%%% ======================================================================
%%% @LaTeX-style-file{
%%% filename = "aps12.sty",
%%% version = "3.0",
%%% date = "October 2, 1992",
%%% ISO-date = "1992.10.02",
%%% time = "15:41:54.18 EDT",
%%% author = "American Physical Society",
%%% contact = "Christopher B. Hamlin",
%%% address = "APS Publications Liaison Office
%%% 500 Sunnyside Blvd.
%%% Woodbury, NY 11797",
%%% telephone = "(516) 576-2390",
%%% FAX = "(516) 349-7817",
%%% email = "mis@aps.org (Internet)",
%%% supported = "yes",
%%% archived = "pinet.aip.org/pub/revtex,
%%% Niord.SHSU.edu:[FILESERV.REVTEX]",
%%% keywords = "REVTeX, version 3.0, preprint print style,
%%% American Physical Society",
%%% codetable = "ISO/ASCII",
%%% checksum = "64602 428 855 13714",
%%% docstring = "This is the internally called style for
%%% preprint-format output for the American
%%% Physical Society under REVTeX 3.0
%%% (release of November 10, 1992).
%%%
%%% The checksum field above contains a CRC-16
%%% checksum as the first value, followed by the
%%% equivalent of the standard UNIX wc (word
%%% count) utility output of lines, words, and
%%% characters. This is produced by Robert
%%% Solovay's checksum utility."
%%% }
%%% ======================================================================
% ****** Start of file aps12.sty ******
%
%
% This file is part of the APS files in the REVTeX 3.0 distribution.
% Version 3.0 of REVTeX, November 10, 1992.
%
% Copyright (c) 1992 The American Physical Society.
%
% See the REVTeX 3.0 README file for restrictions and more information.
%
\typeout{Filename: aps12.sty, v3.0 <2 October 1992>}
\lineskip 1pt
\normallineskip 1pt
\edef\baselinestretch{\if@tightenlines1\else1.655\fi}
\def\@normalsize{\@setsize\normalsize{14.5pt}\xiipt\@xiipt
\abovedisplayskip 12\p@ plus3\p@ minus7\p@
\belowdisplayskip \abovedisplayskip
\abovedisplayshortskip \z@ plus3\p@
\belowdisplayshortskip 6.5\p@ plus3.5\p@ minus3\p@
\let\@listi\@listI}
\def\small{\@setsize\small{14.5pt}\xipt\@xipt
\abovedisplayskip 11\p@ plus3\p@ minus6\p@
\belowdisplayskip \abovedisplayskip
\abovedisplayshortskip \z@ plus3\p@
\belowdisplayshortskip 6.5\p@ plus3.5\p@ minus3\p@
\def\@listi{\leftmargin\leftmargini
\parsep 4.5\p@ plus2\p@ minus\p@ \itemsep \parsep
\topsep 9\p@ plus3\p@ minus5\p@}}
\def\footnotesize{\@setsize\footnotesize{14.5pt}\xpt\@xpt
\abovedisplayskip 10\p@ plus2\p@ minus5\p@
\belowdisplayskip \abovedisplayskip
\abovedisplayshortskip \z@ plus3\p@
\belowdisplayshortskip 6\p@ plus3\p@ minus3\p@
\def\@listi{\leftmargin\leftmargini
\topsep 6\p@ plus2\p@ minus2\p@\parsep 3\p@ plus2\p@ minus\p@
\itemsep \parsep}}
\def\scriptsize{\@setsize\scriptsize{9.5pt}\viiipt\@viiipt}
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\def\large{\@setsize\large{18pt}\xivpt\@xivpt}
\def\Large{\@setsize\Large{22pt}\xviipt\@xviipt}
\def\LARGE{\@setsize\LARGE{25pt}\xxpt\@xxpt}
\def\huge{\@setsize\huge{30pt}\xxvpt\@xxvpt}
\let\Huge=\huge
\normalsize
\if@twoside
\oddsidemargin .25in
\evensidemargin -.25in
\marginparwidth 60pt
\else
\oddsidemargin 0pt
\evensidemargin 0pt
\marginparwidth 44pt
\fi
\marginparsep 10pt
\topmargin -37pt
\headheight 12pt
