% Blackwell Science MN journal document style

% v1.4, released 14th September 1995

%

% Copyright (C) Cambridge University Press 1994

%    for LaTeX version 2.09, 1988, by Leslie Lamport

%    based on the original LaTeX ARTICLE DOCUMENT STYLE

%    modifications by Sue Brooks, Alison Woollatt and Mark Reed 1993, 1994

%

% > Incorporating also parts of authordate.sty

%   by David Rhead, Cripps Computing Centre (Feb 1990).

% > Incorporating special symbol code from laa.sty v1.1 (25th Feb 1991)

%   used with the permission of Springer Verlag.

% > Incorporating parts of mssymb.tex (8th July 1987).

% > Incorporating newfont.sty vALPHA pl 8 (16th August 1994), by M. Reed

%

% v0.1.01  SFB text area, abstract heading, secnumdepth, 

%          \dblfloatpagefraction

% v0.1.02  SFB landscape, galley and referee options;

%          new catchline; enumerated lists; correct raggedright 

%          on section headings;

% v0.1.03  SFB continued floats with \caption* (removed now),

%          short captions centred

% v0.1.04  SFB appendices, unnumbered list (using description)

% v0.1.05  AJW roman catchline, final statement

% v1.0     RM  BSP note, \bsp, added to cup specials

% v1.1     AJW / MR, 28th January 1994. NFSS 1/2 compatible, 

%          Springer-Verlag macros added

% v1.2     AJW, 18th July 1994. Improved cont. captions, 

%          MR font selection check improved,

%          MR removed some redundant code, AW \sevensize added,

%          MR Added MR's `NewFont' support, MR Improved NFSS 1/2 support,

%          MR Added support for Bold math and AMS symbols for NFSS 1,

%          MR par's in abstract now have par indents.

%          MR added \ifCUPmtlplainloaded switch for use in documents.

%          MR Added mnsym.tex (for Times version).

% v1.25    MR, not released to authors 16th August 1994.

%          Replaced existing Newfont.sty code with updated code, after

%          discovering several bugs. This version not released to authors

%          because they are unlikely to find the bugs unless:

%          1) they have an extremely long article,

%          2) have used many \New.. commands (no docs were supplied for

%          these anyway).

% v1.3     MR, 5 September 1994. Added printing of style file version to

%          'Printed' info in catchline. Will help us identify how the 

%          article was produced (TeX/LaTeX) and the version number of the

%          macros.

%          MR Tables and Figures no longer get double spaced when using the

%          `referee' or `doublespacing' options.

%          MR Corrected 7th footnote symbol: made a \star\star (was **).

%          MR Corrected problem where some headings were not upper-case

%          when they should have been (\section*).

% v1.4     AJW, 14th September 1995. Add footlines and \newauthor,

%          correct \listparindent in enumerate environment.



\newif\ifoldfss

\newif\ifnfssone

\newif\ifnfsstwo

\def\f@s@s{}



\@ifundefined{DeclareFontShape}%

  {%

   \@ifundefined{selectfont}%

    {\global\oldfsstrue\let\reset@font=\relax%

     \def\f@s@s{with OFSS,\space}}% old font selection scheme

    {\global\nfssonetrue\def\f@s@s{with NFSS release 1,\space}}%

  }%

  {\global\nfsstwotrue\def\f@s@s{with NFSS release 2,\space}}%



\def\@version{1.4}



\typeout{Document Style `MN' \f@s@s v\@version, released 14th September 1995}



%  Journals use two-sided printing.

%

\@twosidetrue

\@twocolumntrue

\@mparswitchtrue

\def\ds@draft{\overfullrule 5pt}

\def\ds@twocolumn{\@twocolumntrue}

\def\ds@onecolumn{\@twocolumnfalse}



% letters option

%

\newif\if@letters

\def\ds@letters{\@letterstrue}



% landscape option

%

\newif\ifSFB@landscape

\def\ds@landscape{\SFB@landscapetrue}



% galley option

%

\newif\ifSFB@galley

\def\ds@galley{\SFB@galleytrue}



% referee option

%

\newif\ifSFB@referee

\def\ds@referee{%

 \SFB@refereetrue

 \@twocolumnfalse

}

\newif\ifdoublesp@cing

\def\ds@doublespacing{%

 \doublesp@cingtrue

}%

\@options

%

%  ****************************************

%  *               FONTS                  *

%  ****************************************

%

\lineskip 1pt

\normallineskip 1pt

\ifSFB@referee

  \def\baselinestretch{1.5}

\else

  \ifdoublesp@cing

  \def\baselinestretch{2}

\else

  \def\baselinestretch{1}

\fi\fi

\if@twocolumn

  \def\@normalsize{\@setsize\normalsize{11pt}\ixpt\@ixpt

   \abovedisplayskip 6pt plus 2pt minus 2pt

   \belowdisplayskip \abovedisplayskip

   \abovedisplayshortskip 6pt plus 2pt

   \belowdisplayshortskip \abovedisplayshortskip

   \let\@listi\@listI}

 \else

 \ifSFB@referee

  \def\@normalsize{\@setsize\normalsize{14pt}\xiipt\@xiipt

   \abovedisplayskip 4pt plus 1pt minus 1pt

   \belowdisplayskip \abovedisplayskip

   \abovedisplayshortskip 4pt plus 1pt

   \belowdisplayshortskip \abovedisplayshortskip

   \let\@listi\@listI}

 \else

  \def\@normalsize{\@setsize\normalsize{12pt}\ixpt\@ixpt

   \abovedisplayskip 4pt plus 1pt minus 1pt

   \belowdisplayskip \abovedisplayskip

   \abovedisplayshortskip 4pt plus 1pt

   \belowdisplayshortskip \abovedisplayshortskip

   \let\@listi\@listI}

 \fi

\fi

\def\small{\@setsize\small{10pt}\viiipt\@viiipt

 \abovedisplayskip 4pt plus 1pt minus 1pt

 \belowdisplayskip \abovedisplayskip

 \abovedisplayshortskip 4pt plus 1pt

 \belowdisplayshortskip \abovedisplayshortskip

 \def\@listi{\leftmargin\leftmargini

  \topsep 2pt plus 1pt minus 1pt

  \parsep \z@

  \itemsep 2pt}}

\def\footnotesize{\@setsize\footnotesize{10pt}\viiipt\@viiipt

 \abovedisplayskip 4pt plus 1pt minus 1pt

 \belowdisplayskip \abovedisplayskip

 \abovedisplayshortskip 4pt plus 1pt

 \belowdisplayshortskip \abovedisplayshortskip

 \def\@listi{\leftmargin\leftmargini

  \topsep 2pt plus 1pt minus 1pt

  \parsep \z@

  \itemsep 2pt}}

\def\scriptsize{\@setsize\scriptsize{8pt}\vipt\@vipt}

\def\tiny{\@setsize\tiny{6pt}\vpt\@vpt}

%

\if@twocolumn

  \def\large{\@setsize\large{11pt}\xpt\@xpt}

 \else

  \def\large{\@setsize\large{12pt}\xpt\@xpt}

 \fi

\def\Large{\@setsize\Large{14pt}\xiipt\@xiipt}

\def\LARGE{\@setsize\LARGE{17pt}\xivpt\@xivpt}

\def\huge{\@setsize\huge{20pt}\xviipt\@xviipt}

\def\Huge{\@setsize\Huge{25pt}\xxpt\@xxpt}

%

\def\sevensize{\@setsize\sevensize{8pt}\viipt\@viipt}

%

\normalsize



%%%%%%%%%%%%%%%%%%%%%%%% Extra Math / Symbol code %%%%%%%%%%%%%%%%%%%%%%%%



\def\hexnumber#1{\ifcase#1 0\or1\or2\or3\or4\or5\or6\or7%

  \or8\or9\or A\or B\or C\or D\or E\or F\fi}



\def\setboxz@h{\setbox\z@\hbox}

\def\wdz@{\wd\z@}

\def\boxz@{\box\z@}

\def\setbox@ne{\setbox\@ne}

\def\wd@ne{\wd\@ne}



\def\math@atom#1#2{%

   \binrel@{#1}\binrel@@{#2}}

\def\binrel@#1{\setboxz@h{\thinmuskip0mu

  \medmuskip\m@ne mu\thickmuskip\@ne mu$#1\m@th$}%

 \setbox@ne\hbox{\thinmuskip0mu\medmuskip\m@ne mu\thickmuskip

  \@ne mu${}#1{}\m@th$}%

 \setbox\tw@\hbox{\hskip\wd@ne\hskip-\wdz@}}

\def\binrel@@#1{\ifdim\wd2<\z@\mathbin{#1}\else\ifdim\wd\tw@>\z@

 \mathrel{#1}\else{#1}\fi\fi}



% These must be here because \newif and \newtoks are defined \outer.

\newif\iffirstta

\newtoks\math@groups

\newif\ifd@f



\ifoldfss

%

% newfont.sty

% ALPHA VERSION patchlevel 8, 16th August 1994, M. Reed



% \addtom@thgroup{math font loading info}

% Adds to internal \math@groups definition, which is executed at the end

% of each size changing command. It is called by \NewSymbolFont.



\math@groups={}

\def\addtom@thgroup#1#2{#1\expandafter{\the#1#2}} %  \mac={new\the\mac}





% Redefine \@setsize to allow math fonts to be reloaded automatically.

% \@setsize\SIZE{BASELINESKIP}\FONTSIZE\@FONTSIZE

% \@setsize\tiny{6pt}\vpt\@vpt



\def\@setsize#1#2#3#4{\@nomath#1\let\@currsize#1\baselineskip

   #2\setbox\strutbox\hbox{\vrule height.7\baselineskip

      depth.3\baselineskip width\z@}\baselineskip\baselinestretch\baselineskip

   \normalbaselineskip\baselineskip#3#4\relax

   \the\math@groups

}





% Make LaTeX change the values of \s@ze, \ss@ze, \sss@ze when \@npt is

% executed. This makes it possible for math characters to be loaded

% at the correct size automatically when the size is changed.



