{resume}
French abstract.
\end{resume}

\begin{abstr}
English abstract.
\end{abstr}

\bigskip
\section{Introduction}

\begin{definition}
This is a definition.
\end{definition}


\begin{proposition}
This is a proposition.
\end{proposition}

\begin{proposition}
This is another proposition.
\end{proposition}

\begin{lemma}
Let $f, g\in  A(X)$ and let $E$, $F$ be cozero
sets in $X$.
\begin{enumerate}
\item If $f$ is $E$-regular and $F\subseteq E$, then $f$ is $F$-regular.

\item If $f$ is $E$-regular and $F$-regular, then $f$ is $E\cup
F$-regular.

\item If $f(x)\ge c>0$ for all $x\in E$, then $f$ is $E$-regular.

\end{enumerate}
\end{lemma}

The following is an example of a proof.

\begin{proof} Set $j(\nu)=\max(I\backslash a(\nu))-1$. Then we have
\[
\sum_{i\notin a(\nu)}t_i\sim t_{j(\nu)+1}
  =\prod^{j(\nu)}_{j=0}(t_{j+1}/t_j).
\]
Hence we have
\begin{equation}
\begin{split}
\prod_\nu\biggl(\sum_{i\notin
  a(\nu)}t_i\biggr)^{{a(\nu-1)}-{a(\nu)}}
&\sim\prod_\nu\prod^{j(\nu)}_{j=0}
  (t_{j+1}/t_j)^{{a(\nu-1)}-{a(\nu)}}\\
&=\prod_{j\ge 0}(t_{j+1}/t_j)^{
  \sum_{j(\nu)\ge j}({a(\nu-1)}-{a(\nu)})}.
\end{split}
\end{equation}
By definition, we have $a(\nu(j))\supset c(j)$. Hence, ${c(j)}=n-j$
implies (5.4). If $c(j)\notin a$, $a(\nu(j))c(j)$ and hence
we have (5.5).
\end{proof}

\section{conclusion}

\begin{quotation}
This is an example of an `extract'. The magnetization $M_0$ of the Ising
model is related to the local state probability $P(a):M_0=P(1)-P(-1)$.
The equivalences are shown in Table~\ref{eqtable}.
\end{quotation}

\begin{table}[ht]
\caption{}\label{eqtable}
\renewcommand\arraystretch{1.5}
\noindent\[
\begin{array}{|c|c|c|}
\hline
&{-\infty}&{+\infty}\\
\hline
{f_+(x,k)}&e^{\sqrt{-1}kx}+s_{12}(k)e^{-\sqrt{-1}kx}&s_{11}(k)e^
{\sqrt{-1}kx}\\
\hline
{f_-(x,k)}&s_{22}(k)e^{-\sqrt{-1}kx}&e^{-\sqrt{-1}kx}+s_{21}(k)e^{\sqrt
{-1}kx}\\
\hline
\end{array}
\]
\end{table}

\begin{definition}
This is an example of a `definition' element.
For $f\in A(X)$, we define
\begin{equation}
\mathcal{Z} (f)=\{E\in Z[X]: \text{$f$ is $E^c$-regular}\}.
\end{equation}
\end{definition}

\begin{remark}
This is an example of a `remark' element.
For $f\in A(X)$, we define
\begin{equation}
\mathcal{Z} (f)=\{E\in Z[X]: \text{$f$ is $E^c$-regular}\}.
\end{equation}
\end{remark}

\begin{example}
This is an example of an `example' element.
For $f\in A(X)$, we define
\begin{equation}
\mathcal{Z} (f)=\{E\in Z[X]: \text{$f$ is $E^c$-regular}\}.
\end{equation}
\end{example}


The following is an example of a numbered list.

\begin{enumerate}
\item First item.
In the case where in $G$ there is a sequence of subgroups
\[
G = G_0, G_1, G_2, \dots, G_k = e
\]
such that each is an invariant subgroup of $G_i$.

\item Second item.
Its action on an arbitrary element $X = \lambda^\alpha X_\alpha$ has the
form
\begin{equation}\label{eq:action}
[e^\alpha X_\alpha, X] = e^\alpha \lambda^\beta
[X_\alpha X_\beta] = e^\alpha c^\gamma_{\alpha \beta}
 \lambda^\beta X_\gamma,
\end{equation}

\begin{enumerate}
\item First subitem.
\[
- 2\psi_2(e) =  c_{\alpha \gamma}^\delta c_{\beta \delta}^\gamma
e^\alpha e^\beta.
\]

\item Second subitem.
\begin{enumerate}
\item First subsubitem.
In the case where in $G$ there is a sequence of subgroups
\[
G = G_0, G_1, G_2, \ldots, G_k = e
\]
such that each subgroup $G_{i+1}$ is an invariant subgroup of $G_i$ and
each quotient group $G_{i+1}/G_{i}$ is abelian, the group $G$ is called
\textit{solvable}.

\item Second subsubitem.
\end{enumerate}
\item Third subitem.
\end{enumerate}
\item Third item.
\end{enumerate}

Here is an example of a cite. See \cite{ref3}.

\begin{theorem}
This is an example of a theorem.
\end{theorem}

\begin{theorem}[Marcus Theorem]
This is an example of a theorem with a parenthetical note in the
heading.
\end{theorem}



\begin{thebibliography}{xx}

\bibitem{ref1} \textsc{W. W. Adams}, 
\textit{Simultaneous diophantine approximations and cubic irrationals}.
Pacific J. Math. {\bf30} (1969), 1--14.

\bibitem{ref2} {\sc W. W. Adams}, 
\textit{Simultaneous Asymptotic diophantine Approximations to a Basis
of a Real Cubic Field}. 
{J. Number Theory} {\bf1} (1969), 179--194.

\bibitem{ref3} {\sc P. Bachmann}, 
\textit{Zur Theory von Jacobi's Kettenbruch-Algorithmen}. 
J. Reine Angew. Math. {\bf75} (1873), 25--34.

\bibitem{ref4} {\sc A. J. Brentjes}, 
\textit{Multi-dimensional continued fraction algorithms}. 
Mathematics Center Tracts {\bf155}, Amsterdam, 1982.

\bibitem{ref5} {\sc J. W. S. Cassels}, 
\textit{An introduction to diophantine approximation}. 
Cambridge University Press, 1965.
\end{thebibliography}

\end{document}