\headsep 25pt
\topskip 10pt
\footskip 30pt
\if@tightenlines
\textheight = 44\baselineskip
\else
\textheight = 27\baselineskip
\fi
\advance\textheight by \topskip
\textwidth 468pt
\displaywidth\textwidth %
\linewidth\textwidth %
\let\narrowtext=\relax
\let\mediumtext=\relax
\let\widetext=\relax
\columnsep 10pt
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\footnotesep 2pc
\skip\footins 25.25pt plus 4pt minus 2pt
\def\footnoterule{\kern-5.25pt\hrule width.5in\kern4.85pt}
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\@lowpenalty 51
\@medpenalty 151
\@highpenalty 301
\@beginparpenalty -\@lowpenalty
\@endparpenalty -\@lowpenalty
\@itempenalty -\@lowpenalty
\newif\if@mainhead
\def\section{\@mainheadtrue
\@startsection {section}{1}{\z@}{0.8cm plus1ex minus
.2ex}{0.5cm plus1ex minus.2ex}{\reset@font\small\bf\centering}}
\def\subsection{\@mainheadfalse
\@startsection{subsection}{2}{\z@}{0.8cm plus1ex minus
.2ex}{0.5cm plus1ex minus.2ex}{\reset@font\small\bf\centering}}
\def\subsubsection{\@mainheadfalse
\@startsection{subsubsection}{3}{\z@}{.8cm plus1ex minus
.2ex}{0.5cm plus1ex minus.2ex}{\reset@font\small\it\centering}}
\def\paragraph{\@mainheadfalse
\@startsection{paragraph}{4}{\parindent}{\z@}{-1em}{\reset@font
\normalsize\it}}
\def\subparagraph{\@mainheadfalse
\@startsection{subparagraph}{4}{\parindent}{3.25ex plus1ex minus
.2ex}{-1em}{\reset@font\normalsize\bf}}
\setcounter{secnumdepth}{4}
\newif\ifappendixon \global\appendixonfalse
\def\appendix{\par\global\appendixontrue
\setcounter{section}{0}
\setcounter{subsection}{0}
\setcounter{subsubsection}{0}
\def\thesection{\Alph{section}}
\def\thesubsection{\arabic{subsection}}
\def\thesubsubsection{\alph{subsubsection}}
\def\theequation@prefix{\thesection}
\@addtoreset{equation}{section}
\addcontentsline{toc}{section}{\protect\numberline{APPENDIXES\hskip
0pt plus1fill minus1fill\relax}{}}
}
\leftmargini 2.5em
\leftmarginii 2.2em
\leftmarginiii 1.87em
\leftmarginiv 1.7em
\leftmarginv 1em
\leftmarginvi 1em
\leftmargin\leftmargini
\labelsep .5em
\labelwidth\leftmargini\advance\labelwidth-\labelsep
\def\@listI{\leftmargin\leftmargini \parsep 5\p@ plus2.5\p@ minus\p@
\topsep 10\p@ plus4\p@ minus6\p@
\itemsep 5\p@ plus2.5\p@ minus\p@}
\let\@listi\@listI
\@listi
\def\@listii{\leftmargin\leftmarginii
\labelwidth\leftmarginii\advance\labelwidth-\labelsep
\topsep 5\p@ plus2.5\p@ minus\p@
\parsep 2.5\p@ plus\p@ minus\p@
\itemsep \parsep}
\def\@listiii{\leftmargin\leftmarginiii
\labelwidth\leftmarginiii\advance\labelwidth-\labelsep
\topsep 2.5\p@ plus\p@ minus\p@
\parsep \z@ \partopsep \p@ plus\z@ minus\p@
\itemsep \topsep}
\def\@listiv{\leftmargin\leftmarginiv
\labelwidth\leftmarginiv\advance\labelwidth-\labelsep}
\def\@listv{\leftmargin\leftmarginv
\labelwidth\leftmarginv\advance\labelwidth-\labelsep}
\def\@listvi{\leftmargin\leftmarginvi
\labelwidth\leftmarginvi\advance\labelwidth-\labelsep}
\if@amssymbols %
\def\@tempa{%
\let\gtrsim\undefined \let\lesssim\undefined
\let\precsim\undefined \let\succsim\undefined
\def\corresponds{\triangleq}%
\@ifundefined{selectfont}%
{}%
{\input{amssymb.sty}%
\let\Finv\undefined \newsymbol\Finv 2060
