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dsa.cls
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%%
%% This is file `amsart.cls',
%% generated with the docstrip utility.
%%
%% The original source files were:
%%
%% amsclass.dtx (with options: `amsart')
%%
%%% ====================================================================
%%% @LaTeX-file{
%%% filename = "amsclass.dtx",
%%% version = "1.2r",
%%% date = "1997/03/26",
%%% time = "09:49:00 EST",
%%% checksum = "12277 3427 13562 126088",
%%% author = "American Mathematical Society",
%%% copyright = "Copyright (C) 1996 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",
%%% email = "[email protected] (Internet)",
%%% codetable = "ISO/ASCII",
%%% keywords = "latex, amslatex, ams-latex",
%%% supported = "yes",
%%% abstract = "This is part of the AMS-\LaTeX{} distribution.
%%% It produces output conforming to the style
%%% conventions of American Mathematical Society
%%% publications. The file \fn{amsclass.dtx} is
%%% converted by the installation procedure
%%% into three document classes:
%%% \cls{amsart}, \cls{amsproc}, and \cls{amsbook},
%%% which are intended, respectively,
%%% for articles and books containing mathematical
%%% research; both class files will also carry this
%%% heading, and the particular class should be
%%% determined from the external file name.",
%%% 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.",
%%% }
%%% ====================================================================
\NeedsTeXFormat{LaTeX2e}% LaTeX 2.09 can't be used (nor non-LaTeX)
[1994/12/01]% LaTeX date must December 1994 or later
\ProvidesClass{amsart}[1997/03/26 v1.2r]
\def\@tempa#1#2\@nil{\edef\@classname{#1}}
\expandafter\@tempa\@currnamestack{}{}{}\@nil
\ifx\@classname\@empty \edef\@classname{\@currname}\fi
\DeclareOption{a4paper}{\paperheight 297mm\paperwidth 210mm
\textheight 54.5pc }
\DeclareOption{letterpaper}{\paperheight 11in\paperwidth 8.5in }
\DeclareOption{landscape}{\@tempdima\paperheight
\paperheight\paperwidth \paperwidth\@tempdima}
\DeclareOption{portrait}{}
\DeclareOption{oneside}{\@twosidefalse \@mparswitchfalse}
\DeclareOption{twoside}{\@twosidetrue \@mparswitchtrue}
\DeclareOption{draft}{\overfullrule5\p@ }
\DeclareOption{final}{\overfullrule\z@ }
\def\dateposted#1{\def\@dateposted{\ (#1)}}%
\let\@dateposted\@empty
\DeclareOption{e-only}{%
\def\volinfo{Volume \currentvolume}%
\dateposted{Xxxx XX, XXXX}%
}
\newif\if@titlepage
\DeclareOption{titlepage}{\@titlepagetrue}
\DeclareOption{notitlepage}{\@titlepagefalse}
\newif\if@openright
\DeclareOption{openright}{\@openrighttrue}
\DeclareOption{openany}{\@openrightfalse}
\DeclareOption{onecolumn}{\@twocolumnfalse}
\DeclareOption{twocolumn}{\@twocolumntrue}
\DeclareOption{nomath}{}
\DeclareOption{noamsfonts}{}
\DeclareOption{psamsfonts}{%
\PassOptionsToPackage{psamsfonts}{amsfonts}%
\PassOptionsToPackage{cmex10}{amsmath}}
\newif\iftagsleft@
\DeclareOption{leqno}{%
\tagsleft@true \PassOptionsToPackage{leqno}{amsmath}}
\DeclareOption{reqno}{%
\tagsleft@false \PassOptionsToPackage{reqno}{amsmath}}
\newif\ifctagsplit@
\DeclareOption{centertags}{%
\ctagsplit@true \PassOptionsToPackage{centertags}{amsmath}}
\DeclareOption{tbtags}{%
\ctagsplit@false \PassOptionsToPackage{tbtags}{amsmath}}
\DeclareOption{fleqn}{%
\def\[{\relax
\ifmmode\@badmath
\else
\begin{trivlist}%
\@beginparpenalty\predisplaypenalty
\@endparpenalty\postdisplaypenalty
\item[]\leavevmode
\hbox to\linewidth\bgroup$\displaystyle
\hskip\mathindent\bgroup
\fi}%
\def\]{\relax
\ifmmode
\egroup \m@th$\hfil \egroup
\end{trivlist}%
\else \@badmath
\fi}%
\renewenvironment{equation}{%
\@beginparpenalty\predisplaypenalty
\@endparpenalty\postdisplaypenalty
\refstepcounter{equation}%
\@topsep\abovedisplayskip \trivlist
\item[]\leavevmode
\hbox to\linewidth\bgroup\hskip\mathindent$\displaystyle
}{%
\m@th$\hfil \displaywidth\linewidth \hbox{\@eqnnum}\egroup
\endtrivlist
}%
