%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% AMSART.STY						    July 1990      %
%                                                                          %
% This file is part of the AMS-LaTeX Version 1.0 distribution              %
%   American Mathematical Society, Technical Support Group,                %
%   P. O. Box 6248, Providence, RI 02940                                   %
%   800-321-4AMS (321-4267) or 401-455-4080                                %
%   Internet: Tech-Support@Math.AMS.com                                    %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% This is file `ldd:amsart.sty' generated
%% on <1990/7/10> with the docstrip utility (v1.1j). 
%% 
%% The original source file was `ldd:amsart.doc'.
%% 
\def\fileversion{v1.0c}
\def\filedate{90/06/26}
\def\docdate{90/06/26}

%% \CheckSum{1978}
%% \CharacterTable
%%  {Upper-case    \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z
%%   Lower-case    \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z
%%   Digits        \0\1\2\3\4\5\6\7\8\9
%%   Exclamation   \!     Double quote  \"     Hash (number) \#
%%   Dollar        \$     Percent       \%     Ampersand     \&
%%   Acute accent  \'     Left paren    \(     Right paren   \)
%%   Asterisk      \*     Plus          \+     Comma         \,
%%   Minus         \-     Point         \.     Solidus       \/
%%   Colon         \:     Semicolon     \;     Less than     \<
%%   Equals        \=     Greater than  \>     Question mark \?
%%   Commercial at \@     Left bracket  \[     Backslash     \\
%%   Right bracket \]     Circumflex    \^     Underscore    \_
%%   Grave accent  \`     Left brace    \{     Vertical bar  \|
%%   Right brace   \}     Tilde         \~}
\ifx\undefined\if@article % If \if@article is undefined,
\expandafter\let          % we will end up with \let\if@article\iftrue
\else \expandafter\@gobbletwo\fi % otherwise \@gobbletwo\if@article\iftrue
\if@article\iftrue       % which removes this line.
\if@article %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% ARTICLE ONLY
\immediate\write\sixt@@n{%
  Document style `AMSART' \fileversion\space <\filedate> (RK, MJD)}
\immediate\write\sixt@@n{%
  English documentation \space\@spaces\@spaces <\docdate> (MJD)}
\fi %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% ARTICLE ONLY

\input amstex.sty
\def\@ptsize{0}
\@namedef{ds@11pt}{\def\@ptsize{1}}
\@namedef{ds@12pt}{\def\@ptsize{2}}
\@namedef{ds@twoside}{\@empty}

\def\ds@draft{\overfullrule 5\p@}
\@namedef{ds@twocolumn}{\typeout{Sorry---the `twocolumn' option
      is not available in the AMSART and AMSBOOK documentstyles.}}
\@namedef{ds@openbib}{\typeout{Sorry---the `openbib' option
      is not available in the AMSART and AMSBOOK documentstyles.}}
\@namedef{ds@fleqn}{\typeout{Sorry---the `fleqn' option
      is not available in the AMSART and AMSBOOK documentstyles.}}
\if@article %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% ARTICLE ONLY
\@namedef{ds@titlepage}{\typeout{Sorry---the `titlepage' option
      is not available in the AMSART documentstyle.}}
\fi %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% ARTICLE ONLY

