\catcode`\@=11
\message{Loading utility definitions,}
\def\identity@#1{#1}
\def\nofrills@@#1{%
 \DN@{#1}%
 \ifx\next\nofrills \let\frills@\eat@
   \expandafter\expandafter\expandafter\next@\expandafter\eat@
  \else \let\frills@\identity@\expandafter\next@\fi}
\def\nofrillscheck#1{\def\nofrills@{\nofrills@@{#1}}%
  \futurelet\next\nofrills@}
\Invalid@\usualspace
\def\addto#1#2{\csname \expandafter\eat@\string#1@\endcsname
  \expandafter{\the\csname \expandafter\eat@\string#1@\endcsname#2}}
\newdimen\bigsize@
\def\big@#1#2{{\hbox{$\left#2\vcenter to#1\bigsize@{}%
  \right.\nulldelimiterspace\z@\m@th$}}}
\def\big{\big@\@ne}
\def\Big{\big@{1.5}}
\def\bigg{\big@\tw@}
\def\Bigg{\big@{2.5}}
\def\raggedcenter@{\leftskip\z@ plus.4\hsize \rightskip\leftskip
  \parfillskip\z@ \parindent\z@ \spaceskip.3333em \xspaceskip.5em
  \pretolerance9999\tolerance9999 \exhyphenpenalty\@M
  \hyphenpenalty\@M \let\\\linebreak}
\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$#2${\uppercase{#1}%
  \ifx\skipmath@#2\else$#2$\expandafter\skipmath@\fi}
\def\add@missing#1{\expandafter\ifx\envir@end#1%
  \Err@{You seem to have a missing or misspelled
  \expandafter\string\envir@end ...}%
  \envir@end
\fi}
\newtoks\revert@
\def\envir@stack#1{\toks@\expandafter{\envir@end}%
  \edef\next@{\def\noexpand\envir@end{\the\toks@}%
    \revert@{\the\revert@}}%
  \revert@\expandafter{\next@}%
  \def\envir@end{#1}}
\begingroup
\catcode`\ =11
\gdef\revert@envir#1{\expandafter\ifx\envir@end#1%
\the\revert@%
\else\ifx\envir@end\enddocument \Err@{Extra \string#1}%
\else\expandafter\add@missing\envir@end\revert@envir#1%
\fi\fi}
\xdef\enddocument {\string\enddocument}%
\global\let\envir@end\enddocument %%%%%% don't remove the final space!
\endgroup\relax
\def\first@#1#2\end{#1}
\def\true@{TT}
\def\false@{TF}
\def\empty@{}
\begingroup  \catcode`\-=3
\long\gdef\notempty#1{%
  \expandafter\ifx\first@#1-\end-\empty@ \false@\else \true@\fi}
\endgroup
\message{more fonts,}
\font@\tensmc=cmcsc10 \relax
\let\sevenex=\tenex % needs special handling in \PSAMSFonts
\font@\sevenit=cmti7 \relax
\font@\eightrm=cmr8 \relax % preloaded in plain.tex
\font@\sixrm=cmr6 \relax % preloaded in plain.tex
\font@\eighti=cmmi8 \relax     \skewchar\eighti='177 % preloaded
\font@\sixi=cmmi6 \relax       \skewchar\sixi='177   % preloaded
\font@\eightsy=cmsy8 \relax    \skewchar\eightsy='60 % preloaded
\font@\sixsy=cmsy6 \relax      \skewchar\sixsy='60   % preloaded
\let\eightex=\tenex % needs special handling in \PSAMSFonts
\font@\eightbf=cmbx8 \relax % preloaded in plain.tex
\font@\sixbf=cmbx6 \relax   % preloaded in plain.tex
\font@\eightit=cmti8 \relax % preloaded in plain.tex
\font@\eightsl=cmsl8 \relax % preloaded in plain.tex
\font@\eighttt=cmtt8 \relax % preloaded in plain.tex
\let\eightsmc=\nullfont % needs special handling in \PSAMSFonts
\newtoks\tenpoint@
\def\tenpoint{\normalbaselineskip12\p@
 \abovedisplayskip12\p@ plus3\p@ minus9\p@
 \belowdisplayskip\abovedisplayskip
 \abovedisplayshortskip\z@ plus3\p@
 \belowdisplayshortskip7\p@ plus3\p@ minus4\p@
 \textonlyfont@\rm\tenrm \textonlyfont@\it\tenit
 \textonlyfont@\sl\tensl \textonlyfont@\bf\tenbf
 \textonlyfont@\smc\tensmc \textonlyfont@\tt\tentt
 \ifsyntax@ \def\big##1{{\hbox{$\left##1\right.$}}}%
  \let\Big\big \let\bigg\big \let\Bigg\big
 \else
   \textfont\z@\tenrm  \scriptfont\z@\sevenrm
       \scriptscriptfont\z@\fiverm
   \textfont\@ne\teni  \scriptfont\@ne\seveni
       \scriptscriptfont\@ne\fivei
   \textfont\tw@\tensy \scriptfont\tw@\sevensy
       \scriptscriptfont\tw@\fivesy
   \textfont\thr@@\tenex \scriptfont\thr@@\sevenex
        \scriptscriptfont\thr@@\sevenex
   \textfont\itfam\tenit \scriptfont\itfam\sevenit
        \scriptscriptfont\itfam\sevenit
   \textfont\bffam\tenbf \scriptfont\bffam\sevenbf
        \scriptscriptfont\bffam\fivebf
   \setbox\strutbox\hbox{\vrule height8.5\p@ depth3.5\p@ width\z@}%
   \setbox\strutbox@\hbox{\lower.5\normallineskiplimit\vbox{%
        \kern-\normallineskiplimit\copy\strutbox}}%
   \setbox\z@\vbox{\hbox{$($}\kern\z@}\bigsize@1.2\ht\z@
  \fi
  \normalbaselines\rm\dotsspace@1.5mu\ex@.2326ex\jot3\ex@
  \the\tenpoint@}
\newtoks\eightpoint@
\def\eightpoint{\normalbaselineskip10\p@
 \abovedisplayskip10\p@ plus2.4\p@ minus7.2\p@
 \belowdisplayskip\abovedisplayskip
 \abovedisplayshortskip\z@ plus2.4\p@
 \belowdisplayshortskip5.6\p@ plus2.4\p@ minus3.2\p@
 \textonlyfont@\rm\eightrm \textonlyfont@\it\eightit
 \textonlyfont@\sl\eightsl \textonlyfont@\bf\eightbf
 \textonlyfont@\smc\eightsmc \textonlyfont@\tt\eighttt
 \ifsyntax@\def\big##1{{\hbox{$\left##1\right.$}}}%
  \let\Big\big \let\bigg\big \let\Bigg\big
 \else
  \textfont\z@\eightrm \scriptfont\z@\sixrm
       \scriptscriptfont\z@\fiverm
  \textfont\@ne\eighti \scriptfont\@ne\sixi
       \scriptscriptfont\@ne\fivei
  \textfont\tw@\eightsy \scriptfont\tw@\sixsy
       \scriptscriptfont\tw@\fivesy
  \textfont\thr@@\eightex \scriptfont\thr@@\sevenex
   \scriptscriptfont\thr@@\sevenex
  \textfont\itfam\eightit \scriptfont\itfam\sevenit
   \scriptscriptfont\itfam\sevenit
  \textfont\bffam\eightbf \scriptfont\bffam\sixbf
   \scriptscriptfont\bffam\fivebf
 \setbox\strutbox\hbox{\vrule height7\p@ depth3\p@ width\z@}%
 \setbox\strutbox@\hbox{\raise.5\normallineskiplimit\vbox{%
   \kern-\normallineskiplimit\copy\strutbox}}%
 \setbox\z@\vbox{\hbox{$($}\kern\z@}\bigsize@1.2\ht\z@
 \fi
 \normalbaselines\eightrm\dotsspace@1.5mu\ex@.2326ex\jot3\ex@
 \the\eightpoint@}
\def\linespacing#1{%
  \addto\tenpoint{\normalbaselineskip=#1\normalbaselineskip
    \normalbaselines
    \setbox\strutbox=\hbox{\vrule height.7\normalbaselineskip
      depth.3\normalbaselineskip width\z@}%
    \setbox\strutbox@\hbox{\raise.5\normallineskiplimit
      \vbox{\kern-\normallineskiplimit\copy\strutbox}}%
  }%
  \addto\eightpoint{\normalbaselineskip=#1\normalbaselineskip
    \normalbaselines
    \setbox\strutbox=\hbox{\vrule height.7\normalbaselineskip
      depth.3\normalbaselineskip width\z@}%
    \setbox\strutbox@\hbox{\raise.5\normallineskiplimit
      \vbox{\kern-\normallineskiplimit\copy\strutbox}}%
  }%
}
\def\extrafont@#1#2#3{\font#1=#2#3\relax}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newif\ifPSAMSFonts
\def\PSAMSFonts{%
  \def\extrafont@##1##2##3{%
    \font##1=##2%
      \ifnum##3=9 10 at9pt%
      \else\ifnum##3=8 10 at8pt%
      \else\ifnum##3=6 7 at6pt%
              \else ##3\fi\fi\fi\relax}%
  \font@\eightsmc=cmcsc10 at 8pt
  \font@\eightex=cmex10 at 8pt
  \font@\sevenex=cmex10 at 7pt
  \PSAMSFontstrue
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\def\loadextrasizes@#1#2#3#4#5#6#7{%
 \ifx\undefined#1%
 \else \extrafont@{#4}{#2}{8}\extrafont@{#6}{#2}{6}%
   \ifsyntax@
   \else
     \addto\tenpoint{\textfont#1#3\scriptfont#1#5%
       \scriptscriptfont#1#7}%
    \addto\eightpoint{\textfont#1#4\scriptfont#1#6%
       \scriptscriptfont#1#7}%
   \fi
 \fi
}
\newtoks\loadextrafonts@@
\def\loadextrafonts@{%
  \loadextrasizes@\msafam{msam}%
    \tenmsa\eightmsa\sevenmsa\sixmsa\fivemsa
  \loadextrasizes@\msbfam{msbm}%
    \tenmsb\eightmsb\sevenmsb\sixmsb\fivemsb
  \loadextrasizes@\eufmfam{eufm}%
    \teneufm\eighteufm\seveneufm\sixeufm\fiveeufm
  \loadextrasizes@\eufbfam{eufb}%
    \teneufb\eighteufb\seveneufb\sixeufb\fiveeufb
  \loadextrasizes@\eusmfam{eusm}%
    \teneusm\eighteusm\seveneusm\sixeusm\fiveeusm
  \loadextrasizes@\eusbfam{eusb}%
    \teneusb\eighteusb\seveneusb\sixeusb\fiveeusb
  \loadextrasizes@\eurmfam{eurm}%
    \teneurm\eighteurm\seveneurm\sixeurm\fiveeurm
  \loadextrasizes@\eurbfam{eurb}%
    \teneurb\eighteurb\seveneurb\sixeurb\fiveeurb
  \loadextrasizes@\cmmibfam{cmmib}%
    \tencmmib\eightcmmib\sevencmmib\sixcmmib\fivecmmib
  \loadextrasizes@\cmbsyfam{cmbsy}%
    \tencmbsy\eightcmbsy\sevencmbsy\sixcmbsy\fivecmbsy
  \let\loadextrafonts@\empty@
  \ifPSAMSFonts
  \else
    \font@\eightsmc=cmcsc8 \relax
    \font@\eightex=cmex8 \relax
    \font@\sevenex=cmex7 \relax
  \fi
  \the\loadextrafonts@@
}
\message{page dimension settings,}
\parindent1pc
\newdimen\normalparindent \normalparindent\parindent
\normallineskiplimit\p@
\newdimen\indenti \indenti=2pc
\let\magnification=\mag
\topskip10pt \relax
\message{top matter,}
\def\topmatter{\loadextrafonts@ \let\topmatter\relax}
\def\chapterno@{\uppercase\expandafter{\romannumeral\chaptercount@}}
\newcount\chaptercount@
\def\chapter{\let\savedef@\chapter
  \def\chapter##1{\let\chapter\savedef@
  \leavevmode\hskip-\leftskip
   \rlap{\vbox to\z@{\vss\centerline{\eightpoint
   \frills@{CHAPTER\space\afterassignment\chapterno@
       \global\chaptercount@=}%
   ##1\unskip}\baselineskip2pc\null}}\hskip\leftskip}%
 \nofrillscheck\chapter}
\newbox\titlebox@
\def\title{\let\savedef@\title
  \def\title##1\endtitle{\let\title\savedef@
    \global\setbox\titlebox@\vtop{\tenpoint\bf
      \raggedcenter@
      \baselineskip1.3\baselineskip
      \frills@\uppercasetext@{##1}\endgraf}%
    \ifmonograph@
      \edef\next{\the\leftheadtoks}\ifx\next\empty@ \leftheadtext{##1}\fi
    \fi
    \edef\next{\the\rightheadtoks}\ifx\next\empty@ \rightheadtext{##1}\fi
  }%
  \nofrillscheck\title}
\newbox\authorbox@
\def\author#1\endauthor{\global\setbox\authorbox@
  \vbox{\tenpoint\smc\raggedcenter@ #1\endgraf}\relaxnext@
  \edef\next{\the\leftheadtoks}%
  \ifx\next\empty@\leftheadtext{#1}\fi}
\newbox\affilbox@
\def\affil#1\endaffil{\global\setbox\affilbox@
  \vbox{\tenpoint\raggedcenter@#1\endgraf}}
\newcount\addresscount@
\addresscount@\z@
\def\address#1\endaddress{\global\advance\addresscount@\@ne
  \expandafter\gdef\csname address\number\addresscount@\endcsname
  {\nobreak\vskip12\p@ minus6\p@\indent\eightpoint\smc#1\par}}
\def\curraddr{\let\savedef@\curraddr
  \def\curraddr##1\endcurraddr{\let\curraddr\savedef@
  \toks@\expandafter\expandafter\expandafter{%
       \csname address\number\addresscount@\endcsname}%
  \toks@@{##1}%
  \expandafter\xdef\csname address\number\addresscount@\endcsname
  {\the\toks@\endgraf\noexpand\nobreak
    \indent{\noexpand\rm
    \frills@{{\noexpand\it Current address\noexpand\/}:\space}%
    \def\noexpand\usualspace{\space}\the\toks@@\unskip}}}%
  \nofrillscheck\curraddr}
\def\email{\let\savedef@\email
  \def\email##1\endemail{\let\email\savedef@
  \toks@{\def\usualspace{{\it\enspace}}\endgraf\indent\eightpoint}%
  \toks@@{\tt##1\par}%
  \expandafter\xdef\csname email\number\addresscount@\endcsname
  {\the\toks@\frills@{{\noexpand\it E-mail address\noexpand\/}:%
     \noexpand\enspace}\the\toks@@}}%
  \nofrillscheck\email}
\def\tildechar{{\tt\char`\~}}
\def\urladdr{\let\savedef@\urladdr
  \def\urladdr##1\endurladdr{\let\urladdr\savedef@
  \toks@{\def\usualspace{{\it\enspace}}\endgraf\indent\eightpoint}%
  \toks@@{\tt##1\par}%
  \expandafter\xdef\csname urladdr\number\addresscount@\endcsname
  {\the\toks@\frills@{{\noexpand\it URL\noexpand\/}:%
     \noexpand\enspace}\the\toks@@}}%
  \nofrillscheck\urladdr}
\def\thedate@{}
\def\date#1\enddate{\gdef\thedate@{\tenpoint#1\unskip}}
\def\thethanks@{}
\def\thanks#1\endthanks{%
  \ifx\thethanks@\empty@ \gdef\thethanks@{\eightpoint#1}%
  \else
    \expandafter\gdef\expandafter\thethanks@\expandafter{%
     \thethanks@\endgraf#1}%
  \fi}
\def\thekeywords@{}
\def\keywords{\let\savedef@\keywords
  \def\keywords##1\endkeywords{\let\keywords\savedef@
  \toks@{\def\usualspace{{\it\enspace}}\eightpoint}%
  \toks@@{##1\unskip.}%
  \edef\thekeywords@{\the\toks@\frills@{{\noexpand\it
    Key words and phrases.\noexpand\enspace}}\the\toks@@}}%
 \nofrillscheck\keywords}
\def\thesubjclass@{}
\def\subjclass{\let\savedef@\subjclass
 \def\subjclass##1\endsubjclass{\let\subjclass\savedef@
   \toks@{\def\usualspace{{\rm\enspace}}\eightpoint}%
   \toks@@{##1\unskip.}%
   \edef\thesubjclass@{\the\toks@
     \frills@{{\noexpand\rm1991 {\noexpand\it Mathematics Subject
       Classification}.\noexpand\enspace}}%
     \the\toks@@}}%
  \nofrillscheck\subjclass}
\newbox\abstractbox@
\def\abstract{\let\savedef@\abstract
  \def\abstract{\let\abstract\savedef@
    \setbox\abstractbox@\vbox\bgroup\noindent$$\vbox\bgroup
      \def\envir@end{\endabstract}\advance\hsize-2\indenti
      \def\usualspace{\enspace}\eightpoint \noindent
      \frills@{{\smc Abstract.\enspace}}}%
  \nofrillscheck\abstract}
\def\endabstract{\par\unskip\egroup$$\egroup}
\def\widestnumber{\begingroup \let\head\relax\let\subhead\relax
  \let\subsubhead\relax \expandafter\endgroup\setwidest@}
\def\setwidest@#1#2{%
   \ifx#1\head\setbox\tocheadbox@\hbox{#2.\enspace}%
   \else\ifx#1\subhead\setbox\tocsubheadbox@\hbox{#2.\enspace}%
   \else\ifx#1\subsubhead\setbox\tocsubheadbox@\hbox{#2.\enspace}%
   \else\ifx#1\key
       \if C\refstyle@ \else\refstyle A\fi
       \setboxz@h{\refsfont@\keyformat{#2}}%
       \refindentwd\wd\z@
   \else\ifx#1\no\refstyle C%
       \setboxz@h{\refsfont@\keyformat{#2}}%
       \refindentwd\wd\z@
   \else\ifx#1\page\setbox\z@\hbox{\quad\bf#2}%
       \pagenumwd\wd\z@
   \else\ifx#1\item
       \setboxz@h{(#2)}\rosteritemwd\wdz@
   \else\message{\string\widestnumber\space not defined for this
      option (\string#1)}%
\fi\fi\fi\fi\fi\fi\fi}
\newif\ifmonograph@
\def\Monograph{\monograph@true \let\headmark\rightheadtext
  \let\varindent@\indent \def\headfont@{\bf}\def\proclaimheadfont@{\smc}%
  \def\remarkheadfont@{\smc}}
\let\varindent@\noindent
\newbox\tocheadbox@    \newbox\tocsubheadbox@
\newbox\tocbox@
\newdimen\pagenumwd
\def\toc{\toc@{Contents}}
\def\newtocdefs{%
   \def \title##1\endtitle
       {\penaltyandskip@\z@\smallskipamount
        \hangindent\wd\tocheadbox@\noindent{\bf##1}}%
   \def \chapter##1{%
        Chapter \uppercase\expandafter{%
              \romannumeral##1.\unskip}\enspace}%
   \def \specialhead##1\endspecialhead
       {\par\hangindent\wd\tocheadbox@ \noindent##1\par}%
   \def \Head##1 ##2
       {\par\hangindent\wd\tocheadbox@ \noindent
        \if\notempty{##1}\hbox to\wd\tocheadbox@{\hfil##1\enspace}\fi
        ##2\par}%
   \def \subhead##1 ##2\endsubhead
       {\par\vskip-\parskip {\normalbaselines
        \advance\leftskip\wd\tocheadbox@
        \hangindent\wd\tocsubheadbox@ \noindent
        \if\notempty{##1}%
              \hbox to\wd\tocsubheadbox@{##1\unskip\hfil}\fi
         ##2\par}}%
   \def \subsubhead##1 ##2\endsubsubhead
       {\par\vskip-\parskip {\normalbaselines
        \advance\leftskip\wd\tocheadbox@
        \hangindent\wd\tocsubheadbox@ \noindent
        \if\notempty{##1}%
              \hbox to\wd\tocsubheadbox@{##1\unskip\hfil}\fi
        ##2\par}}}
\def\toc@#1{\relaxnext@
 \DN@{\ifx\next\nofrills\DN@\nofrills{\nextii@}%
      \else\DN@{\nextii@{{#1}}}\fi
      \next@}%
 \DNii@##1{%
\ifmonograph@\bgroup\else\setbox\tocbox@\vbox\bgroup
   \centerline{\headfont@\ignorespaces##1\unskip}\nobreak
   \vskip\belowheadskip \fi
   \def\page####1%
       {\unskip\penalty\z@\null\hfil
        \rlap{\hbox to\pagenumwd{\quad\hfil####1}}%
              \hfilneg\penalty\@M}%
   \setbox\tocheadbox@\hbox{0.\enspace}%
   \setbox\tocsubheadbox@\hbox{0.0.\enspace}%
   \leftskip\indenti \rightskip\leftskip
   \setboxz@h{\bf\quad000}\pagenumwd\wd\z@
   \advance\rightskip\pagenumwd
   \newtocdefs
 }%
 \FN@\next@}
\def\endtoc{\par\egroup}
\let\pretitle\relax
\let\preauthor\relax
\let\preaffil\relax
\let\predate\relax
\let\preabstract\relax
\let\prepaper\relax
\def\dedicatory #1\enddedicatory{\def\preabstract{{\medskip
  \eightpoint\it \raggedcenter@#1\endgraf}}}
\def\thetranslator@{}
\def\translator{%
  \let\savedef@\translator
  \def\translator##1\endtranslator{\let\translator\savedef@
    \edef\thetranslator@{\noexpand\nobreak\noexpand\medskip
      \noexpand\line{\noexpand\eightpoint\hfil
      \frills@{Translated by \uppercase}{##1}\qquad\qquad}%
       \noexpand\nobreak}}%
  \nofrillscheck\translator}
\outer\def\endtopmatter{\add@missing\endabstract
  \edef\next{\the\leftheadtoks}%
  \ifx\next\empty@
    \expandafter\leftheadtext\expandafter{\the\rightheadtoks}%
  \fi
  \ifmonograph@\else
    \ifx\thesubjclass@\empty@\else \makefootnote@{}{\thesubjclass@}\fi
    \ifx\thekeywords@\empty@\else \makefootnote@{}{\thekeywords@}\fi
    \ifx\thethanks@\empty@\else \makefootnote@{}{\thethanks@}\fi
  \fi
  \inslogo@
  \pretitle
  \begingroup % to localize variant topskip
  \ifmonograph@ \topskip7pc \else \topskip4pc \fi
  \box\titlebox@
  \endgroup
  \preauthor
  \ifvoid\authorbox@\else \vskip2.5pcplus1pc\unvbox\authorbox@\fi
  \preaffil
  \ifvoid\affilbox@\else \vskip1pcplus.5pc\unvbox\affilbox@\fi
  \predate
  \ifx\thedate@\empty@\else
    \vskip1pcplus.5pc\line{\hfil\thedate@\hfil}\fi
  \preabstract
  \ifvoid\abstractbox@\else
    \vskip1.5pcplus.5pc\unvbox\abstractbox@ \fi
  \ifvoid\tocbox@\else\vskip1.5pcplus.5pc\unvbox\tocbox@\fi
  \prepaper
  \vskip2pcplus1pc\relax
}
\def\document{%
  \loadextrafonts@
  \let\fontlist@\relax\let\alloclist@\relax
  \tenpoint}
\message{section heads,}
\newskip\aboveheadskip       \aboveheadskip\bigskipamount
\newdimen\belowheadskip      \belowheadskip6\p@
\def\headfont@{\smc}
\def\penaltyandskip@#1#2{\par\skip@#2\relax
  \ifdim\lastskip<\skip@\relax\removelastskip
      \ifnum#1=\z@\else\penalty@#1\relax\fi\vskip\skip@
  \else\ifnum#1=\z@\else\penalty@#1\relax\fi\fi}
\def\nobreak{\penalty\@M
  \ifvmode\gdef\penalty@{\global\let\penalty@\penalty\count@@@}%
  \everypar{\global\let\penalty@\penalty\everypar{}}\fi}
\let\penalty@\penalty
\def\heading#1\endheading{\head#1\endhead}
\def\subheading{\DN@{\ifx\next\nofrills
    \expandafter\subheading@
  \else \expandafter\subheading@\expandafter\empty@
  \fi}%
  \FN@\next@
}
\def\subheading@#1#2{\subhead#1#2\endsubhead}
\newskip\abovespecialheadskip
\abovespecialheadskip=\aboveheadskip
\def\specialheadfont@{\bf}
\outer\def\specialhead{%
  \add@missing\endroster \add@missing\enddefinition
  \add@missing\enddemo \add@missing\endexample
  \add@missing\endproclaim
  \penaltyandskip@{-200}\abovespecialheadskip
  \begingroup\interlinepenalty\@M\rightskip\z@ plus\hsize
  \let\\\linebreak
  \specialheadfont@\noindent}
\def\endspecialhead{\par\endgroup\nobreak\vskip\belowheadskip}
\outer\def\head#1\endhead{%
  \add@missing\endroster \add@missing\enddefinition
  \add@missing\enddemo \add@missing\endexample
  \add@missing\endproclaim
  \penaltyandskip@{-200}\aboveheadskip
  {\headfont@\raggedcenter@\interlinepenalty\@M
  #1\endgraf}\headmark{#1}%
  \nobreak
  \vskip\belowheadskip}
\let\headmark\eat@
\def\restoredef@#1{\relax\let#1\savedef@\let\savedef@\relax}
\newskip\subheadskip       \subheadskip\medskipamount
\def\subheadfont@{\bf}
\outer\def\subhead{%
  \add@missing\endroster \add@missing\enddefinition
  \add@missing\enddemo \add@missing\endexample
  \add@missing\endproclaim
  \let\savedef@\subhead \let\subhead\relax
  \def\subhead##1\endsubhead{\restoredef@\subhead
    \penaltyandskip@{-100}\subheadskip
    {\def\usualspace{\/{\subheadfont@\enspace}}%