\renewenvironment{eqnarray}{%
\stepcounter{equation}\let\@currentlabel\theequation
\global\@eqnswtrue \global\@eqcnt\z@ \tabskip\mathindent
\let\\=\@eqncr \abovedisplayskip\topsep
\ifvmode \advance\abovedisplayskip\partopsep \fi
\belowdisplayskip\abovedisplayskip
\belowdisplayshortskip\abovedisplayskip
\abovedisplayshortskip\abovedisplayskip
$$\everycr{}\halign to\linewidth\bgroup
\hskip\@centering
$\displaystyle\tabskip\z@skip####\m@th$&%
\@eqnsel \global\@eqcnt\@ne
\hfil${}####{}\m@th$\hfil&%
\global\@eqcnt\tw@
$\displaystyle ####\m@th$\hfil\tabskip\@centering&%
\global\@eqcnt\thr@@
\hbox to \z@\bgroup\hss####\egroup\tabskip\z@skip\cr
}{%
\@@eqncr \egroup \global\advance\c@equation\m@ne$$%
\global\@ignoretrue
}%
\newdimen\mathindent \mathindent\leftmargini
}
\newcommand{\@mainsize}{10}
\newcommand{\@ptsize}{0}
\newcommand{\larger}[1][1]{%
\count@\@currsizeindex \advance\count@#1\relax
\ifnum\count@<\z@ \count@\z@ \else\ifnum\count@>12 \count@12 \fi\fi
\ifcase\count@
\Tiny\or\Tiny\or\tiny\or\SMALL\or\Small\or\small
\or\normalsize
\or\large\or\Large\or\LARGE\or\huge\or\Huge\else\Huge
\fi
}
\newcommand{\smaller}[1][1]{\larger[-#1]}
\def\@adjustvertspacing{%
\bigskipamount.7\baselineskip plus.7\baselineskip
\medskipamount\bigskipamount \divide\medskipamount\tw@
\smallskipamount\medskipamount \divide\smallskipamount\tw@
\abovedisplayskip\medskipamount
\belowdisplayskip \abovedisplayskip
\abovedisplayshortskip\abovedisplayskip
\advance\abovedisplayshortskip-1\abovedisplayskip
\belowdisplayshortskip\abovedisplayshortskip
\advance\belowdisplayshortskip 1\smallskipamount
\jot\baselineskip \divide\jot 4 \relax
}
\renewcommand\normalsize{\@xsetfontsize\normalsize 6%
\@adjustvertspacing \let\@listi\@listI}
\newcommand\Tiny{\@xsetfontsize\Tiny 1}
\newcommand\tiny{\@xsetfontsize\tiny 2}
\newcommand\SMALL{\@xsetfontsize\SMALL 3}
\newcommand\Small{\@xsetfontsize\Small 4%
\@adjustvertspacing
\def\@listi{\topsep\smallskipamount \parsep\z@skip \itemsep\z@skip}}
\newcommand\small{\@xsetfontsize\small 5\@adjustvertspacing}
\def\footnotesize{\Small}
\def\scriptsize{\SMALL}
\newcommand\large{\@xsetfontsize\large 7\@adjustvertspacing}
\newcommand\Large{\@xsetfontsize\Large 8\@adjustvertspacing}
\newcommand\LARGE{\@xsetfontsize\LARGE 9}
\newcommand\huge{\@xsetfontsize\huge{10}}
\newcommand\Huge{\@xsetfontsize\Huge{11}}
\def\@xsetfontsize#1#2{%
\chardef\@currsizeindex#2\relax
\edef\@tempa{\@nx\@setfontsize\@nx#1%
\@xp\ifcase\@xp\@currsizeindex\@typesizes
\else{99}{99}\fi}%
\@tempa
}
\chardef\@currsizeindex=6
\widowpenalty=10000
\clubpenalty=10000
\brokenpenalty=10000
\newdimen\linespacing
\lineskip=1pt \lineskiplimit=1pt
\normallineskip=1pt \normallineskiplimit=1pt
\let\baselinestretch=\@empty
\headheight=5pt \headsep=14pt
\footskip=12pt
\textheight=50.5pc \topskip=10pt
\textwidth=30pc
\columnsep=10pt \columnseprule=0pt
\marginparwidth=90pt
\marginparsep=11pt
\marginparpush=5pt
\AtBeginDocument{\settoheight{\footnotesep}{\footnotesize M$^1$}}
\skip\footins=7pt plus11pt
\skip\@mpfootins=\skip\footins
\fboxsep=3pt \fboxrule=.4pt
\arrayrulewidth=.4pt \doublerulesep=2pt
\labelsep=5pt \arraycolsep=\labelsep
\tabcolsep=\labelsep \tabbingsep=\labelsep
\floatsep=15pt plus 12pt \dblfloatsep=15pt plus 12pt
\textfloatsep=\floatsep \dbltextfloatsep=15pt plus 12pt
\intextsep=\floatsep
\@fptop=0pt plus1fil \@dblfptop=0pt plus1fil
\@fpbot=0pt plus1fil \@dblfpbot=0pt plus1fil
\@fpsep=8pt plus2fil \@dblfpsep=8pt plus2fil\relax
\parskip=0pt \relax
\newdimen\normalparindent
\normalparindent=12pt
\parindent=\normalparindent
\partopsep=0pt \relax \parsep=0pt \relax \itemsep=0pt \relax
\@lowpenalty=51 \@medpenalty=151 \@highpenalty=301
\@beginparpenalty=-\@lowpenalty
\@endparpenalty=-\@lowpenalty
\@itempenalty=-\@lowpenalty
\DeclareOption{10pt}{\def\@mainsize{10}\def\@ptsize{0}%
\def\@typesizes{%
\or{5}{6}\or{6}{7}\or{7}{8}\or{8}{10}\or{9}{11}%
\or{10}{12}% normalsize
\or{\@xipt}{13}\or{\@xiipt}{14}\or{\@xivpt}{17}%