\@options
\let\ds@twocolumn\relax       \let\ds@openbib\relax
\let\ds@fleqn\relax
\if@article %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% ARTICLE ONLY
\let\ds@titlepage\relax
\fi %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% ARTICLE ONLY
\input{margid.sty}
\def\@plus{plus}
\def\@string{\expandafter\@gobble\string}
\def\@ifempty#1{\ifx\@@end#1\@@end\expandafter\@leftmark
    \else \expandafter\@rightmark\fi}
\long\def\@leftmark#1#2{#1}
\long\def\@rightmark#1#2{#2}
\def\@andify#1#2{%
  \expandafter\in@\expandafter\and\expandafter{#2}%
  \ifin@
  \begingroup\global\toks\@ne{}% initialize to empty
  \def\and##1\and{\@ifempty{##1}{}{\advance\@tempcnta\@ne\and}}%
  \@tempcnta\z@\expandafter\and#2\and%
  \ifnum\@tempcnta>\tw@
    \def\and##1\and{\advance\@tempcnta\m@ne
      \global\toks\@ne\expandafter{\the\toks\@ne ##1}%
      \edef\@tempa{\the\toks\@ne\ifnum\@tempcnta=\@ne\unskip,#1\else
          \ifnum\@tempcnta>\@ne\unskip,\ \fi\fi}%
      \global\toks\@ne\expandafter{\@tempa \ignorespaces}%
      \ifnum\@tempcnta>\z@\expandafter\and\fi}%
  \else % if NOT > 2
    \def\and##1\and{\advance\@tempcnta\m@ne
       \global\toks\@ne\expandafter{\the\toks\@ne ##1}%
       \edef\@tempa{\the\toks\@ne
         \ifnum\@tempcnta=\@ne\unskip#1\ignorespaces\fi}%
       \global\toks\@ne\expandafter{\@tempa}%
       \ifnum\@tempcnta>\z@\expandafter\and\fi}%
  \fi % ifnum
 \expandafter\and#2\relax\endgroup
 \edef#2{\the\toks\@ne}%
\fi % ifin@
}
\def\uppercasetext@#1{%
   {\spaceskip1.3\fontdimen2\the\font plus1.3\fontdimen3\the\font
    \def\ss{SS}\let\i=I\let\j=J\let\ae\AE\let\oe\OE\let\o\O\let\aa\AA\let\l\L
    \skipmath@#1$\skipmath@$}}

\def\skipmath@#1$#2${\skipmath@b#1\(\skipmath@b\)%
  \ifx\skipmath@#2\else$#2$\expandafter\skipmath@\fi}

\def\skipmath@b#1\(#2\){\uppercase{#1}%
  \ifx\skipmath@b#2\else\(#2\)\expandafter\skipmath@b\fi}
\def\today{\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}
\def\LaTeX{L\raise.42ex\hbox{\kern-.33em\protect\scriptsize A\kern-.15em}\TeX}
\def\@ifundefined#1{\expandafter\ifx\csname#1\endcsname\relax
        \expandafter\@leftmark
        \else\expandafter\@rightmark\fi}
\def\ref#1{\@ifundefined{r@#1}{{\normalshape\bf ??}\iffirstchoice@
  \@warning{Reference `#1' on page \thepage \space undefined}\fi}%
  {\rom{\expandafter\expandafter\expandafter
    \@car\csname r@#1\endcsname\@nil\null}}}
\def\defaultfont{\family\default@family \series\default@series
  \shape\default@shape \selectfont}
\def\title{\@dblarg{\@title}}
\def\thetitle@{}

\if@article %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% ARTICLE ONLY
\def\@title[#1]#2{\def\sh@rttitle{\def\\{\unskip, \ignorespaces}%
   \ignorespaces#1\unskip}%
   \def\thetitle@{\ignorespaces#2\unskip}}

\def\sh@rttitle{}
\fi %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% ARTICLE ONLY
\def\author{\@dblarg{\@author}}
\def\theauthors@{}
\if@article %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% ARTICLE ONLY
\def\@author[#1]#2{\expandafter\def\expandafter
  \theauthors@\expandafter{\theauthors@#2\and}%
  \expandafter\def\expandafter\sh@rtauthor\expandafter{\sh@rtauthor#1\and}}

\def\sh@rtauthor{}
\fi %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% ARTICLE ONLY

\newbox\addressb@x  \setbox\addressb@x\copy\voidb@x
\def\address#1{\setbox\addressb@x\vbox{%
\def\\{\unskip, \ignorespaces}%
\let\@nodocument\@empty
  \ifvoid\addressb@x\indent
\vrule\@height16\p@\@width\z@\else
  \dimen@\dp\addressb@x \unvbox\addressb@x \prevdepth\dimen@
  \medskip\indent\fi \ignorespaces{\small\sc#1%
  \interlinepenalty\@M\par}}}
\def\email#1{\ifvoid\addressb@x\errmessage{\string\email\space
  can't precede \string\address.}\fi
  \setbox\addressb@x\vbox{%
\let\@nodocument\@empty
  \dimen@\dp\addressb@x \unvbox\addressb@x \prevdepth\dimen@
  \vskip2\p@\indent{\small{\it E-mail\/}:\enspace
  \ignorespaces#1\interlinepenalty\@M\par}}}