     \varindent@\subheadfont@\ignorespaces##1\unskip\frills@{.\enspace}}%
    \ignorespaces}%
  \nofrillscheck\subhead}
\newskip\subsubheadskip       \subsubheadskip\medskipamount
\def\subsubheadfont@{\it}
\outer\def\subsubhead{%
  \add@missing\endroster \add@missing\enddefinition
  \add@missing\enddemo
  \add@missing\endexample \add@missing\endproclaim
  \let\savedef@\subsubhead \let\subsubhead\relax
  \def\subsubhead##1\endsubsubhead{\restoredef@\subsubhead
    \penaltyandskip@{-50}\subsubheadskip
    {\def\usualspace{\/{\subsubheadfont@\enspace}}%
     \subsubheadfont@##1\unskip\frills@{.\enspace}}\ignorespaces}%
  \nofrillscheck\subsubhead}
\message{theorems/proofs/definitions/remarks,}
\def\proclaimheadfont@{\bf}
\def\proclaimfont{\it}
\newskip\preproclaimskip  \preproclaimskip=\medskipamount
\newskip\postproclaimskip \postproclaimskip=\medskipamount
\outer\def\proclaim{%
  \let\savedef@\proclaim \let\proclaim\relax
  \add@missing\endroster \add@missing\enddefinition
  \add@missing\endproclaim \envir@stack\endproclaim
  \def\proclaim##1{\restoredef@\proclaim
    \penaltyandskip@{-100}\preproclaimskip
    {\def\usualspace{\/{\proclaimheadfont@\enspace}}%
     \varindent@\proclaimheadfont@\ignorespaces##1\unskip
     \frills@{.\enspace}}%
    \proclaimfont\ignorespaces}%
  \nofrillscheck\proclaim}
\def\endproclaim{\revert@envir\endproclaim \par\rm
  \penaltyandskip@{55}\postproclaimskip}
\def\remarkheadfont@{\it}
\def\remarkfont{\rm}
\newskip\remarkskip  \remarkskip=\medskipamount
\def\remark{\let\savedef@\remark \let\remark\relax
  \add@missing\endroster \add@missing\endproclaim
  \envir@stack\endremark
  \def\remark##1{\restoredef@\remark
    \penaltyandskip@\z@\remarkskip
    {\def\usualspace{\/{\remarkheadfont@\enspace}}%
     \varindent@\remarkheadfont@\ignorespaces##1\unskip
     \frills@{.\enspace}}%
    \remarkfont\ignorespaces}%
  \nofrillscheck\remark}
\def\endremark{\par\revert@envir\endremark}
\def\qed{\ifhmode\unskip\nobreak\fi\quad
  \ifmmode\square\else$\m@th\square$\fi}
\newskip\postdemoskip  \postdemoskip=\medskipamount
\def\demo{\DN@{\ifx\next\nofrills
    \DN@####1####2{\remark####1{####2}\envir@stack\enddemo
      \ignorespaces}%
  \else
    \DN@####1{\remark{####1}\envir@stack\enddemo\ignorespaces}%
  \fi
  \next@}%
\FN@\next@}
\def\enddemo{\par\revert@envir\enddemo \endremark\vskip\postdemoskip}
\def\definitionfont{\rm}
\newskip\predefinitionskip  \predefinitionskip=\medskipamount
\newskip\postdefinitionskip  \postdefinitionskip=\medskipamount
\def\definition{\let\savedef@\definition \let\definition\relax
  \add@missing\endproclaim \add@missing\endroster
  \add@missing\enddefinition \envir@stack\enddefinition
  \def\definition##1{\restoredef@\definition
    \penaltyandskip@{-100}\predefinitionskip
    {\def\usualspace{\/{\proclaimheadfont@\enspace}}%
     \varindent@\proclaimheadfont@\ignorespaces##1\unskip
     \frills@{.\proclaimheadfont@\enspace}}%
    \definitionfont\ignorespaces}%
  \nofrillscheck\definition}
\def\enddefinition{\revert@envir\enddefinition
  \par\vskip\postdefinitionskip}
\def\example{%
  \DN@{\ifx\next\nofrills
    \DN@####1####2{\definition####1{####2}\envir@stack\endexample
      \ignorespaces}%
  \else
    \DN@####1{\definition{####1}\envir@stack\endexample\ignorespaces}%
  \fi
  \next@}%
\FN@\next@}
\def\endexample{\revert@envir\endexample \enddefinition }
\message{rosters,}
\newdimen\rosteritemwd
\rosteritemwd16pt % approximately the width of (iii) in 10 point text
\newcount\rostercount@
\newif\iffirstitem@
\let\plainitem@\item
\newtoks\everypartoks@
\def\par@{\everypartoks@\expandafter{\the\everypar}\everypar{}}
\def\leftskip@{}
\def\roster{%
  \envir@stack\endroster
  \edef\leftskip@{\leftskip\the\leftskip}%
  \relaxnext@
  \rostercount@\z@% Initialize \rostercount@ to 0.
  \def\item{\FN@\rosteritem@}%      \item, now redefined, has
  \DN@{\ifx\next\runinitem\let\next@\nextii@
    \else\let\next@\nextiii@
    \fi\next@}%
  \DNii@\runinitem% If \runinitem occurs, \nextii@ must kill it off.
    {\unskip% This unskips any space before the original \roster.
     \DN@{\ifx\next[\let\next@\nextii@
       \else\ifx\next"\let\next@\nextiii@\else\let\next@\nextiv@\fi
       \fi\next@}%
     \DNii@[####1]{\rostercount@####1\relax
       \enspace\therosteritem{\number\rostercount@}~\ignorespaces}%
     \def\nextiii@"####1"{\enspace{\rm####1}~\ignorespaces}%
     \def\nextiv@{\enspace\therosteritem1\rostercount@\@ne~}%
     \par@\firstitem@false% Before doing any of this we still change
     \FN@\next@}%      End of definition of \nextii@\runinitem.
  \def\nextiii@{\par\par@% End the present paragraph, change \everypar
    \penalty\@m\smallskip\vskip-\parskip
    \firstitem@true}%
  \FN@\next@}
\def\rosteritem@{\iffirstitem@\firstitem@false
  \else\par\vskip-\parskip\fi
 \leftskip\rosteritemwd \advance\leftskip\normalparindent
 \advance\leftskip.5em \noindent
 \DNii@[##1]{\rostercount@##1\relax\itembox@}%
 \def\nextiii@"##1"{\def\therosteritem@{\rm##1}\itembox@}%
 \def\nextiv@{\advance\rostercount@\@ne\itembox@}%
 \def\therosteritem@{\therosteritem{\number\rostercount@}}%
 \ifx\next[\let\next@\nextii@\else\ifx\next"\let\next@\nextiii@\else
  \let\next@\nextiv@\fi\fi\next@}
\def\itembox@{\llap{\hbox to\rosteritemwd{\hss
  \kern\z@ % kern to thwart \unskip in \rom
  \therosteritem@}\enspace}\ignorespaces}
\def\therosteritem#1{\rom{(\ignorespaces#1\unskip)}}
\newif\ifnextRunin@
\def\endroster{\relaxnext@
 \revert@envir\endroster % restore \envir@end
 \par\leftskip@% End the paragraph, and restore the \leftskip.
 \global\rosteritemwd16\p@ % restore default value
 \penalty-50 \vskip-\parskip\smallskip% Add a good break and
 \DN@{\ifx\next\Runinitem\let\next@\relax
  \else\nextRunin@false\let\item\plainitem@% Otherwise, set
   \ifx\next\par% moreover, if \endroster is followed by \par,
    \DN@\par{\everypar\expandafter{\the\everypartoks@}}%
   \else% but if the \endroster isn't followed by a new paragraph,
    \DN@{\noindent\everypar\expandafter{\the\everypartoks@}}%
  \fi\fi\next@}%
 \FN@\next@}
\newcount\rosterhangafter@
\def\Runinitem#1\roster\runinitem{\relaxnext@
  \envir@stack\endroster
 \rostercount@\z@
 \def\item{\FN@\rosteritem@}%
 \def\runinitem@{#1}%
 \DN@{\ifx\next[\let\next\nextii@\else\ifx\next"\let\next\nextiii@
  \else\let\next\nextiv@\fi\fi\next}%
 \DNii@[##1]{\rostercount@##1\relax
  \def\item@{\therosteritem{\number\rostercount@}}\nextv@}%
 \def\nextiii@"##1"{\def\item@{{\rm##1}}\nextv@}%
 \def\nextiv@{\advance\rostercount@\@ne
  \def\item@{\therosteritem{\number\rostercount@}}\nextv@}%
 \def\nextv@{\setbox\z@\vbox
  {\ifnextRunin@\noindent\fi
  \runinitem@\unskip\enspace\item@~\par
  \global\rosterhangafter@\prevgraf}%
  \firstitem@false% Set \firstitem@false for future \item's.
  \ifnextRunin@\else\par\fi
  \hangafter\rosterhangafter@\hangindent3\normalparindent
  \ifnextRunin@\noindent\fi
  \runinitem@\unskip\enspace%  Put in all the stored stuff
  \item@~\ifnextRunin@\else\par@\fi% and the \item@, and
  \nextRunin@true\ignorespaces}%% Here's where we set \nextRunin@true.
 \FN@\next@}
\message{footnotes,}
\def\footmarkform@#1{$\m@th^{#1}$}
\let\thefootnotemark\footmarkform@
\def\makefootnote@#1#2{\insert\footins
 {\interlinepenalty\interfootnotelinepenalty
 \eightpoint\splittopskip\ht\strutbox\splitmaxdepth\dp\strutbox
 \floatingpenalty\@MM\leftskip\z@skip\rightskip\z@skip
 \spaceskip\z@skip\xspaceskip\z@skip\noindent         % DF (added \noindent)
 \leavevmode{#1}\footstrut\ignorespaces#2\unskip\lower\dp\strutbox 
 \vbox to\dp\strutbox{}}}
\newcount\footmarkcount@
\footmarkcount@\z@
\def\footnotemark{\let\@sf\empty@\relaxnext@
 \ifhmode\edef\@sf{\spacefactor\the\spacefactor}\/\fi
 \DN@{\ifx[\next\let\next@\nextii@\else
  \ifx"\next\let\next@\nextiii@\else
  \let\next@\nextiv@\fi\fi\next@}%
 \DNii@[##1]{\footmarkform@{##1}\@sf}%
 \def\nextiii@"##1"{{##1}\@sf}%
 \def\nextiv@{\iffirstchoice@\global\advance\footmarkcount@\@ne\fi
  \footmarkform@{\number\footmarkcount@}\@sf}%
 \FN@\next@}
\def\footnotetext{\relaxnext@
 \DN@{\ifx[\next\let\next@\nextii@\else
  \ifx"\next\let\next@\nextiii@\else
  \let\next@\nextiv@\fi\fi\next@}%
 \DNii@[##1]##2{\makefootnote@{\footmarkform@{##1}}{##2}}%
 \def\nextiii@"##1"##2{\makefootnote@{##1}{##2}}%
 \def\nextiv@##1{\makefootnote@{\footmarkform@%
  {\number\footmarkcount@}}{##1}}%
 \FN@\next@}
\def\footnote{\let\@sf\empty@\relaxnext@
 \ifhmode\edef\@sf{\spacefactor\the\spacefactor}\/\fi
 \DN@{\ifx[\next\let\next@\nextii@\else
  \ifx"\next\let\next@\nextiii@\else
  \let\next@\nextiv@\fi\fi\next@}%
 \DNii@[##1]##2{\footnotemark[##1]\footnotetext[##1]{##2}}%
 \def\nextiii@"##1"##2{\footnotemark"##1"\footnotetext"##1"{##2}}%
 \def\nextiv@##1{\footnotemark\footnotetext{##1}}%
 \FN@\next@}
\def\adjustfootnotemark#1{\advance\footmarkcount@#1\relax}
\def\footnoterule{\kern-4\p@
  \hrule width5pc\kern 3.6\p@}%      the \hrule is .4pt high
\message{figures and captions,}
\def\captionfont@{\smc}
\def\topcaption#1#2\endcaption{%
  {\dimen@\hsize \advance\dimen@-\captionwidth@
   \rm\raggedcenter@ \advance\leftskip.5\dimen@ \rightskip\leftskip
  {\captionfont@#1}%
  \if\notempty{#2}.\enspace\ignorespaces#2\fi
  \endgraf}\nobreak\bigskip}
\def\botcaption#1#2\endcaption{%
  \nobreak\bigskip
  \setboxz@h{\captionfont@#1\if\notempty{#2}.\enspace\rm\ignorespaces#2\fi}%
  {\dimen@\hsize \advance\dimen@-\captionwidth@
   \leftskip.5\dimen@ \rightskip\leftskip
   \noindent \ifdim\wdz@>\captionwidth@
   \else\hfil\fi
  {\captionfont@#1}%
  \if\notempty{#2}.\enspace\rm\ignorespaces#2\fi\endgraf}}
\def\@ins{\par\begingroup\def\vspace##1{\vskip##1\relax}%
  \def\captionwidth##1{\captionwidth@##1\relax}%
  \setbox\z@\vbox\bgroup} % start a \vbox
\message{miscellaneous,}
\def\block{\RIfMIfI@\nondmatherr@\block\fi
       \else\ifvmode\noindent$$\predisplaysize\hsize
         \else$$\fi
  \def\endblock{\par\egroup$$}\fi
  \vbox\bgroup\advance\hsize-2\indenti\noindent}
\def\endblock{\par\egroup}
\def\cite#1{\rom{[{\citefont@\m@th#1}]}}
\def\citefont@{\rm}
\def\rom#1{\leavevmode
  \edef\prevskip@{\ifdim\lastskip=\z@ \else\hskip\the\lastskip\relax\fi}%
  \unskip
  \edef\prevpenalty@{\ifnum\lastpenalty=\z@ \else
    \penalty\the\lastpenalty\relax\fi}%
  \unpenalty \/\prevpenalty@ \prevskip@ {\rm #1}}
\message{references,}
\def\refsfont@{\eightpoint}
\def\refsheadfont@{\headfont@}
\newdimen\refindentwd
\newdimen\refafterindentwd
\setboxz@h{\refsfont@ 00.\enspace}
\refindentwd\wdz@
\refafterindentwd\wdz@
\def\Refsname{References}
\outer\def\Refs{\add@missing\endroster \add@missing\endproclaim
 \let\savedef@\Refs \let\Refs\relax % because of \outer-ness
 \def\Refs##1{\restoredef@\Refs
   \if\notempty{##1}\penaltyandskip@{-200}\aboveheadskip
     \begingroup \raggedcenter@\refsheadfont@
       \ignorespaces##1\endgraf\endgroup
     \penaltyandskip@\@M\belowheadskip
   \fi
   \begingroup\def\envir@end{\endRefs}\refsfont@\sfcode`\.\@m
   }%
 \nofrillscheck{\csname Refs\expandafter\endcsname
  \frills@{{\Refsname}}}}
\def\endRefs{\par % This will check for a missing \endref, also
  \endgroup}
\newif\ifbook@ \newif\ifprocpaper@
\def\nofrills{%
  \expandafter\ifx\envir@end\endref
    \let\do\relax
    \xdef\nofrills@list{\nofrills@list\do\curbox}%
  \else\errmessage{\Invalid@@ \string\nofrills}%
  \fi}%
\def\defaultreftexts{\gdef\edtext{ed.}\gdef\pagestext{pp.}%
  \gdef\voltext{vol.}\gdef\issuetext{no.}}
\defaultreftexts
\def\ref{\par
  \begingroup \def\envir@end{\endref}%
  \noindent\hangindent\refafterindentwd
  \def\par{\add@missing\endref}%
  \global\let\nofrills@list\empty@
  \refbreaks
  \procpaper@false \book@false \moreref@false
  \def\curbox{\z@}\setbox\z@\vbox\bgroup
}
\let\keyhook@\empty@
\def\endref{%
  \setbox\tw@\box\thr@@
  \makerefbox?\thr@@{\endgraf\egroup}%
  \endref@
  \endgraf
  \endgroup
  \keyhook@
  \global\let\keyhook@\empty@ % \global to conserve save stack
}
\def\key{\gdef\key{\makerefbox\key\keybox@\empty@}\key} \newbox\keybox@
\def\no{\gdef\no{\makerefbox\no\keybox@\empty@}%
  \gdef\keyhook@{\refstyle C}\no}
\def\by{\makerefbox\by\bybox@\empty@} \newbox\bybox@
\let\manyby\by % for backward compatibility
\def\bysame{\by\hbox to3em{\hrulefill}\thinspace\kern\z@}
\def\paper{\makerefbox\paper\paperbox@\it} \newbox\paperbox@
\def\paperinfo{\makerefbox\paperinfo\paperinfobox@\empty@}%
  \newbox\paperinfobox@
\def\jour{\makerefbox\jour\jourbox@
  {\aftergroup\book@false \aftergroup\procpaper@false}} \newbox\jourbox@
\def\issue{\makerefbox\issue\issuebox@\empty@} \newbox\issuebox@
\def\yr{\makerefbox\yr\yrbox@\empty@} \newbox\yrbox@
\def\pages{\makerefbox\pages\pagesbox@\empty@} \newbox\pagesbox@
\def\page{\gdef\pagestext{p.}\makerefbox\page\pagesbox@\empty@}
\def\ed{\makerefbox\ed\edbox@\empty@} \newbox\edbox@
\def\eds{\gdef\edtext{eds.}\makerefbox\eds\edbox@\empty@}
\def\book{\makerefbox\book\bookbox@
  {\it\aftergroup\book@true \aftergroup\procpaper@false}}
  \newbox\bookbox@
\def\bookinfo{\makerefbox\bookinfo\bookinfobox@\empty@}%
  \newbox\bookinfobox@
\def\publ{\makerefbox\publ\publbox@\empty@} \newbox\publbox@
\def\publaddr{\makerefbox\publaddr\publaddrbox@\empty@}%
  \newbox\publaddrbox@
\def\inbook{\makerefbox\inbook\bookbox@
  {\aftergroup\procpaper@true \aftergroup\book@false}}
\def\procinfo{\makerefbox\procinfo\procinfobox@\empty@}%
  \newbox\procinfobox@
\def\finalinfo{\makerefbox\finalinfo\finalinfobox@\empty@}%
  \newbox\finalinfobox@
\def\miscnote{\makerefbox\miscnote\miscnotebox@\empty@}%
  \newbox\miscnotebox@
\def\toappear{\miscnote to appear}
\def\lang{\makerefbox\lang\langbox@\empty@} \newbox\langbox@
\newbox\morerefbox@
\def\vol{\makerefbox\vol\volbox@{\ifbook@ \else
  \ifprocpaper@\else\bf\fi\fi}}
\newbox\volbox@
\define\MR#1{\makerefbox\MR\MRbox@\empty@
  \def\next@##1:##2:##3\next@{\ifx @##2\empty@##1\else{\bf##1:}##2\fi}%
  MR \next@#1:@:\next@}
\newbox\MRbox@
\define\AMSPPS#1{\makerefbox\AMSPPS\MRbox@\empty@ AMS\-PPS \##1}
\define\CMP#1{\makerefbox\CMP\MRbox@\empty@ CMP #1}
\newbox\holdoverbox
\def\makerefbox#1#2#3{\endgraf
  \setbox\z@\lastbox
  \global\setbox\@ne\hbox{\unhbox\holdoverbox
    \ifvoid\z@\else\unhbox\z@\unskip\unskip\unpenalty\fi}%
  \egroup
  \setbox\curbox\box\ifdim\wd\@ne>\z@ \@ne \else\voidb@x\fi
  \ifvoid#2\else\Err@{Redundant \string#1; duplicate use, or
     mutually exclusive information already given}\fi
  \def\curbox{#2}\setbox\curbox\vbox\bgroup \hsize\maxdimen \noindent
  #3}
\def\refbreaks{%
  \def\refconcat##1{\setbox\z@\lastbox \setbox\holdoverbox\hbox{%
       \unhbox\holdoverbox \unhbox\z@\unskip\unskip\unpenalty##1}}%
  \def\holdover##1{%
    \RIfM@
      \penalty-\@M\null
      \hfil$\clubpenalty\z@\widowpenalty\z@\interlinepenalty\z@
      \offinterlineskip\endgraf
      \setbox\z@\lastbox\unskip \unpenalty
      \refconcat{##1}%
      \noindent
      $\hfil\penalty-\@M
    \else
      \endgraf\refconcat{##1}\noindent
    \fi}%
  \def\break{\holdover{\penalty-\@M}}%
  \let\vadjust@\vadjust
  \def\vadjust##1{\holdover{\vadjust@{##1}}}%
  \def\newpage{\vadjust{\vfill\break}}%
}
\def\refstyle#1{\uppercase{%
  \gdef\refstyle@{#1}%
  \if#1A\relax \def\keyformat##1{[##1]\enspace\hfil}%
  \else\if#1B\relax
    \refindentwd\parindent
    \def\keyformat##1{\aftergroup\kern
              \aftergroup-\aftergroup\refindentwd}%
 \else\if#1C\relax
   \def\keyformat##1{\hfil##1.\enspace}%
 \fi\fi\fi}% end of \uppercase
}
\refstyle{A}
\def\finalpunct{\ifnum\lastkern=\m@ne\unkern\else.\spacefactor2000 \fi
       \refquotes@\refbreak@}%
\def\continuepunct#1#2#3#4{}%
\def\endref@{%
  \hskip\refindentwd
  \keyhook@
  \def\nofrillscheck##1{%
    \def\do####1{\ifx##1####1\let\frills@\eat@\fi}%
    \let\frills@\identity@ \nofrills@list}%
  \ifvoid\bybox@
    \ifvoid\edbox@
    \else\setbox\bybox@\hbox{\unhbox\edbox@\breakcheck
      \nofrillscheck\edbox@\frills@{\space(\edtext)}\refbreak@}\fi
  \fi
  \ifvoid\keybox@\else\llap{\hbox to\refindentwd{%
       \keyformat{\unhbox\keybox@}}}\fi
  \ifmoreref@
    \commaunbox@\morerefbox@
  \else
    \kern-\tw@ sp\kern\m@ne sp
  \fi
  \ppunbox@\empty@\empty@\bybox@\empty@
  \ifbook@ % Case 1: \book etc.
    \commaunbox@\bookbox@ \commaunbox@\bookinfobox@
    \ppunbox@\empty@{ (}\procinfobox@)%
    \ppunbox@,{ vol.~}\volbox@\empty@
    \ppunbox@\empty@{ (}\edbox@{, \edtext)}%
    \commaunbox@\publbox@ \commaunbox@\publaddrbox@
    \commaunbox@\yrbox@
    \ppunbox@,{ \pagestext~}\pagesbox@\empty@
  \else
    \commaunbox@\paperbox@ \commaunbox@\paperinfobox@
    \ifprocpaper@ % Case 2: \paper ... \inbook
      \commaunbox@\bookbox@
      \ppunbox@\empty@{ (}\procinfobox@)%
      \ppunbox@\empty@{ (}\edbox@{, \edtext)}%
      \commaunbox@\bookinfobox@
      \ppunbox@,{ \voltext~}\volbox@\empty@
      \commaunbox@\publbox@ \commaunbox@\publaddrbox@
      \commaunbox@\yrbox@
      \ppunbox@,{ \pagestext~}\pagesbox@\empty@
    \else % Case 3: \paper ... \jour
      \commaunbox@\jourbox@
      \ppunbox@\empty@{ }\volbox@\empty@
      \ppunbox@\empty@{ (}\yrbox@)%
      \ppunbox@,{ \issuetext~}\issuebox@\empty@
      \commaunbox@\publbox@ \commaunbox@\publaddrbox@
      \commaunbox@\pagesbox@
    \fi
  \fi
  \commaunbox@\finalinfobox@
  \ppunbox@\empty@{ (}\miscnotebox@)%
  \finalpunct
  \ppunbox@\empty@{ (}\langbox@{)\spacefactor1001 }%
  \ifnum\spacefactor>\@m \ppunbox@{}{ }\MRbox@\empty@
  \else \commaunbox@\MRbox@
  \fi
  \defaultreftexts
}
\def\punct@#1{#1}
\def\ppunbox@#1#2#3#4{\ifvoid#3\else
  \let\prespace@\relax
  \ifnum\lastkern=\m@ne \unkern\let\punct@\eat@
    \ifnum\lastkern=-\tw@ \unkern\let\prespace@\ignorespaces \fi
  \fi
  \nofrillscheck#3%
  \punct@{#1}\refquotes@\refbreak@
  \let\punct@\identity@
  \prespace@
  \frills@{#2\eat@}\space
  \unhbox#3\breakcheck
  \frills@{#4\eat@}{\kern\m@ne sp}\fi}
\def\commaunbox@#1{\ppunbox@,\space{#1}\empty@}
\def\breakcheck{\edef\refbreak@{\ifnum\lastpenalty=\z@\else
  \penalty\the\lastpenalty\relax\fi}\unpenalty}
\def\endquotes{\def\refquotes@{''\let\refquotes@\empty@}}
\let\refquotes@\empty@
\let\refbreak@\empty@
\newif\ifmoreref@
\def\moreref{%
  \setbox\tw@\box\thr@@
  \makerefbox?\thr@@{\endgraf\egroup}%
  \let\savedef@\finalpunct  \let\finalpunct\empty@
  \endref@
  \def\punct@##1##2{##2;}%
  \global\let\nofrills@list\empty@ % global, to conserve save stack
  \let\finalpunct\savedef@
  \moreref@true
  \def\curbox{\morerefbox@}%
  \setbox\morerefbox@\vbox\bgroup \hsize\maxdimen \noindent
}
\def\transl{\moreref}
\message{end of document,}
\ifx\plainend\undefined \let\plainend\end \fi
\outer\def\enddocument{\par% \par will do a runaway check for \endref
  \add@missing\endRefs
  \add@missing\endroster \add@missing\endproclaim
  \add@missing\enddefinition
  \add@missing\enddemo \add@missing\endremark \add@missing\endexample
  \enddocument@text
  \vfill\supereject\plainend}