% \addtosizeh@ok{x}{10}{7}{5}



\def\addtosizeh@ok#1#2#3#4{%

  \expandafter\def\csname @#1pt\endcsname{%

    \def\s@ze{#2}\def\ss@ze{#3}\def\sss@ze{#4}%

  }%

}





% \resetsizehook allows the size parameters to be reset after \addtosizeh@ok

% has been called (it re-defines \@npt).

% e.g JFM which requires \xpt to have 10.5pt instead of 10pt.

% Note: \resetsizehook must be used BEFORE \begin{document}, and BEFORE any

% \New... commands.



% e.g. \resetsizehook{x}{10.5}{7}{5}



\let\resetsizehook=\addtosizeh@ok





% Standard LaTeX sizes



\ifx\CUP@mtlplain@loaded\undefined

  \addtosizeh@ok{v}    {5}     {5}     {5}

  \addtosizeh@ok{vi}   {6}     {6}     {6}

  \addtosizeh@ok{vii}  {7}     {6}     {5}

  \addtosizeh@ok{viii} {8}     {6}     {5}

  \addtosizeh@ok{ix}   {9}     {6}     {5}

  \addtosizeh@ok{x}    {10}    {7}     {5}

  \addtosizeh@ok{xi}   {10.95} {8}     {6}

  \addtosizeh@ok{xii}  {12}    {8}     {6}

  \addtosizeh@ok{xiv}  {14.4}  {10}    {7}

  \addtosizeh@ok{xvii} {17.28} {12}    {10}

  \addtosizeh@ok{xx}   {20.74} {14.4}  {12}

  \addtosizeh@ok{xxv}  {24.88} {20.74} {17.28}

\else

  \addtosizeh@ok{v}    {5} {5}  {5}

  \addtosizeh@ok{vi}   {6} {6}  {6}

  \addtosizeh@ok{vii}  {7} {6}  {5}

  \addtosizeh@ok{viii} {8} {6}  {5}

  \addtosizeh@ok{ix}   {9} {6}  {5}

  \addtosizeh@ok{x}    {10}{7}  {5}

  \addtosizeh@ok{xi}   {11}{8}  {6}

  \addtosizeh@ok{xii}  {12}{8}  {6}

  \addtosizeh@ok{xiv}  {14}{10} {7}

  \addtosizeh@ok{xvii} {17}{12}{10}

  \addtosizeh@ok{xx}   {20}{14}{12}

  \addtosizeh@ok{xxv}  {25}{20}{17}

\fi





\def\get@font#1#2#3{%

  \edef\fonts@ze{\romannumeral#3}%         10 -> x

  \edef\fontn@me{\fonts@ze#1}%             AMSa -> xAMSa

  \@ifundefined{\fontn@me}%

    {%%\typeout{defining \fontn@me}%

     \global\expandafter\font\csname \fontn@me\endcsname=#2 at #3pt}%

    {}%

}



\def\ass@tfont#1#2{%

  \xdef\fam@name{\csname #1\endcsname}%

  \xdef\font@name{\csname #2\endcsname}%

  \let\textfont@name\font@name

  \textfont\fam@name\textfont@name

}



\def\ass@sfont#1#2{%

  \xdef\fam@name{\csname #1\endcsname}%

  \xdef\font@name{\csname #2\endcsname}%

  \let\textfont@name\font@name

  \scriptfont\fam@name\textfont@name

}



\def\ass@ssfont#1#2{%

  \xdef\fam@name{\csname #1\endcsname}%

  \xdef\font@name{\csname #2\endcsname}%

  \let\textfont@name\font@name

  \scriptscriptfont\fam@name\textfont@name

}





%                fam name  base font  (allocates a \newfam)

% \NewSymbolFont {AMSa}    {mtxm10}



\def\NewSymbolFont#1#2{%

  \expandafter\ifx\csname sym#1fam\endcsname\relax % if not defined

    \expandafter\newfam\csname sym#1fam\endcsname

    \expandafter\edef\csname sym#1fam\endcsname{\the\allocationnumber}%

    \addtom@thgroup\math@groups{%

      \get@font{#1}{#2}{\s@ze}%

      \ass@tfont{sym#1fam}{\fontn@me}%

      \get@font{#1}{#2}{\ss@ze}%

      \ass@sfont{sym#1fam}{\fontn@me}%

      \get@font{#1}{#2}{\sss@ze}%

      \ass@ssfont{sym#1fam}{\fontn@me}%

    }%

  \else

    \errmessage{Family `#1' already defined}%

  \fi

}





%                symbol         type fam    pos (hex)

% \NewMathSymbol {\blacksquare} {0}  {AMSa} {04}



\def\NewMathSymbol#1#2#3#4{%

  \edef\f@mly{\expandafter\hexnumber{\csname sym#3fam\endcsname}}%

  \mathchardef#1="#2\f@mly#4\relax

}





%                  macro name  type  fam1   pos  fam2   pos

% \NewMathDelimiter{\ulcorner} {4}   {AMSa} {70} {AMSb} {70}



\def\NewMathDelimiter#1#2#3#4#5#6{%

  \d@ftrue

  \expandafter\ifx\csname sym#3fam\endcsname\relax

    \d@ffalse \errmessage{Family `#3' is not defined}%

  \fi

  \expandafter\ifx\csname sym#5fam\endcsname\relax

    \d@ffalse \errmessage{Family `#5' is not defined}%

  \fi

  \ifd@f

    \edef\f@mly{\expandafter\hexnumber{\csname sym#3fam\endcsname}}%

    \edef\f@mlytw@{\expandafter\hexnumber{\csname sym#5fam\endcsname}}%

    \xdef#1{\delimiter"#2\f@mly #4\f@mlytw@ #6\relax}%

  \fi

}





%                  macro name  base font  skewchar setting e.g '60 (octal)

% \NewMathAlphabet {mathbssi}  {mtmisb10} {}



\def\m@thit{1}



\def\set@skchar#1{\global\expandafter\skewchar

  \csname\fontn@me\endcsname=#1\relax}



\def\NewMathAlphabet#1#2#3{%

  \def\tst{#3}%

  \ifx\tst\empty\else % if a \skewchar setting is present

    \expandafter\gdef\csname #1@sc\endcsname{}%  \def\cmd@sc{..}

  \fi

  %

  \expandafter\def\csname #1\endcsname{%  \def\cmd{\protect\@cmd}

    \protect\csname @#1\endcsname}%

  %

  \expandafter\def\csname @#1\endcsname##1{%  \def\@cmd{..}

    {%

    \begingroup

      \get@font{#1}{#2}{\s@ze}%

      \@ifundefined{#1@sc}{}{\set@skchar{#3}}%

      \ass@tfont{m@thit}{\fontn@me}%

      \get@font{#1}{#2}{\ss@ze}%

      \@ifundefined{#1@sc}{}{\set@skchar{#3}}%

      \ass@sfont{m@thit}{\fontn@me}%

      \get@font{#1}{#2}{\sss@ze}%

      \@ifundefined{#1@sc}{}{\set@skchar{#3}}%

      \ass@ssfont{m@thit}{\fontn@me}%

      %

      \math@atom{##1}{%

      \mathchoice%

        {\hbox{$\m@th\displaystyle##1$}}%

        {\hbox{$\m@th\textstyle##1$}}%

        {\hbox{$\m@th\scriptstyle##1$}}%

        {\hbox{$\m@th\scriptscriptstyle##1$}}}%

    \endgroup

    }%

  }%

}





%                  macro name  base font  hyphenchar setting e.g -1 (off)

% \NewTextAlphabet {textbfit}  {mtbxti10} {}



% save a family if \NewTextAlphabet is not used.

