% use commenced in July 05 for 11-18.
% This is nyj.cls, the document class for latex2e publications in the
% New York Journal of Mathematics. It is a modified version of the AMS
% amsart class, prepared and maintained by Mark Steinberger.
% It includes contributions by Phil Hirschhorn.
%
% If you like the style and want to use it for documents other than NYJM
% submissions, use the declaration \documentclass[np]{nyj}. The np option
% turns off the special handling features to make space for the logo, etc.
%
% The np option should definitely _not_ be used in papers being prepared
% for submission to the journal, as it will change all the pagebreaks.
%
% With the hyp option, this style may be used to create HyperTeX
% documents, adding automatic hypertext links and anchors to table of
% contents entries and sectional headings, as well as to \cite,
% \bibitem, \ref, and \label commands. It also enables authors to put
% their own links in via the new commands \href and \hlabel (for
% internal references), as well as \hyperlink for links to external
% resources. The syntax is:
%
% \hlabel{label of "name" anchor}
% \href{label of "name" anchor referenced}{text highlighted by link}
%
% In both of these cases, the # is inserted automatically by the macro.
% The syntax for \hyperlink is
%
% \hyperlink{full URL for external reference}{text highlighted by link}
%
% You may use \hyperhash in the URL to insert a #.
%
% Warning: \label does not insert hypertext anchors in amslatex
% equation environments: "name" anchor \specials do not function in
% those environments. So you should use a construction like:
%
% \hlabel{foo}\begin{equation}\label{foo}
%
% The hypertex macros are set up in such a way that if you omit "hyp"
% from your documentclass options, the hypertex macros will be
% nonfunctional, but will not cause error messages.
%
\NeedsTeXFormat{LaTeX2e}% LaTeX 2.09 can't be used (nor non-LaTeX)
[1994/12/01]% LaTeX date must December 1994 or later
\ProvidesClass{nyj}[2005/04/09]
\def\@tempa#1#2\@nil{\edef\@classname{#1}}
\expandafter\@tempa\@currnamestack{}{}{}\@nil
\ifx\@classname\@empty \edef\@classname{\@currname}\fi
\newcommand{\runhdfnt}{\scshape}%{\itshape\bfseries\mathversion{bold}}
\newif\ifpub
\pubtrue
\newif\iffin
\newif\ifhyp
\newif\ifyandy
\newif\ifnc
\newif\ifcomment
\newif\ifposh
\newif\ifaltposh
\newif\ifnoblue
\DeclareOption{np}{\pubfalse}
\DeclareOption{production}{\fintrue}
\DeclareOption{hyp}{\hyptrue}
\DeclareOption{yandy}{\yandytrue}
\DeclareOption{ph}{\poshtrue}
\DeclareOption{ph2}{\altposhtrue}
\DeclareOption{noblue}{\nobluetrue}
\DeclareOption{nc}{\nctrue}
\DeclareOption{comment}{\commenttrue}
\DeclareOption{dvips}{}
\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}}
\newif\ifrokcolor
\DeclareOption{rokcolor}{\rokcolortrue}
\newif\if@bspage