\def\enddocument@text{%
  \ifmonograph@ % do nothing
  \else
    \nobreak
    \thetranslator@
    \count@\z@
    \loop\ifnum\count@<\addresscount@\advance\count@\@ne
      \csname address\number\count@\endcsname
      \csname email\number\count@\endcsname
      \csname urladdr\number\count@\endcsname
    \repeat
  \fi
}

\message{output routine,}
\def\folio{{\foliofont@\ifnum\pageno<\z@ \romannumeral-\pageno
 \else\number\pageno \fi}}
\def\foliofont@{\eightrm}
\def\headlinefont@{\eightpoint}
\def\leftheadline{\rlap{\folio}\hfill \iftrue\topmark\fi \hfill}
\def\rightheadline{\hfill \expandafter\iffalse\botmark\fi
  \hfill \llap{\folio}}
\newtoks\leftheadtoks
\newtoks\rightheadtoks
\def\leftheadtext{\let\savedef@\leftheadtext
  \def\leftheadtext##1{\let\leftheadtext\savedef@
    \leftheadtoks\expandafter{\frills@\uppercasetext@{##1}}%
    \mark{\the\leftheadtoks\noexpand\else\the\rightheadtoks}
    \ifsyntax@\setboxz@h{\def\\{\unskip\space\ignorespaces}%
        \headlinefont@##1}\fi}%
  \nofrillscheck\leftheadtext}
\def\rightheadtext{\let\savedef@\rightheadtext
  \def\rightheadtext##1{\let\rightheadtext\savedef@
    \rightheadtoks\expandafter{\frills@\uppercasetext@{##1}}%
    \mark{\the\leftheadtoks\noexpand\else\the\rightheadtoks}%
    \ifsyntax@\setboxz@h{\def\\{\unskip\space\ignorespaces}%
        \headlinefont@##1}\fi}%
  \nofrillscheck\rightheadtext}
\headline={\def\\{\unskip\space\ignorespaces}\headlinefont@
  \def\chapter{%
    \def\chapter##1{%
      \frills@{\afterassignment\chapterno@ \chaptercount@=}##1.\space}%
    \nofrillscheck\chapter}%
  \ifodd\pageno \rightheadline \else \leftheadline\fi}
\def\NoRunningHeads{\global\runheads@false\global\let\headmark\eat@}
\def\NoPageNumbers{\gdef\folio{}}
\newif\iffirstpage@     \firstpage@true
\newif\ifrunheads@      \runheads@true
\output={\output@}
\newdimen\headlineheight \newdimen\headlinespace
\newdimen\dropfoliodepth