\def\date#1{\def\thedate@{#1}}
\def\thedate@{}

\def\thanks#1{\ifx\@empty\thethanks@
   \def\thethanks@{\ignorespaces#1\unskip.}%
 \else \expandafter\def\expandafter\thethanks@\expandafter
   {\thethanks@\@@par\ignorespaces#1\unskip.}\fi
}
\def\thethanks@{}

\def\dedicatory#1{\def\thededicatory@{#1}}
\def\thededicatory@{}

\def\keywords#1{\def\thekeywords@{#1}}
\def\thekeywords@{}

\def\subjclass#1{\def\thesubjclass@{#1}}
\def\thesubjclass@{}

\def\translator#1{\def\thetranslator@{#1}}
\def\thetranslator@{}

\if@article %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% ARTICLE ONLY
\def\maketitle{\par
  \@topnum\z@ % this prevents figures from falling at the top of page 1
  \begingroup
  \@maketitle
  \endgroup
  \@andify{ AND }\sh@rtauthor
  \thispagestyle{plain}%
  \c@footnote\z@
  \def\do##1{\let##1\relax}%
  \do\maketitle \do\@maketitle
  \do\title \do\@title \do\thetitle@
  \do\author \do\@author \do\theauthors@
  \do\dedicatory \do\thededicatory@
  \do\thanks \do\thethanks@
  \do\keywords \do\thekeywords@
  \do\subjclass \do\thesubjclass@
  \do\@andify
}
\def\@maketitle{%
  \defaultfont\normalsize
  \let\@makefnmark\relax  \let\@thefnmark\relax
  \ifx\@empty\thesubjclass@\else
   \@footnotetext{1980 {\it Mathematics Subject
     Classification} (1985 {\it Revision\/}).\enspace
        Primary \thesubjclass@.}\fi
  \ifx\@empty\thekeywords@\else
   \@footnotetext{{\it Key words and phrases.}\enspace \thekeywords@.}\fi
\ifx\@empty\thethanks@\else
   \@footnotetext{\thethanks@}\fi
\topskip66\p@ % 6.5 picas to the base of the first title line
  \vtop{\centering{\baselineskip14\p@\bf
    \expandafter\uppercasetext@\expandafter{\thetitle@}\@@par}%
   \global\dimen@i\prevdepth}%
  \prevdepth\dimen@i
  \ifx\@empty\theauthors@
  \else
    \baselineskip32\p@
    \vtop{\@andify{ AND }\theauthors@
      \centering{\small
  \expandafter\uppercasetext@\expandafter{\theauthors@}\@@par}%
         \global\dimen@i\prevdepth}\relax
    \prevdepth\dimen@i
  \fi
  \ifx\@empty\thededicatory@
  \else
    \baselineskip18\p@
  \vtop{\centering{\small\it\thededicatory@\@@par}%
      \global\dimen@i\prevdepth}\prevdepth\dimen@i
  \fi
  \ifx\@empty\thedate@\else
  \baselineskip24\p@
    \vtop{\centering\thedate@\@@par
      \global\dimen@i\prevdepth}\prevdepth\dimen@i
  \fi
  \normalbaselines
  \dimen@32\p@ \advance\dimen@-\baselineskip
  \vskip\dimen@\@plus14\p@
  } % end \@maketitle
\fi %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% ARTICLE ONLY
\def\abstractname{Abstract}
\def\abstract{%
\vskip-4\p@\@plus-14\p@
  \moveright 3pc\vtop \bgroup
  \advance \hsize -6pc\bgroup % extra \bgroup to localize \small
   \defaultfont\small \noindent
  {\sc\abstractname}.\enspace\ignorespaces
\global\let\abstract\relax}