\or{\@xviipt}{20}\or{\@xxpt}{24}}%
\normalsize \linespacing=\baselineskip
}
\DeclareOption{11pt}{\def\@mainsize{11}\def\@ptsize{1}%
\def\@typesizes{%
\or{6}{7}\or{7}{8}\or{8}{10}\or{9}{11}\or{10}{12}%
\or{\@xipt}{13}% normalsize
\or{\@xiipt}{14}\or{\@xivpt}{17}\or{\@xviipt}{20}%
\or{\@xxpt}{24}\or{\@xxvpt}{30}}%
\normalsize \linespacing=\baselineskip
}
\DeclareOption{12pt}{\def\@mainsize{12}\def\@ptsize{2}%
\def\@typesizes{%
\or{7}{8}\or{8}{10}\or{9}{11}\or{10}{12}\or{\@xipt}{13}%
\or{\@xiipt}{14}% normalsize
\or{\@xivpt}{17}\or{\@xviipt}{20}\or{\@xxpt}{24}%
\or{\@xxvpt}{30}\or{\@xxvpt}{30}}%
\normalsize \linespacing=\baselineskip
}
\DeclareOption{8pt}{\def\@mainsize{8}\def\@ptsize{8}%
\def\@typesizes{%
\or{5}{6}\or{5}{6}\or{5}{6}\or{6}{7}\or{7}{8}%
\or{8}{10}% normalsize
\or{9}{11}\or{10}{12}\or{\@xipt}{13}%
\or{\@xiipt}{14}\or{\@xivpt}{17}}%
\normalsize \linespacing=\baselineskip
}
\DeclareOption{9pt}{\def\@mainsize{9}\def\@ptsize{9}%
\def\@typesizes{%
\or{5}{6}\or{5}{6}\or{6}{7}\or{7}{8}\or{8}{10}%
\or{9}{11}% normalsize
\or{10}{12}\or{\@xipt}{13}\or{\@xiipt}{14}%
\or{\@xivpt}{17}\or{\@xviipt}{20}}%
\normalsize \linespacing=\baselineskip
}
\def\ps@empty{\let\@mkboth\@gobbletwo
\let\@oddhead\@empty \let\@evenhead\@empty
\let\@oddfoot\@empty \let\@evenfoot\@empty
\global\topskip\normaltopskip}
\def\ps@plain{\ps@empty
\def\@oddfoot{\normalfont\scriptsize \hfil\thepage\hfil}%
\let\@evenfoot\@oddfoot}
\def\ps@headings{\ps@empty
\def\@evenhead{\normalfont\scriptsize
\rlap{\thepage}\hfil \leftmark{}{}\hfil}%
\def\@oddhead{\normalfont\scriptsize \hfil
\rightmark{}{}\hfil \llap{\thepage}}%
\let\@mkboth\markboth
}
\let\sectionname\@empty
\let\subsectionname\@empty
\let\subsubsectionname\@empty
\let\paragraphname\@empty
\let\subparagraphname\@empty
\def\leftmark{\expandafter\@firstoftwo\topmark{}{}}
\def\rightmark{\expandafter\@secondoftwo\botmark{}{}}
\def\ps@firstpage{\ps@plain
\def\@oddfoot{\normalfont\scriptsize \hfil\thepage\hfil
\global\topskip\normaltopskip}%
\let\@evenfoot\@oddfoot
\def\@oddhead{\@serieslogo\hss}%
\let\@evenhead\@oddhead % in case an article starts on a left-hand page
}
\long\def\@nilgobble#1\@nil{}
\def\markboth#1#2{%
\begingroup
\@temptokena{{#1}{#2}}\xdef\@themark{\the\@temptokena}%
\mark{\the\@temptokena}%
\endgroup
\if@nobreak\ifvmode\nobreak\fi\fi}
\def\ps@myheadings{\ps@headings \let\@mkboth\@gobbletwo}
\newskip\normaltopskip
\normaltopskip=10pt \relax
\let\sectionmark\@gobble
\let\subsectionmark\@gobble
\let\subsubsectionmark\@gobble
\let\paragraphmark\@gobble
\DeclareOption{makeidx}{}
\input{amsgen.sty}
\ExecuteOptions{leqno,centertags,letterpaper,portrait,%
10pt,twoside,onecolumn,final}
\ProcessOptions\relax
\if@compatibility
\def\@tempa{\RequirePackage{amstex}\relax}
\else
\@ifclasswith{\@classname}{nomath}{%
\let\@tempa\relax
}{%
\def\@tempa{\RequirePackage{amsmath}\relax}%
}%
\fi
\@tempa % load amstex.sty or amsmath.sty
\providecommand\numberwithin[2]{%
\@ifundefined{c@#1}{\@nocounterr{#1}}{%
\@ifundefined{c@#2}{\@nocounterr{#2}}{%
\@addtoreset{#1}{#2}%
\toks@\@xp\@xp\@xp{\csname the#1\endcsname}%
\@xp\xdef\csname the#1\endcsname
{\@xp\@nx\csname the#2\endcsname
.\the\toks@}}}}
\if@compatibility
\else
\@ifclasswith{\@classname}{noamsfonts}{%
% amsfonts package is not wanted
}{%
% amsfonts package IS wanted; test whether a recent enough version
% seems to be installed
\begingroup \fontencoding{U}\fontfamily{msa}\try@load@fontshape\endgroup
\global\@xp\let\csname U+msa\endcsname\relax % reset
\@ifundefined{U/msa/m/n}{%
\ClassError{\@classname}{%
Package `amsfonts' not installed, or version too old?\MessageBreak
Unable to get font info for the `msam' fonts in the expected form%
}{%
The amsfonts package will not be loaded, to avoid probable\MessageBreak
incompatibility problems. You can (a) use the `noamsfonts'
documentclass\MessageBreak
option next time, or (b) check that the amsfonts package is
installed\MessageBreak
