% Before you compile the tex file please add the class file %
% cmr.cls to the local folder where your tex file resides.  %
%%%%%%%%%%%%%%%%%%%%%%%  CMR  Begin %%%%%%%%%%%%%%%%%%%%%%%%%
\documentclass[mathpazo]{cmr}

%%%%% author macros %%%%%%%%%
% place your own macros HERE
%%%%% end %%%%%%%%%
 

\begin{document}

%%%%% title : short title may not be used but TITLE is required.
% \title{TITLE}
% \title[short title]{TITLE}

\title{Here is the Sample File for CMR}

%%%%% author(s):%%%%%%%%%%%%%
% Single author:
% \author[name in running head]{AUTHOR\corrauth}
% [name in running head] is NOT OPTIONAL, it is a MUST.
% Use \corrauth to indicate the corresponding author.
% Use \email to provide email address of author.
% Use \address to provide complete address with post code of the institution where the work was done.
\author[O.~Author]{Only Author\corrauth}
\address{School of Mathematics,
         Jilin University,
         Changchun, Jilin  130012, P.R. China. } %complete address with Post Code
\email{{\tt author@email} (O.~Author)}

%% Multiple authors:
%% Note the use of \affil and \affilnum to link names and addresses.
%% The author for correspondence is marked by \corrauth.
%% use \emails to provide email addresses of authors.
%% e.g. below example has 3 authors, first author is also the corresponding author,
%%      author 1 and 3 having the same address.
%\author[Z. Zhang, A. Chan and A. Zhao]{ Zhengru Zhang\affil{1}\comma\corrauth,
%                                        Author Chan\affil{2}~and Author Zhao\affil{1} }
%\address{\affilnum{1}\ School of Mathematical Sciences,
%                       Beijing Normal University,
%                       Beijing, 100875, P.R. China. \\
%         \affilnum{2}\ School of Mathematics,
%                       Jilin University,
%                       Changchun, Jilin, 130012, P.R. China.}
%\emails{{\tt zhang@email} (Z.~Zhang),
%        {\tt chan@email}  (A.~Chan),
%        {\tt zhao@email}  (A.~Zhao)  }

% \footnote and \thanks are not used in the heading section.
% Another acknowlegments/support of grants, state in Acknowledgments section
% \section*{Acknowledgments}


%%%%% Begin Abstract %%%%%%%%%%%
\begin{abstract}
This is a Sample File showing the right templates
for Communications in Mathematical Research Prepared in \LaTeX.
Please read the instructions in the tex file very carefully including those proceeded by \% sign.
\end{abstract}
%%%%%  end %%%%%%%%%%%

%%%%% AMS/Keywords %%%%%%%%%%%
\ams{xxxxx, xxxxx}    %AMS subject classification can be found in http://mathscinet.ams.org/msc/msc2010.html
\keywords{xxxxxx, xxxxxx, xxxxxx, xxxxxx.}    %List 3 to 8 keywords


%%%% maketitle %%%%%
\maketitle

%%%%%% Start %%%%%%%%%%%%%%%%%
\section{Introduction}\label{sec1}

\renewcommand{\baselinestretch}{1.05}

Here are some important instructions on how to prepare your \LaTeX\ files
for Communications in Mathematical Research.

\subsection{Equations\label{subsec2.1}}

Equations should be typewritten by using \verb"equation, align, multline"
environments.
\begin{equation}\label{testequation1}
\text{This is a  sample equation:}\quad ax=c.
\end{equation}
Please \textbf{avoid the obsolete} \verb"\eqnarray" environment, which has several bugs.

\subsection{Numbered multi-line equations}

Numbered multi-line equations can be written in the following form:

\begin{example}\label{exm1}
\begin{align}
&v_h(x_A,y_A)=V_1(x_B,y_B),\label{eq1}\\
&v_h^+(x_D,y_D)=v_h^-(x_D,y_D).\label{eq2}
\end{align}
 \end{example}
 
\begin{example}\label{exm2}
\begin{equation}\label{eq3}
\begin{aligned}
u(t_{n+1})&=e^{\mathbf{L}h}u(t_{n})+e^{t_{n}\mathbf{L}}\int_{t_{n}}^{t_{n}+h}e^{-\tau \mathbf{L}}\mathbf{N}(\tau,u(\tau))\,d\tau,\\
v(t_{n+1})&=e^{\mathbf{L}h}u(t_{n})+\int_{0}^{h}e^{(h-\tau) \mathbf{L}}\mathbf{R}(t_{n}+\tau,u(t_{n}+\tau))\,d\tau.
\end{aligned}
\end{equation}
 \end{example}

\begin{example}\label{exm3}
\begin{align}
u(t_{n+1})&=e^{\mathbf{L}h}u(t_{n})+e^{t_{n}\mathbf{L}}\int_{t_{n}}^{t_{n}+h}e^{-\tau \mathbf{L}}\mathbf{N}(\tau,u(\tau))\,d\tau \nonumber\\
&\quad -e^{\mathbf{L}h}u(t_{n})+\int_{0}^{h}e^{(h-\tau) \mathbf{L}}\mathbf{R}(t_{n}+\tau,u(t_{n}+\tau))\,d\tau.\label{eq4}
\end{align}
 \end{example}

Equations should be cited by using the \verb"\eqref" command and the form \\ \verb"Eq.~\eqref{testequation1}" or simply\/ \verb"\eqref{testequation1}". In the text they appear as Eq.~\eqref{testequation1} or \eqref{testequation1}.

