%%
%% 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 = "1.2q",
%%% date = "1996/11/05",
%%% time = "11:55:19 EST",
%%% checksum = "63668 3423 13546 125878",
%%% 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 = "tech-support@ams.org (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}[1996/11/05 v1.2q]
\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}{}
\def\mathfrak{needed}
\DeclareOption{noamsfonts}{\let\mathfrak\relax}
\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#1{\let\mathfrak\relax
\RequirePackage{amstex}\relax}\expandafter\@tempa
\else
\expandafter\@iden
\fi
{% if native mode
\@ifclasswith{\@classname}{nomath}{%
\def\numberwithin#1#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@}}}}%
}{%
\RequirePackage{amsmath}\relax
}
\@ifclasswith{\@classname}{noamsfonts}{%
}{%
\let\mathfrak\relax
\IfFileExists{Umsa.fd}{%
\RequirePackage{amsfonts}\relax
}{%
\ClassError{\@classname
}{%
Font description files Umsa.fd et al. not found; amsfonts.sty
not loaded.
}{%
A font description (.fd) file is needed for every font being used;
these files may be in the inputs area along with other style and
class files, or in a dedicated subdirectory if your system uses
a TDS structure.
}%
}%
}
}% end native mode 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}}
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\else
\insert\copyins{\hsize\textwidth
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\everypar{}%
\vskip-\skip\copyins \nointerlineskip
\noindent\vrule\@width\z@\@height\skip\copyins
\copyright\copyrightyear\ \copyrightholder
\par
\kern\z@}%
\fi\fi
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Classification}
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\@title
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\def\@setkeywords{%
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\def\@setthanks{\def\thanks##1{\par##1\@addpunct.}\thankses}
\newbox\abstractbox
\newenvironment{abstract}{%
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\item[\hskip\labelsep\scshape\abstractname.]%
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\def\@setabstract{\@setabstracta \global\let\@setabstract\relax}
\def\@setabstracta{%
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}
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\itemindent\z@
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\def\makelabel##1{\upshape##1}}
\renewenvironment{enumerate}{%
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{\@enumctr}\def\makelabel##1{\hss\llap{\upshape##1}}}\fi
}{%
\endlist
}
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\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
}
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\labelwidth\z@ \let\makelabel\descriptionlabel}%
}{
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\@afterindenttrue
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\def\appendix{\par\c@section\z@ \c@subsection\z@
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\def\thesection{\@Alph\c@section}}
\def\appendixname{Appendix}
\def\@Roman#1{\@xp\@slowromancap
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\begingroup \hyphenpenalty\@M
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\def\@tempa{#1}%
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\def\fnum@figure{\figurename\ \thefigure}
\def\figurename{Figure}
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\@float{figure}%
}{%
\end@float
}
\newcounter{table}
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\def\ext@table{lot}
\def\fnum@table{\tablename\ \thetable}
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\@float{table}%
}{%
\end@float
}
\def\@floatboxreset{\global\@minipagefalse \centering}
\long\def\@makecaption#1#2{%
\setbox\@tempboxa\vbox{\color@setgroup
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\@captionfont\@captionheadfont#1\@xp\@ifnotempty\@xp
{\@cdr#2\@nil}{.\@captionfont\upshape\enspace#2}%
