\documentclass{MBE}
\usepackage{amsmath}
 \usepackage{paralist}
  \usepackage{graphics}
   \usepackage{epsfig}
    \usepackage[colorlinks=true]{hyperref}
%%%%%%%%%%%%%%%%%%%%Please use the following color setup command for all future papers
 \hypersetup{urlcolor=blue, citecolor=red}

  \textheight=8.2 true in
   \textwidth=5.0 true in
    \topmargin 30pt
     \setcounter{page}{1}

\def\currentvolume{xx}
 \def\currentissue{xx}
  \def\currentyear{20xx}
   \def\currentmonth{xx}
    \def\ppages{1--xx}
     \def\DOI{10.3934/mbe.2009.xx.xx}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%The guidelines on how to assign DOIs%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%%%%%%%%%%%%%1. The DOI number (e.g. 10.3934/mbe.2009.6.1) of each regular paper includes the following number
%10.3934:number assigned to AIMS
%mbe:journal name
%2009:Year issue published
%6:Volume
%1:starting page number of a paper
%%%%%%%%%%%%%%%2. The DOI number (e.g. 10.3934/dcds.2009.8.1i) of Preface of the first special issue in 2009
%%%%%%%%%%%%%%%includes the following number:

%10.3934:number assigned to AIMS
%mbe:journal name
%2009:Year issue published
%6:Volume
%1i: 1 represents the issue number; i represents starting page number of the preface



\newtheorem{theorem}{Theorem}[section]
\newtheorem{corollary}{Corollary}
\newtheorem*{main}{Main Theorem}
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{conjecture}{Conjecture}
\newtheorem*{problem}{Problem}
\theoremstyle{definition}
\newtheorem{definition}[theorem]{Definition}
\newtheorem{remark}{Remark}
\newtheorem*{notation}{Notation}
\newcommand{\ep}{\varepsilon}
\newcommand{\eps}[1]{{#1}_{\varepsilon}}


%% Place the running title of the paper with 40 letters or less in []
 %% and the full title of the paper in { }.
\title[Running heading with forty characters or less]
      {The Full Title of Your Paper: Sample \LaTeX\ File for AIMS Journals }

%% Place all authors' names in [ ] shown as running head;
 %% No more than 40 letters. Leave { } empty
 %% Please use `and' to connect the last two names if appliable
\author[first-name1 last-name1 and first-name2 last-name2]{}

%% It is required to enter MSC and Keywords.
\subjclass{Primary: 58F15, 58F17; Secondary: 53C35}
 \keywords{Dimension theory, Poincar\'e recurrences, multifractal analysis}

%% Email address of the comuncating author is required.
%% You may list email addresses of all other authors, seperatly.
 \email{email1@smsu.edu}
 \email{email2@aimSciences.org}

%% Put your short thanks below. For long thanks/acknowlegements,
%%please go to the last acknowlegement section.
\thanks{The first author is supported by NSF grant xx-xxxx}

\begin{document}
\maketitle

%% Enter the first author's name and address:
\centerline{\scshape First-name1 last-name1 }
\medskip
{\footnotesize
 %% please put the address of the first author
 \centerline{First line of the address of the first author}
   \centerline{Other lines, Springfield, MO 65801-2604, USA}
} %% Do not forget to end the {\footnotesize by the sign }

\medskip

\centerline{\scshape First-name2 last-name2 }
\medskip
{\footnotesize
 %% please put the address of the second author
 \centerline{ First line of the address of the second author}
   \centerline{Other lines, Springfield, MO 65801-2604, USA}
} %

\bigskip

%% The name of the associate editor 
\centerline{(Communicated by the associate editor name)}


\begin{abstract}
This fictitious paper is meant to  serve only as the template for
AIMS' journals: DCDS-A, DCDS-B, CPAA, JIMO, NHM, JMD, AMC, IPI,
DCDS-S, KRM and ERA-MS. Please read the instructions in the tex file
very carefully. The sample file for  MBE may be downloaded at
http://www.mbejournal.org/.
\end{abstract}