\dropfoliodepth=1pc
\headlineheight=5pt
\headlinespace=24pt

\def\pagewidth#1{\hsize#1%
   \captionwidth@\hsize \advance\captionwidth@-2\indenti}

\def\pageheight#1{%
  \vsize=#1 % target height
  \advance\vsize -\headlineheight % subtract height of running head
  \advance\vsize -\headlinespace % subtract space below running head
  \advance\vsize \topskip % but the 24pt is base-to-base, so we need to
                          % compensate for topskip
}

\pagewidth{30pc}\pageheight{50.5pc}

\newinsert\copyins
\skip\copyins=12\p@
\dimen\copyins=40pc
\count\copyins=1000
\def\inslogo@{\insert\copyins{\logo@}}
\def\logo@{\rightline{\eightpoint Typeset by \AmSTeX}}
\def\nologo{\let\logo@\empty@ \let\inslogo@\empty@}
\let\flheadline\hfil \let\frheadline\hfil
\newif\ifplain@  \plain@false
\def\output@{%
  \def\break{\penalty-\@M}\let\par\endgraf
  \shipout\vbox{%
    \ifplain@
      \let\makeheadline\relax \let\makefootline\relax
    \else
      \iffirstpage@ \global\firstpage@false
        \let\rightheadline\frheadline
        \let\leftheadline\flheadline
      \else
        \ifrunheads@ \let\makefootline\relax
        \else \let\makeheadline\relax \fi
      \fi
    \fi
    \makeheadline \pagebody \makefootline
  }%
  \advancepageno \ifnum\outputpenalty>-\@MM\else\dosupereject\fi
}
\def\pagecontents{%
  \ifvoid\topins\else\unvbox\topins\fi
  \dimen@=\dp\@cclv \unvbox\@cclv % open up \box255
  \ifvoid\footins
  \else % footnote info is present
    \vskip\skip\footins
    \footnoterule
    \unvbox\footins
  \fi
  \ifr@ggedbottom \kern-\dimen@ \vfil \fi
  \ifvoid\copyins \else \vskip\skip\copyins \unvbox\copyins \fi
}
\def\makeheadline{%
  \leftskip=\z@
  \vbox{%
    \vbox to\headlineheight{\vss
      \hbox to\hsize{\hskip\z@ plus\hsize\the\headline}%
      \kern-\prevdepth
    }%
    \vskip\headlinespace
    \vskip-\topskip
  }%
  \nointerlineskip
}
\def\makefootline{%
  \relax\ifdim\prevdepth>\z@ \ifdim\prevdepth>\maxdepth \else
    \vskip-\prevdepth \fi\fi
  \nointerlineskip
  \vbox to\z@{\hbox{}%
    \baselineskip\dropfoliodepth
    \hbox to\hsize{\hskip\z@ plus\hsize\the\footline}%
    \vss}}

\message{hyphenation exceptions (U.S. English)}
\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 Brown-ian Eng-lish Euler-ian Feb-ru-ary Gauss-ian
Grothen-dieck Hamil-ton-ian Her-mit-ian Jan-u-ary Japan-ese Kor-te-weg
Le-gendre Lip-schitz Lip-schitz-ian Mar-kov-ian Noe-ther-ian
No-vem-ber Rie-mann-ian Schwarz-schild Sep-tem-ber}
\loadeufm \loadmsam \loadmsbm
\message{symbol names}\UseAMSsymbols\message{,}

%%   The following definition can be used to provide a \square for
%%   \qed in lieu of the normal \UseAMSsymbols route.
%%\define\square{\vrule width.6em height.5em depth.1em\relax}

\tenpoint


\W@{}
\csname amsppt.sty\endcsname
%% 
%% End of file `amsppt.sty'.

%    Then load specs that are shared between ams-m and ams-p.

\brokenpenalty=10000
\clubpenalty=10000
\widowpenalty=10000

\catcode`\@=11

%    Dummy definition of \keyboarder, for now [mjd,1995/04/03]
\def\keyboarder#1{}%

%    Page dimensions = 30pc x 50.5pc
\def\pagewidth#1{\hsize#1
  \captionwidth@24pc}

\pagewidth{30pc}

\parindent=18\p@
\normalparindent\parindent

\parskip=\z@

\def\foliofont@{\sevenrm}
\def\headlinefont@{\sevenpoint}

%  Heading styles are different from AMSPPT.STY:

\def\specialheadfont@{\elevenpoint\smc}
\def\headfont@{\bf}
\def\subheadfont@{\bf}
\def\refsheadfont@{\bf}
\def\abstractfont@{\smc}
\def\proclaimheadfont@{\smc}
\def\xcaheadfont@{\smc}
\def\captionfont@{\smc}
\def\citefont@{\bf}
\def\refsfont@{\eightpoint}

\font\sixsy=cmsy6

%    Added \msbfam and \eufmfam to all additional sizes so that \Bbb
%    and \frak can be used in titles, running heads.  [bnb, 1996/05/07]

%    Twelvepoint (12/14) used for titles
\font@\twelverm=cmr10 scaled \magstep1
\font@\twelvebf=cmbx10 scaled \magstep1
\font@\twelveit=cmti10 scaled \magstep1
\font@\twelvesl=cmsl10 scaled \magstep1
\font@\twelvesmc=cmcsc10 scaled \magstep1
\font@\twelvett=cmtt10 scaled \magstep1
\font@\twelvei=cmmi10 scaled \magstep1
\font@\twelvesy=cmsy10 scaled \magstep1
\font@\twelveex=cmex10 scaled \magstep1
\font@\twelvemsb=msbm10 scaled \magstep1
\font@\twelveeufm=eufm10 scaled \magstep1

\newtoks\twelvepoint@
\def\twelvepoint{\normalbaselineskip14\p@
  \abovedisplayskip12\p@ plus3\p@ minus9\p@
  \belowdisplayskip\abovedisplayskip
  \abovedisplayshortskip\z@ plus3\p@
  \belowdisplayshortskip7\p@ plus3\p@ minus4\p@
  \textonlyfont@\rm\twelverm \textonlyfont@\it\twelveit
  \textonlyfont@\sl\twelvesl \textonlyfont@\bf\twelvebf
  \textonlyfont@\smc\twelvesmc \textonlyfont@\tt\twelvett
  \ifsyntax@ \def\big##1{{\hbox{$\left##1\right.$}}}%
    \let\Big\big \let\bigg\big \let\Bigg\big
  \else
    \textfont\z@\twelverm  \scriptfont\z@\eightrm
       \scriptscriptfont\z@\sixrm
    \textfont\@ne\twelvei  \scriptfont\@ne\eighti
       \scriptscriptfont\@ne\sixi
    \textfont\tw@\twelvesy \scriptfont\tw@\eightsy
       \scriptscriptfont\tw@\sixsy
    \textfont\thr@@\twelveex \scriptfont\thr@@\eightex
        \scriptscriptfont\thr@@\eightex
    \textfont\itfam\twelveit \scriptfont\itfam\eightit
        \scriptscriptfont\itfam\eightit
    \textfont\bffam\twelvebf \scriptfont\bffam\eightbf
        \scriptscriptfont\bffam\sixbf
    \textfont\msbfam\twelvemsb \scriptfont\msbfam\eightmsb
        \scriptscriptfont\msbfam\sixmsb
    \textfont\eufmfam\twelveeufm \scriptfont\eufmfam\eighteufm
        \scriptscriptfont\eufmfam\sixeufm
    \setbox\strutbox\hbox{\vrule height8.5\p@ depth3.5\p@ width\z@}%
    \setbox\strutbox@\hbox{\lower.5\normallineskiplimit\vbox{%
        \kern-\normallineskiplimit\copy\strutbox}}%
    \setbox\z@\vbox{\hbox{$($}\kern\z@}\bigsize@1.2\ht\z@
  \fi
  \normalbaselines\rm\dotsspace@1.5mu\ex@.2326ex\jot3\ex@
  \the\twelvepoint@}

%    Elevenpoint (11/13) used for authors in proceedings.
\font@\elevenrm=cmr10 scaled \magstephalf
\font@\elevenbf=cmbx10 scaled \magstephalf
\font@\elevenit=cmti10 scaled \magstephalf
\font@\elevensl=cmsl10 scaled \magstephalf
\font@\elevensmc=cmcsc10 scaled \magstephalf
\font@\eleventt=cmtt10 scaled \magstephalf
\font@\eleveni=cmmi10 scaled \magstephalf
\font@\elevensy=cmsy10 scaled \magstephalf
\font@\elevenex=cmex10 scaled \magstephalf
\font@\elevenmsb=msbm10 scaled \magstephalf
\font@\eleveneufm=eufm10 scaled \magstephalf

\newtoks\elevenpoint@
\def\elevenpoint{\normalbaselineskip13\p@
  \abovedisplayskip12\p@ plus3\p@ minus9\p@
  \belowdisplayskip\abovedisplayskip
  \abovedisplayshortskip\z@ plus3\p@
  \belowdisplayshortskip7\p@ plus3\p@ minus4\p@
  \textonlyfont@\rm\elevenrm \textonlyfont@\it\elevenit
  \textonlyfont@\sl\elevensl \textonlyfont@\bf\elevenbf
  \textonlyfont@\smc\elevensmc \textonlyfont@\tt\eleventt
  \ifsyntax@ \def\big##1{{\hbox{$\left##1\right.$}}}%
    \let\Big\big \let\bigg\big \let\Bigg\big
  \else
    \textfont\z@\elevenrm  \scriptfont\z@\eightrm
       \scriptscriptfont\z@\sixrm
    \textfont\@ne\eleveni  \scriptfont\@ne\eighti
       \scriptscriptfont\@ne\sixi
    \textfont\tw@\elevensy \scriptfont\tw@\eightsy
       \scriptscriptfont\tw@\sixsy
    \textfont\thr@@\elevenex \scriptfont\thr@@\eightex
        \scriptscriptfont\thr@@\eightex
    \textfont\itfam\elevenit \scriptfont\itfam\eightit
        \scriptscriptfont\itfam\eightit
    \textfont\bffam\elevenbf \scriptfont\bffam\eightbf
        \scriptscriptfont\bffam\sixbf
    \textfont\msbfam\elevenmsb \scriptfont\msbfam\eightmsb
        \scriptscriptfont\msbfam\sixmsb
    \textfont\eufmfam\eleveneufm \scriptfont\eufmfam\eighteufm
        \scriptscriptfont\eufmfam\sixeufm
    \setbox\strutbox\hbox{\vrule height8.5\p@ depth3.5\p@ width\z@}%
    \setbox\strutbox@\hbox{\lower.5\normallineskiplimit\vbox{%
        \kern-\normallineskiplimit\copy\strutbox}}%
    \setbox\z@\vbox{\hbox{$($}\kern\z@}\bigsize@1.2\ht\z@
  \fi
  \normalbaselines\rm\dotsspace@1.5mu\ex@.2326ex\jot3\ex@
  \the\elevenpoint@}

