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\usepackage{latexsym}
\newtheorem{theorem}{Theorem}[section]
\newtheorem{definition}{Definition}[section]
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\begin{document}
\title{
\begin{flushleft}
{\small{\it Advanced Nonlinear Studies} {\bf 1} (2001), xxx--xxx}
\end{flushleft}
\vspace{0.5in}
{\bf\Large  The Title of the Paper}}
\author{{\bf\large Name}\footnote{The author acknowledges the support...}\hspace{2mm}
{\bf\large Name}\vspace{1mm}\\
{\it\small Department of Mathematics}\\ {\it\small University of Texas},
{\it\small San Antonio, Texas 78249}\\
{\it\small e-mail: address}}\vspace{1mm}
\date{\small{Received ---------------} \\
{\it\small Communicated by ----------}}
\maketitle
\begin{center}
{\bf\small Abstract}
\vspace{3mm}
\hspace{.05in}\parbox{4.5in}
{{\small The abstract should be around 300 words, but an attempt should be made not
\indent
to exceed 400 words.}}
\end{center}
\noindent
{\it \footnotesize 1991 Mathematics Subject Classification}. {\scriptsize 12345, 54321}.\\
{\it \footnotesize Key words}. {\scriptsize Differential operator, Hilbert space}
\section{\bf Introduction}
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\begin{definition}
{\rm The texts of Definition, Remark, and Examples must be in roman.}
\end{definition}
\begin{proposition}
This is the proposition.
\end{proposition}
\noindent
\proof
\noindent
This is the end of the proof.
\begin{lemma}
This is the lemma.
\end{lemma}
\begin{corollary}
This is the corollary.
\end{corollary}
\section{\bf Title of this section}
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\begin{eqnarray}
A+B=c+d
\end{eqnarray}
$$
\alpha+\beta=\gamma+\delta
$$
The references are cited as \cite{BO89} and \cite{RA83}. {\bf Note that the text and the
mathematical expressions should be adjusted or split so that they do not exceed the right margin}.

\section{\bf Title of this section}
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\begin{definition}
{\rm The texts of Definition, Remark, and Examples must be in roman.}
\end{definition}
\begin{theorem}
This is the theorem.
\end{theorem}

\begin{theorem}
This is another theorem in the same section.
\end{theorem}

\begin{thebibliography}{777}
\bibitem{BO89} N. Bourbaki,
Algebra I,
Springer-Verlag, Berlin, 1989.
\bibitem{RA83} J. Rawnsley, W. Schmid, and J.A. Wolf,
{\it Singular unitary representations and indefinite harmonic theory},
J. Funct. Anal. {\bf 51} (1983), 1--114.

\end{thebibliography}
\end{document}