\newif\ifsm@bspage
\DeclareOption{abspage}{\@bspagetrue\pubfalse}
\DeclareOption{smabspage}{\sm@bspagetrue\@bspagetrue\pubfalse}
\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=10pt \headsep=16pt
\footskip=24pt
\textheight=50pc \topskip=10pt
\textwidth=30pc
\columnsep=10pt \columnseprule=0pt
\marginparwidth=90pt
\marginparsep=11pt
\marginparpush=5pt
\AtBeginDocument{\settoheight{\footnotesep}{\footnotesize M$^1$}%
\ifsm@bspage\RequirePackage{crop}\begin{cropbox}\hidecontrols\fi}
\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
\def\@oddhead{\hyper@anchor{page.\thepage}{}} \let\@evenhead\@oddhead
\let\@oddfoot\@empty \let\@evenfoot\@empty
\global\topskip\normaltopskip}
\def\ps@plain{\ps@empty
\def\@oddfoot{\normalfont \hfil\thepage\hfil}% removed \scriptsize
\let\@evenfoot\@oddfoot}
\def\ps@headings{\ps@empty
\def\@evenhead{\normalfont\normalsize
\rlap{\hyper@anchor{page.\thepage}\thepage}\hfil \runhdfnt\leftmark{}{}\hfil}%
\def\@oddhead{\normalsize\runhdfnt \hfil
\rightmark{}{}\hfil \normalfont\llap{\hyper@anchor{page.\thepage}\thepage}}%
\let\@mkboth\markboth
}
\def\ps@void{\let\@oddfoot\@empty\let\@evenfoot\@empty
\let\@oddhead\@empty\let\@evenhead\@empty}
\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 \hfil\thepage\hfil % removed \scriptsize
% \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
\ifrokcolor\def\bluetext#1{\special{color push rgb 0 0 1}#1\special{color
pop}}\else\def\bluetext#1{#1}\fi
\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
\ifhyp %%%%%%%%%%%%%%%%%%%%%% If using hypertex macros
\newcommand{\hyper@quote}{\string"}
\edef\hyper@hash{\string#}
\edef\hyperhash{\string#}
\newcommand{\hyper@link}[2]{%
\special{html:}\bluetext{#2}%
\special{html:}}
\newcommand{\hyper@anchor}[1]{%
\special{html:}\special{html:}}
\newcommand{\anchor@ref}[2]{\hyper@link{\hyper@hash#1}{%
\bluetext{#2}}}
\newcommand{\anchor@longref}[2]{\hyper@link{\hyper@hash#1}{%
\bluetext{#2}}}
\else %%%%%%%%%%%%%%%%%%%%%%% If not using hypertex macros
\newcommand{\hyper@link}[2]{#2}
\edef\hyperhash{}
\newcommand{\hyper@anchor}[1]{}
\newcommand{\anchor@ref}[2]{#2}
\newcommand{\anchor@longref}[2]{#2}
\fi %%%%%%%%%%%%%%%%%%%%%%% End of conditional for for hypertex
\ifposh \RequirePackage{posh}\fi%%%%% conditional for posh
\ifaltposh \RequirePackage{posh2}\fi%%%%% conditional for posh2
\ifyandy
\ifnoblue\def\bluetext#1{\special{color push}\special{color rgb 0 0 0}#1\special{color pop}}%
\else\def\bluetext#1{\special{color push}\special{color rgb 0 0 1}#1\special{color pop}}\fi
\newcount\height
\newcount\width
\long\def\anchor@ref#1#2{\leavevmode\setbox0\hbox{#2}\height=\ht0\width=\wd0%
\special{button: \the\width\space \the\height\space #1}\bluetext{\box0}}
\long\def\anchor@longref#1#2{\leavevmode\setbox0\hbox{#2}\height=\ht0\width=\wd0%