\addto\tenpoint{\normalbaselineskip12\p@
 \abovedisplayskip6\p@ plus6\p@ minus0\p@
 \belowdisplayskip6\p@ plus6\p@ minus0\p@
 \abovedisplayshortskip0\p@ plus3\p@ minus0\p@
 \belowdisplayshortskip2\p@ plus3\p@ minus0\p@
 \ifsyntax@
 \else
  \setbox\strutbox\hbox{\vrule height9\p@ depth4\p@ width\z@}%
  \setbox\strutbox@\hbox{\vrule height8\p@ depth3\p@ width\z@}%
 \fi
 \normalbaselines\rm}

%    Add sevenpoint for running heads.
\newtoks\sevenpoint@
\def\sevenpoint{\normalbaselineskip9\p@
 \textonlyfont@\rm\sevenrm \textonlyfont@\it\sevenit
 \textonlyfont@\sl\sevensl \textonlyfont@\bf\sevenbf
 \textonlyfont@\smc\sevensmc \textonlyfont@\tt\seventt
  \textfont\z@\sevenrm \scriptfont\z@\sixrm
       \scriptscriptfont\z@\fiverm
  \textfont\@ne\seveni \scriptfont\@ne\sixi
       \scriptscriptfont\@ne\fivei
  \textfont\tw@\sevensy \scriptfont\tw@\sixsy
       \scriptscriptfont\tw@\fivesy
  \textfont\thr@@\sevenex \scriptfont\thr@@\sevenex
   \scriptscriptfont\thr@@\sevenex
  \textfont\itfam\sevenit \scriptfont\itfam\sevenit
   \scriptscriptfont\itfam\sevenit
  \textfont\bffam\sevenbf \scriptfont\bffam\sixbf
   \scriptscriptfont\bffam\fivebf
  \textfont\msbfam\sevenmsb \scriptfont\msbfam\sixmsb
   \scriptscriptfont\msbfam\fivemsb
  \textfont\eufmfam\seveneufm \scriptfont\eufmfam\sixeufm
   \scriptscriptfont\eufmfam\fiveeufm
 \setbox\strutbox\hbox{\vrule height7\p@ depth3\p@ width\z@}%
 \setbox\strutbox@\hbox{\raise.5\normallineskiplimit\vbox{%
   \kern-\normallineskiplimit\copy\strutbox}}%
 \setbox\z@\vbox{\hbox{$($}\kern\z@}\bigsize@1.2\ht\z@
 \normalbaselines\sevenrm\dotsspace@1.5mu\ex@.2326ex\jot3\ex@
 \the\sevenpoint@}

%    Differences from amsppt.sty:
%    - own skips above and below, not the same as \head
%    - centered, not flush left
\newskip\abovespecheadskip   \abovespecheadskip20\p@ plus8\p@ minus2\p@
\newdimen\belowspecheadskip  \belowspecheadskip6\p@
\outer\def\specialhead{%
  \add@missing\endroster \add@missing\enddefinition
  \add@missing\enddemo \add@missing\endexample
  \add@missing\endproclaim
  \penaltyandskip@{-200}\abovespecheadskip
  \begingroup\interlinepenalty\@M\rightskip\z@ plus\hsize
  \let\\\linebreak
  \specialheadfont@\raggedcenter@\noindent}
\def\endspecialhead{\endgraf\endgroup\nobreak\vskip\belowspecheadskip}

\let\varindent@\indent

\def\num#1{{\rm #1\enspace}}

%    Differences from amsppt.sty:
%    - no \penaltyandskip@ before
\let\subsubhead\relax
\outer\def\subsubhead{%
  \add@missing\endroster \add@missing\enddefinition
  \add@missing\enddemo
  \add@missing\endexample \add@missing\endproclaim
  \let\savedef@\subsubhead \let\subsubhead\relax
  \def\subsubhead##1\endsubsubhead{\restoredef@\subsubhead
      {\def\usualspace{\/{\subsubheadfont@\enspace}}%
    \subsubheadfont@##1\unskip\frills@{.\enspace}}\ignorespaces}%
  \nofrillscheck\subsubhead}

%    Indentation for \proclaim, \demo, etc., are the same as for
%    \subhead, and are taken care of by \varindent.
%    \proclaim head font is small caps, and the text font is italic
%    (not \sl). Vertical space only above proclaim, no added space to
%    other math environments.

\newskip\abstractindent 	\abstractindent=3pc
\long\def\block #1\endblock{\vskip 6pt
	{\leftskip=\abstractindent \rightskip=\abstractindent
	\noindent #1\endgraf}\vskip 6pt}

\long\def\ext #1\endext{\removelastskip\block #1\endblock}

\outer\def\xca{\let\savedef@\xca \let\xca\relax
  \add@missing\endproclaim \add@missing\endroster
  \add@missing\endxca \envir@stack\endxca
  \def\xca##1{\restoredef@\xca
    \penaltyandskip@{-100}\medskipamount
    \bgroup{\def\usualspace{{\xcaheadfont@\enspace}}%
      \varindent@\xcaheadfont@\ignorespaces##1\unskip
      \frills@{.\xcaheadfont@\enspace}}%
      \ignorespaces}%
  \nofrillscheck\xca}
\def\endxca{\egroup\revert@envir\endxca
  \par\medskip}

%    Differences from amsppt.sty:
%    - font is \smc, not \it
%    - good break point before
%    - skip after
\def\remarkheadfont@{\smc}
\def\remark{\let\savedef@\remark \let\remark\relax
  \add@missing\endroster \add@missing\endproclaim
  \envir@stack\endremark
  \def\remark##1{\restoredef@\remark
    \penaltyandskip@{-100}\medskipamount
    {\def\usualspace{{\remarkheadfont@\enspace}}%
     \varindent@\remarkheadfont@\ignorespaces##1\unskip
     \frills@{.\enspace}}\rm
    \ignorespaces}\nofrillscheck\remark}
\def\endremark{\par\revert@envir\endremark\medskip}

%    Differences from amsppt.sty:
%    - square is flush right
\def\qed{\ifhmode\unskip\nobreak\fi\hfill
  \ifmmode\square\else$\m@th\square$\fi}


%%%%%%

%    Expand rosters to three item levels
%    This is identical to code in ams-j.sty except for the width setting
%    of \rosteritemitemitemwd (here "iii"; "ii" in ams-j.sty).
\newdimen\rosteritemsep
\rosteritemsep=.5pc

\newdimen\rosteritemitemwd
\newdimen\rosteritemitemitemwd

\newbox\setwdbox
\setbox\setwdbox\hbox{0.}\rosteritemwd=\wd\setwdbox
\setbox\setwdbox\hbox{0.\hskip.5pc(c)}\rosteritemitemwd=\wd\setwdbox
\setbox\setwdbox\hbox{0.\hskip.5pc(c)\hskip.5pc(iii)}%
  \rosteritemitemitemwd=\wd\setwdbox

%    Differences from amsppt.sty:
%    - adds \itemitem, \itemitemitem
%    - omits \enspace before item label
%    - omits \smallskip following item
\def\roster{%
  \envir@stack\endroster
  \edef\leftskip@{\leftskip\the\leftskip}%
  \relaxnext@
  \rostercount@\z@% Initialize \rostercount@ to 0.
  \def\item{\FN@\rosteritem@}%
  \def\itemitem{\FN@\rosteritemitem@}%
  \def\itemitemitem{\FN@\rosteritemitemitem@}%
  \DN@{\ifx\next\runinitem\let\next@\nextii@
    \else\let\next@\nextiii@
    \fi\next@}%
  \DNii@\runinitem% If \runinitem occurs, \nextii@ must kill it off.
    {\unskip% This unskips any space before the original \roster.
     \DN@{\ifx\next[\let\next@\nextii@
       \else\ifx\next"\let\next@\nextiii@\else\let\next@\nextiv@\fi
       \fi\next@}%
     \DNii@[####1]{\rostercount@####1\relax
       \therosteritem{\number\rostercount@}~\ignorespaces}%
     \def\nextiii@"####1"{{\rm####1}~\ignorespaces}%
     \def\nextiv@{\therosteritem1\rostercount@\@ne~}%
     \par@\firstitem@false% Before doing any of this we still change
     \FN@\next@}%      End of definition of \nextii@\runinitem.
  \def\nextiii@{\par\par@% End the present paragraph, change \everypar
    \penalty\@m\vskip-\parskip
    \firstitem@true}%
  \FN@\next@}

%    Differences from amsppt.sty:
%    - \leftskip = .5pc, not .5em
\def\rosteritem@{\iffirstitem@\firstitem@false
  \else\par\vskip-\parskip
  \fi
  \leftskip\rosteritemwd \advance\leftskip\normalparindent
  \advance\leftskip.5pc \noindent
  \DNii@[##1]{\rostercount@##1\relax\itembox@}%
  \def\nextiii@"##1"{\def\therosteritem@{\rm##1}\itembox@}%
  \def\nextiv@{\advance\rostercount@\@ne\itembox@}%
  \def\therosteritem@{\therosteritem{\number\rostercount@}}%
  \ifx\next[\let\next@\nextii@
  \else\ifx\next"\let\next@\nextiii@\else\let\next@\nextiv@\fi
  \fi\next@}

%    Differences from amsppt.sty:
%    - \skip after label = .5pc, not \enspace
\def\itembox@{\llap{\hbox to\rosteritemwd{\hss
  \kern\z@ % kern to thwart \unskip in \rom
  \therosteritem@}\hskip.5pc}\ignorespaces}

%    Differences from amsppt.sty:
%    - period after, no parentheses around label
\def\therosteritem#1{\rom{\ignorespaces#1.\unskip}}

%    Two new levels.
\def\rosteritemitem@{\iffirstitem@\firstitem@false
  \else\par\vskip-\parskip
  \fi
  \leftskip\rosteritemitemwd \advance\leftskip\normalparindent
  \advance\leftskip.5pc \noindent
  \DNii@[##1]{\rostercount@##1\relax\itemitembox@}%
  \def\nextiii@"##1"{\def\therosteritemitem@{\rm##1}\itemitembox@}%
  \def\nextiv@{\advance\rostercount@\@ne\itemitembox@}%
  \def\therosteritemitem@{\therosteritemitem{\number\rostercount@}}%
  \ifx\next[\let\next@\nextii@
  \else\ifx\next"\let\next@\nextiii@\else\let\next@\nextiv@\fi
  \fi\next@}

\def\itemitembox@{\llap{\hbox to\rosteritemitemwd{\hss
  \kern\z@ % kern to thwart \unskip in \rom
  \therosteritemitem@}\hskip.5pc}\ignorespaces}

\def\therosteritemitem#1{\rom{(\ignorespaces#1\unskip)}}

\def\rosteritemitemitem@{\iffirstitem@\firstitem@false
  \else\par\vskip-\parskip
  \fi
  \leftskip\rosteritemitemitemwd \advance\leftskip\normalparindent
  \advance\leftskip.5pc \noindent
  \DNii@[##1]{\rostercount@##1\relax\itemitemitembox@}%
  \def\nextiii@"##1"{\def\therosteritemitemitem@{\rm##1}\itemitemitembox@}%
  \def\nextiv@{\advance\rostercount@\@ne\itemitemitembox@}%
  \def\therosteritemitemitem@{\therosteritemitemitem{\number\rostercount@}}%
  \ifx\next[\let\next@\nextii@
  \else\ifx\next"\let\next@\nextiii@\else\let\next@\nextiv@\fi
  \fi\next@}

\def\itemitemitembox@{\llap{\hbox to\rosteritemitemitemwd{\hss
  \kern\z@ % kern to thwart \unskip in \rom
  \therosteritemitemitem@}\hskip.5pc}\ignorespaces}

\def\therosteritemitemitem#1{\rom{(\ignorespaces#1\unskip)}}

\def\endroster{\relaxnext@
  \revert@envir\endroster % restore \envir@end
  \par\leftskip@% End the paragraph, and restore the \leftskip.
  \penalty-50 % \vskip-\parskip% Add a good break
  \DN@{\ifx\next\Runinitem\let\next@\relax
    \else\nextRunin@false\let\item\plainitem@% Otherwise, set
      \ifx\next\par% moreover, if \endroster is followed by \par,
        \DN@\par{\everypar\expandafter{\the\everypartoks@}}%
      \else% but if the \endroster isn't followed by a new paragraph,
        \DN@{\noindent\everypar\expandafter{\the\everypartoks@}}%
      \fi
    \fi\next@}%
  \FN@\next@}

%%%%%%%%%%

%    Differences with amsppt.sty (all address-related items):
%    - break not suppressed before \address
%    - \addressfont@ specified
\def\address#1\endaddress{\global\advance\addresscount@\@ne
  \expandafter\gdef\csname address\number\addresscount@\endcsname
  {\vskip12\p@ minus6\p@\indent\addressfont@\smc\ignorespaces#1\par}}

%  Current addresses as well as permanent ones must be accommodated.
%  Check on the skip before the address; it may be a fixed 6pt.
%  \smallskip has been assumed before the current address, as that
%  is what has been used for \email.

\def\curraddr{\let\savedef@\curraddr
  \def\curraddr##1\endcurraddr{\let\curraddr\savedef@
  \toks@\expandafter\expandafter\expandafter{%
       \csname address\number\addresscount@\endcsname}%
  \toks@@{##1}%
  \expandafter\xdef\csname address\number\addresscount@\endcsname
  {\the\toks@\endgraf\noexpand\nobreak
    \indent\noexpand\addressfont@{\noexpand\rm
    \frills@{{\noexpand\it Current address\noexpand\/}:\space}%
    \def\noexpand\usualspace{\space}\the\toks@@\unskip}}}%
  \nofrillscheck\curraddr}

\def\email{\let\savedef@\email
  \def\email##1\endemail{\let\email\savedef@
  \toks@{\def\usualspace{{\it\enspace}}\endgraf\indent\addressfont@}%
  \toks@@{{\tt ##1}\par}%
  \expandafter\xdef\csname email\number\addresscount@\endcsname
  {\the\toks@\frills@{{\noexpand\it E-mail address\noexpand\/}:%
     \noexpand\enspace}\the\toks@@}}%
  \nofrillscheck\email}


\def\rom#1{{\rm #1}}

%    Differences from amsppt.sty:
%    - rule is 2pc, not 3em
\def\bysame{\by\hbox to2pc{\hrulefill}\thinspace\kern\z@}

%    Differences from amsppt.sty:
%    - indent differs in style B
\def\refstyle#1{\uppercase{%
  \gdef\refstyle@{#1}%
  \if#1A\relax \def\keyformat##1{[##1]\enspace\hfil}%
  \else\if#1B\relax
    \refindentwd2pc
    \def\keyformat##1{\aftergroup\kern
              \aftergroup-\aftergroup\refindentwd}%
  \else\if#1C\relax
    \refindentwd30pt \refafterindentwd39pt
    \def\keyformat##1{\hfil##1.\enspace}%
  \fi\fi\fi}% end of \uppercase
}

\refstyle{C}




\catcode`\@=11

%    Heading styles are different from AMSPPT.STY:

\def\addressfont@{\tenpoint}

\skip\footins=\bigskipamount % space added when footnote is present

%  \titlefont is 14/18 (in ams-p.sty it is 12/14)
\font@\titlebf=cmbx10 scaled \magstep2	% 14/18
\font@\titlei=cmmi10 scaled \magstep2
\font@\titlesy=cmsy10 scaled \magstep2
\font@\titlemsb=msbm10 scaled \magstep2
\font@\titleeufm=eufm10 scaled \magstep2
\def\titlefont{\normalbaselineskip18\p@
  \textonlyfont@\bf\titlebf
  \ifsyntax@\else
    \textfont\z@\titlebf  \scriptfont\z@\tenbf  \scriptscriptfont\z@\sevenbf
    \textfont\@ne\titlei  \scriptfont\@ne\teni  \scriptscriptfont\@ne\seveni
    \textfont\tw@\titlesy \scriptfont\tw@\tensy \scriptscriptfont\tw@\sevensy
    \textfont\thr@@\tenex \scriptfont\thr@@\tenex \scriptscriptfont\thr@@\tenex
    \textfont\msbfam\titlemsb \scriptfont\msbfam\tenmsb
      \scriptscriptfont\msbfam\sevenmsb
    \textfont\eufmfam\titleeufm \scriptfont\eufmfam\teneufm
      \scriptscriptfont\eufmfam\seveneufm
  \fi
  \normalbaselines\titlebf}

%  added \specialpart to allow suppression of ``Part n'' element; bnb, 30May96
\newif\ifpart	\partfalse
\newif\ifspecialpart  \specialpartfalse

\font\partnofont=cmbx10 scaled \magstep3
%  \partfont is 20/25
%  amplified \partfont to accommodate math; bnb, 21Sep96
%\font\partfont=cmbx10 scaled \magstep4
\font@\partbf=cmbx10 scaled \magstep4
\font@\parti=cmmi10 scaled \magstep4
\font@\partsy=cmsy10 scaled \magstep4
\font@\partmsb=msbm10 scaled \magstep4
\font@\parteufm=eufm10 scaled \magstep4
\def\partfont{\normalbaselineskip25\p@
  \textonlyfont@\bf\partbf
  \ifsyntax@\else
    \textfont\z@\partbf  \scriptfont\z@\titlebf  \scriptscriptfont\z@\tenbf
    \textfont\@ne\parti  \scriptfont\@ne\titlei  \scriptscriptfont\@ne\teni
    \textfont\tw@\partsy \scriptfont\tw@\titlesy \scriptscriptfont\tw@\tensy
    \textfont\thr@@\tenex \scriptfont\thr@@\tenex \scriptscriptfont\thr@@\tenex
    \textfont\bffam\partbf \scriptfont\bffam\titlebf
      \scriptscriptfont\bffam\tenbf
    \textfont\msbfam\partmsb \scriptfont\msbfam\titlemsb
      \scriptscriptfont\msbfam\tenmsb
    \textfont\eufmfam\parteufm \scriptfont\eufmfam\titleeufm
      \scriptscriptfont\eufmfam\teneufm
  \fi
  \normalbaselines\partbf}

%  To get proper inter-word spacing, \raggedcenter@ must follow font change.
\def\part#1\\#2\endpart{\global\parttrue
  \gdef\thepart{\def\\{\hfil\break}%
    {\partnofont\raggedcenter@ \ifspecialpart\null \else Part #1\fi \endgraf}%
    \vskip 20pt
    {\partfont\raggedcenter@ #2\endgraf}}%
  }

\def\specialpart#1\endspecialpart{%
  \global\specialparttrue
  \part\\#1\endpart}

\def\title#1\endtitle{%
  \global\setbox\titlebox@\vtop{\titlefont
   \raggedcenter@
   #1\endgraf}%
 \ifmonograph@ \edef\next{\the\leftheadtoks}%
    \ifx\next\empty@
    \leftheadtext{#1}\fi
 \fi
 \edef\next{\the\rightheadtoks}\ifx\next\empty@ \rightheadtext{#1}\fi
 }

% chapter heading in ten point

\def\romanchapternum{\gdef\chapterno@{\uppercase\expandafter{\romannumeral
    \chaptercount@}}}

\def\chapterno@{\the\chaptercount@}

\def\chapter{\let\savedef@\chapter
  \def\chapter##1{\let\chapter\savedef@
  \leavevmode\hskip-\leftskip
   \rlap{\vbox to\z@{\vss\centerline{\tenpoint
   \frills@{CHAPTER\space\afterassignment\chapterno@
       \global\chaptercount@=}%
   ##1\unskip}\baselineskip36pt\null}}\hskip\leftskip}%
 \nofrillscheck\chapter}


%  authors are set in all caps

\def\author{\let\savedef@\author
  \def\author##1\endauthor{\global\setbox\authorbox@
 \vbox{\tenpoint\raggedcenter@
  \frills@{\ignorespaces##1}\endgraf}
 \edef\next{\the\leftheadtoks}%
 \ifx\next\empty@\expandafter\uppercase{\leftheadtext{##1}}\fi}
\nofrillscheck\author}

%  \abstract differs from the one in AMSPPT.STY by the use of a slightly
%  larger indentation.

\def\abstract{\let\savedef@\abstract
 \def\abstract{\let\abstract\savedef@
  \setbox\abstractbox@\vbox\bgroup\noindent$$\vbox\bgroup\indenti=0pt
  \def\envir@end{\endabstract}\advance\hsize-2\indenti
  \def\usualspace{\enspace}\tenpoint \noindent
  \frills@{{\abstractfont@ Abstract.\enspace}}}%
 \nofrillscheck\abstract}


\def\thanks#1\endthanks{%
  \gdef\thethanks@{{\tenpoint#1\endgraf}}}

\def\keywords{\let\savedef@\keywords
  \def\keywords##1\endkeywords{\let\keywords\savedef@
  \toks@{\def\usualspace{{\it\enspace}}\raggedcenter@\tenpoint}%
  \toks@@{##1\unskip.\endgraf}%
  \edef\thekeywords@{{\the\toks@\frills@{{\noexpand\it
    Key words and phrases.\noexpand\enspace}}\the\toks@@}}}%
 \nofrillscheck\keywords}

\def\subjclass{\let\savedef@\subjclass
 \def\subjclass##1\endsubjclass{\let\subjclass\savedef@
   \toks@{\def\usualspace{{\rm\enspace}}\tenpoint\raggedcenter@}%
   \toks@@{##1\unskip.\endgraf}%
   \edef\thesubjclass@{{\the\toks@
     \frills@{{\noexpand\rm1991 {\noexpand\it Mathematics Subject
       Classification}.\noexpand\enspace}}%
     \the\toks@@}}}%
  \nofrillscheck\subjclass}

%  More generous skips above some section headings, not as much shrink.
\abovespecheadskip=24\p@ plus12\p@ minus\z@
\aboveheadskip=12\p@ plus4\p@ minus2\p@
\subheadskip=6\p@ plus2\p@ minus\z@

\newskip\xcskip   \newskip\afterxcskip
\xcskip=10pt plus2pt minus0pt
\afterxcskip=0pt
\long\def\xcb#1{\par\ifnum\lastskip<\xcskip
  \removelastskip\penalty-100\vskip\xcskip\fi
  \noindent{\bf#1}%
  \nobreak\bgroup
  \xcbrosterdefs}

\def\xcbrosterdefs{\normalparindent=0pt
\setbox\setwdbox\hbox{0.}\rosteritemwd=\wd\setwdbox\relax
  \setbox\setwdbox\hbox{0.\hskip.5pc(c)}\rosteritemitemwd=\wd\setwdbox\relax
  \setbox\setwdbox\hbox{0.\hskip.5pc(c)\hskip.5pc(iii)}%
	\rosteritemitemitemwd=\wd\setwdbox\relax
}

\def\endxcb{\par\egroup}

\outer\def\endtopmatter{\add@missing\endabstract
  \edef\next{\the\leftheadtoks}%
  \ifx\next\empty@
    \expandafter\leftheadtext\expandafter{\the\rightheadtoks}%
  \fi
  \ifpart
%	%  AMS-LaTeX spacing: \null\vfil\thepart\vfil\vfil\newpage
%	%  Fix this at the same distance as a part with 1-line title.
    \global\plain@true
    \null\vskip146\p@
    \thepart
    \vfill\eject
    \null\vfill\eject
  \fi
  \global\plain@false
  \global\firstpage@true
  \begingroup % to localize variant topskip
    \topskip90\p@
    \box\titlebox@
  \endgroup
  \ifvoid\authorbox@\else \vskip2.5pc plus1pc\unvbox\authorbox@\fi
  \ifnum\addresscount@>\z@
    \vfill
    Author address\ifnum\addresscount@>1 es\fi:
    \count@\z@
    \loop\ifnum\count@<\addresscount@\advance\count@\@ne
      \csname address\number\count@\endcsname
      \csname email\number\count@\endcsname
    \repeat
    \vfill\eject
  \fi
  \ifvoid\affilbox@\else \vskip1pcplus\unvbox\affilbox@\fi
  \ifx\thesubjclass@\empty@\else \vfil\thesubjclass@\fi
  \ifx\thekeywords@\empty@\else \vfil\thekeywords@\fi
  \ifx\thethanks@\empty@\else \vfil\thethanks@\fi
  \ifvoid\abstractbox@\else \vfil\unvbox\abstractbox@\vfil\eject \fi
  \ifvoid\tocbox@\else \vskip1.5pcplus.5pc\unvbox\tocbox@\fi
  \prepaper
  \vskip22pt\relax
}

\def\raggedleft@{\leftskip\z@ plus.4\hsize \rightskip\z@
  \parfillskip\z@ \parindent\z@ \spaceskip.3333em \xspaceskip.5em
  \pretolerance9999\tolerance9999 \exhyphenpenalty\@M
  \hyphenpenalty\@M \let\\\linebreak}

\def\aufm #1\endaufm{\vskip-\prevdepth
  \vskip12pt{\raggedleft@ #1\endgraf}}

\widestnumber\key{M} % set default lettered ref style

%%%% table of contents

\begingroup
\let\head\relax \let\specialhead\relax \let\subhead\relax
\let\subsubhead\relax \let\title\relax \let\chapter\relax
\newbox\tocchapbox@

\gdef\newtocdefs{%
  \def\ptitle##1\endptitle
       {\penalty\z@ \vskip8\p@
        \hangindent\wd\tocheadbox@\noindent{\bf ##1}\endgraf}%
  \def\title##1\endtitle
       {\penalty\z@ \vskip8\p@
        \hangindent\wd\tocchapbox@\noindent{##1}\endgraf}%
  \def\chapter##1{\par
        Chapter ##1.\unskip\enspace}%
  \def\part##1{\par
        {\bf Part ##1.}\unskip\enspace}%
  \def\specialhead##1 ##2\endspecialhead{\par
    \begingroup \hangindent.5em \noindent
    \if\notempty{##1}%
      \leftskip\wd\tocheadbox@
      \llap{\hbox to\wd\tocheadbox@{\hfil##1}}\enspace
    \else
      \leftskip\parindent
    \fi
    ##2\endgraf
    \endgroup}%
  \def\head##1 ##2\endhead{\par
    \begingroup \hangindent.5em \noindent
    \if\notempty{##1}%
      \leftskip\wd\tocheadbox@
      \llap{\hbox to\wd\tocheadbox@{\hfil##1}}\enspace
    \else
      \leftskip\parindent
    \fi
    ##2\endgraf
    \endgroup}%
%    Added subhead and subsubhead to prevent \widestnumber error.
%    Style for these in the toc is unspecified; just provide something
%    ad hoc for now. [mjd,1995/03/28]
%    modify sub(sub)heads so that extra lines are hangindented [bnb,1996/07/03]
  \def\subhead##1 ##2\endsubhead{\par
    \begingroup \leftskip4.5pc
    \noindent\llap{##1\enspace}##2\endgraf \endgroup}%
  \def\subsubhead##1 ##2\endsubsubhead{\par
    \begingroup \leftskip7pc
    \noindent\llap{\hss##1\enspace}##2\endgraf \endgroup}%
}%
\gdef\toc@#1{\relaxnext@
  \DN@{\ifx\next\nofrills\DN@\nofrills{\nextii@}%
      \else\DN@{\nextii@{{#1}}}%
      \fi
      \next@}%
  \DNii@##1{%
    \ifmonograph@\bgroup
    \else\setbox\tocbox@\vbox\bgroup
      \centerline{\headfont@\ignorespaces##1\unskip}\nobreak
      \vskip\belowheadskip
    \fi
    \def\page####1%
       {\unskip\penalty\z@\null\hfil
        \rlap{\hbox to\pagenumwd{\quad\hfil\rm ####1}}%
    \global\setbox\tocchapbox@\hbox{Chapter 1.\enspace}%
    \global\setbox\tocheadbox@\hbox{\hskip18pt \S0.0.}%
         \hfilneg\penalty\@M}%
    \leftskip\z@ \rightskip\leftskip
    \setboxz@h{\bf\quad000}\pagenumwd\wd\z@
    \advance\rightskip\pagenumwd
    \newtocdefs
    }%
  \FN@\next@
}%
\endgroup

\def\logo@{}

\def\makefootline{\baselineskip18\p@\line{\the\footline}}

\Monograph

\catcode`\@=13

\def\amsversion{2.1c}

\catcode`\@=11

\def\pretitle{\vskip84pt}

\aboveheadskip=12\p@ plus 9\p@

\newskip\abovesubheadskip
\abovesubheadskip=9\p@ plus 6\p@


\newskip\abovesubsubheadskip
\abovesubsubheadskip=6\p@ plus 6\p@

\belowheadskip=6\p@

%  Page numbers and running heads are provided by default, as defined
%  in AMSPPT.STY.  Headline text is centered, and page numbers are
%  positioned at the outside corners.  To suppress page numbers and/or
%  running heads, include \NoPageNumbers and/or \NoRunningHeads in the
%  input file, as appropriate.

\def\foliofont@{\eightbf}
\def\headlinefont@{\eightpoint}           %DF

\newif\iflecture@ \lecture@false

\newif\ifLogoOn  \LogoOnfalse
\def\LogoOn{\global\LogoOntrue
  \def\inslogo@{\insert\copyins{\logo@}}%
  }

\def\Monograph{\monograph@true
  \nologo \nojourlogo
  \let\headmark\rightheadtext
  \let\varindent@\noindent
  \def\abstractfont@{\bf}
  \def\addressfont@{\tenpoint}
  \def\specialheadfont@{\twelvepoint\bf}%
  \def\headfont@{\elevenpoint\bf}%
  \def\proclaimheadfont@{\bf}%
  \def\remarkheadfont@{\bf}}


%  Heading styles are different from AMSPPT.STY:

\def\subheadfont@{\bf}
\def\refheadfont@{\headfont@}

\outer\def\specialhead{%
  \add@missing\endroster \add@missing\enddefinition
  \add@missing\enddemo \add@missing\endexample
  \add@missing\endproclaim
  \penaltyandskip@{-200}\abovespecheadskip
  \begingroup\interlinepenalty\@M\rightskip\z@ plus\hsize
  \let\\\linebreak
  \specialheadfont@\raggedright\noindent}
\def\endspecialhead{\endgraf\endgroup\nobreak\vskip\belowspecheadskip\noindent}


\font@\fourteenrm=cmr10 scaled \magstep2
\font@\fourteenbf=cmbx10 scaled \magstep2
\font@\fourteenit=cmti10 scaled \magstep2
\font@\fourteensl=cmsl10 scaled \magstep2
\font@\fourteensmc=cmcsc10 scaled \magstep2
\font@\fourteentt=cmtt10 scaled \magstep2
\font@\fourteeni=cmmi10 scaled \magstep2
\font@\fourteensy=cmsy10 scaled \magstep2
\font@\fourteenex=cmex10 scaled \magstep2

\newtoks\fourteenpoint@
\def\fourteenpoint{\normalbaselineskip16\p@
 \abovedisplayskip12\p@ plus3\p@ minus9\p@
 \belowdisplayskip\abovedisplayskip
 \abovedisplayshortskip\z@ plus3\p@
 \belowdisplayshortskip7\p@ plus3\p@ minus4\p@
 \textonlyfont@\rm\fourteenrm \textonlyfont@\it\fourteenit
 \textonlyfont@\sl\fourteensl \textonlyfont@\bf\fourteenbf
 \textonlyfont@\smc\fourteensmc \textonlyfont@\tt\fourteentt
 \ifsyntax@ \def\big##1{{\hbox{$\left##1\right.$}}}%
  \let\Big\big \let\bigg\big \let\Bigg\big
 \else
   \textfont\z@\fourteenrm  \scriptfont\z@\tenrm
       \scriptscriptfont\z@\eightrm
   \textfont\@ne\fourteeni  \scriptfont\@ne\teni
       \scriptscriptfont\@ne\eighti
   \textfont\tw@\fourteensy \scriptfont\tw@\tensy
       \scriptscriptfont\tw@\eightsy
   \textfont\thr@@\fourteenex \scriptfont\thr@@\tenex
        \scriptscriptfont\thr@@\tenex
   \textfont\itfam\fourteenit \scriptfont\itfam\tenit
        \scriptscriptfont\itfam\tenit
   \textfont\bffam\fourteenbf \scriptfont\bffam\tenbf
        \scriptscriptfont\bffam\eightbf
   \setbox\strutbox\hbox{\vrule height8.5\p@ depth3.5\p@ width\z@}%
   \setbox\strutbox@\hbox{\lower.5\normallineskiplimit\vbox{%
        \kern-\normallineskiplimit\copy\strutbox}}%
   \setbox\z@\vbox{\hbox{$()$}\kern\z@}\bigsize@1.2\ht\z@
  \fi
  \normalbaselines\rm\dotsspace@1.5mu\ex@.2326ex\jot3\ex@
  \the\fourteenpoint@}