\firsttatrue



\def\set@hchar#1{\global\expandafter\hyphenchar

  \csname\fontn@me\endcsname=#1\relax}



\def\NewTextAlphabet#1#2#3{%

  \iffirstta

    \global\firsttafalse

    \newfam\scratchfam

    \edef\scrt@fam{\the\allocationnumber}%

  \fi

  \def\tst{#3}%

  \ifx\tst\empty\else % if a \hyphenchar setting is required

    \expandafter\gdef\csname #1@hc\endcsname{}%  \def\cmd@sc{..}

  \fi

  %

  \expandafter\def\csname #1\endcsname{%  \def\cmd{\protect\t@cmd}

    \protect\csname t@#1\endcsname}%

  %

  \long\expandafter\def\csname t@#1\endcsname##1{%  \def\t@cmd{..}

    \ifmmode

      \typeout{Warning: do not use \expandafter\string\csname #1\endcsname

        \space in math mode}\fi%

    {%

      \get@font{#1}{#2}{\s@ze}\let\t@xtfnt=\fontn@me\relax

      \@ifundefined{#1@hc}{}{\set@hchar{#3}}%

      \ass@tfont{scrt@fam}{\fontn@me}%

      \get@font{#1}{#2}{\ss@ze}%

      \@ifundefined{#1@hc}{}{\set@hchar{#3}}%

      \ass@sfont{scrt@fam}{\fontn@me}%

      \get@font{#1}{#2}{\sss@ze}%

      \@ifundefined{#1@hc}{}{\set@hchar{#3}}%

      \ass@ssfont{scrt@fam}{\fontn@me}%

      \fam\scratchfam\csname\t@xtfnt\endcsname

    ##1%

    }%

  }%

  %

  \expandafter\def\csname #1shape%  \def\cmdshape{\protect\@cmdshape}

    \endcsname{\protect\csname @#1shape\endcsname}%

  %

  \expandafter\def\csname @#1shape\endcsname{%  \def\@cmdshape

    \ifmmode

      \typeout{Warning: do not use \expandafter\string\csname

        #1shape\endcsname \space in math mode}\fi

      %

      \get@font{#1}{#2}{\s@ze}\let\t@xtfnt=\fontn@me\relax

      \@ifundefined{#1@hc}{}{\set@hchar{#3}}%

      \ass@tfont{scrt@fam}{\fontn@me}%

      \get@font{#1}{#2}{\ss@ze}%

      \@ifundefined{#1@hc}{}{\set@hchar{#3}}%

      \ass@sfont{scrt@fam}{\fontn@me}%

      \get@font{#1}{#2}{\sss@ze}%

      \@ifundefined{#1@hc}{}{\set@hchar{#3}}%

      \ass@ssfont{scrt@fam}{\fontn@me}%

      \fam\scratchfam\csname\t@xtfnt\endcsname

  }%

}





% \bmath{math text}



\ifx\CUP@mtlplain@loaded\undefined

  \def\math@itfnt{cmmib10}

  \def\math@syfnt{cmbsy10}

\else

  \def\math@itfnt{mtmib10}

  \def\math@syfnt{mtbsy10}

\fi



\def\m@thsy{2}



\def\bmath{\protect\@bmath}

\def\@bmath#1{%

  {%

  \begingroup

    \get@font{mthit}{\math@itfnt}{\s@ze}\set@skchar{'177}%

    \ass@tfont{m@thit}{\fontn@me}%

    \get@font{mthit}{\math@itfnt}{\ss@ze}\set@skchar{'177}%

    \ass@sfont{m@thit}{\fontn@me}%

    \get@font{mthit}{\math@itfnt}{\sss@ze}\set@skchar{'177}%

    \ass@ssfont{m@thit}{\fontn@me}%

    %

    \get@font{mthsy}{\math@syfnt}{\s@ze}\set@skchar{'60}%

    \ass@tfont{m@thsy}{\fontn@me}%

    \get@font{mthsy}{\math@syfnt}{\ss@ze}\set@skchar{'60}%

    \ass@sfont{m@thsy}{\fontn@me}%

    \get@font{mthsy}{\math@syfnt}{\sss@ze}\set@skchar{'60}%

    \ass@ssfont{m@thsy}{\fontn@me}%

    %

    \math@atom{#1}{%

    \mathchoice%

      {\hbox{$\m@th\displaystyle#1$}}%

      {\hbox{$\m@th\textstyle#1$}}%

      {\hbox{$\m@th\scriptstyle#1$}}%

      {\hbox{$\m@th\scriptscriptstyle#1$}}}%

  \endgroup

  }%

}

%

\fi % End of ofss



% Make these do nothing (for backwards compatibility}

\let\loadboldmathitalic=\relax

\let\loadboldgreek=\relax



\ifoldfss % if NFSS release 1 or 2

\else

  %

  \def\mathch{\protect\p@mathch}

  \def\p@mathch#1#2{%

    \begingroup

    \let\@nomath\@gobble \mathversion{#1}%

    \math@atom{#2}{%

    \mathchoice%

      {\hbox{$\m@th\displaystyle#2$}}%

      {\hbox{$\m@th\textstyle#2$}}%

      {\hbox{$\m@th\scriptstyle#2$}}%

      {\hbox{$\m@th\scriptscriptstyle#2$}}}%

  \endgroup}

  %

  \def\bmath{\protect\p@boldm}

  \def\p@boldm#1{\mathch{bold}{#1}}

  %

\fi





% Define lowercase bold Greek.

% Use \boldeta for bold \eta (clashes with \beta).



\ifnfsstwo % if OFSS or NFSS release 1

\else

%

  \def\balpha{\bmath{\alpha}}

  \def\bbeta{\bmath{\beta}}

  \def\bgamma{\bmath{\gamma}}

  \def\bdelta{\bmath{\delta}}

  \def\bepsilon{\bmath{\epsilon}}

  \def\bzeta{\bmath{\zeta}}

  \def\boldeta{\bmath{\eta}}

  \def\btheta{\bmath{\theta}}

  \def\biota{\bmath{\iota}}

  \def\bkappa{\bmath{\kappa}}

  \def\blambda{\bmath{\lambda}}

  \def\bmu{\bmath{\mu}}

  \def\bnu{\bmath{\nu}}

  \def\bxi{\bmath{\xi}}

  \def\bpi{\bmath{\pi}}

  \def\brho{\bmath{\rho}}

  \def\bsigma{\bmath{\sigma}}

  \def\btau{\bmath{\tau}}

  \def\bupsilon{\bmath{\upsilon}}

  \def\bphi{\bmath{\phi}}

  \def\bchi{\bmath{\chi}}

  \def\bpsi{\bmath{\psi}}

  \def\bomega{\bmath{\omega}}

  \def\bvarepsilon{\bmath{\varepsilon}}

  \def\bvartheta{\bmath{\vartheta}}

  \def\bvarpi{\bmath{\varpi}}

  \def\bvarrho{\bmath{\varrho}}

  \def\bvarsigma{\bmath{\varsigma}}

  \def\bvarphi{\bmath{\varphi}}

  %

\fi



\ifnfsstwo

  %

  \let\mit=\mathnormal

  %

  % The following is needed beause NFSS release 2 does not define the bold

  % math symbol font to be available!

  %

  \SetSymbolFont{symbols}{bold}{OMS}{cmsy}{b}{n}

  %

  \DeclareSymbolFont{bmisymbols}{OML}{cmm}{b}{it}

  \DeclareMathSymbol{\balpha}{0}{bmisymbols}{"0B}

  \DeclareMathSymbol{\bbeta}{0}{bmisymbols}{"0C}

  \DeclareMathSymbol{\bgamma}{0}{bmisymbols}{"0D}

  \DeclareMathSymbol{\bdelta}{0}{bmisymbols}{"0E}

  \DeclareMathSymbol{\bepsilon}{0}{bmisymbols}{"0F}

  \DeclareMathSymbol{\bzeta}{0}{bmisymbols}{"10}

  \DeclareMathSymbol{\boldeta}{0}{bmisymbols}{"11}

  \DeclareMathSymbol{\btheta}{0}{bmisymbols}{"12}

  \DeclareMathSymbol{\biota}{0}{bmisymbols}{"13}

  \DeclareMathSymbol{\bkappa}{0}{bmisymbols}{"14}

  \DeclareMathSymbol{\blambda}{0}{bmisymbols}{"15}

  \DeclareMathSymbol{\bmu}{0}{bmisymbols}{"16}

  \DeclareMathSymbol{\bnu}{0}{bmisymbols}{"17}

  \DeclareMathSymbol{\bxi}{0}{bmisymbols}{"18}

  \DeclareMathSymbol{\bpi}{0}{bmisymbols}{"19}

  \DeclareMathSymbol{\brho}{0}{bmisymbols}{"1A}

  \DeclareMathSymbol{\bsigma}{0}{bmisymbols}{"1B}

  \DeclareMathSymbol{\btau}{0}{bmisymbols}{"1C}

  \DeclareMathSymbol{\bupsilon}{0}{bmisymbols}{"1D}

  \DeclareMathSymbol{\bphi}{0}{bmisymbols}{"1E}

  \DeclareMathSymbol{\bchi}{0}{bmisymbols}{"1F}

  \DeclareMathSymbol{\bpsi}{0}{bmisymbols}{"20}

  \DeclareMathSymbol{\bomega}{0}{bmisymbols}{"21}

  \DeclareMathSymbol{\bvarepsilon}{0}{bmisymbols}{"22}

  \DeclareMathSymbol{\bvartheta}{0}{bmisymbols}{"23}

  \DeclareMathSymbol{\bvarpi}{0}{bmisymbols}{"24}

  \DeclareMathSymbol{\bvarrho}{0}{bmisymbols}{"25}

  \DeclareMathSymbol{\bvarsigma}{0}{bmisymbols}{"26}

  \DeclareMathSymbol{\bvarphi}{0}{bmisymbols}{"27}

  %

\fi





% Define font shapes for Euler upright Math, bold upright Math,

% AMS symbol fonts A and B, sans-serif bold, bold text italic,

% math italic bold and bold math symbol.

% These font shapes are defined in mnsym.tex to use Times fonts.