\special{button: \the\width\space \the\height\space #1}\bluetext{\unhbox0}}
\def\hyper@anchor#1{\special{mark: #1}}
\def\hyper@link#1#2{\leavevmode\setbox0\hbox{#2}\height=\ht0\width=\wd0%
\special{button: \the\width\space \the\height\space #1}\bluetext{\unhbox0}}
\fi %%%%%%%%%%%%%%%%%%%% End of conditional for yandy
\newcommand{\mailurl}[1]{\hyper@link{mailto:#1}{#1}}
\newcommand{\bib@link}[2]{\anchor@ref{bibcite#1}{#2}}
\newcommand{\bib@anchor}[1]{\hyper@anchor{bibcite#1}}
\newcommand{\hyperlink}[2]{\hyper@link{#1}{#2}}
\newcommand{\hlabel}[1]{\hyper@anchor{#1}}
\newcommand{\shlabel}[1]{\hyper@anchor{#1}{#1}}
\newcommand{\href}[2]{\anchor@ref{#1}{#2}}
\newcommand{\shref}[1]{\anchor@ref{#1}{#1}}
\newcommand{\shyperlink}[1]{\hyper@link{#1}{#1}}
\newcommand{\mrev}[1]{\hyperlink{http://www.ams.org/mathscinet-getitem?mr=#1}%
{MR#1}}
\newcommand{\mrold}[2]{\hyperlink{%
http://www.ams.org/mathscinet-getitem?mr=#1:#2}%
{MR#1~\##2}}
\newcommand{\mrolder}[2]{\hyperlink{%
http://www.ams.org/mathscinet-getitem?mr=#1:#2}%
{MR#1,#2}}
\newcommand{\mscmp}[3]{\hyperlink{%
http://www.ams.org/mathscinet-getitem?mr=#1#2#3}{MR#1~#2~#3}}
\newcommand{\zbl}[1]{\hyperlink{http://www.emis.de/cgi-bin/MATH-item?#1}{Zbl~#1}}
\newcommand{\jfm}[1]{\hyperlink{http://www.emis.de/cgi-bin/MATH-item?#1}{JFM~#1}}
\newcommand{\eram}[1]{\hyperlink{http://www.emis.de/cgi-bin/MATH-item?#1}{ERAM~#1}}
\newcommand{\arx}[1]{\hyperlink{http://arXiv.org/abs/#1}{#1}}
%%@ Here are hypertex versions of various macros defined in the format
\def\@citex[#1]#2{%
\let\@citea\@empty
\@cite{\@for\@citeb:=#2\do
{\@citea\def\@citea{,\penalty\@m\ }%
\edef\@citeb{\expandafter\@iden\@citeb}%
\if@filesw\immediate\write\@auxout{\string\citation{\@citeb}}\fi
\@ifundefined{b@\@citeb}{{\reset@font\bfseries ?}%
\G@refundefinedtrue\@latex@warning
{Citation `\@citeb' on page \thepage \space undefined}}%
{\hbox{\bib@link{\@citeb}{\csname b@\@citeb\endcsname}}}}}{#1}}
\def\@bibitem#1{\item\if@filesw \immediate\write\@auxout
{\string\bibcite{#1}{\the\value{\@listctr}}}\fi%
\hyper@anchor{bibcite#1}\ignorespaces}
\def\@lbibitem[#1]#2{\item[\@biblabel{\bib@anchor{#2}#1}\hfill]\if@filesw
{\let\protect\noexpand
\immediate
\write\@auxout{\string\bibcite{#2}{#1}}}\fi\ignorespaces}
%\def\@setref#1#2#3{\ifx#1\relax
% \protect\@noref{#3}%
% \else
% \anchor@ref{#3}{\protect\textup{\expandafter#2#1\hbox{}}}%
% \fi}
\newcommand{\@noref}[1]{%
\G@refundefinedtrue
\nfss@text{\reset@font\bfseries ??}%
\@latex@warning{Reference `#1' on page \thepage\space undefined}%
}
\def\old@setref#1#2#3{\ifx#1\relax
\protect\@noref{#3}%
\else
\protect\textup{\expandafter#2#1\hbox{}}%
\fi}
\def\page@setref#1#2#3{\ifx#1\relax
\protect\@noref{#3}%
\else
\anchor@ref{page.\expandafter#2#1}{\protect\textup{\expandafter#2#1\hbox{}}}%
\fi}
\def\sectionlabel#1{\@bsphack
\protected@write\@auxout{}%