\font@\titlebf=cmbx10 scaled \magstep3  % 17/22
\font@\titlei=cmmi10 scaled \magstep3
\font@\titlesy=cmsy10 scaled \magstep3
\def\titlefont{\normalbaselineskip22\p@
 \textonlyfont@\bf\titlebf
 \ifsyntax@\else
  \textfont\z@\titlebf  \scriptfont\z@\tenbf  \scriptscriptfont\z@\sevenbf
  \textfont\@ne\titlei  \scriptfont\@ne\teni  \scriptscriptfont\@ne\seveni
  \textfont\tw@\titlesy \scriptfont\tw@\tensy \scriptscriptfont\tw@\sevensy
  \textfont\thr@@\tenex \scriptfont\thr@@\tenex \scriptscriptfont\thr@@\tenex
 \fi
 \normalbaselines\titlebf}

\def\raggedleft{\leftskip\z@ plus 1fil
\parfillskip\z@ \parindent\z@ \spaceskip\z@ \xspaceskip\z@
 \pretolerance9999\tolerance9999 \exhyphenpenalty\@M}

\def\raggedright{\rightskip\z@ plus 1fil
\parfillskip\z@ \parindent\z@ \spaceskip\z@ \xspaceskip\z@
 \pretolerance9999\tolerance9999 \exhyphenpenalty\@M}


\newif\ifpart   \partfalse

\newif\ifNoNewpage \NoNewpagefalse
\def\NoNewPage{\NoNewpagetrue}

\font\partnofont=cmbx10 scaled \magstep1
\font\partfont=cmbx10 scaled \magstep3

\def\partno#1{{\titlefont Part #1}}

\def\part#1\\#2\endpart{\global\parttrue
  \gdef\thepart{\def\\{\break}%
    {\raggedleft
     \noindent\partnofont PART #1\unskip\vskip5pt
     \partfont\baselineskip=25pt
     \noindent#2\unskip\break\endgraf}}}

\def\series #1\endseries{\global\parttrue
  \def\sauth ##1\endsauth{\gdef\thesauth{{%
                \fourteenpoint\bf ##1\unskip\endgraf}}}%
  \gdef\thepart{\def\\{\break}%
    {\raggedleft
     \partfont\baselineskip=25pt
     \noindent#1\unskip\vskip\baselineskip
     \if\notempty{\thesauth}%
       \thesauth
     \fi
     \endgraf}}}

\newif\ifContents \Contentsfalse
\def\contents{\global\Contentstrue}

\setbox\titlebox@\vbox{}

\def\title#1\endtitle{%
  \def\\{\break}%
  \global\setbox\titlebox@\vtop{\titlefont
   \ifodd\pageno
     \ifContents\raggedright
     \else\raggedleft
     \fi
   \else\raggedright
   \fi
   \noindent#1\unskip\break}%
 \ifmonograph@ \edef\next{\the\leftheadtoks}%
    \ifx\next\empty
    \leftheadtext{#1}\fi
 \fi
 \edef\next{\the\rightheadtoks}\ifx\next\empty \rightheadtext{#1}\fi
 }

\def\shortauthtitle #1\endshortauthtitle{%       %DF 
  \leftheadtext{\uppercase{\ignorespaces#1\unskip}}}

\def\thelecture{}
\def\thelecturelabel{Lecture}                     %DF
\def\thenewlecturelabel{Lecture}                     %DF
\def\lecturelabel#1{\def\thenewlecturelabel{#1}}  %DF   (to get headings right)
\def\lecture#1{%
  \ifNoNewpage\else\vfill\eject\fi               %DF
  \global\lecture@true
  \gdef\lectnomark{#1}%
  \gdef\thelecture{%
    \begingroup\raggedleft
      \twelvepoint\bf
      \expandafter\uppercase\expandafter{\thelecturelabel}
      {\fourteenbf #1\unskip}\break
  }}

\def\lecturename #1\endlecturename{%
  \gdef\lectnamemark{#1}%
  \gdef\shortlectnamemark{\uppercase{\ignorespaces#1\unskip}}%          %DF
  \gdef\thelecturename{%
      \def\\{\break}%
      \baselineskip=16pt #1\unskip\endgraf
    \endgroup}}

\def\shortlecturename #1\endshortlecturename{%  %DF
  \gdef\shortlectnamemark{\uppercase{\ignorespaces#1\unskip}}}          %DF

\def\chapter{\let\savedef@\chapter
  \def\chapter##1{\let\chapter\savedef@
  \leavevmode\hskip-\leftskip
   \rlap{\vbox to\z@{\vss
   \ifodd\pageno
   \rightline{\twelvepoint\bf
   \frills@{CHAPTER\fourteenpoint\bf\space\afterassignment\chapterno@
       \global\chaptercount@=}%
   ##1\unskip}%
   \else
   \leftline{\twelvepoint
   \frills@{CHAPTER\fourteenpoint\bf\space\afterassignment\chapterno@
       \global\chaptercount@=}%
   ##1\unskip}%
   \fi
\baselineskip44pt\null}}\hskip\leftskip}%
 \nofrillscheck\chapter}


\def\author{\let\savedef@\author
  \def\author##1\endauthor{\global\setbox\authorbox@\vbox{%
        \fourteenpoint\bf\raggedleft
  \ignorespaces##1\unskip\break\endgraf}%
 \edef\next{\the\leftheadtoks}%
 \ifx\next\empty{\leftheadtext{##1}}\fi}\author}

\def\address#1\endaddress{%
  \global\advance\addresscount@\@ne
  \expandafter\gdef\csname address\number\addresscount@\endcsname
  {{\ignorespaces#1\unskip}}}

%  Current addresses as well as permanent ones must be accommodated.
%  Check on the skip before the address; it may be a fixed 6pt.

\def\email{\let\savedef@\email
  \def\email##1\endemail{\let\email\savedef@
  \toks@{\def\usualspace{{\bf\enspace}}}%
  \toks@@{{\tt ##1\unskip}}%
  \expandafter\xdef\csname email\number\addresscount@\endcsname
  {\endgraf\noindent\the\toks@\frills@{{\noexpand\bf E-mail address
        \noexpand\/}\rm :%
     \noexpand\enspace}\the\toks@@}}%
  \nofrillscheck\email}


\def\curraddr{\let\savedef@\curraddr
  \def\curraddr##1\endcurraddr{\let\curraddr\savedef@
  \toks@\expandafter\expandafter\expandafter{%
       \csname address\number\addresscount@\endcsname}%
  \toks@@{##1\unskip}%
  \expandafter\xdef\csname address\number\addresscount@\endcsname
  {\the\toks@\endgraf\noindent
    {\noexpand\rm
    \frills@{{\noexpand\bf Current address\noexpand\/}:\space}%
    \def\noexpand\usualspace{\space}\the\toks@@\unskip}}}%
  \nofrillscheck\curraddr}


\def\setaddress@{%
% \iflecture@\else\vfill\eject\fi        %COMMENTED OUT BY DF
{\parskip=0pt\ifnum\addresscount@>\z@
 \count@\z@ \loop\ifnum\count@<\addresscount@\advance\count@\@ne
 \makefootnote@{$^{\number\count@}$}%
        {\csname address\number\count@\endcsname
        \csname email\number\count@\endcsname}%
 \repeat
\fi
}\adjustfootnotemark{\number\addresscount@}
\addresscount@\z@}			%ADDED BY DF


\outer\def\head#1\endhead{%
  \add@missing\endroster \add@missing\enddefinition
  \add@missing\enddemo \add@missing\endexample
  \add@missing\endproclaim
  \penaltyandskip@{-200}\aboveheadskip
  {\headfont@\interlinepenalty\@M
  \noindent #1\unskip\endgraf}\iflecture@\else\headmark{#1}\fi%
  \penalty10000
  \parskip=\belowheadskip\noindent\parskip0pt\relax}


\outer\def\subhead#1\endsubhead{%
  \add@missing\endroster \add@missing\enddefinition
  \add@missing\enddemo \add@missing\endexample
  \add@missing\endproclaim
  \par
  \ifdim\lastskip=\belowheadskip\else
          \penaltyandskip@{-200}\abovesubheadskip\fi
  {\subheadfont@\interlinepenalty\@M
  \noindent #1\unskip\endgraf}%
  \penalty999
  \parskip=\belowheadskip\noindent\parskip0pt\relax}


\let\subsubhead\relax
\def\subsubhead{%
  \add@missing\endroster \add@missing\enddefinition
  \add@missing\enddemo
  \add@missing\endexample \add@missing\endproclaim
  \let\savedef@\subsubhead \let\subsubhead\relax
  \def\subsubhead##1\endsubsubhead{\restoredef@\subsubhead
  \par
  \ifdim\lastskip=\belowheadskip\else
          \penaltyandskip@{-50}\abovesubsubheadskip\fi
      {\def\usualspace{\/{\it\enspace}}%
    \noindent \it##1\unskip\frills@{.\enspace}}}%
  \nofrillscheck\subsubhead}

\def\endtopmatter{\add@missing\endabstract
  \edef\next{\the\leftheadtoks}%
  \ifx\next\empty
    \expandafter\leftheadtext\expandafter{\the\rightheadtoks}%
  \fi
  \ifpart
     \partfalse				% DF
     \global\plain@true
     \null\vskip11pc
     \thepart
     \vfill\eject
     \null\vfill\eject
     \global\firstpage@true	%DF
  \fi
  \global\plain@false
  \ifLogoOn
     \inslogo@ \let\logo@=\relax   %DF
  \fi
  \iflecture@                            %DF
    \ifNoNewpage\NoNewpagefalse\else     %DF
    \ifodd\pageno\global\firstpage@true  %DF
    \else\plain@true\null\vfill\eject    %DF
    \global\plain@false\global\firstpage@true    %DF
  \fi\fi  % DF 
  \fi
  \let\thelecturelabel\thenewlecturelabel    %DF      (to get headings right)
  \null\pretitle
  \box\titlebox@
  \topskip10pt
  \ifvoid\authorbox@
  \else
     \ifLogoOn \vskip-.8\baselineskip \else \vskip5pt\fi
     \unvbox\authorbox@
  \fi
  \ifLogoOn
     \vskip13pt
  \else
     \iflecture@ \vskip4pt \fi
  \fi
  \iflecture@
     \ifLogoOn\else\vskip12pt\fi
     \thelecture
     \thelecturename
     \rightheadtext{\uppercase\expandafter{\thelecturelabel\  %   %DF
     \lectnomark.\ \shortlectnamemark}}%  %DF 
  \fi
  \ifnum\addresscount@>\z@
     \setaddress@
  \fi
  \ifvoid\affilbox@
  \else
        \vskip1pcplus\unvbox\affilbox@
  \fi
  \ifx\thesubjclass@\empty\else \vfil\thesubjclass@\fi
  \ifx\thekeywords@\empty\else \vfil\thekeywords@\fi
  \ifx\thethanks@\empty\else \vfil\thethanks@\fi
  \ifvoid\abstractbox@\else \vfil\unvbox\abstractbox@\vfil\eject \fi
  \ifvoid\tocbox@\else\vskip1.5pcplus.5pc\unvbox\tocbox@\fi
  \iflecture@ \vskip2pc\fi
}

\def\xcaheadfont@{\bf}
\def\xcbheadfont@{\headfont@}

% figure
\def\endinsert{\egroup % finish the \vbox
  \if@mid \dimen@\ht\z@ \advance\dimen@\dp\z@ \advance\dimen@12\p@
    \advance\dimen@\pagetotal \advance\dimen@-\pageshrink
    \ifdim\dimen@>\pagegoal\@midfalse\p@gefalse\fi\fi
  \if@mid \bigskip\box\z@\bigbreak
  \else\insert\topins{\penalty100 % floating insertion
    \splittopskip\z@skip
    \splitmaxdepth\maxdimen \floatingpenalty\z@
    \ifp@ge \dimen@\dp\z@
    \vbox to\vsize{\unvbox\z@\kern-\dimen@}% depth is zero
    \else \box\z@\nobreak\vskip 12\p@ plus 12\p@\fi}\fi\endgroup}

\iflecture@
   \def\refsfont@{\eightpoint}%
\else
   \def\refsfont@{\tenpoint}%
   \widestnumber\key{M}
\fi

\def\leftheadtext{\let\savedef@\leftheadtext
  \def\leftheadtext##1{\let\leftheadtext\savedef@
    \leftheadtoks\expandafter{\frills@{##1}}%
    \mark{\the\leftheadtoks\noexpand\else\the\rightheadtoks}
    \ifsyntax@\setboxz@h{\def\\{\unskip\space\ignorespaces}%
        \headlinefont@##1\unskip}\fi}%
  \nofrillscheck\leftheadtext}
\def\rightheadtext{\let\savedef@\rightheadtext
  \def\rightheadtext##1{\let\rightheadtext\savedef@
    \rightheadtoks\expandafter{\frills@{##1}}%
    \mark{\the\leftheadtoks\noexpand\else\the\rightheadtoks}%
    \ifsyntax@\setboxz@h{\def\\{\unskip\space\ignorespaces}%
        \headlinefont@##1\unskip}\fi}%
  \nofrillscheck\rightheadtext}

\def\captionfont@{\bf}

\def\topcaption#1#2\endcaption{%
  {\dimen@\hsize \advance\dimen@-\captionwidth@
   \rm\raggedcenter@ \advance\leftskip.5\dimen@ \rightskip\leftskip
  {\captionfont@#1}%
  \if\notempty{#2}\enspace\ignorespaces#2\unskip\fi
  \endgraf}\nobreak\bigskip}
\def\botcaption#1#2\endcaption{%
  \nobreak\bigskip
  \setboxz@h{\captionfont@#1\if\notempty{#2}.\enspace\rm#2\unskip\fi}%
  {\dimen@\hsize \advance\dimen@-\captionwidth@
   \leftskip.5\dimen@ \rightskip\leftskip
   \noindent \ifdim\wdz@>\captionwidth@
   \else\hfil\fi\eightpoint
  {\captionfont@#1\unskip}%
  \if\notempty{#2}.\enspace\rm#2\fi\endgraf}}



%%%% table of contents


\begingroup
\let\head\relax
\let\specialhead\relax
\let\subhead\relax
\let\subsubhead\relax
\let\title\relax
\let\chapter\relax


