	%===============   PTPTEX.sty   ===================================
%
%                                       ver.0.1      July 29, 1995
%                                       ver.0.7     March 25, 1996
%                                       ver.0.8    August 11, 1997
%                                       ver.1.0       May 22, 1999
%
% based on JJAPTEX.sty for (C) Japanese Journal of Applied Physics
%             Release 2.1, date : 9 September, '94
%
%=================================================================
% This PTPTEX.sty contains the following freeware style files
% at the final parts of the file:  
%   1. SUBEQN.STY for Subequations Environment 
%         made by Stephen Gildea
%   2. SUBEQNA.STY for Subeqnarray DOCUMENT-STYLE option
%         Copyright (C) 1988 by Johannes Braams, Dr Neher Laboratories
%   3. CITE.STY for compress numerical citations
%         Copyright (C) 1989,1990 by Donald Arseneau
% The original authors' notes are kept there.
%-------------------------------------------------------------------
\typeout{***** Document Style <<PTPTeX.sty>> ver.1.0 ****}
\def\@typeset{\sf typeset using \PTPTeX.sty $<$ver.1.0$>$}

\def\notypesetlogo{\def\@typeset{}}
\def\PTPTeX{\raisebox{-.2ex}{$\cal P$}\kern-.05em{$\cal T$}\kern-.18em%
\raisebox{-.2ex}{$\cal P$}\kern-.03em\TeX}
%\raggedbottom

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%       default       \@prtstyle=1    for full paper
%       [letter]      \@prtstyle=2    for letter
%       [supplement]  \@prtstyle=3    for supplement
%       [preprint]    \@prtstyle=0    for preprint
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\def\@prtstyle{1} 
\@namedef{ds@preprint}{\def\@prtstyle{0}}
\@namedef{ds@letter}{\def\@prtstyle{2}}
\@namedef{ds@letters}{\def\@prtstyle{2}}
\@namedef{ds@supple}{\def\@prtstyle{3}
\gdef\@supple{Progress of Theoretical Physics Supplement }}
\@namedef{ds@supplement}{\def\@prtstyle{3}
\gdef\@supple{Progress of Theoretical Physics Supplement }}
\@namedef{ds@addenda}{\def\@addenda{Addenda}}
\@namedef{ds@errata}{\def\@addenda{Errata}}
\def\ds@twoside{\@twosidetrue \@mparswitchtrue}
\newif\if@seceq \@seceqfalse
\def\ds@seceq{\@seceqtrue}
\newif\if@wrapfig \@wrapfigfalse
\def\ds@wrapfig{\@wrapfigtrue}
%\newif\if@pageFN \@pageFNfalse
%\def\ds@editorial{\@pageFNtrue}
\@twosidetrue

%%--- optional setting for PTP ---
 \def\@secapp{\secsymbol}  \def\@rm{\rm}
%%-------------------------------

\@options               %read option inputs
\if 0\@prtstyle                 %if preprint
  \input ptp-prep.sty\relax
\else
  \input ptp-text.sty\relax
\fi
\if@wrapfig
  \input wrapft.sty
\fi

%%%%% Followings are to make Greek Letters italic for PTP %%%%%
%%%%% "70xx are changed into "71xx                        %%%%%
\mathchardef\Gamma="7100
\mathchardef\Delta="7101
\mathchardef\Theta="7102
\mathchardef\Lambda="7103
\mathchardef\Xi="7104
\mathchardef\Pi="7105
\mathchardef\Sigma="7106
\mathchardef\Upsilon="7107
\mathchardef\Phi="7108
\mathchardef\Psi="7109
\mathchardef\Omega="710A
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\def\labelenumi{\arabic{enumi}.}
\def\theenumi{\arabic{enumi}}
\def\labelenumii{(\alph{enumii})}
\def\theenumii{\alph{enumii}}
\def\p@enumii{\theenumi}
\def\labelenumiii{\roman{enumiii}.}
\def\theenumiii{\roman{enumiii}}
\def\p@enumiii{\theenumi(\theenumii)}
\def\labelenumiv{\Alph{enumiv}.}
\def\theenumiv{\Alph{enumiv}}
\def\p@enumiv{\p@enumiii\theenumiii}

\def\labelitemi{$\bullet$}
\def\labelitemii{\bf --}
\def\labelitemiii{$\ast$}
\def\labelitemiv{$\cdot$}

\def\verse{\let\\=\@centercr
 \list{}{\itemsep\z \itemindent -1.5em\listparindent \itemindent
 \rightmargin\leftmargin\advance\leftmargin 1.5em}\item[]}
\let\endverse\endlist
\def\quotation{\list{}{\listparindent 1.5em
 \itemindent\listparindent
 \rightmargin\leftmargin\parsep 0pt plus 1pt}\item[]}
\let\endquotation=\endlist
\def\quote{\list{}{\rightmargin\leftmargin}\item[]}
\let\endquote=\endlist