{\string\newlabel{#1}{{\@currentlabel}{\thepage}}}%
\protected@write\@auxout{}%
{\string\newlabel{sectionlabel@#1}{sectunit\thetoclink}}%
\@esphack\hyper@anchor{#1}}
\def\@setref#1#2#3{\ifx#1\relax
\protect\@noref{#3}%
\else
\@ifundefined{r@sectionlabel@#3}{\anchor@ref{#3}}%
{\anchor@ref{\csname r@sectionlabel@#3\endcsname}}%
{\protect\textup{\expandafter#2#1\hbox{}}}%
\fi}
%\def\ref#1{\expandafter\@setref\csname r@#1\endcsname\@firstoftwo{#1}}
%\def\label#1{\@bsphack
% \protected@write\@auxout{}%
% {\string\newlabel{#1}{{\@currentlabel}{\thepage}}}%
% \@esphack\hyper@anchor{#1}}
\def\oldlabel#1{\@bsphack
\protected@write\@auxout{}%
{\string\newlabel{#1}{{\@currentlabel}{\thepage}}}%
\@esphack}
\def\bothlabel#1{\hlabel{#1}\label{#1}}
\def\oldpageref#1{\expandafter\old@setref\csname r@#1\endcsname
\@secondoftwo{#1}}
\def\pageref#1{\expandafter\page@setref\csname r@#1\endcsname
\@secondoftwo{#1}}
\newcounter{totfootns}
\def\footnote{\stepcounter{totfootns}\@ifnextchar[\@xfootnote{\stepcounter\@mpfn
\protected@xdef\@thefnmark{\thempfn}%
\h@footnotemark\h@footnotetext}}
\def\@xfootnote[#1]{%
\begingroup
\csname c@\@mpfn\endcsname #1\relax
\unrestored@protected@xdef\@thefnmark{\thempfn}%
\endgroup
\h@footnotemark\@hfootnotetext}
\long\def\h@footnotetext#1{\insert\footins{%
\normalfont\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%
\hyper@anchor{footnote\thetotfootns}#1\unskip\strut\par}}}
\def\h@footnotemark{%
\leavevmode
\ifhmode\edef\@x@sf{\the\spacefactor}\nobreak\fi
\anchor@ref{footnote\thetotfootns}{\@makefnmark}
\ifhmode\spacefactor\@x@sf\fi
\relax}
%% End of redefinitions for hypertex
\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
}
\newcommand{\papnum}[1]{\def\papnumber{#1}}
\edef\author{\@nx\@dblarg
\@xp\@nx\csname\string\author\endcsname}
\let\shortauthors\@empty \let\authors\@empty
\let\addresses\@empty \let\thankses\@empty \let\papernum\@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{\if@bspage
\else\ifx\@empty\@translators\else\@settranslators\fi\fi
\ifsm@bspage\end{cropbox}
\else\ifx\@empty\addresses\else\@setaddresses\fi\iffin\@setpaphomepage\fi\fi
\iffin\label{finalpage}\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\noindent
\@ifnotempty{##1}{(\ignorespaces##1\unskip) }%
{\scshape\ignorespaces##2}\par\endgroup}%
\def\curraddr##1##2{\begingroup
\@ifnotempty{##2}{\nobreak\noindent{\itshape Current address}%
\@ifnotempty{##1}{, \ignorespaces##1\unskip}\/:\space\scshape
##2\par\endgroup}}%
\def\email##1##2{\begingroup
\@ifnotempty{##2}{\nobreak\noindent%{\itshape E-mail address}%
\@ifnotempty{##1}{\ignorespaces##1\unskip\/:\space}%
##2\par\endgroup}}%
\def\urladdr##1##2{\begingroup
\@ifnotempty{##2}{\nobreak\noindent%{\itshape URL}%
\@ifnotempty{##1}{\ignorespaces##1\unskip\/:\space}%
\shyperlink{##2}\par\endgroup}}%
\addresses