\def\endabstract{\par\egroup
\global\dimen@i\prevdepth \egroup \prevdepth\dimen@i
\dimen@32\p@ \advance\dimen@-\normalbaselineskip
  \vskip\dimen@\@plus14\p@ \relax
\global\let\endabstract\relax}
\def\titlepage{\thispagestyle{empty}\c@page\z@}
\def\endtitlepage{\newpage}
\def\labelenumi{(\@arabic\c@enumi)}
\def\theenumi{\@arabic\c@enumi}
\def\labelenumii{(\@alph\c@enumii)}
\def\theenumii{\@alph\c@enumii}
\def\p@enumii{\theenumi}
\def\labelenumiii{(\@roman\c@enumiii)}
\def\theenumiii{\@roman\c@enumiii}
\def\p@enumiii{\theenumi(\theenumii)}
\def\labelenumiv{(\@Alph\c@enumiv)}
\def\theenumiv{\@Alph\c@enumiv}
\def\p@enumiv{\p@enumiii\theenumiii}

\def\labelitemi{$\m@th\bullet$}
\def\labelitemii{\bf --}% \normalshape already done by \itemize
\def\labelitemiii{$\m@th\ast$}
\def\labelitemiv{$\m@th\cdot$}
\def\verse{\let\\\@centercr
 \list{}{\itemsep\z@ \itemindent -1.5em\listparindent\itemindent
 \rightmargin\leftmargin \advance\leftmargin 1.5em}\item[]}
\let\endverse=\endlist
\def\quotation{\list{}{\listparindent 1.5em\itemindent\listparindent
 \rightmargin\leftmargin \parsep\z@ \@plus\p@}\item[]}
\let\endquotation=\endlist
\def\quote{\list{}{\rightmargin\leftmargin}\item[]}
\let\endquote=\endlist
\def\trivlist{\parsep\parskip
  \@trivlist \labelwidth\z@ \leftmargin\z@
  \itemindent\z@ \def\makelabel##1{\normalshape##1}}

\def\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{\normalshape##1}}}\fi}

\def\itemize{\ifnum\@itemdepth>3 \@toodeep
  \else \advance\@itemdepth\@ne
  \edef\@itemitem{labelitem\romannumeral\the\@itemdepth}%
  \list{\csname\@itemitem\endcsname}%
  {\def\makelabel##1{\hss\llap{\normalshape##1}}}\fi}

\def\descriptionlabel#1{\hspace\labelsep \normalshape\bf #1:}
\def\description{\list{}{%
\advance\leftmargin6\p@ \itemindent-6\p@
  \labelwidth\z@ \let\makelabel\descriptionlabel}}
\let\enddescription=\endlist
\input amsart1\@ptsize.sty\relax
\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\@sect#1#2#3#4#5#6[#7]#8{%
\ifnum #2>\c@secnumdepth
   \let\@svsec\@empty
 \else
   \refstepcounter{#1}%
\edef\@svsec{\ifnum#2<\@m
             \@ifundefined{#1name}{}{\csname #1name\endcsname\ }\fi
\noexpand\rom{\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
   \if@article\else\csname #1mark\endcsname{%
        \ifnum \c@secnumdepth >#2\relax\csname the#1\endcsname. \fi#7}\fi
\ifnum#2>\@m \else
       \addcontentsline{toc}{#1}%
{\ifnum #2>\c@secnumdepth \else
             \protect\numberline{%
               \ifnum#2<\@m
               \@ifundefined{#1name}{}{\csname #1name\endcsname\ }\fi
               \csname the#1\endcsname.}\fi
           #7}%
     \fi
 \else
  \def\@svsechd{#6\hskip #3\@svsec \ignorespaces#8\unskip.%
        \ifnum#2>\@m \else
          \addcontentsline{toc}{#1}%
            {\ifnum #2>\c@secnumdepth \else
              \protect\numberline{%
                \ifnum#2<\@m
                \@ifundefined{#1name}{}{\csname #1name\endcsname\ }\fi
                \csname the#1\endcsname.}\fi
             #7}\fi}%
 \fi
\@xsect{#5}}

\def\@xsect#1{\@tempskipa #1\relax
 \ifdim \@tempskipa>\z@ % then this is not a run-in heading
   \par \nobreak \vskip\@tempskipa
   \@afterheading
 \else % otherwise it IS a run-in heading
   \global\@nobreakfalse \global\@noskipsectrue
   \everypar{\if@noskipsec \global\@noskipsecfalse
               \clubpenalty\@M \kern-\parindent
               \begingroup \@svsechd \endgroup \hskip -#1\relax
             \else \clubpenalty \@clubpenalty\everypar{}\fi
            }%
 \fi\ignorespaces}

\def\@afterheading{\global\@nobreaktrue
   \everypar{\if@nobreak \global\@nobreakfalse \clubpenalty\@M
               \if@afterindent \else {\setbox\z@\lastbox}\fi
             \else \clubpenalty\@clubpenalty \everypar{}\fi}}
\def\@hangfrom#1{\setboxz@h{#1}\hangindent\wdz@ \noindent\box\z@}

\let\@ssect\relax % to save memory.  \@ssect not needed in amsart.sty.