\ifx\CUP@mtlplain@loaded\undefined

  %

  \ifnfssone

    %

    \new@fontshape{eur}{m}{n}{%

      <5>eurm5<6>eurm6<7>eurm7<8>eurm8<9>eurm9<10>eurm10%

      <11>eurm10 at 10.95pt<12>eurm10 at 12pt<14>eurm10 at 14.4pt%

      <17>eurm10 at 17.28pt<20>eurm10 at 20.74pt<25>eurm10 at 24.88pt}{}

    %

    \new@fontshape{eur}{b}{n}{%

      <5>eurb5<6>eurb6<7>eurb7<8>eurb8<9>eurb9<10>eurb10%

      <11>eurb10 at 10.95pt<12>eurb10 at 12pt<14>eurb10 at 14.4pt%

      <17>eurb10 at 17.28pt<20>eurb10 at 20.74pt<25>eurb10 at 24.88pt}{}

    %

    \new@fontshape{msa}{m}{n}{%

      <5>msam5<6>msam6<7>msam7<8>msam8<9>msam9<10>msam10%

      <11>msam10 at 10.95pt<12>msam10 at 12pt<14>msam10 at 14.4pt%

      <17>msam10 at 17.28pt<20>msam10 at 20.74pt<25>msam10 at 24.88pt}{}

    %

    \new@fontshape{msb}{m}{n}{%

      <5>msbm5<6>msbm6<7>msbm7<8>msbm8<9>msbm9<10>msbm10%

      <11>msbm10 at 10.95pt<12>msbm10 at 12pt<14>msbm10 at 14.4pt%

      <17>msbm10 at 17.28pt<20>msbm10 at 20.74pt<25>msbm10 at 24.88pt}{}

    %

    \new@fontshape{cmss}{bx}{n}{%

      <5>cmssbx10 at5pt<6>cmssbx10 at6pt<7>cmssbx10 at7pt<8>cmssbx10 at8pt%

      <9>cmssbx10 at9pt<10>cmssbx10<11>cmssbx10 at10.95pt<12>cmssbx10 at12pt%

      <14>cmssbx10 at14.4pt<17>cmssbx10 at17.28pt<20>cmssbx10 at20.74pt%

      <25>cmssbx10 at24.88pt}{}

    %

    \new@fontshape{cmr}{bx}{it}{%

      <5>cmbxti10 at5pt<6>cmbxti10 at6pt<7>cmbxti10 at7pt<8>cmbxti10 at8pt%

      <9>cmbxti10 at9pt<10>cmbxti10<11>cmbxti10 at10.95pt<12>cmbxti10 at12pt%

      <14>cmbxti10 at14.4pt<17>cmbxti10 at17.28pt<20>cmbxti10 at20.74pt%

      <25>cmbxti10 at24.88pt}{}

    %

    \new@fontshape{cmm}{b}{it}{%

      <5>cmmib10 at5pt<6>cmmib10 at6pt<7>cmmib10 at7pt<8>cmmib10 at8pt%

      <9>cmmib10 at9pt<10>cmmib10<11>cmmib10 at10.95pt<12>cmmib10 at12pt%

      <14>cmmib10 at14.4pt<17>cmmib10 at17.28pt<20>cmmib10 at20.74pt%

      <25>cmmib10 at24.88pt}{}

      %

    \new@fontshape{cmsy}{b}{n}{%

      <5>cmbsy10 at5pt<6>cmbsy10 at6pt<7>cmbsy10 at7pt<8>cmbsy10 at8pt%

      <9>cmbsy10 at9pt<10>cmbsy10<11>cmbsy10 at10.95pt<12>cmbsy10 at12pt%

      <14>cmbsy10 at14.4pt<17>cmbsy10 at17.28pt<20>cmbsy10 at20.74pt%

      <25>cmbsy10 at24.88pt}{}

    %

    \def\UseAMStwoboldmath{%

      \new@fontshape{cmm}{b}{it}{%

        <5>cmmib5<6>cmmib6<7>cmmib7<8>cmmib8<9>cmmib9<10>cmmib10%

        <11>cmmib10 at10.95pt<12>cmmib10 at12pt<14>cmmib10 at14.4pt%

        <17>cmmib10 at17.28pt<20>cmmib10 at20.74pt<25>cmmib10 at24.88pt}{}

      %

      \new@fontshape{cmsy}{b}{n}{%

        <5>cmbsy5<6>cmbsy6<7>cmbsy7<8>cmbsy8<9>cmbsy9<10>cmbsy10%

        <11>cmbsy10 at10.95pt<12>cmbsy10 at12pt<14>cmbsy10 at14.4pt%

        <17>cmbsy10 at17.28pt<20>cmbsy10 at20.74pt<25>cmbsy10 at24.88pt}{}

    }%

    %

  \fi % End of NFSS release 1

\else

  \let\UseAMStwoboldmath=\relax

\fi





% Astronomy and Astrophysics symbol macros



\def\la{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil

$\reset@font\displaystyle##$\hfil\cr<\cr\sim\cr}}}

{\vcenter{\offinterlineskip\halign{\hfil$\reset@font\textstyle##$\hfil\cr

<\cr\sim\cr}}}

{\vcenter{\offinterlineskip\halign{\hfil$\reset@font\scriptstyle##$\hfil\cr

<\cr\sim\cr}}}

{\vcenter{\offinterlineskip\halign{\hfil$\reset@font\scriptscriptstyle##$\hfil\cr

<\cr\sim\cr}}}}}



\def\ga{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil

$\reset@font\displaystyle##$\hfil\cr>\cr\sim\cr}}}

{\vcenter{\offinterlineskip\halign{\hfil$\reset@font\textstyle##$\hfil\cr

>\cr\sim\cr}}}

{\vcenter{\offinterlineskip\halign{\hfil$\reset@font\scriptstyle##$\hfil\cr

>\cr\sim\cr}}}

{\vcenter{\offinterlineskip\halign{\hfil$\reset@font\scriptscriptstyle##$\hfil\cr

>\cr\sim\cr}}}}}



\def\getsto{\mathrel{\mathchoice {\vcenter{\offinterlineskip

\halign{\hfil

$\reset@font\displaystyle##$\hfil\cr\gets\cr\to\cr}}}

{\vcenter{\offinterlineskip\halign{\hfil$\reset@font\textstyle##$\hfil\cr\gets

\cr\to\cr}}}

{\vcenter{\offinterlineskip\halign{\hfil$\reset@font\scriptstyle##$\hfil\cr\gets

\cr\to\cr}}}

{\vcenter{\offinterlineskip\halign{\hfil$\reset@font\scriptscriptstyle##$\hfil\cr

\gets\cr\to\cr}}}}}



\def\cor{\mathrel{\mathchoice {\hbox{$\widehat=$}}{\hbox{$\widehat=$}}

{\hbox{$\reset@font\scriptstyle\hat=$}}

{\hbox{$\reset@font\scriptscriptstyle\hat=$}}}}



\def\lid{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil

$\reset@font\displaystyle##$\hfil\cr<\cr\noalign{\vskip1.2pt}=\cr}}}

{\vcenter{\offinterlineskip\halign{\hfil$\reset@font\textstyle##$\hfil\cr<\cr

\noalign{\vskip1.2pt}=\cr}}}

{\vcenter{\offinterlineskip\halign{\hfil$\reset@font\scriptstyle##$\hfil\cr<\cr

\noalign{\vskip1pt}=\cr}}}

{\vcenter{\offinterlineskip\halign{\hfil$\reset@font\scriptscriptstyle##$\hfil\cr

<\cr

\noalign{\vskip0.9pt}=\cr}}}}}



\def\gid{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil

$\reset@font\displaystyle##$\hfil\cr>\cr\noalign{\vskip1.2pt}=\cr}}}

{\vcenter{\offinterlineskip\halign{\hfil$\reset@font\textstyle##$\hfil\cr>\cr

\noalign{\vskip1.2pt}=\cr}}}

{\vcenter{\offinterlineskip\halign{\hfil$\reset@font\scriptstyle##$\hfil\cr>\cr

\noalign{\vskip1pt}=\cr}}}

{\vcenter{\offinterlineskip\halign{\hfil$\reset@font\scriptscriptstyle##$\hfil\cr

>\cr

\noalign{\vskip0.9pt}=\cr}}}}}



\def\sol{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil

$\reset@font\displaystyle##$\hfil\cr\sim\cr<\cr}}}

{\vcenter{\offinterlineskip\halign{\hfil$\reset@font\textstyle##$\hfil\cr\sim\cr

<\cr}}}

{\vcenter{\offinterlineskip\halign{\hfil$\reset@font\scriptstyle##$\hfil\cr\sim\cr

<\cr}}}

{\vcenter{\offinterlineskip\halign{\hfil$\reset@font\scriptscriptstyle##$\hfil\cr

\sim\cr<\cr}}}}}



\def\sog{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil

$\reset@font\displaystyle##$\hfil\cr\sim\cr>\cr}}}

{\vcenter{\offinterlineskip\halign{\hfil$\reset@font\textstyle##$\hfil\cr\sim\cr

>\cr}}}

{\vcenter{\offinterlineskip\halign{\hfil$\reset@font\scriptstyle##$\hfil\cr

\sim\cr>\cr}}}

{\vcenter{\offinterlineskip\halign{\hfil$\reset@font\scriptscriptstyle##$\hfil\cr

\sim\cr>\cr}}}}}



\def\lse{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil

$\reset@font\displaystyle##$\hfil\cr<\cr\simeq\cr}}}

{\vcenter{\offinterlineskip\halign{\hfil$\reset@font\textstyle##$\hfil\cr

<\cr\simeq\cr}}}

{\vcenter{\offinterlineskip\halign{\hfil$\reset@font\scriptstyle##$\hfil\cr

<\cr\simeq\cr}}}

{\vcenter{\offinterlineskip\halign{\hfil$\reset@font\scriptscriptstyle##$\hfil\cr

<\cr\simeq\cr}}}}}



\def\gse{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil

$\reset@font\displaystyle##$\hfil\cr>\cr\simeq\cr}}}

{\vcenter{\offinterlineskip\halign{\hfil$\reset@font\textstyle##$\hfil\cr

>\cr\simeq\cr}}}

{\vcenter{\offinterlineskip\halign{\hfil$\reset@font\scriptstyle##$\hfil\cr

>\cr\simeq\cr}}}

{\vcenter{\offinterlineskip\halign{\hfil$\reset@font\scriptscriptstyle##$\hfil\cr

>\cr\simeq\cr}}}}}



\def\grole{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil

$\reset@font\displaystyle##$\hfil\cr>\cr\noalign{\vskip-1.5pt}<\cr}}}

{\vcenter{\offinterlineskip\halign{\hfil$\reset@font\textstyle##$\hfil\cr

>\cr\noalign{\vskip-1.5pt}<\cr}}}

{\vcenter{\offinterlineskip\halign{\hfil$\reset@font\scriptstyle##$\hfil\cr

>\cr\noalign{\vskip-1pt}<\cr}}}

{\vcenter{\offinterlineskip\halign{\hfil$\reset@font\scriptscriptstyle##$\hfil\cr