\endgroup
}
\let\@date\@empty
\newcommand\recdate[1]{\gdef\@recdate{#1}}
\let\@recdate\@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
\ifx\@empty\shortauthors \let\shortauthors\shorttitle
\else \andify\shortauthors \fi
\@maketitle@hook
\begingroup
\@maketitle
\toks@\@xp{\shortauthors}\@temptokena\@xp{\shorttitle}%
\edef\@tempa{\@nx\markboth{\the\toks@}{\the\@temptokena}}\@tempa
\endgroup
\if@bspage\thispagestyle{void}\else\thispagestyle{firstpage}\fi%
\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\@setrecdate{\ifx\@empty\@recdate%
\@footnotetext{\bfseries Please supply date!}
\else\@footnotetext{Received \@recdate.}\fi}
\def\@maketitle{%
\normalfont\normalsize
\let\@makefnmark\relax \let\@thefnmark\relax
\ifpub\iffin\@setrecdate\else\@footnotetext{\phantom{Received}}\fi\fi
\ifpub\else\if@bspage
\else\ifx\@empty\@date\else\@footnotetext{\@setdate}\fi\fi\fi
\if@bspage\else\ifx\@empty\@subjclass\else\@footnotetext{\@setsubjclass}\fi\fi
\if@bspage\else\ifx\@empty\@keywords\else\@footnotetext{\@setkeywords}\fi\fi
\if@bspage\else\ifx\@empty\thankses\else \@footnotetext{%
\def\par{\let\par\@par}\@setthanks}\fi\fi
\@mkboth{\@nx\shortauthors}{\@nx\shorttitle}%
\if@bspage\else\global\topskip42\p@\relax\fi % 5.5pc " " " " "
\ifsm@bspage\else\@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\fi
\@setabstract
\normalsize
\if@titlepage
\newpage
\else
\dimen@20\p@ \advance\dimen@-\baselineskip
\vskip\dimen@ plus 14\p@\relax
\fi
} % end \@maketitle
\@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\@combinefloats{%
\ifx \@toplist\@empty \else \@cflt \fi
\ifx \@botlist\@empty \else \@cflb \fi
\ifvoid\copyins \else \@cflci \fi
}
\newcommand{\abstractname}{Abstract}
\newcommand{\keywordsname}{Key words and phrases}
\newcommand{\subjclassname}{Mathematics Subject
Classification}
\def\@tempb{nyj}
\ifx\@classname\@tempb
\newcommand{\datename}{Date}
\else
\newcommand{\datename}{Received}
\fi
\def\@settitle{\begin{center}\LARGE\bfseries\mathversion{bold}\@title\end{center}}
\def\@setauthors{%
\begingroup
\trivlist
\centering\footnotesize \@topsep28\p@\relax
\advance\@topsep by -\baselineskip
\item\relax
\andify\authors \Large\bfseries
\leavevmode\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\ifsm@bspage\else\Small
\Small\fi
\list{}{\labelwidth\z@
\leftmargin3pc \rightmargin\leftmargin
\listparindent\normalparindent \itemindent\z@
\parsep\z@ \@plus\p@
\let\fullwidthdisplay\relax
}%
\item[\hskip\labelsep\scshape\abstractname.]%
}{%
\endlist\egroup
\ifx\@setabstract\relax \@setabstracta \fi
}
\def\@setabstract{\@setabstracta \global\let\@setabstract\relax}
\def\@setabstracta{%
\ifvoid\abstractbox
\else
\ifsm@bspage\else\skip@24\p@ plus 10\p@ \advance\skip@-\lastskip
\advance\skip@-\baselineskip \vskip\skip@\fi
\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{\bfseries}