\newcounter{part}
\newcounter{section}
\newcounter{subsection}[section]
\newcounter{subsubsection}[subsection]

\def\thepart{\@Roman\c@part}
\def\thesection{\@arabic\c@section}
\def\thesubsection{\thesection.\@arabic\c@subsection}
\def\thesubsubsection{\thesubsection.\@arabic\c@subsubsection}
\setcounter{secnumdepth}{3}
\def\@pnumwidth{1.6em}
\def\@tocrmarg {2.6em}
\setcounter{tocdepth}{2}
\if@article %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% ARTICLE ONLY
\def\tableofcontents{%
\removelastskip\vskip\z@skip
  \@startsection{}\@M\z@{12\p@\@plus12\p@}{6\p@}%
        {\centering\sc}\contentsname
 \@starttoc{toc}%
 \addvspace{32\p@\@plus14\p@}%
\let\tableofcontents\relax
\let\l@part\relax \let\l@section\relax
\let\l@subsection\relax \let\l@subsubsection\relax
}
\fi %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% ARTICLE ONLY

\def\contentsname{Contents}
\def\@tocline#1#2#3#4#5{\par
  \addpenalty\@secpenalty\addvspace{#1}%
  \begingroup   \@tempdima#2\relax % used by \numberline
  \parindent\z@ \rightskip\@pnumwidth \parfillskip-\@pnumwidth
  {#3\leavevmode #4\hfil \hbox to\@pnumwidth{\hss #5}}\par\nobreak
  \endgroup}

\def\l@part{\@tocline\bigskipamount{2em}{\normalshape\bf}}

\def\l@section{\@tocline\medskipamount{2em}{\normalshape\bf}}
\def\@dottedtocline#1#2#3#4#5{\ifnum #1>\c@tocdepth \else
  \vskip \z@\@plus\p@
  {\leftskip #2\relax \rightskip\@tocrmarg \parfillskip-\rightskip
   \parindent #2\relax \@afterindenttrue
   \interlinepenalty\@M \leavevmode
   \@tempdima #3\relax \advance\leftskip\@tempdima
    \null \hskip-\leftskip #4\nobreak
        \hfill\nobreak
  \ifnum#1<\c@tocdepth\hbox to\@pnumwidth{\hfil\normalshape#5}\fi
  \null\par}\fi}
\def\numberline#1{\setboxz@h{#1\enspace}\ifdim\wdz@>\@tempdima
  \box\z@\else \hbox to\@tempdima{#1\hfil}\fi}
\def\l@subsection{\@dottedtocline\tw@{1.5em}{2.3em}}
\def\l@subsubsection{\@dottedtocline\thr@@{3.8em}{3.2em}}
\def\l@paragraph{\@dottedtocline4{7em}{4.1em}}
\def\refname{References}
\def\bibname{Bibliography}

\if@article %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% ARTICLE ONLY
\def\thebibliography#1{\section*\refname
  \defaultfont\small\labelsep .5em\relax
  \list{\@arabic\c@enumi.}{\settowidth\labelwidth{#1.}%
  \leftmargin\labelwidth \advance\leftmargin\labelsep
  \usecounter{enumi}}%
  \sloppy \clubpenalty4000\relax \widowpenalty\clubpenalty
  \sfcode`\.\@m}
\let\endthebibliography=\endlist
\fi %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% ARTICLE ONLY

\def\footnoterule{\kern-.4\p@
        \hrule\@width 5pc\kern11\p@\kern-\footnotesep}