\def\descriptionlabel#1{\hspace\labelsep \bf #1}
\def\description{\list{}{\labelwidth\z@ \itemindent-\leftmargin 
\itemindent -1em
\labelsep 0pt \leftmargin 1em \itemsep 10pt
\let\makelabel\descriptionlabel}}
\let\enddescription\endlist
\newdimen\descriptionmargin
\descriptionmargin=3em

\arraycolsep 6pt \tabcolsep 6pt \arrayrulewidth \hruleheight 
\tabbingsep \labelsep

\skip\@mpfootins = \skip\footins
\fboxsep = 3pt \fboxrule = .4pt

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

\def\thesection {\arabic{section}}
\def\thesubsection {\@rm \arabic{section}.\arabic{subsection}}
\def\thesubsubsection {\@rm \thesubsection.\arabic{subsubsection}}

\font\tensyb=cmbsy10\relax
\def\secsymbol{\mbox{\tensyb\symbol{'170}}}

%%%%%% tableofcontents %%%%%%
\def\@pnumwidth{\ifnum\value{page}<100 1.4em \else\ifnum\value{page}<1000 
1.6em \else 2.2em \fi\fi}
\def\@tocrmarg {3em}
\def\@dotsep{4.5}
\setcounter{tocdepth}{2}

\def\tableofcontents{\section*{Contents\@mkboth{CONTENTS}{CONTENTS}}
 \@starttoc{toc}}
\def\l@section#1#2{\addpenalty{\@secpenalty} \addvspace{0em plus 1pt}
\@tempdima 1.7em \begingroup
 \parindent \z@ \rightskip \@pnumwidth 
 \parfillskip -\@pnumwidth 
 \bf \leavevmode \advance\leftskip\@tempdima \hskip -\leftskip #1\nobreak\hfil
\nobreak\hbox to\@pnumwidth{\hss #2}\par
 \endgroup}
 
\def\l@subsection{\@dottedtocline{2}{2.1em}{1.9em}}
\def\l@subsubsection{\@dottedtocline{3}{4.2em}{2.7em}}
\def\listoffigures{\section*{List of Figures\@mkboth
 {LIST OF FIGURES}{LIST OF FIGURES}}\@starttoc{lof}}
\def\l@figure{\@dottedtocline{1}{1.5em}{2.3em}}
\def\listoftables{\section*{List of Tables\@mkboth
 {LIST OF TABLES}{LIST OF TABLES}}\@starttoc{lot}}
\let\l@table\l@figure
%%%%%%%%%%%%%%%%%

\if@seceq
\@addtoreset{equation}{section}
\def\theequation{\arabic{section}\raise.5ex\hbox{.}\arabic{equation}}
\else
\def\theequation{\arabic{equation}}
\fi

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\def\thebibliography#1{\if 0\@prtstyle\section*{References}\else%
\vspace{-.1\baselineskip}\refsize
\section*{\if 2\@prtstyle%                                 %if letter
\vbox{\hrule width 71pt height 7.2pt depth -7pt}
\else{\refsize\bf References}\fi}\vspace{-.7\baselineskip}\fi
\list{\arabic{enumi})}{\settowidth
 \labelwidth{#1)} \leftmargin\labelwidth
 \advance\leftmargin\parindent \advance\leftmargin\labelsep
 \usecounter{enumi}}
 \def\newblock{\hskip .11em plus .33em minus .07em}
 \sloppy\clubpenalty4000\widowpenalty4000
 \sfcode`\.=1000\relax}
\let\endthebibliography=\endlist