\let\Game\undefined \newsymbol\Game 2061
\let\Bbbk\undefined \newsymbol\Bbbk 207C
\let\diagup\undefined \newsymbol\diagup 231E
\let\diagdown\undefined \newsymbol\diagdown 231F
\endinput}%
}
\else %
\if@amsfonts %
\def\@tempa{\@ifundefined{selectfont}{}{\input{amsfonts.sty}\endinput}}
\else %
\let\@tempa\endinput
\fi
\fi
\@tempa
\def\frak{\protect\pfrak} \def\Bbb{\protect\pBbb}
\newfam\msamfam
\font\frtnmsam=msam10\@magscale2 \font\twlmsam=msam10\@magscale1
\font\elvmsam=msam10\@halfmag \font\egtmsam=msam8 \font\sixmsam=msam6
\newfam\msbmfam
\font\frtnmsbm=msbm10\@magscale2 \font\twlmsbm=msbm10\@magscale1
\font\elvmsbm=msbm10\@halfmag \font\egtmsbm=msbm8 \font\sixmsbm=msbm6
\newfam\euffam
\font\frtneufm=eufm10\@magscale2 \font\twleufm=eufm10\@magscale1
\font\elveufm=eufm10\@halfmag \font\egteufm=eufm8 \font\sixeufm=eufm6
\def\fontextras#1#2#3{%
\def\pfrak{\fam\euffam\elveufm}\textfont\euffam\elveufm
\scriptfont\euffam\egteufm \scriptscriptfont\euffam\sixeufm
\textfont\msamfam\elvmsam \scriptfont\msamfam\egtmsam
\scriptscriptfont\msamfam\sixmsam
\def\pBbb{\fam\msbmfam\elvmsbm}\textfont\msbmfam\elvmsbm
\scriptfont\msbmfam\egtmsbm \scriptscriptfont\msbmfam\sixmsbm
\def\boldmath{\@ifundefined{#1elvmib}%
{\expandafter\global\expandafter\def\csname#1elvmib\endcsname{}%
\global\font\elvmib=cmmib10\@halfmag\global\font\egtmib=cmmib8\global
\font\sixmib=cmmib6%
\global\font\elvbsy=cmbsy10\@halfmag\global\font\egtbsy=cmbsy8\global
\font\sixbsy=cmbsy6%
\global\font\elveufb=eufb10\@halfmag\global\font\egteufb=eufb8\global
\font\sixeufb=eufb6\global\font#2=#3\relax
\expandafter\@addfontinfo\csname#1\endcsname
{\def\boldmath{\@prtct\@nomathbold
\everymath{\mit}\everydisplay{\mit}%
\textfont\@ne\elvmib \scriptfont\@ne\egtmib \scriptscriptfont\@ne\sixmib
\textfont\tw@\elvbsy \scriptfont\tw@\egtbsy \scriptscriptfont\tw@\sixbsy
\textfont\euffam\elveufb \scriptfont\euffam\egteufb
\scriptscriptfont\euffam\sixeufb
\textfont\lyfam#2\relax
\@prtct\@boldtrue}%
}%
}%
{}\csname#1\endcsname\boldmath
}%
}
\expandafter\def\expandafter\xpt\expandafter{\xpt%
\fontextras{@xpt}\tenlyb{lasyb10}%
}
\expandafter\def\expandafter\xipt\expandafter{\xipt%
\fontextras{@xipt}\elvlyb{lasyb10\@halfmag}%
}
\expandafter\def\expandafter\xiipt\expandafter{\xiipt%
\def\pfrak{\fam\euffam\twleufm}\textfont\euffam\twleufm
\scriptfont\euffam\egteufm \scriptscriptfont\euffam\sixeufm
\textfont\msamfam\twlmsam \scriptfont\msamfam\egtmsam
\scriptscriptfont\msamfam\sixmsam
\def\pBbb{\fam\msbmfam\twlmsbm}\textfont\msbmfam\twlmsbm
\scriptfont\msbmfam\egtmsbm \scriptscriptfont\msbmfam\sixmsbm
\def\boldmath{\@ifundefined{twlmib}%
{\global\font\twlmib=cmmib10\@magscale1\global\font\egtmib=cmmib8\global
\font\sixmib=cmmib6%
\global\font\twlbsy=cmbsy10\@magscale1\global\font\egtbsy=cmbsy8\global
\font\sixbsy=cmbsy6%
\global\font\twleufb=eufb10\@magscale1\global\font\egteufb=eufb8\global
\font\sixeufb=eufb6
\global\font\twllyb=lasyb10\@magscale1\relax
\@addfontinfo\@xiipt{\def\boldmath{\@prtct\@nomathbold
\everymath{\mit}\everydisplay{\mit}%
\textfont\@ne\twlmib \scriptfont\@ne\egtmib \scriptscriptfont\@ne\sixmib
\textfont\tw@\twlbsy \scriptfont\tw@\egtbsy \scriptscriptfont\tw@\sixbsy