>\cr\noalign{\vskip-0.5pt}<\cr}}}}}



\def\leogr{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil

$\reset@font\displaystyle##$\hfil\cr<\cr\noalign{\vskip-1.5pt}>\cr}}}

{\vcenter{\offinterlineskip\halign{\hfil$\reset@font\textstyle##$\hfil\cr

<\cr\noalign{\vskip-1.5pt}>\cr}}}

{\vcenter{\offinterlineskip\halign{\hfil$\reset@font\scriptstyle##$\hfil\cr

<\cr\noalign{\vskip-1pt}>\cr}}}

{\vcenter{\offinterlineskip\halign{\hfil$\reset@font\scriptscriptstyle##$\hfil\cr

<\cr\noalign{\vskip-0.5pt}>\cr}}}}}



\def\loa{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil

$\reset@font\displaystyle##$\hfil\cr<\cr\approx\cr}}}

{\vcenter{\offinterlineskip\halign{\hfil$\reset@font\textstyle##$\hfil\cr

<\cr\approx\cr}}}

{\vcenter{\offinterlineskip\halign{\hfil$\reset@font\scriptstyle##$\hfil\cr

<\cr\approx\cr}}}

{\vcenter{\offinterlineskip\halign{\hfil$\reset@font\scriptscriptstyle##$\hfil\cr

<\cr\approx\cr}}}}}



\def\goa{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil

$\reset@font\displaystyle##$\hfil\cr>\cr\approx\cr}}}

{\vcenter{\offinterlineskip\halign{\hfil$\reset@font\textstyle##$\hfil\cr

>\cr\approx\cr}}}

{\vcenter{\offinterlineskip\halign{\hfil$\reset@font\scriptstyle##$\hfil\cr

>\cr\approx\cr}}}

{\vcenter{\offinterlineskip\halign{\hfil$\reset@font\scriptscriptstyle##$\hfil\cr

>\cr\approx\cr}}}}}



\def\sun{\hbox{$\odot$}}

\def\degr{\hbox{$^\circ$}}

\def\diameter{{\ifmmode\mathchoice

{\ooalign{\hfil\hbox{$\reset@font\displaystyle/$}\hfil\crcr

{\hbox{$\reset@font\displaystyle\mathchar"20D$}}}}

{\ooalign{\hfil\hbox{$\reset@font\textstyle/$}\hfil\crcr

{\hbox{$\reset@font\textstyle\mathchar"20D$}}}}

{\ooalign{\hfil\hbox{$\reset@font\scriptstyle/$}\hfil\crcr

{\hbox{$\reset@font\scriptstyle\mathchar"20D$}}}}

{\ooalign{\hfil\hbox{$\reset@font\scriptscriptstyle/$}\hfil\crcr

{\hbox{$\reset@font\scriptscriptstyle\mathchar"20D$}}}}

\else{\ooalign{\hfil/\hfil\crcr\mathhexbox20D}}%

\fi}}



\def\sq{\ifmmode\squareforqed\else{\unskip\nobreak\hfil

\penalty50\hskip1em\null\nobreak\hfil\squareforqed

\parfillskip=0pt\finalhyphendemerits=0\endgraf}\fi}

\def\squareforqed{\hbox{\rlap{$\sqcap$}$\sqcup$}}



\ifoldfss

  \newcommand{\r@mn}[1] {{\rm #1}}%

\else

  \newcommand{\r@mn}[1] {\mathrm{#1}}%

\fi



\def\fd{\hbox{$.\!\!^{\reset@font\r@mn{d}}$}}

\def\fh{\hbox{$.\!\!^{\reset@font\r@mn{h}}$}}

\def\fm{\hbox{$.\!\!^{\reset@font\r@mn{m}}$}}

\def\fs{\hbox{$.\!\!^{\reset@font\r@mn{s}}$}}

\def\fdg{\hbox{$.\!\!^\circ$}}

\def\farcm{\hbox{$.\mkern-4mu^\prime$}}

\def\farcs{\hbox{$.\!\!^{\prime\prime}$}}

\def\fp{\hbox{$.\!\!^{\reset@font\scriptscriptstyle\r@mn{p}}$}}

\def\arcmin{\hbox{$^\prime$}}

\def\arcsec{\hbox{$^{\prime\prime}$}}



%%%%%%%%%%%%%%%%%%%%% End of Extra Math / Symbol code %%%%%%%%%%%%%%%%%%%%%



%  ****************************************

%  *            PAGE LAYOUT               *

%  ****************************************

%

% SIDE MARGINS:

\if@twocolumn

 \oddsidemargin -2.5pc \evensidemargin -2.5pc

\else

 \ifSFB@referee

  \oddsidemargin \z@  \evensidemargin \z@

 \else

  \oddsidemargin -2pc  \evensidemargin -2pc

 \fi

\fi

\marginparwidth 4pc

\marginparsep 0.5pc



% VERTICAL SPACING:

%\if@twocolumn

% \topmargin -2pc

%\else

 \topmargin \z@

%\fi

\headheight 14pt

\headsep    15pt

\topskip     9pt

\footheight 11pt

\footskip   22pt % was 26pt

%

% DIMENSION OF TEXT: % SFB 0.1.01

%

\newdimen\SFB@measure

\SFB@measure 42pc

%

\textheight 682pt

\textwidth \SFB@measure

%

\ifSFB@landscape

 \textwidth \textheight

 \textheight \SFB@measure

\fi

\ifSFB@referee

 \textwidth 39pc

\fi

\columnsep 2pc

\columnseprule 0pt



% FOOTNOTES:

\footnotesep 6pt

\skip\footins 19.5pt plus 12pt minus 1pt



% FLOATS:

\floatsep 12pt plus 5.5pt minus 1pt

\textfloatsep 12pt plus 7.5pt 

\intextsep 12pt plus 5.5pt minus 2pt

\@maxsep 15pt

\dblfloatsep 12pt plus 5.5pt minus 2pt

\dbltextfloatsep 15pt plus 4.5pt minus 3pt

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\@fptop 0pt plus 0fil

\@fpsep 12pt plus 0fil

\@fpbot 0pt plus 0fil% 3fil ajw

\@dblfptop 0pt plus 0fil

\@dblfpsep 12pt plus 0fil

\@dblfpbot 0pt plus 0fil% 3fil ajw

\marginparpush 5pt



%  ****************************************

%  *           PARAGRAPHING               *

%  ****************************************

%

\newdimen\realparindent % needed for abstract

\parskip \z@ plus .1pt

\parindent 18pt

\realparindent=\parindent

\partopsep 0pt plus 1pt

\@lowpenalty   51

\@medpenalty  151

\@highpenalty 301

\@beginparpenalty -\@lowpenalty

\@endparpenalty -\@lowpenalty

\@itempenalty -\@lowpenalty

\clubpenalty=0

\widowpenalty=10000



%  ****************************************

%  *       PARTS & SECTIONS NUMBERS       *

%  ****************************************

%

\newcounter {part}

\newcounter {section}

\newcounter {subsection}[section]

\newcounter {subsubsection}[subsection]

\newcounter {paragraph}[subsubsection]

\newcounter {subparagraph}[paragraph]

\def\thepart {\arabic{part}}

\def\thesection {\arabic{section}}

\def\thesubsection    {\thesection.\arabic{subsection}}

\def\thesubsubsection {\thesubsection.\arabic{subsubsection}}

\def\theparagraph     {\thesubsubsection.\arabic{paragraph}}

\def\thesubparagraph  {\theparagraph.\arabic{subparagraph}}



%  ****************************************

%  *                PARTS                 *

%  ****************************************

%

\def\part{\par \addvspace{4ex}\@afterindentfalse

 \secdef\@part\@spart}

\def\@part[#1]#2{\ifnum \c@secnumdepth >\m@ne

  \refstepcounter{part}

  \addcontentsline{toc}{part}{Part \thepart: #1}

 \else \addcontentsline{toc}{part}{#1}

 \fi

 {\parindent 0pt \raggedright

  \ifnum \c@secnumdepth >\m@ne

   \reset@font\large\rm PART

   \ifcase\thepart \or ONE \or TWO \or THREE \or FOUR \or FIVE

    \or SIX \or SEVEN \or EIGHT \or NINE \or TEN \else \fi

   \par \nobreak

  \fi

  \reset@font\LARGE \rm #2 \markboth{}{}\par }

 \nobreak \vskip 3ex \@afterheading}

\def\@spart#1{{\parindent 0pt \raggedright

  \reset@font\LARGE \rm #1\par}

 \nobreak \vskip 3ex \@afterheading}



%  ****************************************

%  *               SECTIONS               *

%  ****************************************

%

% \@startsection modified to leave less space before \subsection

%    if it immediately follows \section



% \@startsection {NAME}{LEVEL}{INDENT}{BEFORESKIP}{AFTERSKIP}{STYLE}



\newif\if@levelone



\def\@startsection#1#2#3#4#5#6{\if@noskipsec \leavevmode \fi

   \par \@tempskipa #4\relax

   \@afterindenttrue

   \ifnum #2=\@ne  % if level=1 ie. section

     \global\@levelonetrue

   \else

     \global\@levelonefalse

   \fi

   \ifdim \@tempskipa <\z@ \@tempskipa -\@tempskipa \@afterindentfalse\fi

   \if@nobreak

     \everypar{}\ifnum#2=2 \vskip 0pt plus1pt\fi % was 6pt

   \else

     \addpenalty{\@secpenalty}\addvspace{\@tempskipa}

   \fi \@ifstar

     {\@ssect{#3}{#4}{#5}{#6}}{\@dblarg{\@sect{#1}{#2}{#3}{#4}{#5}{#6}}}}



%\def\SFB@hangraggedright{\rightskip\@flushglue \let\\=\newline}

%\def\SFB@raggedright{\rightskip\@flushglue \let\\=\@centercr

% \parindent=\SFB@indent}



\def\SFB@hangraggedright{\rightskip=\@flushglue \let\\=\@centercr \parindent=0pt}