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\setcounter{footnote}{0}%
\def\footnoterule{\kern-3\p@
 \hrule width .3\columnwidth height \hruleheight \kern 2.6\p@}
\long\def\@makefntext#1{%
\parindent 1.5em\noindent \footnotesize %
\hbox to 2.5em{\hss$^{\@thefnmark}$}\hskip3pt#1}
\gdef\@thanks{}
%% The following is a macro by S.Fujita 1995/06/06
%% to reset the footnote number properly at each page.
%% Fujita's original macro is modified such that the resetting is made on 
%% the new counter {f@@tn@te} but not on the original counter {footnote}. 
\newcounter{f@@tn@te}\setcounter{f@@tn@te}{0}%
\newcount\CurrP@ge \CurrP@ge\z@%
\@ifundefined{hyperlink}%                    
{\def\thefootnote{\fnsymbol{f@@tn@te})}}     %<-- if not hyperlatex
{\def\thefootnote{\fnsymbol{f@@tn@te}}}      %<-- if hyperlatex
\def\ftnt@page#1#2{\@tempcnta=#2 \ifnum\@tempcnta>\CurrP@ge%
\expandafter\gdef\csname @ftnt@#1\endcsname{#2}%
\CurrP@ge=\@tempcnta\fi}
\let\fo@tnote=\footnote%
\long\def\f@@tnote#1{\stepcounter{f@@tn@te}\fo@tnote{#1}}%
\long\def\footnote#1{%
\@tempcnta=\c@footnote%
\@ifundefined{@ftnt@\the\@tempcnta}{\f@@tnote{#1}}%
{\c@f@@tn@te\z@\f@@tnote{#1}}%
\edef\the@fn@t{\the\@tempcnta}%
{\let\the\z@ \edef\next{\write\@auxout{%
\string\ftnt@page{\the@fn@t}{\the\c@page}}}\next}}
%%since \@addtoreset{footnote}{page} does not work well
%%%%%%%%% JJAP %%%%%%%%%%%%%%%%%%%%%%
%    definition of footnote mark
%%%%%%%%% JPSJ %%%%%%%%%%%%%%%%%%%%%%
%            modified
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\def\@fnsymbol#1{\ifcase#1\or *\or **\or ***\or \dagger\or
   \dagger\dagger\or \dagger\dagger\dagger\or \ddagger\or
   \ddagger\ddagger\or \ddagger\ddagger\ddagger\else\@roman{#1}\fi}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\setcounter{topnumber}{5}
\def\topfraction{0.9}
\setcounter{bottomnumber}{5}
\def\bottomfraction{0.9}
\setcounter{totalnumber}{7}
\def\textfraction{0.1}
\def\floatpagefraction{0.9}
\setcounter{dbltopnumber}{2}
\def\dbltopfraction{.7}
\def\dblfloatpagefraction{1}

%%%%%%%%% JJAP %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%    definition of @makecaption and tabular environment
%%%%%%%%% PTP %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%            modified
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\def\@tableflag{table}

\long\def\@makecaption#1#2{\captionsize
\ifx\@captype\@tableflag\else
\ifdim\topsep=\z@\vskip0.5\baselineskip\fi \fi
 \setbox\@tempboxa\hbox{#1.\hskip.8em#2}
 \ifdim \wd\@tempboxa > \hsize
     \hangindent=1.75em {#1.\hskip.8em#2\par} 
   \else \hbox to \hsize{\hfil\box\@tempboxa\hfil} 
 \fi}

\let\@Ttabular\tabular
\def\tabular{\vskip.25\baselineskip\tabularsize\@Ttabular}

\newcounter{figure}
\def\thefigure{\@arabic\c@figure}
\def\fps@figure{htbp}
\def\ftype@figure{1}
\def\ext@figure{lof}
\def\fnum@figure{Fig.\hskip.35em\thefigure}
\def\figure{\@float{figure}}
\let\endfigure\end@float
\newcounter{table}
\def\thetable{\@Roman\c@table}
\def\fps@table{tbhp}
\def\ftype@table{2} 
\def\ext@table{lot}
\def\fnum@table{Table\hskip.35em\thetable}
\def\table{\@float{table}}
\let\endtable\end@float

%%%%%%%%% PTP %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%    \figurebox{width}{height}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newif\if@figbox \@figboxtrue
\def\nofigureboxrule{\@figboxfalse}
\def\figurebox#1#2{% #1: fig-width  #2: fig-height
\begin{center}
\if@figbox \else \fboxrule 0pt \fi
\fbox{\rule{0cm}{#2}\hspace{#1}}
\end{center}}

%%%%%%%%% JJAP %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%    definition of maketitle
%%%%%%%%% JPSJ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%            modified
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\def\maketitle{\par
 \begingroup
 %\def\thefootnote{\fnsymbol{footnote}}
 %\def\@makefnmark{\hbox to 0pt{$^{\@thefnmark}$\hss}} 
 \if@twocolumn
 \twocolumn[\@maketitle]
 \else \newpage
 \global\@topnum\z@ \@maketitle \fi\thispagestyle{headings}\@thanks
 \endgroup
 \if 0\@prtstyle \newpage \fi%               %if preprint
 %\setcounter{footnote}{0}
 \let\maketitle\relax
 \let\@maketitle\relax
 \gdef\@thanks{}\gdef\@author{}\gdef\@title{}\let\thanks\relax}

%%%% \def\@maketitle was moved into PTP-text.sty and PTP-prep.sty files %%%%

\long\def\title#1{\gdef\@title{#1}}
\long\def\subtitle#1{\gdef\@subtitle{#1}}
\long\def\author#1{\gdef\@author{#1}}
\long\def\inst#1{\gdef\@inst{#1}}
\long\def\abst#1{\gdef\@abst{#1}}
\def\pubvolno<#1,#2,#3>{#1,#2}
\def\pubmonthyear<#1,#2,#3>{#3}
\def\pubinfo#1{\gdef\@pubinfo{#1}
\if 2\@prtstyle \gdef\@letterinfo{\pubvolno<#1>}
\gdef\@letterdate{\pubmonthyear<#1>}\fi}
\def\preprintnumber{\@ifnextchar[{\@preptnumber}{\@preptnumber[30mm]}}
\def\@preptnumber[#1]#2{\gdef\@preprtnumwidth{#1}\gdef\@preprtnum{#2}}
\def\publishedin#1{\gdef\@publishedin{#1}}
\def\recdate#1{\gdef\@recdate{#1}}