correctly, and is not too old to be compatible.%
}%
}{%
\RequirePackage{amsfonts}[1995/01/01]\relax
}%
}
\fi % end yesamsfonts branch
\newcommand{\uppercasenonmath}[1]{\toks@\@emptytoks
\@xp\@skipmath\@xp\@empty#1$$%
\edef#1{\@nx\@upprep\the\toks@}%
}
\newcommand{\@upprep}{%
\spaceskip1.3\fontdimen2\font plus1.3\fontdimen3\font
\upchars@}
\newcommand{\upchars@}{%
\def\ss{SS}\def\i{I}\def\j{J}\def\ae{\AE}\def\oe{\OE}%
\def\o{\O}\def\aa{\AA}\def\l{\L}\def\Mc{M{\scshape c}}}
\newcommand{\@skipmath}{}
\long\def\@skipmath#1$#2${%
\@xskipmath#1\(\)%
\@ifnotempty{#2}{\toks@\@xp{\the\toks@$#2$}\@skipmath\@empty}}%
\newcommand{\@xskipmath}{}
\long\def\@xskipmath#1\(#2\){%
\uppercase{\toks@\@xp\@xp\@xp{\@xp\the\@xp\toks@#1}}%
\@ifnotempty{#2}{\toks@\@xp{\the\toks@\(#2\)}\@xskipmath\@empty}}%
\newcommand{\today}{%
\relax\ifcase\month\or
January\or February\or March\or April\or May\or June\or
July\or August\or September\or October\or November\or December\fi
\space\number\day, \number\year}
\DeclareOldFontCommand{\rm}{\normalfont\rmfamily}{\mathrm}
\DeclareOldFontCommand{\sf}{\normalfont\sffamily}{\mathsf}
\DeclareOldFontCommand{\tt}{\normalfont\ttfamily}{\mathtt}
\DeclareOldFontCommand{\bf}{\normalfont\bfseries}{\mathbf}
\DeclareOldFontCommand{\it}{\normalfont\itshape}{\mathit}
\DeclareOldFontCommand{\sl}{\normalfont\slshape}{\@nomath\sl}
\DeclareOldFontCommand{\sc}{\normalfont\scshape}{\@nomath\sc}
\renewcommand*{\title}[2][]{\gdef\shorttitle{#1}\gdef\@title{#2}}
\edef\title{\@nx\@dblarg
\@xp\@nx\csname\string\title\endcsname}
\renewcommand{\author}[2][]{%
\ifx\@empty\authors
\gdef\shortauthors{#1}\gdef\authors{#2}%
\else
\g@addto@macro\shortauthors{\and#1}%
\g@addto@macro\authors{\and#2}%
\g@addto@macro\addresses{\author{}}%
\fi
}
\edef\author{\@nx\@dblarg
\@xp\@nx\csname\string\author\endcsname}
\let\shortauthors\@empty \let\authors\@empty
\let\addresses\@empty \let\thankses\@empty
\newcommand{\address}[2][]{\g@addto@macro\addresses{\address{#1}{#2}}}
\newcommand{\curraddr}[2][]{\g@addto@macro\addresses{\curraddr{#1}{#2}}}
\newcommand{\email}[2][]{\g@addto@macro\addresses{\email{#1}{#2}}}
\newcommand{\urladdr}[2][]{\g@addto@macro\addresses{\urladdr{#1}{#2}}}
\renewcommand{\thanks}[1]{\g@addto@macro\thankses{\thanks{#1}}}
\def\enddoc@text{\ifx\@empty\@translators \else\@settranslators\fi
\ifx\@empty\addresses \else\@setaddresses\fi}
\AtEndDocument{\enddoc@text}
\def\@setaddresses{\par
\nobreak \begingroup
\footnotesize
\def\author##1{\nobreak\addvspace\bigskipamount}%
\def\\{\unskip, \ignorespaces}%
\interlinepenalty\@M
\def\address##1##2{\begingroup
\par\addvspace\bigskipamount\indent
\@ifnotempty{##1}{(\ignorespaces##1\unskip) }%
{\scshape\ignorespaces##2}\par\endgroup}%
\def\curraddr##1##2{\begingroup
\@ifnotempty{##2}{\nobreak\indent{\itshape Current address}%
\@ifnotempty{##1}{, \ignorespaces##1\unskip}\/:\space
##2\par\endgroup}}%
\def\email##1##2{\begingroup
\@ifnotempty{##2}{\nobreak\indent{\itshape E-mail address}%
\@ifnotempty{##1}{, \ignorespaces##1\unskip}\/:\space
\ttfamily##2\par\endgroup}}%
\def\urladdr##1##2{\begingroup
\@ifnotempty{##2}{\nobreak\indent{\itshape URL}%
\@ifnotempty{##1}{, \ignorespaces##1\unskip}\/:\space
\ttfamily##2\par\endgroup}}%
\addresses
\endgroup
}
\let\@date\@empty
\def\dedicatory#1{\def\@dedicatory{#1}}
\let\@dedicatory=\@empty
\def\keywords#1{\def\@keywords{#1}}
\let\@keywords=\@empty
\def\subjclass#1{\def\@subjclass{#1}}
\let\@subjclass=\@empty
\def\commby#1{\def\@commby{(Communicated by #1)}}
\let\@commby=\@empty
\def\translator#1{%
\ifx\@empty\@translators \def\@translators{#1}%
\else\g@addto@macro\@translators{\and#1}\fi}
\let\@translators=\@empty
\def\@settranslators{\par\begingroup
\addvspace{6\p@\@plus9\p@}%
\hbox to\columnwidth{\hss\normalfont\normalsize
Translated by %
\andify\@translators \uppercasenonmath\@translators
\@translators}
\endgroup
}
\newcommand{\xandlist}[4]{\@andlista{{#1}{#2}{#3}}#4\and\and}