\setcounter{tocdepth}{2}
\newcounter{toclink}\setcounter{toclink}{\m@ne}
\def\@sect#1#2#3#4#5#6[#7]#8{\stepcounter{toclink}%
\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\hyper@anchor{sectunit\thetoclink}%
\@hangfrom{\hskip #3\relax\@svsec}{\interlinepenalty\@M #8\par}%
\endgroup
\ifnum#2>\@m \else \@tocwrite{#1}{\protect\anchor@longref{sectunit\thetoclink}{#7}}\fi
\else
\def\@svsechd{\hyper@anchor{sectunit\thetoclink}#6\hskip #3\@svsec
\@ifnotempty{#8}{\ignorespaces#8\unskip
\@addpunct.}%
\ifnum#2>\c@tocdepth \else
\@tocwrite{#1}{\protect\anchor@longref{sectunit\thetoclink}{#7}}\fi
}%
\fi
\global\@nobreaktrue
\@xsect{#5}}
\let\@ssect\relax
\newcounter{part}
\newcounter{section}
\newcounter{subsection}[section]
\newcounter{subsubsection}[subsection]
\newcounter{paragraph}[subsubsection]
\renewcommand\thepart {\Roman{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\Large\bfseries\mathversion{bold}\centering}}
\def\specialsection{\@startsection{section}{1}%
\z@{\linespacing\@plus\linespacing}{.5\linespacing}%
{\normalfont\Large\bfseries\mathversion{bold}\raggedright}}
\def\section{\@startsection{section}{1}%
\z@{.7\linespacing\@plus\linespacing}{.5\linespacing}%
{\normalfont\Large\bfseries\mathversion{bold}\raggedright}}
\def\subsection{\@startsection{subsection}{2}%
\z@{.5\linespacing\@plus.7\linespacing}
{-6.001\p@\@plus2\p@}%was {-.5em}%
{\normalfont\bfseries\mathversion{bold}}}
\def\subsubsection{\@startsection{subsubsection}{3}%
\z@{.5\linespacing\@plus.7\linespacing}{-.5em}%
{\normalfont\bfseries}}
\def\paragraph{\@startsection{paragraph}{4}%
\z@\z@{-\fontdimen2\font}%
{\normalfont\itshape}}
\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{20\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}{2pt}{1pc}{}{}}
\newcommand{\tocsection}[3]{%
\indentlabel{\@ifnotempty{#2}{\ignorespaces#1 #2.\quad}}#3}
\def\l@subsection{\@tocline{2}{2pt}{3pc}{5pc}{}}
\let\tocsubsection\tocsection
\def\l@subsubsection{\@tocline{3}{2pt}{5pc}{7pc}{}}
\let\tocparagraph\tocsection
\let\tocsubsubsection\tocsection
\def\l@part{\@tocline{-1}{12pt plus2pt}{0pt}{}{}}
\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]{%
\if@bspage\else\@xp\section\@xp*\@xp{\refname}\fi%
\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}}%
\sloppy \clubpenalty\@M \widowpenalty\clubpenalty
\sfcode`\.=\@m
}{%
\def\@noitemerr{\@latex@warning{Empty `thebibliography' environment}}%
\endlist
}
\def\bysame{\leavevmode\hbox to3em{\hrulefill}\thinspace}
\def\newblock{}
\newcommand\MR[1]{\relax\ifhmode\unskip\spacefactor3000 \space\fi
\def\@tempa##1:##2:##3\@nil{%
\ifx @##2\@empty##1\else\textbf{##1:}##2\fi}%
\MRhref{#1}{MR \@tempa#1:@:\@nil}}
\newcommand\URL{\begingroup
\def\@sverb##1{%
\def\@tempa####1##1{\@URL{####1}\egroup\endgroup}%
\@tempa}%
\verb}
\let\URLhref\@gobble