\def\abstract{\if@twocolumn
\section*{Abstract}
\else \small 
\begin{center}
{\bf Abstract\vspace{-.5em}\vspace{0pt}} 
\end{center}
\quotation 
\fi}
\def\endabstract{\if@twocolumn\else\endquotation\fi}

\mark{{}{}}

%%%%%%%% header of the first page %%%%%%%%
\def\invitedpaper{\gdef\@invited{INVITED PAPERS}}
\def\ps@headings{
\let\@mkboth\markboth
\if 0\@prtstyle
\def\@oddhead{}
\def\@oddfoot{\hbox to \textwidth{\hfil\rm\thepage\hfil%
\makebox[0pt][r]{\@typeset}}}
\else
\def\@oddfoot{\hfil\@typeset}
\@ifundefined{@supple}{%
\def\@oddhead{\@ifundefined{@invited}{}{%
\fbox{\rule[-.7pt]{0pt}{.84em}\hspace{.5pt}\@invited}}
%\fbox{\hspace{1pt}\@invited}}
\hfil\rm\thepage}
}{% for Supplement
\def\@oddhead{\hbox to \textwidth{\hfil{\footnotesize%
\@supple\@ifundefined{@pubinfo}{}{\@pubinfo}}%
\hfil\makebox[0pt][r]{\rm\thepage}}}
\def\@evenhead{\hbox to \textwidth{\makebox[0pt][l]{\rm\thepage}%
\hfil{\footnotesize\@supple\@ifundefined{@pubinfo}{}{\@pubinfo}}%
\hfil}}}
\fi}
%%%%%%% header for the other pages %%%%%%%%%
\def\ps@myheadings{\let\@mkboth\@gobbletwo
\if 2\@prtstyle%                                %if letter
\def\@oddhead{\hbox to \textwidth{%
\makebox[0pt][l]{\footnotesize%
\@ifundefined{@letterdate}{}{\@letterdate}}\hfil{\it Letters}\hfil%
\makebox[0pt][r]{\rm\thepage}}}
\def\@evenhead{\hbox to \textwidth{\makebox[0pt][l]{\rm\thepage}%
\hfil{\it Letters}\hfil\makebox[0pt][r]{\footnotesize%
\@ifundefined{@letterinfo}{}{\@letterinfo}}}}
\else%                                          %otherwise
\def\@oddhead{\hbox to \textwidth{\hfil\it\rightmark\hfil%
\makebox[0pt][r]{\rm\thepage}}}
\def\@evenhead{\hbox to \textwidth{\makebox[0pt][l]{\rm\thepage}%
\hfil\it\leftmark\hfil}}
\fi
\def\@oddfoot{}
\def\@evenfoot{}\def\sectionmark##1{}\def\subsectionmark##1{}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\def\today{\ifcase\month\or
 January\or February\or March\or April\or May\or June\or
 July\or August\or September\or October\or November\or December\fi
 \space\number\day, \number\year}

\ps@plain \pagenumbering{arabic} \onecolumn 
\if@twoside\else\raggedbottom\fi 
\pagenumbering{arabic} \onecolumn

\def\sloppy{\tolerance=9999 \hfuzz=.5\p@ \vfuzz=.5\p@}

%%%%%%%%% JPSJ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%    acknowledgements 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newcommand{\acknowledgement}{\section*{Acknowledgement}}
\newcommand{\acknowledgements}{\section*{Acknowledgements}}

%%%%%%%%% JJAP %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%    definition of @sect for sections
%%%%%%%%% JPSJ, PTP %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%            modified
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\def\@nullstring{}
\def\@appendixstring{Appendix}
\def\@widerule{\rule[.5ex]{2em}{\hruleheight}}
\def\f@rst#1#2\@@{#1}