\section{Introduction}
With the setting of the template, automatically the text is set in
10 point fonts, while the abstract and references are in 8 point
fonts. All formulas and pictures must be within the limit of
\textbf{5} inches in width. An abstract is needed and not exceeding
\textbf{200} words. Also needed are some \textbf{key words} and
\textbf{AMS subject classifications}. Here are some important
instructions on how to prepare your final \TeX\ files. Please pay
special attention to the following:

\begin{enumerate}

\item To produce a theorem, lemma, proposition, corollary,  conjecture,
etc., you need to use the standard command \verb+\+begin\{\dots\} to
start with, and \verb+\+end\{\dots\} to finish.  All texts in such
environment should be automatically \textbf{\emph{slanted}}.

\item For a definition, remark, or notation, please use the
standard commands \verb+\+begin\{\dots\} and \verb+\+end\{\dots\}.
However all texts in such a environment should be automatically
\textbf{normal}.

\item For all \textbf{proof}s, please use \verb+\+begin\{proof\} and
\verb+\+end\{proof\} commands. Do not define your own macros.

\item Make sure all \textbf{lines}, \textbf{math formulas}
and \textbf{figures} are \textbf{\textbf{within the limit of 5
inches in width}}. In particular, formulas can not run to the right
of equation numbers. Never run out of the bound.

\item The following seven items all address the exact \textbf{reference style}.
Please also follow very closely the reference samples at the end of
this article.
      \begin{compactenum}[i)]

      \item List papers in alphabetic order according to first
      authors.

      \item Always place the first name (or first name initial) first,
      then the middle name initial (optional), followed by the last name.
       If there are multiple authors, use the word `and` to connect the last two authors.
      See references  \cite {A11}, \cite{A22} and \cite{BFL} for details.

      \item If a reference is a paper in a journal,
      the title of the paper should be {\bf \emph{slanted}},
      which can be achieved by putting
      the title inside the braces: \verb+\+emph\{\dots\}.
      Only the first character in a paper's title is in capital.
      When you list a paper from a journal,
       please ignore the issue number since the page numbers and
      volume number yield sufficient information to identify the paper.
      Finally, please pay attention to the correct way
      for \textbf{volume number} (in bold face), \textbf{year},
      \textbf{starting page}--\textbf{ending page}.
      See references  \cite{A22} and \cite{BFL} for details.

       \item If the reference is a book, one should quote the title
       of the book, the first letter of each word should be capitalized.
        See reference
       \cite{rB} for details.

       \item If the reference is a paper in a conference proceeding,
        please see the sample reference \cite{Serrin}.

       \item  If the reference is a thesis, please see the sample reference \cite{Zeng}.

       \item  Please don't list any references you never cited in your paper.

       \item
          It is very valuable to the readers if the references have direct
       links to the Mathematical Reviews (MR) Database and arxiv database. Therefore, it is
       necessary to add the MR number (published paper) or archive number (preprint paper)
       for each reference whenever available.
      Your help in gathering such information (MR numbers or archive numbers)
       will ensure such information's accuracy and expedite the process
       of your paper's publication.
              The quickest way to find the MR numbers is to search
              at the link:
                 \url{http://www.ams.org/mrlookup}  or \url{http://www.ams.org/mathscinet/}.
                 To find the archive number, please click the following  link:\break \url{http://www.arxiv.org}. You may use any two combinations to find
                 MR numbers, e.g.
                 last name of one of the authors and the title (it is not necessary to put the full title)
                 or last name of one of the authors and starting page number. Concerning where to
                 put these MR or archive numbers please refer to the references
               \cite{A22}, \cite{BFL}, \cite{rB}, \cite{Serrin} and \cite{quas}
               at the end of this \TeX\ file. \\

       \end{compactenum}


\end{enumerate}
Please use the AIMS template to prepare your tex file after the
paper is accepted by an AIMS journal. Thank you for your
cooperation.