\def\@URL#1{\URLhref{#1}#1}
\newif\if@restonecol
\def\theindex{\@restonecoltrue\if@twocolumn\@restonecolfalse\fi
\columnseprule\z@ \columnsep 35\p@
\twocolumn[\@xp\section\@xp*\@xp{\indexname}]%
\thispagestyle{plain}%
\let\item\@idxitem
\parindent\z@ \parskip\z@\@plus.3\p@\relax
\footnotesize}
\def\indexname{Index}
\def\@idxitem{\par\hangindent 2em}
\def\subitem{\par\hangindent 2em\hspace*{1em}}
\def\subsubitem{\par\hangindent 3em\hspace*{2em}}
\def\endtheindex{\if@restonecol\onecolumn\else\clearpage\fi}
\def\indexspace{\par\bigskip}
\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{%
\normalfont\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}}}
\hfuzz=1pt \vfuzz=\hfuzz
\def\sloppy{\tolerance9999 \emergencystretch 3em\relax}
\setcounter{topnumber}{4}
\setcounter{bottomnumber}{4}
\setcounter{totalnumber}{4}
\setcounter{dbltopnumber}{4}
\renewcommand{\topfraction}{.97}
\renewcommand{\bottomfraction}{.97}
\renewcommand{\textfraction}{.03}
\renewcommand{\floatpagefraction}{.9}
\renewcommand{\dbltopfraction}{.97}
\renewcommand{\dblfloatpagefraction}{.9}
\setlength{\floatsep}{12pt plus 6pt minus 4pt}
\setlength{\textfloatsep}{15pt plus 8pt minus 5pt}
\setlength{\intextsep}{12pt plus 6pt minus 4pt}
\setlength{\dblfloatsep}{12pt plus 6pt minus 4pt}
\setlength{\dbltextfloatsep}{15pt plus 8pt minus 5pt}
\setlength{\@fptop}{0pt}% removed ``plus 1fil''
\setlength{\@fpsep}{8pt}% removed ``plus 2fil''
\setlength{\@fpbot}{0pt plus 1fil}
\setlength{\@dblfptop}{0pt}% removed ``plus 1fil''
\setlength{\@dblfpsep}{8pt}% removed ``plus 2fil''
\setlength{\@dblfpbot}{0pt plus 1fil}
\newcommand{\fps@figure}{tbp}
\newcommand{\fps@table}{tbp}
\newcounter{figure}
\def\@captionheadfont{\scshape}
\def\@captionfont{\normalfont}
\def\ftype@figure{1}
\def\ext@figure{lof}
\def\fnum@figure{\figurename\ \thefigure}
\def\figurename{Figure}
\newenvironment{figure}{%
\@float{figure}%
}{%
\end@float
}
\newcounter{table}
\def\ftype@table{2}
\def\ext@table{lot}
\def\fnum@table{\tablename\ \thetable}
\def\tablename{Table}
\newenvironment{table}{%
\@float{table}%
}{%
\end@float
}
\def\@floatboxreset{\global\@minipagefalse \centering}
\long\def\@makecaption#1#2{%
\setbox\@tempboxa\vbox{\color@setgroup
\advance\hsize-2\captionindent\noindent
\@captionfont\@captionheadfont#1\@xp\@ifnotempty\@xp
{\@cdr#2\@nil}{.\@captionfont\upshape\enspace#2}%
\unskip\kern-2\captionindent\par
\global\setbox\@ne\lastbox\color@endgroup}%
\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-2\captionindent\box\@ne\hss}%
\else % tempboxa contained more than one line
\setbox\@ne\vbox{\unvbox\@tempboxa\parskip\z@skip
\noindent\unhbox\@ne\advance\hsize-2\captionindent\par}%
\fi
\ifnum\@tempcnta<64 % if the float IS a figure...
\addvspace\abovecaptionskip
\moveright\captionindent\box\@ne
\else % if the float IS NOT a figure...