\def\@sect#1#2#3#4#5#6[#7]#8{%
   \ifnum #2>\c@secnumdepth
      \def\@svsec{}
   \else
      \refstepcounter{#1}
      \ifnum #2=1		% TRUE if \section{}
         \ifx\@secapp\@appendixstring
             \edef\@svsec{\@secapp~\csname the#1\endcsname}
         \else
           \ifx\thesection\@nullstring
             \edef\@svsec{\@secapp \csname the#1\endcsname\hskip .8em}
           \else
             \edef\@svsec{\@secapp \csname the#1\endcsname.\hskip .8em}
           \fi
         \fi
      \else
           \def\@svsec{\csname the#1\endcsname.\hskip .8em}
      \fi
   \fi
   \@tempskipa #5\relax
     \ifdim \@tempskipa>\z@
       \begingroup 
           #6\relax
         \ifnum #2=1          	% TRUE if \section{}
           \center
           \ifx\@secapp\@appendixstring
             \xdef\t@mp{\expandafter\f@rst#8{}\@@}
             \ifx\t@mp\@empty 
               \centerline{\interlinepenalty \@M \@secapp}
             \else
               \@svsec \par\nobreak
               \@hangfrom{\hskip #3\relax\@widerule\ }{%
               \interlinepenalty \@M{\it #8}\ \@widerule \par
                \nobreak \vspace{-.1\baselineskip}}%
             \fi
           \else
            \@hangfrom{\hskip #3\relax\@svsec}{\interlinepenalty \@M #8\par}%
           \fi
         \else
           \@hangfrom{\hskip #3\relax\@svsec}{\interlinepenalty \@M #8\par}%
         \fi
       \endgroup
       \csname #1mark\endcsname{#7}\addcontentsline
         {toc}{#1}{\ifnum #2>\c@secnumdepth \else
                    \ifnum #2=1 
		      \ifx\@secapp\@appendixstring
                        \protect\rm \protect\numberline{\ \ 
                           \csname the#1\endcsname.}\protect\hspace{.7ex}
                      \else
                        \protect\numberline{\@secapp \csname the#1\endcsname.}%
                      \fi
                    \else
                      \protect\numberline{\csname the#1\endcsname.}%
                    \fi\fi
                     #7}
     \else
       \def\@svsechd{#6\hskip #3\@svsec #8\csname #1mark\endcsname
                     {#7}\addcontentsline
         {toc}{#1}{\ifnum #2>\c@secnumdepth \else
                    \ifnum #2=1 
		      \ifx\@secapp\@appendixstring
                         \protect\rm \protect\numberline{\ \ 
                           \csname the#1\endcsname.}\protect\hspace{.7ex}
                      \else
                         \protect\numberline{\@secapp \csname the#1\endcsname.}
                      \fi
                    \else
                      \protect\numberline{\csname the#1\endcsname.}%
                    \fi\fi
                     #7}}
     \fi
     \@xsect{#5}}

\def\@ssect#1#2#3#4#5{\@tempskipa #3\relax
   \ifdim \@tempskipa>\z@
     \begingroup \center
     #4\@hangfrom{\hskip #1}{\interlinepenalty \@M #5\par}\endgroup
   \else \def\@svsechd{#4\hskip #1\relax #5}\fi
    \@xsect{#3}}

%%%%%%%%% JJAP %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%    \appendix
%%%%%%%%% JPSJ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%            modified
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\def\appendix{\par
 \addtocontents{toc}{\protect\vspace{.5ex}
 \protect\numberline{{\protect\bf Appendix}}} 
 \setcounter{section}{0}
 \setcounter{subsection}{0}
 \def\@secapp{Appendix}
 \@addtoreset{equation}{section}
 \def\theequation{\Alph{section}\raise.5ex\hbox{.}\arabic{equation}}
 \def\thesection{\Alph{section}}
 \def\thesubsection{\@rm\Alph{section}.\arabic{subsection}}}