\def\section{\@startsection{section}{1}{\z@}

 {-24pt plus -12pt minus -1pt}{6pt}

 {\SFB@hangraggedright\reset@font\normalsize\bf}}

\def\subsection{\@startsection{subsection}{2}{\z@}

 {-18pt plus -9pt minus -1pt}{6pt}

 {\SFB@hangraggedright\reset@font\normalsize\bf}}

\def\subsubsection{\@startsection{subsubsection}{3}{\z@}

 {-18pt plus -9pt minus -1pt}{6pt}

 {\SFB@hangraggedright\reset@font\normalsize\it}}

\def\paragraph{\@startsection{paragraph}{4}{\z@}

 {12pt plus 2.25pt minus 1pt}{-0.5em}{\reset@font\normalsize\bf}}

\def\subparagraph{\@startsection{subparagraph}{5}{\parindent}

 {12pt plus 2.25pt minus 1pt}{-0.5em}{\reset@font\normalsize\it}}

\setcounter{secnumdepth}{4} % SFB 0.1.01

%

% \@sect{NAME}{LEVEL}{INDENT}{BEFORESKIP}{AFTERSKIP}{STYLE}[ARG1]{ARG2}

\def\@sect#1#2#3#4#5#6[#7]#8{%

  \ifnum #2>\c@secnumdepth

    \def\@svsec{}%

  \else

    \refstepcounter{#1}%

    \if@levelone % is it a \section or \section*

      \ifSFB@appendix

        \edef\@svsec{}%

      \else

        \edef\@svsec{\csname the#1\endcsname\hskip 1em}%

      \fi

    \else

      \edef\@svsec{\csname the#1\endcsname\hskip 1em}%

    \fi

  \fi

  \@tempskipa #5\relax

  \ifdim \@tempskipa>\z@

    \begingroup #6\relax

    \if@levelone

      \ifSFB@appendix

        \@hangfrom{\hskip #3\relax\@svsec}{\interlinepenalty \@M

        APPENDIX \csname the#1\endcsname:\hskip 0.5em\uppercase{#8}\par}%

      \else

        \@hangfrom{\hskip #3\relax\@svsec}{\interlinepenalty \@M

        \uppercase{#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 %ajw

   \protect\numberline{\csname the#1\endcsname}\fi #7}%ajw

 \else

  \def\@svsechd{#6\hskip #3\@svsec \if@levelone \uppercase{#8}\else #8\fi

  \csname #1mark\endcsname{#7}

  \addcontentsline{toc}{#1}{\ifnum #2>\c@secnumdepth \else %ajw

  \protect\numberline{\csname the#1\endcsname}\fi#7}%ajw

  }\fi

 \@xsect{#5}}



% from latex.tex

%   \@ssect{INDENT}{BEFORESKIP}{AFTERSKIP}{STYLE}{ARG}

\def\@ssect#1#2#3#4#5{%

  \@tempskipa #3\relax

    \ifdim \@tempskipa>\z@

      \begingroup #4\@hangfrom{\hskip #1}{%

      \interlinepenalty \@M 

      \if@levelone

        \uppercase{#5}%

      \else {#5}%

      \fi\par}%

     \endgroup

    \else 

      \def\@svsechd{#4\hskip #1\relax

      \if@levelone

        \uppercase{#5}%

      \else {#5}%

      \fi}

    \fi

  \@xsect{#3}%

}



\newif\ifSFB@appendix

\def\appendix{\par

 \SFB@appendixtrue

 \@addtoreset{equation}{section}

 \@addtoreset{table}{section}

 \@addtoreset{figure}{section}

 \setcounter{section}{0}

 \setcounter{equation}{0}

 \setcounter{figure}{0}

 \setcounter{table}{0}

 \def\thesection{\Alph{section}}

 \def\thesubsection{\thesection\arabic{subsection}}

 \def\theequation{\thesection\arabic{equation}}

 \def\thefigure{\thesection\@arabic\c@figure}

 \def\thetable{\thesection\@arabic\c@table}

}



%  ****************************************

%  *               SKIPS                  *

%  ****************************************

%

\newskip\@indentskip

\newskip\smallindent

\newskip\@footindent

\newskip\@leftskip

\@indentskip=18pt

\smallindent=1.5em

\@footindent=\smallindent

\@leftskip=\z@



%  ****************************************

%  *                LISTS                 *

%  ****************************************

%

\leftmargini   \z@

\leftmarginii  1.25pc

\leftmarginiii 1.25pc

\leftmarginiv  1.25pc

\leftmarginv   1pc

\leftmarginvi  1pc

\leftmargin\leftmargini

\labelsep 0.5em

\labelwidth\leftmargini\advance\labelwidth-\labelsep

%

% label macros for Range-Left and Range-Right labels

\def\makeRLlabel#1{\rlap{#1}\hss}

\def\makeRRlabel#1{\hss\llap{#1}}

\def\makenewlabel#1{#1}

%

\def\@listI{\leftmargin\leftmargini

 \parsep \z@

 \topsep 6pt plus 1pt minus 1pt

 \itemsep \z@ plus .1pt

}

\let\@listi\@listI

\@listi

\def\@listii{\leftmargin\leftmarginii

 \labelwidth\leftmarginii\advance\labelwidth-\labelsep

 \topsep 6pt plus 1pt minus 1pt

 \parsep \z@

 \itemsep \z@ plus .1pt

}

\def\@listiii{\leftmargin\leftmarginiii

 \labelwidth\leftmarginiii\advance\labelwidth-\labelsep

 \topsep 6pt plus 1pt minus 1pt

 \parsep \z@

 \partopsep \z@

 \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

}

%

% ITEMIZE

\def\itemize{%

  \ifnum \@itemdepth >3 \@toodeep

  \else \advance\@itemdepth \@ne

   \edef\@itemitem{labelitem\romannumeral\the\@itemdepth}%

   \list{\csname\@itemitem\endcsname}%

   {\let\makelabel\makeRRlabel}%

   \parindent 1em%

   \leftmargin 3.5em\labelsep 0.5em\itemindent 2.0em\labelwidth 0.5em%

  \fi}

\def\labelitemi{$\bullet$}

\def\labelitemii{--}

\def\labelitemiii{$\cdot$}

\def\labelitemiv{*}

%

% ENUMERATE

% SFB -- enumerate with optional argument to set left margin...