\def\@makefnmark{\hbox{$\m@th^{\@thefnmark}$}}

\def\@makefntext{\indent\@makefnmark}
\long\def\@footnotetext#1{\insert\footins{%
    \defaultfont\footnotesize
    \interlinepenalty\interfootnotelinepenalty
    \splittopskip\footnotesep \splitmaxdepth \dp\strutbox
    \floatingpenalty\@MM \hsize\columnwidth
\@parboxrestore \parindent\normalparindent \sloppy
  \edef\@currentlabel{\p@footnote\@thefnmark}\@makefntext
 {\rule\z@\footnotesep\ignorespaces#1\unskip\strut\par}}}
\def\sloppy{\tolerance9999\relax}
\hfuzz=1pt \vfuzz=\hfuzz

\setcounter{topnumber}{2}
\def\topfraction{.7}
\setcounter{bottomnumber}{1}
\def\bottomfraction{.3}
\setcounter{totalnumber}{3}
\def\textfraction{.2}
\def\floatpagefraction{.5}
\setcounter{dbltopnumber}{2}
\def\dbltopfraction{.7}
\def\dblfloatpagefraction{.5}
\long\def\@makecaption#1#2{%
\setbox\@tempboxa\vbox{\advance\hsize-6pc\noindent
    \sc#1\@ifempty{#2}{}{.\normalshape\enspace#2}%
    \unskip\kern-6pc\par
    \global\setbox\@ne\lastbox}%
\ifhbox\@ne % the normal case
  \setbox\@ne\hbox{\unhbox\@ne\unskip\unskip\unpenalty\unkern}%
\fi
  \ifdim\wd\@tempboxa=\z@ % this means caption will fit on one line
    \setbox\@ne\hbox to\columnwidth{\hss\kern-6pc\box\@ne\hss}%
  \else % tempboxa contained more than one line (or other vertical mode stuff)
    \setbox\@ne\vbox{\unvbox\@tempboxa\parskip\z@skip
        \noindent\unhbox\@ne\advance\hsize-6pc\par}%
\fi
  \ifnum\@tempcnta<64 % if the float IS a figure...
    \vskip 1pc%
    \moveright 3pc\box\@ne
  \else % if the float IS NOT a figure...
    \moveright 3pc\box\@ne
    \vskip 1pc%
  \fi
\relax
}

\newcounter{figure}
\def\thefigure{\@arabic\c@figure}
\def\fps@figure{tbp}
\def\ftype@figure{1}
\def\ext@figure{lof}
\def\fnum@figure{\figurename\ \thefigure}
\def\figurename{Figure}
\def\figure{\@float{\@string\figure}}
\let\endfigure=\end@float
\newcounter{table}
\def\thetable{\@arabic\c@table}
\def\fps@table{tbp}
\def\ftype@table{2}
\def\ext@table{lot}
\def\fnum@table{\tablename\ \thetable}
\def\tablename{Table}
\def\table{\@float{\@string\table}}
\let\endtable=\end@float
\input theorem.sty
\theorembodyfont{}
\def\@begintheorem#1#2{\item[\hskip\labelsep \theorem@headerfont
       \theorem@indent#1\ \rom{#2}\unskip.]}
\def\@opargbegintheorem#1#2#3{\item[\hskip\labelsep \theorem@headerfont
       \theorem@indent#1\ \rom{#2}\unskip\ \rom(#3\rom).]}
\def\th@plain{\it}
\def\th@definition{\theorempreskipamount6\p@\@plus6\p@
    \theorempostskipamount\theorempreskipamount
    \normalshape}
\def\th@remark{\theorempreskipamount6\p@\@plus6\p@
    \theorempostskipamount\z@\@plus6\p@
    \def\theorem@headerfont{\it}\normalshape}
\def\theorem@headerfont{\normalshape\bf}
\let\theorem@indent\noindent
\theorempreskipamount=6pt plus9pt
\theorempostskipamount=\theorempreskipamount
\def\@endtheorem{\endtrivlist\@endpefalse }
\if@article %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% ARTICLE ONLY
\newenvironment{pf}{\par\addvspace{6\p@\@plus6\p@}\noindent
  {\it\proofname.}\enspace\ignorespaces}{\qed\par\addvspace{6\p@\@plus6\p@}}