%%%%%%%%% JJAP %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\def\eqnarray{%
  \stepcounter{equation}%
  \let\@currentlabel=\theequation
  \global\@eqnswtrue
  \global\@eqcnt\z@
  \tabskip\@centering
  \let\\=\@eqncr
  $$\halign to \displaywidth\bgroup\@eqnsel\hskip\@centering
  $\displaystyle\tabskip\z@{##}$&\global\@eqcnt\@ne
  \hfil$\displaystyle{{}##{}}$\hfil
  &\global\@eqcnt\tw@$\displaystyle\tabskip\z@{##}$\hfil
  \tabskip\@centering&\llap{##}\tabskip\z@\cr}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\if 0\@prtstyle
\pagestyle{plain}
\else
\pagestyle{myheadings}
\fi
%%%%%%%%% PTP: some small macros %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\def\mib#1{\mbox{\boldmath $#1$}}
\def\dfrac#1#2{{{\displaystyle{#1}} \over {\displaystyle{#2}}}}
\renewcommand{\thanks}{\footnote}
\def\tocite#1{$^{\hbox{\,-}}$\kern-.04em\cite{#1}}%\cite{xx}\tocite{yy}
\def\halftext{.471\textwidth}
\def\@JLone<#1,#2>{#1}
\def\@JLtwo<#1,#2,#3>{#2}
\def\@JLyear<#1,#2,#3,#4>{#3}
\def\@JLpage<#1,#2,#3,#4>{#4}
\def\JL#1{\@JLone<#1>\ {\bf \@JLtwo<#1>} (\@JLyear<#1>), \@JLpage<#1>}
\def\@Jpage<#1,#2,#3>{#3}
\def\andvol#1{{\bf \@JLone<#1>} (\@JLtwo<#1>), \@Jpage<#1>}
\def\PTP#1{Prog.\ Theor.\ Phys.\ \andvol{#1}}
\def\JPSJ#1{J.~Phys.\ Soc.\ Jpn.\ \andvol{#1}}
\def\PR#1{Phys.\ Rev.\ \andvol{#1}}
\def\PRL#1{Phys.\ Rev.\ Lett.\ \andvol{#1}}
\def\PL#1{Phys.\ Lett.\ \andvol{#1}}
\def\NP#1{Nucl.\ Phys.\ \andvol{#1}}
\def\JMP#1{J.~Math.\ Phys.\ \andvol{#1}}
\def\IJMP#1{Int.\ J.~Mod.\ Phys.\ \andvol{#1}}
\def\CMP#1{Commun.\ Math.\ Phys.\ \andvol{#1}}
\def\JP#1{J.~of Phys.\ \andvol{#1}}
\def\ANN#1{Ann.\ of Phys.\ \andvol{#1}}
\def\NC#1{Nouvo Cim.\ \andvol{#1}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%% The following is for using PTPTeX.sty in Japanese %%%%%%%%%%
\let\r@m=\rm \let\i@t=\it
\ifx\gtfam\undefined
\ifx\jasciikanjiskip\undefined\else %i.e., if NTT-jTeX
\def\rm{\r@m\dm} \def\it{\i@t\dm}\fi
\else                               %i.e., in Asci jTeX, pTeX 
\def\rm{\r@m\mc} \def\it{\i@t\mc}
\fi
%%%%%%%%%% This is to replace \psfig into \epsf %%%%%%%%%%%%%%%%%%
%%%%%%%%% you can write e.g., \epsf{file=xxx.eps,width=xcm} %%%%%%
\newif\if@height \newif\if@width
\def\@ps@init@parms{\@heightfalse \@widthfalse
		\def\ptp@sfile{}\def\ptp@sheight{}\def\ptp@swidth{} }
\def\@cs@name#1{\csname #1\endcsname}
\def\@@setparms#1=#2,{\@cs@name{@ptp@@s#1}{#2}}
\def\@parse@ps@parms#1{\@for\@psfiga:=#1\do
		      {\expandafter\@@setparms\@psfiga,}}
\def\@ptp@@sbbllx#1{} \def\@ptp@@sbblly#1{}   \def\@ptp@@sbburx#1{}
\def\@ptp@@sbbury#1{} \def\@ptp@@srheight#1{} \def\@ptp@@srwidth#1{}
\def\@ptp@@sangle#1{} \def\@ptp@@ssilent#1{}  \def\@ptp@@sprolog#1{}
\def\@ptp@@spostlog#1{}
\def\@ptp@@sfile#1{\edef\ptp@sfile{#1}}
\def\@ptp@@sheight#1{\@heighttrue \edef\ptp@sheight{#1}}
\def\@ptp@@swidth#1{\@widthtrue \edef\ptp@swidth{#1}}
\def\@raphic@zapspace#1{#1\ifx\@raphic@zapspace#1\@raphic@zapspace%
  \else\expandafter\@raphic@zapspace \fi}
\def\epsf#1{%
\edef\@temp@{\@raphic@zapspace#1{}}%
\@ps@init@parms \@parse@ps@parms{\@temp@}%
\ifvmode\leavevmode\fi%
\if@width \epsfxsize=\ptp@swidth \fi%
\if@height \epsfysize=\ptp@sheight \fi%
\centerline{\epsfbox{\ptp@sfile}}}

%%%%%%% The following contains several environments %%%%%%%%%

%111%%%%%%%%% The subequations environment %%%%%%%%%%%%%%%%%
%
% Within the subequations environment, the only change is that
% equations are labeled differently.  The number stays the same,
% and lower case letters are appended.  For example, if after doing
% three equations, numbered 1, 2, and 3, you start a subequations
% environmment and do three more equations, they will be numbered
% 4a, 4b, and 4c.  After you end the subequations environment, the
% next equation will be numbered 5.
%
% Both text and equations can be put inside the subequations environment.
%
% If you make any improvements, I'd like to hear about them.
%
% Stephen Gildea
% MIT Earth Resources Lab
% Cambridge, Mass. 02139
% mit-erl!gildea
% gildea@erl.mit.edu
%
\newtoks\@stequation

\def\subequations{\refstepcounter{equation}%
  \edef\@savedequation{\the\c@equation}%
  \@stequation=\expandafter{\theequation}%   %only want \theequation
  \edef\@savedtheequation{\the\@stequation}% %expanded once
  \edef\oldtheequation{\theequation}%
  \setcounter{equation}{0}%
  \def\theequation{\oldtheequation\alph{equation}}}

\def\endsubequations{%
  \setcounter{equation}{\@savedequation}%
  \@stequation=\expandafter{\@savedtheequation}%
  \edef\theequation{\the\@stequation}%
  \global\@ignoretrue}

% More from John Hobby
% Fix Plain's \bigl, \Bigl, etc. macros so that they try to scale with
% LaTeX size changes.  This uses the fact that \@setsize sets \ht\strutbox
% to be 70% of the normal unstretched baselineskip.