\def\enumerate{\ifnum \@enumdepth >3 \@toodeep \else

  \advance\@enumdepth \@ne

  \edef\@enumctr{enum\romannumeral\the\@enumdepth}%

 \fi

 \@ifnextchar [{\@enumeratetwo}{\@enumerateone}%

}

\def\@enumeratetwo[#1]{%

 \list{\csname label\@enumctr\endcsname}%

  {\settowidth\labelwidth{[#1]}

   \leftmargin\z@ 

   \listparindent 1em

   \usecounter{\@enumctr}

   \let\makelabel\makenewlabel}

}

\def\@enumerateone{%

 \list{\csname label\@enumctr\endcsname}%

  {\usecounter{\@enumctr}\itemindent 1em\listparindent 1em

   \let\makelabel\makenewlabel}}

%

\def\labelenumi{\theenumi}

\def\theenumi{(\roman{enumi})}

\def\labelenumii{(\theenumii)}

\def\theenumii{(\alph{enumii})}

\def\p@enumii{\theenumi}

\def\labelenumiii{\theenumiii}

\def\theenumiii{(\arabic{enumiii})}

\def\p@enumiii{\theenumi(\theenumii)}

\def\labelenumiv{\theenumiv}

\def\theenumiv{(\Alph{enumiv})}

\def\p@enumiv{\p@enumiii\theenumiii}

%

% DESCRIPTION

%\def\descriptionlabel#1{\hspace\labelsep \reset@font\bf #1}

%\def\description{\list{}{\labelwidth\z@ \itemindent-\leftmargin

%  \leftmargin 1em

%  \itemindent-1em

%}}

\def\descriptionlabel#1{\reset@font\bf #1}

\def\description{\list{}{\labelwidth\z@

  \leftmargin \z@

  \itemindent 1em

}}

\let\enddescription\endlist



%  ****************************************

%  *            DISPLAYED TEXT            *

%  ****************************************

%

% VERSE

\def\verse{\let\\=\@centercr

 \list{}{\itemsep\z@

  \itemindent -\@indentskip

  \listparindent \itemindent

  \rightmargin\leftmargin

  \advance\leftmargin \@indentskip}\item[]}

\let\endverse\endlist

%

% QUOTATION

\def\quotation{\list{}{\listparindent \smallindent

%  \itemindent\listparindent

  \leftmargin\z@\rightmargin\leftmargin

  \parsep 0pt plus 1pt}\item[]\reset@font\small}

\let\endquotation=\endlist

%

% QUOTE

\def\quote{\list{}{\leftmargin\z@\rightmargin\leftmargin}\item[]%

  \reset@font\small}

\let\endquote=\endlist



%  ****************************************

%  *         OTHER ENVIRONMENTS           *

%  ****************************************

%

% THEOREM

\def\@begintheorem#1#2{\reset@font\rm \trivlist \item[\hskip \labelsep

  {\reset@font\bf #1\ #2.}]}

\def\@opargbegintheorem#1#2#3{\reset@font\rm \trivlist

  \item[\hskip \labelsep{\reset@font\bf #1\ #2.\ (#3)}]}

\def\@endtheorem{\endtrivlist}

%

% PROOF

\def\proof{\reset@font\rm \trivlist \item[\hskip \labelsep

  {\reset@font\it Proof.}]}

\def\endproof{\hspace*{1em}{\begin{picture}(6.5,6.5)%

  \put(0,0){\framebox(6.5,6.5){}}\end{picture}}\endtrivlist}

\@namedef{proof*}{\reset@font\rm \trivlist \item[\hskip \labelsep

  {\reset@font\it Proof.}]}

\@namedef{endproof*}{\endtrivlist}

\def\proofbox{\begin{picture}(6.5,6.5)%

  \put(0,0){\framebox(6.5,6.5){}}\end{picture}}

%

% TITLEPAGE

\def\titlepage{\@restonecolfalse\if@twocolumn\@restonecoltrue\onecolumn

  \else \newpage \fi \thispagestyle{empty}\c@page\z@}

\def\endtitlepage{\if@restonecol\twocolumn \else \newpage \fi}



% ARRAY AND TABULAR

%

\arraycolsep   5pt

\tabcolsep     6pt

\arrayrulewidth .5pt

\doublerulesep 1.5pt



\def\tabular{\def\@halignto{}

 \def\hline{\noalign{\ifnum0=`}\fi

  \vskip 3pt

  \hrule \@height \arrayrulewidth

%   {\hbox to 0.667\textwidth{\hrulefill}}

  \vskip 3pt

  \futurelet \@tempa\@xhline}

 \def\fullhline{\noalign{\ifnum0=`}\fi

  \vskip 3pt

  \hrule \@height \arrayrulewidth

%   {\hbox to \textwidth{\hrulefill}}

  \vskip 3pt

  \futurelet \@tempa\@xhline}

 \def\@xhline{\ifx\@tempa\hline

   \vskip -6pt

   \vskip \doublerulesep

  \fi

  \ifnum0=`{\fi}}

  \def\@arrayrule{\@addtopreamble{\hskip -.5\arrayrulewidth

%                                  \vrule \@width \arrayrulewidth

                                  \hskip .5\arrayrulewidth}}

\@tabular

}

% TABBING

%

\tabbingsep \labelsep



% MINIPAGE

%

\skip\@mpfootins = \skip\footins



% FRAMEBOX

%

% Space left between box and text by \fbox and \framebox.

\fboxsep = 3pt

% Width of rules in box made by \fbox and \framebox.

\fboxrule = \arrayrulewidth



%  ****************************************

%  *         TITLE AND ABSTRACT           *

%  ****************************************

%

\def\maketitle{\par

 \begingroup

  \if@twocolumn

   \twocolumn[\vspace*{17pt}\@maketitle] 

  \else

   \newpage

   \global\@topnum\z@

   \@maketitle

  \fi

  \thispagestyle{titlepage}

 \endgroup

 \let\maketitle\relax

 \let\@maketitle\relax

 \gdef\@author{}

 \gdef\@title{}

 \let\thanks\relax

}

\def\newauthor{%

  \end{author@tabular}\par

  \begin{author@tabular}[t]{@{}l@{}}%

}

\def\and{%

  \end{author@tabular}\vskip 3pt\par

 \begin{author@tabular}[t]{@{}l@{}}%

}

\def\@maketitle{\newpage

 \vspace*{7pt}

 {\raggedright \sloppy

  {\reset@font\huge \bf \@title \par}

  \vskip 23pt

  {\reset@font\LARGE

   \begin{author@tabular}[t]{@{}l@{}}\@author

   \end{author@tabular}\par}

  \vskip 22pt

 }

 \par\noindent

 {\reset@font\small \@date \par}

 \vskip 22pt

}

%

\def\abstract{\if@twocolumn

   \start@SFBbox\@abstract

 \else

   \@abstract

 \fi}

\def\endabstract{\if@twocolumn

   \endlist\finish@SFBbox

 \else

  \endlist

 \fi}

\def\@abstract{\list{}{%

    \listparindent\realparindent

    \itemindent\z@

    \labelwidth\z@ \labelsep\z@ 

    \leftmargin 11pc\rightmargin\z@

    \parsep 0pt plus 1pt}\item[]%

    \reset@font\normalsize{\bf ABSTRACT}\\\reset@font\large

} % SFB 0.1.01 

%

\newif\ifSFB@keywords

\def\keywords{\if@twocolumn

  \start@SFBbox\@keywords

 \else

  \@keywords

 \fi

}

\def\@keywords{\list{}{%

    \labelwidth\z@ \labelsep\z@ 

    \leftmargin 11pc\rightmargin\z@

    \parsep 0pt plus 1pt}\item[]\reset@font\large{\bf Key words: }%

}

\def\endkeywords{\if@twocolumn

  \endlist\addvspace{37pt plus 0.5\baselineskip}\finish@SFBbox 

 \else

  \endlist

 \fi

 \@thanks

 \gdef\@thanks{}

 \SFB@keywordstrue

}

\def\nokeywords{\ifSFB@keywords\else

 \if@twocolumn \start@SFBbox\addvspace{37pt}\finish@SFBbox \fi

 \@thanks

 \gdef\@thanks{}\fi

}



\def\author@tabular{\def\@halignto{}\@authortable}

\let\endauthor@tabular=\endtabular

%

\def\author@tabcrone{\vspace{2pt}{\ifnum0=`}\fi%

  \@xtabularcr[-7pt]\reset@font\small\it

  \let\\=\author@tabcrtwo\ignorespaces}

%

\def\author@tabcrtwo{{\ifnum0=`}\fi\@xtabularcr[-7pt]\reset@font\small\it

 \let\\=\author@tabcrtwo\ignorespaces}

%

\def\@authortable{\leavevmode \hbox \bgroup $\let\@acol\@tabacol

 \let\@classz\@tabclassz \let\@classiv\@tabclassiv

 \let\\=\author@tabcrone\ignorespaces \@tabarray}



\def\start@SFBbox{\@next\@currbox\@freelist{}{}%

 \global\setbox\@currbox

 \vbox\bgroup

  \hsize \textwidth

  \@parboxrestore

}

\def\finish@SFBbox{\par\vskip -\dbltextfloatsep

  \egroup

  \global\count\@currbox\tw@

  \global\@dbltopnum\@ne

  \global\@dbltoproom\maxdimen\@addtodblcol

  \global\vsize\@colht

  \global\@colroom\@colht

}



%  ****************************************

%  *            PAGE STYLES               *

%  ****************************************

%

\mark{{}{}}

\gdef\@author{\mbox{}}

\def\author{\@ifnextchar [{\@authortwo}{\@authorone}}

\def\@authortwo[#1]#2{\gdef\@author{#2}\gdef\@shortauthor{#1}}

\def\@authorone#1{\gdef\@author{#1}\gdef\@shortauthor{#1}}

%\def\shortauthor#1{\gdef\@shortauthor{#1}}

\gdef\@shortauthor{}

\gdef\@title{\mbox{}}

\def\title{\@ifnextchar [{\@titletwo}{\@titleone}}

\def\@titletwo[#1]#2{\gdef\@title{#2}\gdef\@shorttitle{#1}}

\def\@titleone#1{\gdef\@title{#1}\gdef\@shorttitle{#1}}

%\def\shorttitle#1{\gdef\@shorttitle{#1}}

\gdef\@shorttitle{}

\def\volume#1{\gdef\@volume{#1}}

\gdef\@volume{000}

\def\tod@y{\today}

\def\microfiche#1{\gdef\@microfiche{#1}}

\gdef\@microfiche{}

\def\pubyear#1{\gdef\@pubyear{#1}}

\gdef\@pubyear{0000}

\def\pagerange#1{\gdef\@pagerange{#1}}

\gdef\@pagerange{000--000}

\def\journal#1{\gdef\@journal{#1}}

\def\plate#1{\gdef\pl@te{#1}}

\ifx\CUP@mtlplain@loaded\undefined

  \def\@printed{\qquad Printed \tod@y\qquad

    (MN \LaTeX\ style file v\@version)}

\else

  \def\@printed{}

\fi

\gdef\@journal{{Mon.\ Not.\ R.\ Astron.\ Soc.} {\bf \@volume}, \@pagerange\

% (\number\year) \@microfiche\@printed}

  (\@pubyear) \@microfiche\@printed}

%

% \ps@empty and \ps@plain defined in LATEX.TEX

%

\def\@ddell{}

\if@letters

  \def\@ddell{L}

\fi

\def\ps@headings{\let\@mkboth\markboth

 \def\@oddhead{\Large\hfill{\it\@shorttitle}\hspace{1.5em}%

   \rm\@ddell\thepage}

 \def\@oddfoot{\small\copyright\ \@pubyear\ RAS, MNRAS {\bf \@volume}, \@pagerange\hfil}

 \def\@evenhead{\Large\@ddell\thepage\hspace{1.5em}\it\@shortauthor\hfill}

 \def\@evenfoot{\hfil\small\copyright\ \@pubyear\ RAS, MNRAS {\bf \@volume}, \@pagerange}

 \def\sectionmark##1{\markboth{##1}{}}

 \def\subsectionmark##1{\markright{##1}}}



\def\ps@myheadings{\let\@mkboth\@gobbletwo

 \def\@oddhead{\Large\hfill\it\rightmark\hspace{1.5em}\rm\@ddell\thepage}

 \def\@oddfoot{\small\copyright\ \@pubyear\ RAS, MNRAS {\bf \@volume}, \@pagerange\hfil}

 \def\@evenhead{\Large\@ddell\thepage\hspace{1.5em}\it\leftmark\hfill}

 \def\@evenfoot{\hfil\small\copyright\ \@pubyear\ RAS, MNRAS {\bf \@volume}, \@pagerange}