\subsection{Non-numbered equations}

For non-numbered equations, please use the commands
 \verb"equation*", \verb"align*", \verb"multline*" rather than
\verb"$$ $$" and  \verb"\[    \]".





\subsection{Theorems, corollaries, lemmas, definitions}

For theorem, lemma, proposition, corollary, definition, remark, example use predefined environment.


 \begin{definition}\label{def1}
A matrix $A$ is called invertible if there exists a matrix $B$ such that
$AB=BA=E$, where $E$ is the identity matrix.
 \end{definition}

 

\begin{lemma}\label{lem1}
If $A\geq 2-\epsilon$, then the Galerkin method is stable.
 \end{lemma}

Results from other sources can be written in the form

\begin{theorem}[cf.~Author \& Co-Author~\cite{firstauthor}]\label{thm1}
If $a\neq0$, then the Eq.~\eqref{testequation1} has a unique solution.
\end{theorem}

\begin{proof}
A special environment is predefined: the \textit{proof} environment. Please use

\verb"\begin{proof}"

proof of the statement 

\verb"\end{proof}"

for typesetting your proofs. 
\end{proof}
 

\subsection{Figures}


Figures should be in a finished form suitable for publication in eps format. Lettering on drawings should be of professional quality or generated by high-resolution computer graphics and must be large enough to withstand appropriate reduction for publication.
For example, if you use {\sf MATLAB} to do figure plots,
axis labels should be at least point 18. Title should be 24 points or above. Tick marks labels better have 14 points or above. Line width should be 2 (or above). Illustrations in colors will appear in black and white in printed version.

Insert a figure in the text closest to its to where it is first cited.
Number figures consecutively with Arabic numerals according to its sequence in the text,
e.g., Fig.~1, Fig.~2. The caption should be placed at the bottom of the figure.
%Example of inserting a Figure
%\begin{figure}[htp]
%\centering
%  % replace XXX.xxx by your figure file name
%  %\includegraphics[width=2in]{XXX.xxx}
%  %\caption{Here is the Caption of your figure}\label{XXX}
%\end{figure}
 

 
 
   
%%%% Acknowledgments %%%%%%%%
\section*{Acknowledgments}

The author expresses thanks to the people helping with this work.
Financial support also appears in this part, with grant number(s) following. The full title of each fund is required.


%%%% Bibliography  %%%%%%%%%%
 
\begin{thebibliography}{99}

%References should be listed at the end of the paper in alphabetical order according to the surnames of the first author, and should be cited in the text using \verb"\cite" command as \verb"\cite{coutsias1996,firstauthor,Berger,deBoor}". In the text the citations will appear as  \cite{coutsias1996,firstauthor,Berger,deBoor}.

% Abbreviations of titles of periodicals/books should be given by using Math. Reviews, see e.g. \verb"https://mathscinet.ams.org/msnhtml/serials.pdf"

%Please do not list any references you never cited in your paper.

 
 
 \bibitem{firstauthor}  
 F.~Author and A.~Co-Author, \emph{Preparation of manuscript}, Intern. Public.  1 (2018), 12--21.

\bibitem{Berger} 
M. J.~Berger and P.~Collela, {\em Local adaptive mesh
refinement for shock hydrodynamics}, J. Comput. Phys.  82 (1989), 62--84.


\bibitem{deBoor} 
C.~de~Boor, {\em Good approximation by splines with variable knots II}, Springer Lecture  Notes Series  363, Springer-Verlag (1973).


\bibitem{Can09}
C.~Canuto, {\em High-order methods for {PDE}s: Recent advances and new perspectives},
 in:  {\em 6th {I}nternational {C}ongress on {I}ndustrial  and {A}pplied {M}athematics}, pp. 57--87,
 European Mathematical Society (2009).

 \bibitem{coutsias1996}
E.~Coutsias, T.~Hagstrom, J. S. Hesthaven, and D.~Torres,
 \emph{Integration preconditioners for differential operators in spectral
  $\tau$-methods},
 in: {\em Proceedings of the Third International Conference on Spectral
  and High Order Methods}, A.~Ilin and R.~Scott (Eds), pp. 21--38,  Houston Journal of Mathematics (1996).


\bibitem{TanTZ}  
Z. J.~Tan, T.~Tang, and Z. R.~Zhang, {\em A simple moving mesh method for one- and two-dimensional phase-field equations}, J. Comput. Appl. Math. (To appear).

\bibitem{Toro} 
E. F.~Toro,  \emph{Riemann Solvers and Numerical Methods for Fluid Dynamics}, Springer-Verlag, 1999.


\end{thebibliography}

\end{document}