\subsection{Example of definition and theorem }
Definition sample:

\begin{definition} Sample: Let $\phi_{t}$ be an Anosmia flow on a
        compact space $V$ and $A \subset V$ a dense set. Say
        that the upper Lacunae exponents are
        \emph{$\frac{1}{2}$-pinched} on $A$ if
  \begin{equation}\label{Quotient}
        \sup_{x \in A} \frac{\max \{ |\bar{\lambda}|: \bar{\lambda} \
        \text{is a nonzero upper Lyapunov exponent at} \ x \}}
        {\min \{ |\bar{\lambda}|: \bar{\lambda} \ \text{is a
        nonzero upper Lyapunov exponent at} \ x\}}
         \leq 2.
  \end{equation}
\end{definition}


A. B asked in \cite{A22} how to state a theorem in AIMS journal,
here is an example:

\begin{theorem} \label{result1}
        Content of your theorem.
\end{theorem}

\begin{proof}
To refer to equations in your paper, use the commands:
\ref{Quotient}, \ref{Multi} and \ref{Equ3}.
\end{proof}

Now let's move to the next subsection.

\subsection{A sample Lemma}

\begin{lemma} \label{L: Lyapunov exponents} State your lemma here.
\end{lemma}

\begin{proof}
Your proof statements.
\end{proof}


Now let's move to the next section.

\section{The title of your section 2}

PostScript graphics in EPS (Encapsulated PostScript) format can be
included and should be sent as separate files. The preferred macro
package for including EPS graphics files is the LaTeX graphicx
package. Further, please follow the below \textbf{instructions on
figures}:

\begin{enumerate}

\item Notice that all color graphics will be printed in black
and white in the AIMS journals, \textbf{make sure that a black and
white printout of your figure is legible}.

\item All figures should be placed in the body of your paper and
before your Reference.

\item In a page with figures, there should be no unnecessary spare space.
Be sure that a page should be fully occupied by figures and texts.

\item Reduce the physical size of your figures if possible, while keep your figures \textbf{high resolution (clearly
visible)}. For example, an eps figure file with size bigger than 1MB
is usually unacceptable. Paper with poor \textbf{relolution} figures
maybe postponed for publication.

\item Pictures should be in eps format and scalable.

\item Again, be sure that all \textbf{figures} are \textbf{\textbf{within the limit of 5
inches in width}}.  Never run out of the bound.

\end{enumerate}

 See an example below.

\begin{figure}[htp]
\begin{center}
  % Requires \usepackage{graphicx}
  % replace aims_logo.eps by your figure file name
  \includegraphics[width=2in]{aims_logo.eps}\\
  \caption{Here is the Caption of your figure}\label{AIMS}
  \end{center}
\end{figure}


\begin{theorem} \label{result2}
        Content of your second theorem.
\end{theorem}

In both definition and remark, the text should not be slanted.

\begin{remark}
Content of your remarks.
\end{remark}

In the proof below, we would like to show how to align the math
formulas:
\begin{proof}[Proof of Theorem \ref{result1}]
    Please align you math formulas:
\begin{equation}\label{Multi}
 \begin{split}
    \eps{\theta} \wedge d\eps{\theta}^{n-1} &= (\theta_0 + \ep \alpha)
    \wedge (d(\theta_0 + \ep \alpha))^{n-1} \quad \text{since } d\alpha = 0\\
    &= (\theta_0 + \ep \alpha) \wedge
    (d\theta_0)^{n-1} + \theta_0 \wedge d\theta_0^{n-1} - \ep d(\alpha \wedge
    \theta_0 \wedge d\theta_0^{n-2})\\
    & \quad + \theta_0 \wedge d\theta_0^{n-1} + \ep \alpha \wedge
    d\theta_0^{n-1}  \\
    &= \theta_0 \wedge d\theta_0^{n-1} - \ep d(\alpha \wedge
    \theta_0 \wedge d\theta_0^{n-2}),
 \end{split}
\end{equation}
So,
\begin{equation}\label{Equ3}
 \begin{split}
\int_0^T |u_0(t)|^2dt &\leq \delta^{-1} [\int_0^T
(\beta(t)+\gamma(t)) dt\\
& \quad +T^{\frac{2(p-1)}{p}}(\int_0^T
|\dot{u}_0(t)|^pdt)^{\frac{2}{p}}
 +T^{\frac{2(p-1)}{p}}(\int_0^T |\dot{u}_0(t)|^pdt)^{\frac{2}{p}}].
 \end{split}
\end{equation}

