% \iffalse %%% ==================================================================== %%% @LaTeX-file{ %%% author = "American Mathematical Society", %%% version = "1.2beta", %%% date = "11-Oct-1994", %%% time = "15:19:39 EDT", %%% filename = "testart.tex", %%% copyright = "Copyright (C) 1994 American Mathematical Society, %%% all rights reserved. Copying of this file is %%% authorized only if either: %%% (1) you make absolutely no changes to your copy, %%% including name; OR %%% (2) if you do make changes, you first rename it %%% to some other name.", %%% address = "American Mathematical Society, %%% Technical Support, %%% Electronic Products and Services, %%% P. O. Box 6248, %%% Providence, RI 02940, %%% USA", %%% telephone = "401-455-4080 or (in the USA and Canada) %%% 800-321-4AMS (321-4267)", %%% FAX = "401-331-3842", %%% checksum = "53623 302 1069 9672", %%% email = "tech-support@math.ams.org (Internet)", %%% codetable = "ISO/ASCII", %%% keywords = "latex, amslatex, ams-latex, amstex", %%% supported = "yes", %%% abstract = "This file is part of the AMS-\LaTeX{} package. %%% It is a sample document illustrating the use of %%% the ``amsart'' documentclass and the ``amstex'' %%% package.", %%% docstring = "The checksum field above contains a CRC-16 %%% checksum as the first value, followed by the %%% equivalent of the standard UNIX wc (word %%% count) utility output of lines, words, and %%% characters. This is produced by Robert %%% Solovay's checksum utility.", %%% } %%% ==================================================================== % \fi %------------------------------------------------------------------------------ % Beginning of testart.tex %------------------------------------------------------------------------------ % This is a sample file for use with AMS-LaTeX1.2. It provides an example of % how to set up a file to be typeset with AMS-LaTeX. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % \documentclass{amsart} \newtheorem{theorem}{Theorem}[section] \newtheorem{lemma}[theorem]{Lemma} \theoremstyle{definition} \newtheorem{definition}[theorem]{Definition} \newtheorem{example}[theorem]{Example} \newtheorem{xca}[theorem]{Exercise} \theoremstyle{remark} \newtheorem{remark}[theorem]{Remark} \numberwithin{equation}{section} \makeatletter \def\square{\RIfM@\bgroup\else$\bgroup\aftergroup$\fi \vcenter{\hrule\hbox{\vrule\@height.6em\kern.6em\vrule}\hrule}\egroup} \makeatother \begin{document} \title[Sample Article Paper]{Sample Article Paper} \author[AUTHOR ONE AND AUTHOR TWO]{Author One and Author Two} \address{Department of Mathematics, Northeastern University, Boston, Massachusetts\linebreak 02115} % Research address for author one \curraddr{Department of Mathematics and Statistics, Case Western Reserve University, Cleveland, Ohio 43403} \email{xyz@@math.ams.org} \address{Mathematical Research Section, School of Mathematical Sciences, Australian National University, Canberra ACT 2601, Australia} %address for % author two \subjclass{Primary 54C40, 14E20; Secondary 46E25, 20C20} \date{09 October 1994 \\ Version 1.02} % \thanks will become a 1st page footnote. \thanks{The first author was supported in part by NSF Grant \#000000.} \maketitle \begin{abstract} This paper is a sample prepared to illustrate for authors the use of the \AmS-\LaTeX{} Version~1.2 package \texttt{amsart} style. \end{abstract} \section{This is a numbered first-level section head} This is an example of a numbered first-level heading. \section*{This is an unnumbered first-level section head} This is an example of an unnumbered first-level heading. \subsection{This is a numbered second-level section head} This is an example of a numbered second-level heading. \subsection*{This is an unnumbered second-level section head} This is an example of an unnumbered second-level heading. \subsubsection{This is a numbered third-level section head} This is an example of a numbered third-level heading. \subsubsection*{This is an unnumbered third-level section head} This is an example of an unnumbered third-level heading. \begin{lemma} Let $f, g\in A(X)$ and let $E$, $F$ be cozero sets in $X$. \begin{enumerate} \renewcommand{\theenumi}{\alph{enumi}} \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\footnote{Here is an example of a footnote. Notice that this footnote text is running on so that it can stand as an example of how a footnote with separate paragraphs should be keyed.\endgraf And here is the beginning of the second paragraph.}. \begin{pf} 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{pf} \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 the definition style. 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 the remark style. 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 the example style. 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 $$ G = G_0, G_1, G_2, \ldots, G_k = e $$ 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:2.15} [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. $$ - 2\psi_2(e) = c_{\alpha \gamma}^\delta c_{\beta \delta}^\gamma e^\alpha e^\beta. $$ When the form $\psi_1(e)$ is not zero, the expression on the right-hand side of this equation can be written in the form: \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 {\it solvable}. \item Second subsubitem. \end{enumerate} \item Third subitem. \end{enumerate} \item Third item. \end{enumerate} \begin{theorem} This is an example of a theorem. \end{theorem} \begin{theorem}[Marcus Theorem] This is an example of a theorem with the theorem name printed also. \end{theorem} % art work measures 11.5pc for figure 1, 7pc for figure 2 \begin{figure}[tb] \vskip 5pc \caption{This is an example of a figure caption.\label{firstfig}} \end{figure} \begin{figure}[tb] \vskip 3pc \caption{}\label{otherfig} \end{figure} \bibliographystyle{amsalpha} \begin{thebibliography}{BFMO} \bibitem [A1]{A1} T. Aoki, \textit{Calcul exponentiel des op\'erateurs microdifferentiels d'ordre infini.} I, Ann. Inst. Fourier (Grenoble) \textbf{33} (1983), 227--250. \bibitem [A2]{A2} \bysame, \textit{Calcul exponential des op\'erateurs microdifferentiels d'ordre infini.} II, Ann. Inst. Fourier (Grenoble) \textbf{36} (1986), 143--165. \bibitem [AKK]{AKK} T. Aoki, M. Kashiwara, and T. Kawai, \textit{On a class of linear differential operators of infinite order with finite index}, Adv. in Math. \textbf{62} (1986), 155--168. \end{thebibliography} \end{document} %------------------------------------------------------------------------------ % End of testart.tex %------------------------------------------------------------------------------