\moveright\captionindent\box\@ne
\nobreak
\vskip\belowcaptionskip
\fi
\relax
}
\newskip\abovecaptionskip \abovecaptionskip=12pt \relax
\newskip\belowcaptionskip \belowcaptionskip=12pt \relax
\newdimen\captionindent \captionindent=3pc
\RequirePackage{amsthm}[1996/09/24]
\def\@swapped#1#2{#2%
\@ifnotempty{#1}{\@addpunct{.}\quad#1\unskip}}
\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
}
\if@compatibility
\let\@newpf\proof \let\proof\relax \let\endproof\relax
\newenvironment{pf}{\@newpf[\proofname]}{\qed\endtrivlist}
\newenvironment{pf*}[1]{\@newpf[#1]}{\qed\endtrivlist}
\fi
\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
\edef\cite{\@nx\protect\@xp\@nx\csname cite \endcsname}%
}{}
\def\fullwidthdisplay{\displayindent\z@ \displaywidth\columnwidth}
\edef\@tempa{\noexpand\fullwidthdisplay\the\everydisplay}
\everydisplay\expandafter{\@tempa}
\newcommand\seename{see also}%
\newcommand\see[2]{{\em \seename\/} #1}%
\newcommand\printindex{\@input{\jobname.ind}}%
\DeclareRobustCommand\textprime{\leavevmode
\raise.8ex\hbox{\check@mathfonts\the\scriptfont2 \char48 }}
\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}
\def\calclayout{\advance\textheight -\headheight
\advance\textheight -\headsep
\oddsidemargin\paperwidth
\advance\oddsidemargin -\textwidth
\divide\oddsidemargin\tw@
\ifdim\oddsidemargin<.5truein \oddsidemargin.5truein \fi
\advance\oddsidemargin -1truein
\evensidemargin\oddsidemargin
\topmargin\paperheight \advance\topmargin -\textheight
\advance\topmargin -\headheight \advance\topmargin -\headsep
\divide\topmargin\tw@
\ifdim\topmargin<.5truein \topmargin.5truein \fi
\advance\topmargin -1.18truein\relax
}
\calclayout % initialize
\newcounter{pgct}
\newcommand{\paphomepage}[1]{\iffin\def\paphomepageurl{#1}\fi}
\newcommand{\beginningpage}[1]{\iffin\setcounter{page}{#1}\def\beginpage{#1}
\setcounter{pgct}{#1} \stepcounter{pgct}\else\relax\fi}
\newcommand{\pubyr}[1]{\def\copyrightyear{#1}\def\currentyear{#1}}
\newcommand{\pubvol}[1]{\def\currentvolume{#1}}
\iffin\AtBeginDocument{\RequirePackage{nyjlogo}}
\else\setcounter{pgct}{2} \fi
\def\nextpageheight{\begingroup\global\advance\headheight by -\@extrahead
\global\textheight=\subsequentpageheight
\global\@colht=\textheight
\global\@colroom=\textheight
\global\vsize=\textheight
\global\pagegoal=\textheight\endgroup}
\ifpub\newdimen\initialpageheight
\newdimen\subsequentpageheight
\newdimen\@extrahead
\initialpageheight=\textheight
\subsequentpageheight=\textheight
\advance\initialpageheight by -44.4pt
\@extrahead=22.4pt
\begingroup
\global\advance\headheight by \@extrahead
\global\textheight=\initialpageheight
\global\@colht=\textheight
\global\@colroom=\textheight
\global\vsize=\textheight
\global\pagegoal=\textheight
\endgroup
\output=\expandafter{\the\output \ifnum\thepage=\value{pgct}\nextpageheight\fi}
\fi
\pagenumbering{arabic}
\pagestyle{headings}
\thispagestyle{plain}
\renewenvironment{proof}[1][\proofname]{\par
\normalfont
\topsep6\p@\@plus6\p@ \trivlist
\item[\hskip\labelsep\bfseries
#1\@addpunct{.}]\ignorespaces
}{%
\qed\endtrivlist
}
\RequirePackage{amssymb}
\renewcommand{\openbox}{\leavevmode
\hbox to .77778em{\hfil${\square}$\hfil}}
\if@compatibility \else\endinput\fi
\def\tiny{\Tiny}
\def\defaultfont{\normalfont}
\def\rom{\textup}
\endinput
%%
%% End of file `nyj.cls'.