Please use the displaystyle if your formulas fully occupy a
paragraph, while use textstyle among the text.

For two equations:
\begin{align*}
A &= \theta_0 \wedge d\theta_0^{n-1} - \ep d(\alpha \wedge \theta_0 \wedge d\theta_0^{n-2})\\
B&=\theta_1 \wedge d\theta_1^{n-1} - \ep d(\alpha \wedge \theta_1
\wedge d\theta_1^{n-2})
\end{align*}
Please align your formulas nicely. Thanks.
\end{proof}

%For acknowledgements section, please don't number the section, you need to begin with \section*{Acknowledgements}
\section*{Acknowledgements} We would like to thank the
referees very much for their valuable comments and suggestions.

\begin{thebibliography}{99}

\bibitem{A11}
     \newblock FirstName MiddleInitial. LastName, % first name middle initial. and then last name.  Only the first character in the paper title is capitalized.
     \newblock \emph{Title of the paper},
     \newblock Name of the journal, \textbf{Volume} (Year), StaringPage--EndingPage.

% Example of paper with MR number:
\bibitem{A22} (2082924)
     \newblock C. Wolf,
     \newblock \emph{A mathematical model for the propagation of a hantavirus in structured populations},
     \newblock Discrete Continuous Dynam. Systems - B, \textbf{4} (2004), 1065--1089.

% Example of multiple authors:
\bibitem{BFL} (1124979)
    \newblock Y. Benoist, P. Foulon and F. Labourie, % Use `and' connect the last two authors
    \newblock \emph{Flots d'Anosov a distributions stable et instable
     differentiables},
    \newblock J. Amer. Math. Soc., \textbf{5} (1992), 33--75.

% Example of a book in the reference:
\bibitem{rB} (1301779)
     \newblock J. Smoller,
     \newblock ``Shock Waves and Reaction-Diffusion Equations," 2$^{nd}$
     \newblock edition,
     \newblock Springer-Verlag, New York, 1994.

\bibitem{Serrin} (0402274)
    \newblock J. Serrin,
    \newblock  \emph{Gradient estimates for solutions of nonlinear elliptic
                     and parabolic equations},
    \newblock  in ``Contributions to Nonlinear Functional Analysis" (eds. E.H. Zarantonello and Author 2),
                Academic Press, (1971), 33--75.

\bibitem{Zeng}
    \newblock FirstName LastName,
    \newblock  ``Torsion Cycles and Set Theoretic Complete Intersection,"
    \newblock  Ph.D thesis, Washington University in St. Louis, 2006.


\bibitem{quas}
\newblock M. Entov, L. Polterovich and F. Zapolsky,
\newblock \textit{Quasi-morphisms
\newblock and the Poisson bracket}, preprint,
\arXiv{math/0605406}

\bibitem{ckm2}
 \newblock R. Cote, C.E. Kenig and F. Merle,
  \newblock \emph{Scattering below critical energy for the radial 4D Yang-Mills equation and for the 2D corotational wave map system,}
  preprint \arXiv{0709.3222v1}



\end{thebibliography}

\medskip
%%% The received and accepted dates 
Received September 10, 2006; Accepted February 10, 2007.

\medskip

\end{document}