\textfont\euffam\twleufb \scriptfont\euffam\egteufb
\scriptscriptfont\euffam\sixeufb
\textfont\lyfam\twllyb
\@prtct\@boldtrue}%
}%
}%
{}\@xiipt\boldmath
}%
}
\expandafter\def\expandafter\xivpt\expandafter{\xivpt%
\def\pfrak{\fam\euffam\frtneufm}\textfont\euffam\frtneufm
\scriptfont\euffam\elveufm \scriptscriptfont\euffam\egteufm
\textfont\msamfam\frtnmsam \scriptfont\msamfam\elvmsam
\scriptscriptfont\msamfam\egtmsam
\def\pBbb{\fam\msbmfam\frtnmsbm}\textfont\msbmfam\frtnmsbm
\scriptfont\msbmfam\elvmsbm \scriptscriptfont\msbmfam\egtmsbm
\def\boldmath{\@ifundefined{frtnmib}%
{\global\font\frtnmib=cmmib10\@magscale2\global\font\elvmib=cmmib10\@halfmag
\global\font\egtmib=cmmib8%
\global\font\frtnbsy=cmbsy10\@magscale2\global\font\elvbsy=cmbsy10\@halfmag
\global\font\egtbsy=cmbsy8%
\global\font\frtneufb=eufb10\@magscale2\global\font\elveufb=eufb10\@halfmag
\global\font\egteufb=eufb8
\global\font\frtnlyb=lasyb10\@magscale2\relax
\@addfontinfo\@xivpt{\def\boldmath{\@prtct\@nomathbold
\everymath{\mit}\everydisplay{\mit}%
\textfont\@ne\frtnmib \scriptfont\@ne\elvmib \scriptscriptfont\@ne\egtmib
\textfont\tw@\frtnbsy \scriptfont\tw@\elvbsy \scriptscriptfont\tw@\egtbsy
\textfont\euffam\frtneufb \scriptfont\euffam\elveufb
\scriptscriptfont\euffam\egteufb
\textfont\lyfam\frtnlyb
\@prtct\@boldtrue}%
}%
}%
{}\@xivpt\boldmath
}%
}
\def\undefine#1{\let#1\undefined}
\def\newsymbol#1#2#3#4#5{\let\next@\relax
\ifnum#2=\@ne\let\next@\msafam@\else
\ifnum#2=\tw@\let\next@\msbfam@\fi\fi
\mathchardef#1="#3\next@#4#5}
\def\hexnumber@#1{\ifcase#1 0\or 1\or 2\or 3\or 4\or 5\or 6\or 7\or 8\or
9\or A\or B\or C\or D\or E\or F\fi}
\edef\msafam@{\hexnumber@\msamfam}
\mathchardef\dabar@"0\msafam@39
\def\dashrightarrow{\mathrel{\dabar@\dabar@\mathchar"0\msafam@4B}}
\def\dashleftarrow{\mathrel{\mathchar"0\msafam@4C\dabar@\dabar@}}
\let\dasharrow\dashrightarrow
\def\ulcorner{\delimiter"4\msafam@70\msafam@70 }
\def\urcorner{\delimiter"5\msafam@71\msafam@71 }
\def\llcorner{\delimiter"4\msafam@78\msafam@78 }
\def\lrcorner{\delimiter"5\msafam@79\msafam@79 }
\def\yen{{\mathhexbox@\msafam@55 }}
\def\checkmark{{\mathhexbox\msafam@58 }}
\def\circledR{{\mathhexbox\msafam@72 }}
\def\maltese{{\mathhexbox\msafam@7A }}
\edef\msbfam@{\hexnumber@\msbmfam}
\def\widehat#1{\setbox\z@\hbox{$\m@th#1$}%
\ifdim\wd\z@>\tw@ em\mathaccent"0\msbfam@5B{#1}%
\else\mathaccent"0362{#1}\fi}
\def\widetilde#1{\setbox\z@\hbox{$\m@th#1$}%
\ifdim\wd\z@>\tw@ em\mathaccent"0\msbfam@5D{#1}%
\else\mathaccent"0365{#1}\fi}
\undefine\Box \newsymbol\Box 1203
\undefine\Diamond \newsymbol\Diamond 1206
\undefine\leadsto \newsymbol\leadsto 1320
\undefine\lhd \newsymbol\lhd 1343
\undefine\unlhd \newsymbol\unlhd 1345
\undefine\rhd \newsymbol\rhd 1342
\undefine\unrhd \newsymbol\unrhd 1344
\edef\Join{\mathrel{\mathchar"0\msbfam@ 6F\mkern-13.8mu%
\mathchar"0\msbfam@ 6E}}
\if@amssymbols %
\expandafter\def\csname amsfonts.sty\endcsname{}
\input{amssymb.sty}
\undefine\Finv \newsymbol\Finv 2060
\undefine\Game \newsymbol\Game 2061
\undefine\Bbbk \newsymbol\Bbbk 207C
\undefine\diagup \newsymbol\diagup 231E
\undefine\diagdown \newsymbol\diagdown 231F
\fi
\endinput
%
% ****** End of file aps12.sty ******