\def\@andlista#1#2\and#3\and{\@andlistc{#2}\@ifnotempty{#3}{%
\@andlistb#1{#3}}}
\def\@andlistb#1#2#3#4#5\and{%
\@ifempty{#5}{%
\@andlistc{#2#4}%
}{%
\@andlistc{#1#4}\@andlistb{#1}{#3}{#3}{#5}%
}}
\let\@andlistc\@iden
\newcommand{\nxandlist}[4]{%
\def\@andlistc##1{\toks@\@xp{\the\toks@##1}}%
\toks@{\toks@\@emptytoks \@andlista{{#1}{#2}{#3}}}%
\the\@xp\toks@#4\and\and
\edef#4{\the\toks@}%
\let\@andlistc\@iden}
\newcommand{\andify}{%
\nxandlist{\unskip, }{\unskip{} and~}{\unskip, and~}}
\def\and{\unskip{ }and \ignorespaces}
\def\maketitle{\par
\@topnum\z@ % this prevents figures from falling at the top of page 1
\@setcopyright
\uppercasenonmath\shorttitle
\ifx\@empty\shortauthors \let\shortauthors\shorttitle
\else \andify\shortauthors \uppercasenonmath\shortauthors \fi
\@maketitle@hook
\begingroup
\@maketitle
\toks@\@xp{\shortauthors}\@temptokena\@xp{\shorttitle}%
\edef\@tempa{\@nx\markboth{\the\toks@}{\the\@temptokena}}\@tempa
\endgroup
\thispagestyle{firstpage}% this sets first page specifications
\c@footnote\z@
\def\do##1{\let##1\relax}%
\do\maketitle \do\@maketitle \do\title \do\@xtitle \do\@title
\do\author \do\@xauthor \do\address \do\@xaddress
\do\email \do\@xemail \do\curraddr \do\@xcurraddr
\do\commby \do\@commby
\do\dedicatory \do\@dedicatory \do\thanks \do\thankses
\do\keywords \do\@keywords \do\subjclass \do\@subjclass
}
\def\@maketitle@hook{\global\let\@maketitle@hook\@empty}
\def\@maketitle{%
\normalfont\normalsize
\let\@makefnmark\relax \let\@thefnmark\relax
\ifx\@empty\@date\else \@footnotetext{\@setdate}\fi
\ifx\@empty\@subjclass\else \@footnotetext{\@setsubjclass}\fi
\ifx\@empty\@keywords\else \@footnotetext{\@setkeywords}\fi
\ifx\@empty\thankses\else \@footnotetext{%
\def\par{\let\par\@par}\@setthanks}\fi
\@mkboth{\@nx\shortauthors}{\@nx\shorttitle}%
\global\topskip42\p@\relax % 5.5pc " " " " "
\@settitle
\ifx\@empty\authors \else \@setauthors \fi
\ifx\@empty\@dedicatory
\else
\baselineskip18\p@
\vtop{\centering{\footnotesize\itshape\@dedicatory\@@par}%
\global\dimen@i\prevdepth}\prevdepth\dimen@i
\fi
\@setabstract
\normalsize
\if@titlepage
\newpage
\else
\dimen@34\p@ \advance\dimen@-\baselineskip
\vskip\dimen@\relax
\fi
} % end \@maketitle
\AtBeginDocument{%
\@ifundefined{publname}{%
\let\publname\@empty
\let\@serieslogo\@empty
}{%
\def\@serieslogo{%
\vbox to\headheight{%
\parindent\z@ \fontsize{6}{7\p@}\selectfont
\noindent\publname\newline
\volinfo, \pageinfo \@dateposted\newline \@PII\endgraf
\vss
}%
}%
}%
}
\AtBeginDocument{%
\@ifundefined{volinfo}{%
\def\volinfo{%
Volume \currentvolume, Number \number0\currentissue,
\currentmonth\ \currentyear
}%
}{}%
}
\def\issueinfo#1#2#3#4{\def\currentvolume{#1}\def\currentissue{#2}%
\def\currentmonth{#3}\def\currentyear{#4}}
\issueinfo{00}% volume number
{0}% % issue number
{Xxxx}% % month
{XXXX}% % year
\def\copyrightinfo#1#2{\def\copyrightyear{#1}\def\copyrightholder{#2}}
\copyrightinfo{0000}{(copyright holder)}
\def\pagespan#1#2{\setcounter{page}{#1}%
\ifnum\c@page<\z@ \pagenumbering{roman}\setcounter{page}{-#1}\fi
\def\start@page{#1}\def\end@page{#2}}
\pagespan{000}{000}
\@ifundefined{pageinfo}{%
\def\pageinfo{%
\ifnum\start@page=\z@
Pages 000--000
\else
\ifx\start@page\end@page
Page \start@page
\else
Pages \start@page--\end@page
\fi
\fi}%
}{}
\@ifundefined{ISSN}{\def\ISSN{0000-0000}}{}
\newcommand\PII[1]{\def\@PII{#1}}
\PII{S \ISSN(XX)0000-0}
\newinsert\copyins
\skip\copyins=1.5pc
\count\copyins=1000 % magnification factor, 1000 = 100%
\dimen\copyins=.5\textheight % maximum allowed per page
\def\@setcopyright{%
\ifx\@empty\@serieslogo
\else\ifx\@empty\copyrightyear
\else
\insert\copyins{\hsize\textwidth
\parfillskip\z@ \leftskip\z@\@plus.9\textwidth
\fontsize{6}{7\p@}\normalfont\upshape
\everypar{}%
\vskip-\skip\copyins \nointerlineskip
\noindent\vrule\@width\z@\@height\skip\copyins
\copyright\copyrightyear\ \copyrightholder
\par
\kern\z@}%
\fi\fi
}
\def\@combinefloats{%
\ifx \@toplist\@empty \else \@cflt \fi