\@namedef{pf*}#1{\par\begingroup\def\proofname{#1}\pf\endgroup\ignorespaces}
\expandafter\let\csname endpf*\endcsname=\endpf
\fi %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% ARTICLE ONLY
\def\qedsymbol{\RIfM@\bgroup\else$\bgroup\aftergroup$\fi
  \vcenter{\hrule\hbox{\vrule\@height.6em\kern.6em\vrule}\hrule}\egroup}
\def\qed{\RIfM@\else\unskip\nobreak\fi\quad\qedsymbol}
\def\proofname{Proof}
\def\enddocument{\@checkend{document}\par
\if@article %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% ARTICLE ONLY
  \ifx\@empty\thetranslator@ \else
    \addvspace{6\p@\@plus9\p@}%
    \hbox to\columnwidth{\hss\defaultfont\normalsize
     Translated by \expandafter\uppercasetext@\expandafter{\thetranslator@}}%
  \fi
 \removelastskip\unvbox\addressb@x
\fi %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% ARTICLE ONLY
 \clearpage\begingroup
 \if@filesw \immediate\closeout\@mainaux
 \def\global\@namedef##1##2{}\def\newlabel{\@testdef r}%
 \def\bibcite{\@testdef b}\@tempswafalse \makeatletter\input \jobname.aux
 \if@tempswa \@warning{Label(s) may have changed.  Rerun to get
 cross-references right}\fi\fi\endgroup\deadcycles\z@\@@end}
\if@article %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% ARTICLE ONLY
\def\ps@headings{\let\@mkboth\@gobbletwo
  \let\partmark\@gobble\let\sectionmark\@gobble
  \let\subsectionmark\@gobble
  \let\@oddfoot\@empty\let\@evenfoot\@empty%
  \def\@evenhead{\defaultfont\small
      \rlap{\thepage}\hfil
      \expandafter\uppercasetext@\expandafter{\sh@rtauthor}\hfil}%
  \def\@oddhead{\defaultfont\small \hfil
      \expandafter\uppercasetext@\expandafter{\sh@rttitle}\hfil
      \llap{\thepage}}%
}
\fi %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% ARTICLE ONLY

\def\ps@myheadings{\let\@mkboth\@gobbletwo
  \let\@oddfoot\@empty\let\@evenfoot\@empty
  \def\@oddhead{\null\defaultfont\small\rightmark \hfil\thepage}%
  \def\@evenhead{\defaultfont\small \thepage\hfil\leftmark\null}%
}
\def\ps@plain{\let\@mkboth\@gobbletwo
     \let\@oddhead\@empty \let\@evenhead\@empty \let\@evenfoot\@oddfoot
     \def\@oddfoot{\defaultfont\small \hfil\thepage\hfil}}
\def\@cite#1#2{\rom{\mediumseries[{#1\if@tempswa , #2\fi}]}}
\def\rom#1{\leavevmode\skip@\lastskip\unskip\/%
        \ifdim\skip@=\z@\else\hskip\skip@\fi
   {\normalshape#1}}
\def\eqref#1{\rom{\tagform@{\ref{#1}}}}
\def\theequation{\@arabic\c@equation}
\if@article %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% ARTICLE ONLY
\advance\textheight by -\headheight
\advance\textheight by -\headsep
\advance\textheight by -\normalbaselineskip
\advance\textheight by \topskip
\oddsidemargin=8.5 true in % standard U.S. paper width
\advance\oddsidemargin by -\textwidth
\oddsidemargin=.5\oddsidemargin
\ifdim\oddsidemargin < .5 true in
  \oddsidemargin = .5 true in \fi
\advance\oddsidemargin by -1 true in
\evensidemargin=\oddsidemargin
\topmargin=11 true in % standard U.S. paper width
\advance\topmargin by -\textheight
\advance\topmargin by -\headheight
\advance\topmargin by -\headsep
\advance\topmargin by -\footheight
\advance\topmargin by -\footskip
\topmargin=.5\topmargin
\ifdim\topmargin<.5 true in
  \topmargin=.5 true in \fi
\advance\topmargin by -1 true in
\pagenumbering{arabic}
\onecolumn
\@twosidetrue \@mparswitchtrue   % this = `twoside' option
\mark{{}{}}
\ps@headings
\fi %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% ARTICLE ONLY
\endinput
%% 
%% End of file `ldd:amsart.sty'.