\unskip\kern-2\captionindent\par
\global\setbox\@ne\lastbox\color@endgroup}%
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\RequirePackage{amsthm}[1996/09/24]
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\def\thmhead@plain#1#2#3{%
\thmname{#1}\thmnumber{\@ifnotempty{#1}{ }\@upn{#2}}%
\thmnote{ \textmd{\upshape(#3)}}}
\def\swappedhead@plain#1#2#3{%
\thmnumber{\@upn{#2}}\thmname{\@ifnotempty{#2}{. }#1}%
\thmnote{ \textmd{\upshape(#3)}}}
\def\th@plain{%
\let\thmhead\thmhead@plain \let\swappedhead\swappedhead@plain
\thm@preskip.5\baselineskip\@plus.2\baselineskip
\@minus.2\baselineskip
\thm@postskip\thm@preskip
\itshape
}
\def\th@definition{%
\let\thmhead\thmhead@plain \let\swappedhead\swappedhead@plain
\thm@preskip.5\baselineskip\@plus.2\baselineskip
\@minus.2\baselineskip
\thm@postskip\thm@preskip
\upshape
}
\def\th@remark{%
\thm@headfont{\itshape}% heading font bold
\let\thmhead\thmhead@plain \let\swappedhead\swappedhead@plain
\thm@preskip.5\baselineskip\@plus.2\baselineskip
\@minus.2\baselineskip
\thm@postskip\thm@preskip
\upshape
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\if@compatibility
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\newenvironment{pf*}[1]{\@newpf[#1]}{\qed\endtrivlist}
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\def\nonbreakingspace{\unskip\nobreak\ \ignorespaces}
\def~{\protect\nonbreakingspace}
\def\@biblabel#1{\@ifnotempty{#1}{[#1]}}
\def\@cite#1#2{{%
\m@th\upshape\mdseries[{#1\if@tempswa, #2\fi}]}}
\@ifundefined{cite }{%
\expandafter\let\csname cite \endcsname\cite
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\def\fullwidthdisplay{\displayindent\z@ \displaywidth\columnwidth}
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\newcommand\seename{see also}%
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\hyphenation{acad-e-my acad-e-mies af-ter-thought anom-aly anom-alies
an-ti-deriv-a-tive an-tin-o-my an-tin-o-mies apoth-e-o-ses
apoth-e-o-sis ap-pen-dix ar-che-typ-al as-sign-a-ble as-sist-ant-ship
as-ymp-tot-ic asyn-chro-nous at-trib-uted at-trib-ut-able bank-rupt
bank-rupt-cy bi-dif-fer-en-tial blue-print busier busiest
cat-a-stroph-ic cat-a-stroph-i-cally con-gress cross-hatched data-base
de-fin-i-tive de-riv-a-tive dis-trib-ute dri-ver dri-vers eco-nom-ics
econ-o-mist elit-ist equi-vari-ant ex-quis-ite ex-tra-or-di-nary
flow-chart for-mi-da-ble forth-right friv-o-lous ge-o-des-ic
ge-o-det-ic geo-met-ric griev-ance griev-ous griev-ous-ly
hexa-dec-i-mal ho-lo-no-my ho-mo-thetic ideals idio-syn-crasy
in-fin-ite-ly in-fin-i-tes-i-mal ir-rev-o-ca-ble key-stroke
lam-en-ta-ble light-weight mal-a-prop-ism man-u-script mar-gin-al
meta-bol-ic me-tab-o-lism meta-lan-guage me-trop-o-lis
met-ro-pol-i-tan mi-nut-est mol-e-cule mono-chrome mono-pole
mo-nop-oly mono-spline mo-not-o-nous mul-ti-fac-eted mul-ti-plic-able
non-euclid-ean non-iso-mor-phic non-smooth par-a-digm par-a-bol-ic
pa-rab-o-loid pa-ram-e-trize para-mount pen-ta-gon phe-nom-e-non
post-script pre-am-ble pro-ce-dur-al pro-hib-i-tive pro-hib-i-tive-ly
pseu-do-dif-fer-en-tial pseu-do-fi-nite pseu-do-nym qua-drat-ic
quad-ra-ture qua-si-smooth qua-si-sta-tion-ary qua-si-tri-an-gu-lar
quin-tes-sence quin-tes-sen-tial re-arrange-ment rec-tan-gle
ret-ri-bu-tion retro-fit retro-fit-ted right-eous right-eous-ness
ro-bot ro-bot-ics sched-ul-ing se-mes-ter semi-def-i-nite
semi-ho-mo-thet-ic set-up se-vere-ly side-step sov-er-eign spe-cious
spher-oid spher-oid-al star-tling star-tling-ly sta-tis-tics
sto-chas-tic straight-est strange-ness strat-a-gem strong-hold
sum-ma-ble symp-to-matic syn-chro-nous topo-graph-i-cal tra-vers-a-ble
tra-ver-sal tra-ver-sals treach-ery turn-around un-at-tached
un-err-ing-ly white-space wide-spread wing-spread wretch-ed
wretch-ed-ly Eng-lish Euler-ian Feb-ru-ary Gauss-ian
Hamil-ton-ian Her-mit-ian Jan-u-ary Japan-ese Kor-te-weg
Le-gendre Mar-kov-ian Noe-ther-ian No-vem-ber Rie-mann-ian Sep-tem-ber}
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