\ifx \@botlist\@empty \else \@cflb \fi
\ifvoid\copyins \else \@cflci \fi
}
\def\@cflci{%
\if\if@twocolumn \if@firstcolumn F\else T\fi\else T\fi T%
\setbox\@outputbox\vbox{%
\unvbox\@outputbox
\vskip\skip\copyins
\hbox to\columnwidth{%
\hss\vbox to\z@{\vss\unvbox\copyins}}}%
\fi
}
\newcommand{\abstractname}{Abstract}
\newcommand{\keywordsname}{Key words and phrases}
\newcommand{\subjclassname}{\textup{1991} Mathematics Subject
Classification}
\def\@tempb{amsart}
\ifx\@classname\@tempb
\newcommand{\datename}{\textit{Date}:}
\else
\newcommand{\datename}{Received by the editors}
\fi
\def\@settitle{\begin{center}%
\baselineskip14\p@\relax
\bfseries
\uppercasenonmath\@title
\@title
\end{center}%
}
\def\@setauthors{%
\begingroup
\trivlist
\centering\footnotesize \@topsep30\p@\relax
\advance\@topsep by -\baselineskip
\item\relax
\andify\authors
\uppercasenonmath\authors
\authors
\endtrivlist
\endgroup
}
\def\@setdate{\datename\ \@date\@addpunct.}
\def\@setsubjclass{%
{\itshape\subjclassname.}\enspace\@subjclass\@addpunct.}
\def\@setkeywords{%
{\itshape \keywordsname.}\enspace \@keywords\@addpunct.}
\def\@setthanks{\def\thanks##1{\par##1\@addpunct.}\thankses}
\newbox\abstractbox
\newenvironment{abstract}{%
\ifx\maketitle\relax
\ClassWarning{\@classname}{Abstract should precede
\protect\maketitle\space in AMS documentclasses; reported}%
\fi
\global\setbox\abstractbox=\vtop \bgroup
\normalfont\Small
\Small
\list{}{\labelwidth\z@
\leftmargin3pc \rightmargin\leftmargin
\listparindent\normalparindent \itemindent\z@
\parsep\z@ \@plus\p@
\let\fullwidthdisplay\relax
}%
\item[\hskip\labelsep]%
}{%
\endlist\egroup
\ifx\@setabstract\relax \@setabstracta \fi
}
\def\@setabstract{\@setabstracta \global\let\@setabstract\relax}
\def\@setabstracta{%
\ifvoid\abstractbox
\else
\skip@20\p@ \advance\skip@-\lastskip
\advance\skip@-\baselineskip \vskip\skip@
\box\abstractbox
\prevdepth\z@ % because \abstractbox is a vtop
\fi
}
\def\titlepage{%
\clearpage
\thispagestyle{empty}\setcounter{page}{0}}
\def\endtitlepage{\newpage}
\def\labelenumi{\theenumi.}
\def\theenumi{\@arabic\c@enumi}
\def\labelenumii{(\theenumii)}
\def\theenumii{\@alph\c@enumii}
\def\p@enumii{\theenumi}
\def\labelenumiii{(\theenumiii)}
\def\theenumiii{\@roman\c@enumiii}
\def\p@enumiii{\theenumi(\theenumii)}
\def\labelenumiv{(\theenumiv)}
\def\theenumiv{\@Alph\c@enumiv}
\def\p@enumiv{\p@enumiii\theenumiii}
\def\labelitemi{$\m@th\bullet$}
\def\labelitemii{\bfseries --}% \upshape already done by \itemize
\def\labelitemiii{$\m@th\ast$}
\def\labelitemiv{$\m@th\cdot$}
\newenvironment{verse}{\let\\\@centercr
\list{}{\itemsep\z@ \itemindent -1.5em\listparindent\itemindent
\rightmargin\leftmargin \advance\leftmargin 1.5em}\item[]%
}{%
\endlist
}
\let\endverse=\endlist % for efficiency
\newenvironment{quotation}{\list{}{%
\leftmargin3pc \listparindent\normalparindent
\itemindent\z@
\rightmargin\leftmargin \parsep\z@ \@plus\p@}%
\item[]%
}{%
\endlist
}
\let\endquotation=\endlist % for efficiency
\newenvironment{quote}{%
\list{}{\rightmargin\leftmargin}\item[]%
}{%
\endlist
}
\let\endquote=\endlist % for efficiency
\def\trivlist{\parsep\parskip\@nmbrlistfalse
\@trivlist \labelwidth\z@ \leftmargin\z@
\itemindent\z@
\let\@itemlabel\@empty
\def\makelabel##1{\upshape##1}}
\renewenvironment{enumerate}{%
\ifnum \@enumdepth >3 \@toodeep\else
\advance\@enumdepth \@ne
\edef\@enumctr{enum\romannumeral\the\@enumdepth}\list
{\csname label\@enumctr\endcsname}{\usecounter
{\@enumctr}\def\makelabel##1{\hss\llap{\upshape##1}}}\fi
}{%
\endlist
}
\let\endenumerate=\endlist % for efficiency
\renewenvironment{itemize}{%
\ifnum\@itemdepth>3 \@toodeep
\else \advance\@itemdepth\@ne
\edef\@itemitem{labelitem\romannumeral\the\@itemdepth}%
\list{\csname\@itemitem\endcsname}%
{\def\makelabel##1{\hss\llap{\upshape##1}}}%
\fi
}{%
\endlist
}
\let\enditemize=\endlist % for efficiency
\newcommand{\descriptionlabel}[1]{\hspace\labelsep \upshape\bfseries #1:}