\def\big#1{{\hbox{$\left#1\vcenter to1.428\ht\strutbox{}\right.\n@space$}}}
\def\Big#1{{\hbox{$\left#1\vcenter to2.142\ht\strutbox{}\right.\n@space$}}}
\def\bigg#1{{\hbox{$\left#1\vcenter to2.857\ht\strutbox{}\right.\n@space$}}}
\def\Bigg#1{{\hbox{$\left#1\vcenter to3.571\ht\strutbox{}\right.\n@space$}}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%222%%%%%% subeqnarray environment %%%%%%%%%%%%%%%%%%%%
% Subeqnarray DOCUMENT-STYLE option -- Version 1.1 released 15 November 1988
%    for LaTeX version 2.09
%
% Copyright (C) 1988 by Johannes Braams, Dr Neher Laboratories
%
%    This style option defines the subeqnarray and subeqnarray*
%    environment, which behaves like the eqnarray environment,
%    except that the lines are numbered like 1a 1b 1c etc.
%    To refer to these numbers an extra label command \slabel
%    has been defined.
%
%    Many of this code was taken from LaTeX.TeX and modified for
%    this purpose.
%
% Revisions:
%
%    22 December 1988    V1.1    JB    Fixed bug in subeqnarray* environment
%
%-
%\typeout{Documentstyle option `subeqnarray' V1.1;  Released 22 December 1988}
%
%    A new counter for he subequations
%    and a command to generate the number
%
\newcounter{subequation}[equation]
\def\thesubequation{\theequation\@alph\c@subequation}
%
%  \@subeqnnum: Produces the equation number for the
%     subeqnarray environment.  The following definition is for
%     flushright numbers; for flushleft numbers, see leqno.doc.
%     The {\rm ... } puts the subequation number in roman type even if
%     an subeqnarray environment appears in an italic environment.
%     1em space is put after subequation number in PTP (96.4.10) 
%\def\@subeqnnum{{\rm (\thesubequation)}} 
\def\@subeqnnum{{\rm (\thesubequation)\hspace{1em}}} %put space after Eq.#
%
%    A new label command to refer to subequations. It works
%    like the \label command and was taken from LaTeX.TeX
%
%  \slabel{FOO} then writes the following on file \@auxout :
%        \newlabel{FOO}{{eval(\@currentlabel)}{eval(\thepage)}}
%
\def\slabel#1{\@bsphack\if@filesw {\let\thepage\relax
   \xdef\@gtempa{\write\@auxout{\string
      \newlabel{#1}{{\thesubequation}{\thepage}}}}}\@gtempa
   \if@nobreak \ifvmode\nobreak\fi\fi\fi\@esphack}
%
%    Here's the subeqnarray environment,
%        it steps the equation counter,
%        sets the subequation counter equal to 1
%        and behaves much like the eqnarray environment.
%
\def\subeqnarray{\stepcounter{equation}
\let\@currentlabel=\theequation\global\c@subequation\@ne
\global\@eqnswtrue
\global\@eqcnt\z@\tabskip\@centering\let\\=\@subeqncr
$$\halign to \displaywidth\bgroup\@eqnsel\hskip\@centering
  $\displaystyle\tabskip\z@{##}$&\global\@eqcnt\@ne
  \hskip 2\arraycolsep \hfil${##}$\hfil
  &\global\@eqcnt\tw@ \hskip 2\arraycolsep $\displaystyle\tabskip\z@{##}$\hfil
   \tabskip\@centering&\llap{##}\tabskip\z@\cr}

\def\endsubeqnarray{\@@subeqncr\egroup
                     $$\global\@ignoretrue}

\def\@subeqncr{{\ifnum0=`}\fi\@ifstar{\global\@eqpen\@M
    \@ysubeqncr}{\global\@eqpen\interdisplaylinepenalty \@ysubeqncr}}

\def\@ysubeqncr{\@ifnextchar [{\@xsubeqncr}{\@xsubeqncr[\z@]}}

\def\@xsubeqncr[#1]{\ifnum0=`{\fi}\@@subeqncr
   \noalign{\penalty\@eqpen\vskip\jot\vskip #1\relax}}

\def\@@subeqncr{\let\@tempa\relax
    \ifcase\@eqcnt \def\@tempa{& & &}\or \def\@tempa{& &}
      \else \def\@tempa{&}\fi
     \@tempa \if@eqnsw\@subeqnnum\refstepcounter{subequation}\fi
     \global\@eqnswtrue\global\@eqcnt\z@\cr}

% Here's the subeqnarray* environment:

\let\@ssubeqncr=\@subeqncr
\@namedef{subeqnarray*}{\def\@subeqncr{\nonumber\@ssubeqncr}\subeqnarray}
\@namedef{endsubeqnarray*}{\global\advance\c@equation\m@ne%
                           \nonumber\endsubeqnarray}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%333%%%%%%% macros  \cite and \citen %%%%%%%%%%%%%%%%%%
%     CITE.STY -- compress numerical citations.
%     See also OVERCITE.STY.
%
%     Copyright (C) 1989,1990 by Donald Arseneau
%     These macros may be freely transmitted, reproduced, or modified for
%     non-commercial purposes provided that this notice is left intact.
%     
%     Instructions follow \endinput.
%  ------------------------------------
%
%  Pull out the code that writes the aux file citation and formats 
%  the number.  \citen can be used by itself to give citation numbers 
%  without the other formatting; e.g., "See also ref.~\citen{junk}."
%
\def\citen#1{%
\if@filesw \immediate \write \@auxout {\string \citation {#1}}\fi 
\@tempcntb\m@ne \let\@h@ld\relax \def\@citea{}%
\@for \@citeb:=#1\do {%
  \@ifundefined {b@\@citeb}%
    {\@h@ld\@citea\@tempcntb\m@ne{\bf ?}%
    \@warning {Citation `\@citeb ' on page \thepage \space undefined}}%
% else, defined
    {\@tempcnta\@tempcntb \advance\@tempcnta\@ne
    \setbox\z@\hbox\bgroup % check if citation is a number:
    \ifnum0<0\csname b@\@citeb \endcsname) \relax
       \egroup \@tempcntb\number\csname b@\@citeb \endcsname \relax
       \else \egroup \@tempcntb\m@ne \fi
    \ifnum\@tempcnta=\@tempcntb % Number follows previous--hold on to it
       \ifx\@h@ld\relax % first pair of successives
          \edef \@h@ld{\@citea\csname b@\@citeb\endcsname)}% 
       \else % compressible list of successives
%         % use \hbox to avoid easy \exhyphenpenalty breaks 
%          \edef\@h@ld{\hbox{-}\penalty\@highpenalty
          \edef\@h@ld{\penalty\@highpenalty\hskip.15em plus.1em minus.1em
            \hbox{-}\penalty\@highpenalty\hskip.15em plus.1em minus.1em
            \csname b@\@citeb\endcsname)}%
       \fi
    \else   %  non-successor--dump what's held and do this one
       \@h@ld\@citea\csname b@\@citeb \endcsname)\let\@h@ld\relax
    \fi}%
%%    To put space after the comma, use:
 \def\@citea{,\penalty\@highpenalty\hskip.15em plus.1em minus.1em}%
%%    For no space after comma, use:
%% \def\@citea{,\penalty\@highpenalty}% 
%%
}\@h@ld}
% 
%     Replacement for \@citex:
% 
\def\@citex[#1]#2{\@cite{\citen{#2}}{#1}}%
%
%  Replacement for \@cite 
%
\def\@cite#1#2{\leavevmode\unskip
  \ifnum\lastpenalty=\z@\penalty\@highpenalty\fi% highpenalty before
%\ $^{\multiply\@highpenalty 3 #1%             % triple-highpenalties within
   $^{\hskip.15em plus.1em minus.1em \multiply\@highpenalty 3 #1%
      \if@tempswa,\penalty\@highpenalty\ #2\fi % and before note.
    }$\spacefactor\@m}
%
%\endinput
%
%     
%                          CITE.STY
%
%     Modify LaTeX's normal citation mechanism to:
%
%     o Allow, but strongly discourage, line breaks within a series of
%       citations.  Each number is separated by a comma and a small space.
%       A break at the beginning of an optional note is discouraged also.
%
%     o Compress lists of three or more consecutive numbers to one number 
%       range which can be split, with difficulty, after the dash.  No sorting
%       to optimize compression is done.  All numbers should be greater than
%       zero. E.g., if you used to get [5,6,7,9,8,Einstein,6], then this style 
%       will give you [5--7,9,8,Einstein,6]. 
%
%     o Always puts an interword space before the citation and allow a 
%       highpenalty break there (unless you specifically forbid it with ~).
%       E.g.,   Something really stupid \cite{Larry,Curly,Moe}.
%                                      ^-- This space doesn't matter.
%
%     To get just the numbers (and write to the aux file) without the
%     extra formatting, use \citen just like \cite.
%
%     Linebreaks are allowed with triple-highpenalties after dashes
%     and commas; these may have to be taken if TeX sees no other 
%     viable breakpoints.  If you think citations are being split 
%     unnecessarily, try using \sloppy or a sloppypar environment.
%
%     FRAGILE!
%
% Send problem reports to asnd@triumfcl.bitnet or Arseneau@mtsg.ubc.ca
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\endinput