\gdef\newtocdefs{%
   \def \Title##1
       {\penalty\z@ \vskip10\p@
        \noindent{\bf ##1}\endgraf}%
   \def \title##1\endtitle
       {\penalty\z@ \vskip8\p@
        \hangindent\wd\tocheadbox@\noindent{##1}\endgraf}%
   \def \chapter##1{%
        Chapter ##1.\unskip\enspace}%
   \def \part##1{%
        {\bf PART ##1}\hfill\break}%
   \def \specialhead##1 ##2\endspecialhead
       {\par\hangindent\wd\tocheadbox@\parindent=12pt \indent
        \if\notempty{##1}\hbox to\wd\tocheadbox@{\hfil ##1\unskip\enspace}\fi
        {\bf ##2}\par}%
   \def \Head##1##2{\par\hangindent\wd\tocheadbox@\parindent=12pt \indent
        \if\notempty{##1}\hbox to\wd\tocheadbox@{\hfil\S##1\unskip\enspace}\fi
        ##2\par}%
   \def \subhead##1 ##2\endsubhead
       {\par\vskip-\parskip {\normalbaselines
        \advance\leftskip\wd\tocheadbox@
        \hangindent\wd\tocsubheadbox@ \parindent=12pt\indent
        \if\notempty{##1}%
              \hbox to\wd\tocsubheadbox@{##1\unskip\hfil}\fi
         ##2\unskip\par}}%
   \def \subsubhead##1 ##2\endsubsubhead{}% not applicable
}%
\gdef\toc@#1{\relaxnext@
 \DN@{\ifx\next\nofrills\DN@\nofrills{\nextii@}%
      \else\DN@{\nextii@{{#1}}}\fi
      \next@}%
 \DNii@##1{%
  \bgroup
   \def\page####1%
       {\unskip\penalty\z@\null\hfil
        \rlap{\hbox to\pagenumwd{\quad\hfil\rm ####1}}%
              \hfilneg\penalty\@M}%
   \setbox\tocheadbox@\hbox{0.0.\enspace}%
   \setbox\tocsubheadbox@\hbox{0.0.0.\enspace}%
  \leftskip\z@ \rightskip\leftskip
   \setboxz@h{\bf\quad000}\pagenumwd\wd\z@
   \advance\rightskip\pagenumwd
   \vskip-4pt
   \newtocdefs
 }%
 \FN@\next@}%

\endgroup

%%%%%

%       define  a logo for the upper left-hand corner

%\def\nojourlogo{\let\jourlogo\empty@}
\def\nojourlogo{\LogoOnfalse}

\def\jourlogo{%
  \vbox to\headlineheight{%
    \parshape\z@ \leftskip\z@ \rightskip\z@
    \parfillskip\z@ plus1fil\relax
    \eightbf \baselineskip9pt
    \parindent\z@ \frenchspacing
    \vtop{IAS/Park City Mathematics Series\endgraf
      Volume \issuevol@, \issueyear@\par\vss}%
    \vss}%
}

\def\flheadline{\ifLogoOn\jourlogo\global\LogoOnfalse\else\empty@\fi}  % DF
\let\frheadline\flheadline 

%       macros to be put into the \topmatter for the logo

\define\volyear#1#2{\issueinfo{#1}{#1}{}{#2} 
     \let\logo@=\copyrightline@}              % ADDED BY DF

\define\issueinfo#1#2#3#4{%
  \def\issuevol@{#1}\def\issueno@{#2}%
  \def\issuemonth@{#3}\def\issueyear@{#4}}
\issueinfo{00}{0}{}{1997}

\define\copyrightinfo#1#2{\def\cryear@{#1}\def\crholder@{#2}}
\copyrightinfo{\issueyear@}{American Mathematical Society}

\font\sixsy=cmsy6

\def\issn#1{\gdef\issn@{#1}}
\issn{1070-4116}

\skip\copyins=1.5pc
\def\copyrightline@{%
  \rightline{\sixbf \textfont2=\sixsy \copyright\cryear@\ \crholder@}}

\newif\ifplain@  \plain@false

\Monograph

%%%%%%%%%%  Front End to AMS Commands          (DF)        %%%%%%%%%%% 
 
\NoBlackBoxes

\newif\iftajointauthor \tajointauthorfalse 
\newif\iftaassistantauthor \taassistantauthorfalse

\def\Volume#1{\gdef\volumemark{#1}} 
\def\Year#1{\gdef\yearmark{#1}}
\def\SeriesTitle#1{\gdef\seriestitle{#1}%          
		   \gdef\shortseriestitle{\uppercase{#1}}%  
} 
\def\ShortSeriesTitle#1{\gdef\shortseriestitle{\uppercase{#1}}}    %  optional
\def\Author#1{\gdef\authormark{#1}} 
\def\ShortAuthor#1{\gdef\shortauthor{\uppercase{#1}}}
\def\AuthorAddress#1{\gdef\authoraddress{#1}}
\def\AuthorEmail#1{\gdef\authoremail{#1}}
\def\TAIsJointAuthor{\tajointauthortrue}
\def\TAIsAssistantAuthor{\tajointauthortrue\taassistantauthortrue}
\def\TA#1{\gdef\ta{#1}} 
\def\ShortTA#1{\gdef\shortta{\uppercase{#1}}} 
\def\TAAddress#1{\gdef\taaddress{#1}} 
\def\TAEmail#1{\gdef\taemail{#1}}

\def\EndTopInfo{ 
%   \volyear{\volumemark}{\yearmark} 
   \LogoOnfalse
   \topmatter 
%   \series\seriestitle
%   \iftajointauthor
%     \iftaassistantauthor
%       \sauth\authormark\\ \\ {\it with the assistance of\/}\\\ta\endsauth 
%     \else 
%       \sauth\authormark\\\ta\endsauth 
%     \fi
%   \else 
%     \sauth\authormark\endsauth 
%   \fi
%   \endseries 
   \title\seriestitle\endtitle 
   \iftajointauthor
     \iftaassistantauthor
       \author\authormark\\ \\ {\it with the assistance of\/}\\\ta\endauthor 
       \shortauthtitle\shortauthor, \shortseriestitle\endshortauthtitle
     \else 
       \author\authormark\\ \ta\endauthor 
       \shortauthtitle\shortauthor, \shortta, %
         \shortseriestitle\endshortauthtitle 
     \fi
   \else 
     \author\authormark\endauthor 
     \shortauthtitle\shortauthor, \shortseriestitle\endshortauthtitle
   \fi
%   \address\authoraddress\endaddress 
%   \email\authoremail\endemail 
   \iftajointauthor 
     \address\taaddress\endaddress 
     \email\taemail\endemail 
   \fi 
   \endtopmatter
}

\def\Lecture#1#2{ 
   \topmatter
   \lecturelabel{Lecture}
   \lecture{#1}
   \lecturename #2\endlecturename
   \endtopmatter
}

\def\Chapter#1#2{ 
   \topmatter
   \lecturelabel{Chapter}
   \lecture{#1}
   \lecturename #2\endlecturename
   \endtopmatter
}

\def\Notetaker#1{
   \footnotetext""{\bf Notes by #1}
}


\def\ShortLectureName#1{ 
  \gdef\shortlectnamemark{\uppercase{\ignorespaces#1\unskip}}
  \rightheadtext{\uppercase\expandafter{\thelecturelabel\  %
  \lectnomark.\ \shortlectnamemark}}%
}

\def\Exercises{ 
   \topmatter
   \lecturelabel{Exercises}
   \lecture{}
   \lecturename\endlecturename 
   \endtopmatter
   \rightheadtext{EXERCISES} 
}

\def\Bibliography{ 
   \topmatter
   \lecturelabel{Bibliography}
   \lecture{}
   \lecturename\endlecturename 
   \endtopmatter
   \rightheadtext{BIBLIOGRAPHY} 
}

\def\BlankPage{ 
   \plain@true\null\vfill\eject\plain@false
}

\def\Head#1#2{\add@missing\endroster \add@missing\enddefinition
  \add@missing\enddemo \add@missing\endexample
  \add@missing\endproclaim
  \penaltyandskip@{-200}\aboveheadskip
  {\headfont@\interlinepenalty\@M
  \noindent \S#1. #2\unskip\endgraf}%
  \penalty10000
  \parskip=\belowheadskip\flushpar\parskip0pt}

\def\Headnn#1{\add@missing\endroster \add@missing\enddefinition
  \add@missing\enddemo \add@missing\endexample
  \add@missing\endproclaim
  \penaltyandskip@{-200}\aboveheadskip
  {\headfont@\interlinepenalty\@M
  \noindent #1\unskip\endgraf}%
  \penalty10000
  \parskip=\belowheadskip\flushpar\parskip0pt}

\def\Subhead#1#2{%
  \add@missing\endroster \add@missing\enddefinition
  \add@missing\enddemo \add@missing\endexample
  \add@missing\endproclaim
  \par
  \ifdim\lastskip=\belowheadskip\else
          \penaltyandskip@{-200}\abovesubheadskip\fi
  {\subheadfont@\interlinepenalty\@M
  \noindent #1. #2\unskip\endgraf}%
  \penalty999
  \parskip=\belowheadskip\noindent\parskip0pt\relax}


\def\SubHeadnn#1{\add@missing\endroster \add@missing\enddefinition
  \add@missing\enddemo \add@missing\endexample
  \add@missing\endproclaim
  \par
  \ifdim\lastskip=\belowheadskip\else
          \penaltyandskip@{-200}\abovesubheadskip\fi
  {\subheadfont@\interlinepenalty\@M
  \noindent #1\unskip\endgraf}%
  \penalty999
  \parskip=\belowheadskip\flushpar\parskip0pt}

\def\EndTopInfoNoAuthor{ 
%   \volyear{\volumemark}{\yearmark} 
   \LogoOnfalse
   \topmatter 
%   \series\seriestitle
%   \iftajointauthor
%     \iftaassistantauthor
%       \sauth\authormark\\ \\ {\it with the assistance of\/}\\\ta\endsauth 
%     \else 
%       \sauth\authormark\\\ta\endsauth 
%     \fi
%   \else 
%     \sauth\authormark\endsauth 
%   \fi
%   \endseries 
   \title\seriestitle\endtitle 
%   \iftajointauthor
%     \iftaassistantauthor
%       \author\authormark\\ \\ {\it with the assistance of\/}\\\ta\endauthor 
%       \shortauthtitle\shortauthor, \shortseriestitle\endshortauthtitle
%     \else 
%       \author\authormark\\ \ta\endauthor 
%       \shortauthtitle\shortauthor, \shortta, %
%         \shortseriestitle\endshortauthtitle 
%     \fi
%   \else 
%     \author\authormark\endauthor 
%     \shortauthtitle\shortauthor, \shortseriestitle\endshortauthtitle
%   \fi
%   \address\authoraddress\endaddress 
%   \email\authoremail\endemail 
   \iftajointauthor 
     \address\taaddress\endaddress 
     \email\taemail\endemail 
   \fi 
   \endtopmatter
}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%		FOR PROBLEMS 

\setbox0\hbox{(a)\ }  
\newdimen\secwidth \secwidth=\wd0 
\secwidth=0pt
\newcount\probno \probno=0 \newcount\probsecno
\newbox\numbox

\def\prob#1#2{#1.\;\hbox to 40pt{\hrulefill/#2}\hskip25pt}
\long\def\problem#1\endproblem{\bigbreak \global\advance\probno by 1
  \noindent {\parskip2pt plus1pt minus1pt \parindent0pt
  {\bf\problemlabel\number\probno.\enspace}#1}\bigbreak}
\def\probsec{\futurelet\next\probsecc}
\def\probsecc{\bigbreak \global\advance\probno by 1
  \noindent \begingroup  \parskip2pt plus1pt minus1pt \parindent0pt
  \probsecno=0 
  \ifx\next\sec\firstsec\else\firsttext\fi}
\long\def\firsttext#1\sec{{\bf\problemlabel\number\probno.\enspace}#1\sec}
\def\firstsec\else\firsttext\fi\sec#1\sec{\fi\advance\probsecno by 1 
    \leftskip\secwidth\leavevmode{\bf\problemlabel\number\probno.\enspace 
    (\secno\unskip)\ }#1\sec}
\long\def\sec{\par\leftskip\secwidth\smallbreak\advance\probsecno by 1 
  \leavevmode{\bf(\secno\unskip)\ }}
\def\secno{\ifcase\probsecno\or a \or b \or c \or d \or e \or f \or g \or h
  \or i \or j \or k \or l \or m \or n\else\fi}
\def\endprobsec{\par\endgroup\bigbreak}
\def\pretend#1\haswidth#2{\setbox0\hbox{#2}\hbox to \wd0{\hfill #1}}

\def\Solution#1#2{\rightheadtext{SOLUTION TO \uppercase\expandafter{\problemlabel}#1} \Headnn{Solution\footnote{Solution by #2} to %
   \problemlabel#1}}
 
\def\Solutionna#1{\rightheadtext{SOLUTION TO \uppercase\expandafter{\problemlabel}#1}\Headnn{Solution to %
   \problemlabel#1}}



\def\Notes{\begingroup\parindent12pt\eightpoint
\add@missing\endroster \add@missing\enddefinition
  \add@missing\enddemo \add@missing\endexample
  \add@missing\endproclaim
  \penaltyandskip@{-200}\aboveheadskip
  {\tenbf\interlinepenalty\@M
  \noindent References and cross
  references\unskip\endgraf}% 
  \penalty10000
  \parskip=\belowheadskip\flushpar\parskip0pt\refstyle{C}} 

\def\endNotes{\endgroup}
%%%%%%%%%%%%%%%%%%%%%%%%%%% 
 
%	XREF CODES 
 
\newcount\commacount@
\def\first@#1#2\end{#1}
\def\true@{TT}
\def\false@{TF}
\def\empty@{}
\begingroup  \catcode`\-=3
\long\gdef\notempty#1{%
  \expandafter\ifx\first@#1-\end-\empty@ \false@\else \true@\fi}
\endgroup
\def\tcomma#1{\commacount@=0 \testcomma#1\end } 
\def\testcomma#1{\ifx#1\end \let\next=\relax 
  \else\if#1,\commacount@=1\fi\let\next=\testcomma\fi\next}
\def\tperiod#1{\commacount@=0 \testperiod#1\end } 
\def\testperiod#1{\ifx#1\end \let\next=\relax 
  \else\if#1.\commacount@=1\fi\let\next=\testperiod\fi\next}

\def\CODE#1#2#3#4{\if\notempty{#2}\tcomma{#2}\ifnum\commacount@=1[#4-{\bf %
   #1}, \S\S#2]\else \tperiod{#2}\ifnum\commacount@=1[#4-{\bf #1},~\S#2]\else%
   #3#2 of [#4-{\bf #1}]\fi\fi\else[#4-{\bf #1}]\fi}

\def\ASH#1{\CODE{Home\-work}{#1}{Problem~ASH}{I}}
\def\CFT#1{\CODE{CFT}{#1}{Lecture~}{II}}
\def\CF#1{\CODE{Clas\-sical Fields}{#1}{Chapter~}{I}}
\def\DQFT#1{\CODE{Dynam\-ics of QFT}{#1}{Lecture~}{II}}
\def\DQFTP#1{\CODE{Dynam\-ics of QFT, Exercises}{#1}{Problem~}{II}}
\def\DQ#1{\CODE{Quan\-ti\-za\-tion}{#1}{\S }{I}}
\def\DR#1{\CODE{Dim'l Regu\-lar\-iza\-tion}{#1}{\S }{I}}
\def\DS#1{\CODE{Spin\-ors}{#1}{Chapter~}{I}}
\def\FE#1{\CODE{Home\-work}{#1}{Problem~FE}{I}}
\def\FP#1{\CODE{Home\-work}{#1}{Problem~FP}{I}}
\def\HLS#1{\CODE{Symme\-tries}{#1}{\S }{I}}
\def\IQFT#1{\CODE{Axiom\-atics}{#1}{Lecture~}{I}}
\def\IT#1{\CODE{Dirac Index}{#1}{Lecture~}{I}}
\def\KK#1{\CODE{Compact\-ifi\-ca\-tions}{#1}{Lecture~}{II}}
%\def\KQGT#1{\CODE{Kazhdan obsolete}{#1}{Lecture~}{I}}
\def\LSS#1{\CODE{Super\-sym\-metry}{#1}{Chapter~}{I}}
\def\NCFT#1{\CODE{Chiral Alge\-bras}{#1}{\S }{II}}
\def\PQFT#1{\CODE{Pertur\-ba\-tive QFT}{#1}{Lecture~}{I}}
\def\PST#1{\CODE{Strings}{#1}{Lecture~}{II}}
\def\QGT#1{\CODE{Faddeev}{#1}{Lecture~}{I}}
\def\RG#1{\CODE{Renorm Groups}{#1}{Lecture~}{I}}
\def\SCFT#1{\CODE{N=2 SUSY}{#1}{Lecture~}{II}}
\def\SH#1{\CODE{Home\-work}{#1}{Problem~SH}{I}}
\def\SM#1{\CODE{Signs}{#1}{\S }{I}}
\def\SQCD#1{\CODE{N=1 Dy\-nam\-ics}{#1}{Lecture~}{II}}
\def\SS#1{\CODE{Super\-solu\-tions}{#1}{Chapter~}{I}}


%%%%%%%%%%%%%%%%%%%%%%%%%%%

\catcode`\@=13


\def\amsversion{2.1}
\endinput