\newenvironment{description}{\list{}{%
\advance\leftmargini6\p@ \itemindent-12\p@
\labelwidth\z@ \let\makelabel\descriptionlabel}%
}{
\endlist
}
\let\enddescription=\endlist % for efficiency
\let\upn=\textup
\AtBeginDocument{%
\settowidth\leftmargini{\labelenumi\hskip\labelsep}%
\advance\leftmargini by \normalparindent
\settowidth\leftmarginii{\labelenumii\hskip\labelsep}%
\advance\leftmarginii by 6pt
\settowidth\leftmarginiii{\labelenumiii\hskip\labelsep}%
\advance\leftmarginiii by 6pt
\settowidth\leftmarginiv{\labelenumiv\hskip\labelsep}%
\advance\leftmarginiv by 10pt
\leftmarginv=10pt
\leftmarginvi=10pt
\leftmargin=\leftmargini
\labelsep=5pt
\labelwidth=\leftmargini \advance\labelwidth-\labelsep
\@listi}
\newskip\listisep
\listisep\smallskipamount
\def\@listI{\leftmargin\leftmargini \parsep\z@skip
\topsep\listisep \itemsep\z@skip
\listparindent\normalparindent}
\let\@listi\@listI
\def\@listii{\leftmargin\leftmarginii
\labelwidth\leftmarginii \advance\labelwidth-\labelsep
\topsep\z@skip \parsep\z@skip \partopsep\z@skip \itemsep\z@skip}
\def\@listiii{\leftmargin\leftmarginiii
\labelwidth\leftmarginiii \advance\labelwidth-\labelsep}
\def\@listiv{\leftmargin\leftmarginiv
\labelwidth\leftmarginiv \advance\labelwidth-\labelsep}
\def\@listv{\leftmargin\leftmarginv
\labelwidth\leftmarginv \advance\labelwidth-\labelsep}
\def\@listvi{\leftmargin\leftmarginvi
\labelwidth\leftmarginvi \advance\labelwidth-\labelsep}
\def\@startsection#1#2#3#4#5#6{%
\if@noskipsec \leavevmode \fi
\par \@tempskipa #4\relax
\@afterindenttrue
\ifdim \@tempskipa <\z@ \@tempskipa -\@tempskipa \@afterindentfalse\fi
\if@nobreak \everypar{}\else
\addpenalty\@secpenalty\addvspace\@tempskipa\fi
\@ifstar{\@dblarg{\@sect{#1}{\@m}{#3}{#4}{#5}{#6}}}%
{\@dblarg{\@sect{#1}{#2}{#3}{#4}{#5}{#6}}}%
}
\def\@secnumfont{\mdseries}
\def\@sect#1#2#3#4#5#6[#7]#8{%
\edef\@toclevel{\ifnum#2=\@m 0\else\number#2\fi}%
\ifnum #2>\c@secnumdepth \let\@secnumber\@empty
\else \@xp\let\@xp\@secnumber\csname the#1\endcsname\fi
\ifnum #2>\c@secnumdepth
\let\@svsec\@empty
\else
\refstepcounter{#1}%
\edef\@svsec{\ifnum#2<\@m
\@ifundefined{#1name}{}{%
\ignorespaces\csname #1name\endcsname\space}\fi
\@nx\textup{%
\@nx\@secnumfont
\csname the#1\endcsname.}\enspace
}%
\fi
\@tempskipa #5\relax
\ifdim \@tempskipa>\z@ % then this is not a run-in section heading
\begingroup #6\relax
\@hangfrom{\hskip #3\relax\@svsec}{\interlinepenalty\@M #8\par}%
\endgroup
\ifnum#2>\@m \else \@tocwrite{#1}{#8}\fi
\else
\def\@svsechd{#6\hskip #3\@svsec
\@ifnotempty{#8}{\ignorespaces#8\unskip
\@addpunct.}%
\ifnum#2>\@m \else \@tocwrite{#1}{#8}\fi
}%
\fi
\global\@nobreaktrue
\@xsect{#5}}
\let\@ssect\relax
\newcounter{part}
\newcounter{section}
\newcounter{subsection}[section]
\newcounter{subsubsection}[subsection]
\newcounter{paragraph}[subsubsection]
\renewcommand\thepart {\arabic{part}}
\renewcommand\thesection {\arabic{section}}
\renewcommand\thesubsection {\thesection.\arabic{subsection}}
\renewcommand\thesubsubsection {\thesubsection .\arabic{subsubsection}}
\renewcommand\theparagraph {\thesubsubsection.\arabic{paragraph}}
\setcounter{secnumdepth}{3}
\def\partname{Part}
\def\part{\@startsection{part}{0}%
\z@{\linespacing\@plus\linespacing}{.5\linespacing}%
{\normalfont\bfseries\raggedright}}
\def\specialsection{\@startsection{section}{1}%
\z@{\linespacing\@plus\linespacing}{.5\linespacing}%
{\normalfont\centering}}
\def\section{\@startsection{section}{1}%
\z@{.7\linespacing\@plus\linespacing}{.5\linespacing}%
{\normalfont\bfseries\centering}}
\def\subsection{\@startsection{subsection}{2}%
\z@{.5\linespacing\@plus.7\linespacing}{-.5em}%
{\normalfont\bfseries}}
\def\subsubsection{\@startsection{subsubsection}{3}%
\z@{.5\linespacing\@plus.7\linespacing}{-.5em}%
{\normalfont\itshape}}
\def\paragraph{\@startsection{paragraph}{4}%
\z@\z@{-\fontdimen2\font}%
\normalfont}
\def\subparagraph{\@startsection{subparagraph}{5}%
\z@\z@{-\fontdimen2\font}%
\normalfont}
\def\appendix{\par\c@section\z@ \c@subsection\z@
\let\sectionname\appendixname
\def\thesection{\@Alph\c@section}}
\def\appendixname{Appendix}
\def\@Roman#1{\@xp\@slowromancap
\romannumeral#1@}%
\def\@slowromancap#1{\ifx @#1% then terminate
\else
\if i#1I\else\if v#1V\else\if x#1X\else\if l#1L\else\if
c#1C\else\if m#1M\else#1\fi\fi\fi\fi\fi\fi
\@xp\@slowromancap
\fi
}
\newcommand{\@pnumwidth}{1.6em}
\newcommand{\@tocrmarg}{2.6em}
\setcounter{tocdepth}{2}
\def\@starttoc#1#2{\begingroup
\par\removelastskip\vskip\z@skip
\@startsection{}\@M\z@{\linespacing\@plus\linespacing}%
{.5\linespacing}{\centering\scshape}{#2}%
\ifx\contentsname#2%
\else \addcontentsline{toc}{section}{#2}\fi
\makeatletter
\@input{\jobname.#1}%
\if@filesw
\@xp\newwrite\csname tf@#1\endcsname
\immediate\@xp\openout\csname tf@#1\endcsname \jobname.#1\relax
\fi
\global\@nobreakfalse \endgroup
\addvspace{32\p@\@plus14\p@}%
\let\tableofcontents\relax
}
\def\contentsname{Contents}
\def\listfigurename{List of Figures}
\def\listtablename{List of Tables}
\def\tableofcontents{\@starttoc{toc}\contentsname}
\def\listoffigures{\@starttoc{lof}\listfigurename}
\def\listoftables{\@starttoc{lot}\listtablename}
\AtBeginDocument{%
\@for\@tempa:=-1,0,1,2,3\do{%
\@ifundefined{r@tocindent\@tempa}{%
\@xp\gdef\csname r@tocindent\@tempa\endcsname{0pt}}{}%
}%
}
\def\@writetocindents{%
\begingroup
\@for\@tempa:=-1,0,1,2,3\do{%
\immediate\write\@auxout{%
\string\newlabel{tocindent\@tempa}{%
\csname r@tocindent\@tempa\endcsname}}%
}%
\endgroup}
\AtEndDocument{\@writetocindents}
\let\indentlabel\@empty
\def\@tochangmeasure#1{\sbox\z@{#1}%
\ifdim\wd\z@>\csname r@tocindent\@toclevel\endcsname\relax
\@xp\xdef\csname r@tocindent\@toclevel\endcsname{\the\wd\z@}%
\fi
}
\def\@toclevel{0}
\def\@tocline#1#2#3#4#5#6#7{\relax
\ifnum #1>\c@tocdepth % then omit
\else
\par \addpenalty\@secpenalty\addvspace{#2}%
\begingroup \hyphenpenalty\@M
\@ifempty{#4}{%
\@tempdima\csname r@tocindent\number#1\endcsname\relax
}{%
\@tempdima#4\relax
}%
\parindent\z@ \leftskip#3\relax \advance\leftskip\@tempdima\relax
\rightskip\@pnumwidth plus1em \parfillskip-\@pnumwidth
#5\leavevmode\hskip-\@tempdima #6\relax
\hfil\hbox to\@pnumwidth{\@tocpagenum{#7}}\par
\nobreak
\endgroup
\fi}
\def\@tocpagenum#1{\hss{\mdseries #1}}
\def\@tocwrite#1{\@xp\@tocwriteb\csname toc#1\endcsname{#1}}
\def\@tocwriteb#1#2#3{%
\begingroup
\def\@tocline##1##2##3##4##5##6{%
\ifnum##1>\c@tocdepth
\else \sbox\z@{##5\let\indentlabel\@tochangmeasure##6}\fi}%
\csname l@#2\endcsname{#1{\csname#2name\endcsname}{\@secnumber}{}}%
\endgroup
\addcontentsline{toc}{#2}%
{\protect#1{\csname#2name\endcsname}{\@secnumber}{#3}}}
\def\l@section{\@tocline{1}{0pt}{1pc}{}{}}
\newcommand{\tocsection}[3]{%
\indentlabel{\@ifnotempty{#2}{\ignorespaces#1 #2.\quad}}#3}
\def\l@subsection{\@tocline{2}{0pt}{1pc}{5pc}{}}
\let\tocsubsection\tocsection
\def\l@subsubsection{\@tocline{3}{0pt}{1pc}{7pc}{}}
\let\tocsubsubsection\tocsection
\def\l@part{\@tocline{-1}{12pt plus2pt}{0pt}{}{\bfseries}}
\let\tocpart\tocsection
\def\l@chapter{\@tocline{0}{8pt plus1pt}{0pt}{}{}}
\let\tocchapter\tocsection
\let\tocappendix\tocchapter
\def\l@figure{\@tocline{0}{3pt plus2pt}{0pt}{}{}}
\let\l@table=\l@figure
\def\refname{REFERENCES}
\def\bibname{Bibliography}
\def\bibliographystyle#1{%
\if@filesw\immediate\write\@auxout
{\string\bibstyle{#1}}\fi
\def\@tempa{#1}%
\def\@tempb{amsplain}%
\def\@tempc{}%
\ifx\@tempa\@tempb
\def\@biblabel##1{##1.}%
\def\bibsetup{}%
\else
\def\bibsetup{\labelsep6\p@}%
\ifx\@tempa\@tempc
\def\@biblabel##1{}%
\def\bibsetup{\labelwidth\z@ \leftmargin24\p@
\itemindent-24\p@
\labelsep\z@ }%
\fi
\fi}
\newenvironment{thebibliography}[1]{%
\@xp\section\@xp*\@xp{\refname}%
\normalfont\footnotesize\labelsep .5em\relax
\renewcommand\theenumiv{\arabic{enumiv}}\let\p@enumiv\@empty
\list{\@biblabel{\theenumiv}}{\settowidth\labelwidth{\@biblabel{#1}}%
\leftmargin\labelwidth \advance\leftmargin\labelsep
\usecounter{enumiv}}%