 \def\sectionmark##1{}

 \def\subsectionmark##1{}}



\def\ps@titlepage{\let\@mkboth\@gobbletwo

 \def\@oddhead{\footnotesize\@journal\hfill}

 \def\@oddfoot{\small\copyright\ \@pubyear\ RAS\hfil}

 \def\@evenhead{\footnotesize\@journal\hfill}

 \def\@evenfoot{\hfil\small\copyright\ \@pubyear\ RAS}

 \def\sectionmark##1{}

 \def\subsectionmark##1{}}



\def\ps@plate{\let\@mkboth\@gobbletwo

  \def\@oddhead{\footnotesize\pl@te\hfill}

  \def\@oddfoot{\small\copyright\ \@pubyear\ RAS, MNRAS {\bf \@volume},

    \@pagerange\hfil}

  \def\@evenhead{\footnotesize\pl@te\hfill}

  \def\@evenfoot{\hfil\small\copyright\ \@pubyear\ RAS, MNRAS {\bf \@volume},

    \@pagerange}

}



%  ****************************************

%  *         TABLE OF CONTENTS, ETC.      *

%  ****************************************

%

\def\@pnumwidth{1.55em}

\def\@tocrmarg {2.55em}

\def\@dotsep{4.5}

\setcounter{tocdepth}{2}

\def\@undottedtocline#1#2#3#4#5{\ifnum #1>\c@tocdepth

 \else

  \vskip \z@ plus .2pt

  {\hangindent #2\relax

   \rightskip \@tocrmarg \parfillskip -\rightskip

   \parindent #2\relax \@afterindenttrue

   \interlinepenalty\@M \leavevmode

   \@tempdima #3\relax #4\nobreak \hfill \nobreak

   \hbox to\@pnumwidth{\hfil\reset@font\rm \ }\par}\fi}

\def\tableofcontents{\@restonecolfalse

 \if@twocolumn\@restonecoltrue\onecolumn\fi

 \section*{CONTENTS} \@starttoc{toc}

 \if@restonecol\twocolumn\fi \par\vspace{12pt}}

\def\l@part#1#2{\addpenalty{-\@highpenalty}

 \addvspace{2.25em plus 1pt}

 \begingroup

  \parindent \z@ \rightskip \@pnumwidth

  \parfillskip -\@pnumwidth

  {\reset@font\normalsize\rm

   \leavevmode \hspace*{3pc}

   #1\hfil \hbox to\@pnumwidth{\hss \ }}\par

   \nobreak \global\@nobreaktrue

   \everypar{\global\@nobreakfalse\everypar{}}\endgroup}

\def\l@section#1#2{\addpenalty{\@secpenalty}

 \@tempdima 1.5em

 \begingroup

  \parindent \z@ \rightskip \@pnumwidth

  \parfillskip -\@pnumwidth \reset@font\rm \leavevmode

  \advance\leftskip\@tempdima \hskip -\leftskip

  #1\nobreak\hfil \nobreak\hbox to\@pnumwidth{\hss \ }\par

 \endgroup}

\def\l@subsection{\@undottedtocline{2}{1.5em}{2.3em}}

\def\l@subsubsection{\@undottedtocline{3}{3.8em}{3.2em}}

\def\l@paragraph{\@undottedtocline{4}{7.0em}{4.1em}}

\def\l@subparagraph{\@undottedtocline{5}{10em}{5em}}

\def\listoffigures{\@restonecolfalse

 \if@twocolumn\@restonecoltrue\onecolumn\fi

 \section*{LIST OF FIGURES\@mkboth{LIST OF FIGURES}{LIST OF FIGURES}}

 \@starttoc{lof} \if@restonecol\twocolumn\fi}

\def\l@figure{\@undottedtocline{1}{1.5em}{2.3em}}

\def\listoftables{\@restonecolfalse

 \if@twocolumn\@restonecoltrue\onecolumn\fi

 \section*{LIST OF TABLES\@mkboth{LIST OF TABLES}{LIST OF TABLES}}

 \@starttoc{lot} \if@restonecol\twocolumn\fi}

\let\l@table\l@figure



%  ****************************************

%  *             BIBLIOGRAPHY             *

%  ****************************************

%



\newcounter{dummy}

\def\thebibliography#1{\section*{REFERENCES}

 \addcontentsline{toc}{section}{REFERENCES}

 \list{}{\usecounter{dummy}%

         \labelwidth\z@

         \leftmargin 1.5em

         \itemsep \z@

         \itemindent-\leftmargin}

 \reset@font\small

 \parindent\z@

 \parskip\z@ plus .1pt\relax

 \def\newblock{\hskip .11em plus .33em minus .07em}

 \sloppy\clubpenalty4000\widowpenalty4000

 \sfcode`\.=1000\relax

}

\let\endthebibliography=\endlist

\def\@biblabel#1{\hspace*{\labelsep}[#1]}



%  ****************************************

%  *              THE INDEX               *

%  ****************************************

%

\newif\if@restonecol

\def\theindex{\section*{INDEX}

 \addcontentsline{toc}{section}{INDEX}

 \reset@font\footnotesize \parindent\z@ \parskip\z@ plus .1pt\relax

 \let\item\@idxitem}

\def\@idxitem{\par\hangindent 1em}

\def\subitem {\par\hangindent 1em \hspace*{1em}}

\def\subsubitem{\par\hangindent 1em\hspace*{1em}}

\def\endtheindex{\if@restonecol\onecolumn\else\clearpage\fi}

\def\indexspace{\par\vskip\baselineskip \relax}



%  ****************************************

%  *             FOOTNOTES                *

%  ****************************************

%

\def\footnoterule{\kern-3\p@ \hrule width 12pc height \z@ \kern 3\p@}



\renewcommand{\thefootnote}{\mbox{{$\fnsymbol{footnote}$}}}



\def\@fnsymbol#1{\ifcase#1\or \mbox{$\star$}\or \dagger\or \ddagger\or

   \S \or \P \or \|\or \mbox{$\star\star$}\or \dagger\dagger

   \or \ddagger\ddagger\or \S\S\or \P\P\or \|\|\else ***

   \fi\relax}



\long\def\@makefntext#1{\parindent 1em\noindent

  $^{\@thefnmark}$\hspace{4pt}#1}



%\long\def\@makefntext#1{\@setpar{\@@par\@tempdima \hsize

% \advance\@tempdima-18pt\parshape \@ne 18pt\@tempdima}\par

% \noindent \hbox to \z@{\hss$^{\@thefnmark}$\hspace{0.5em}}#1}



%  ****************************************

%  *         FIGURES AND TABLES           *

%  ****************************************

%

\setcounter{topnumber}{2}

\def\topfraction{.9}

\setcounter{bottomnumber}{1}

\def\bottomfraction{.9}

\setcounter{totalnumber}{3}

\def\textfraction{.1}

\def\floatpagefraction{.9}

\setcounter{dbltopnumber}{2}

\def\dbltopfraction{.9}

\def\dblfloatpagefraction{.9}



\newif\ifst@rredfloat

\newcounter{table}

\def\thetable{\@arabic\c@table}

\def\fps@table{tbp}

\def\ftype@table{1}

\def\fstyle@table{\reset@font\small\rm}

\def\ext@table{lot}

\def\fnum@table{Table \thetable}

\def\table{\def\baselinestretch{1}%

  \let\@makecaption=\SFB@maketablecaption%

  \@float{table}\fstyle@table}

\let\endtable\end@float

\@namedef{table*}{\def\baselinestretch{1}\st@rredfloattrue

  \let\@makecaption=\SFB@maketablecaption%

  \@dblfloat{table}\centering\fstyle@table}

\@namedef{endtable*}{\end@dblfloat\st@rredfloatfalse}



\newcounter{figure}

\def\thefigure{\@arabic\c@figure}

\def\fps@figure{tbp}

\def\ftype@figure{2}

\def\fstyle@figure{\reset@font\small\rm}

\def\ext@figure{lof}

\def\fnum@figure{Figure \thefigure}

\def\figure{\def\baselinestretch{1}%

  \let\@makecaption=\SFB@makefigurecaption%

  \@float{figure}\fstyle@figure}

\let\endfigure\end@float

\@namedef{figure*}{\def\baselinestretch{1}\st@rredfloattrue

  \let\@makecaption=\SFB@makefigurecaption%

  \@dblfloat{figure}\centering\fstyle@figure}

\@namedef{endfigure*}{\end@dblfloat\st@rredfloatfalse}



\long\def\SFB@makefigurecaption#1#2{\vskip 6pt

  \setbox\@tempboxa\hbox{\reset@font\small{\bf #1}%

    \if@cont \ -- {\it continued}\else{\bf .}\fi\ {\rm #2}\par}%

 \ifdim \wd\@tempboxa >\hsize

   {\reset@font\small{\bf #1}%

     \if@cont \ -- {\it continued}\else{\bf .}\fi\ {\rm #2}\par}%

 \else

   \ifst@rredfloat

     \hbox to\hsize{\hfill\box\@tempboxa\hfill}%

   \else

     \hbox to\hsize{\hfill\box\@tempboxa\hfill}%

   \fi

 \fi

 \vskip 6pt

 \@contfalse

}



\long\def\SFB@maketablecaption#1#2{\vskip 6pt

  \setbox\@tempboxa\hbox{\reset@font\small{\bf #1}%

    \if@cont \ -- {\it continued}\else{\bf .}\fi\ {\rm #2}\par}%

 \ifdim \wd\@tempboxa >\hsize

    {\reset@font\small{\bf #1}%

    \if@cont \ -- {\it continued}\else{\bf .}\fi\ {\rm #2}\par}%

 \else

   \hbox to\hsize{\box\@tempboxa\hfill}%

 \fi

 \vskip 6pt

 \@contfalse

}



\newif\if@cont

\def\caption{\refstepcounter\@captype \@dblarg{\@caption\@captype}}

\def\contcaption{\@conttrue\SFB@caption\@captype}



\long\def\SFB@caption#1#2{%\par

 \begingroup

  \@parboxrestore

  \reset@font\normalsize

  \@makecaption{\csname fnum@#1\endcsname}{\ignorespaces #2}\par

 \endgroup}



%  ****************************************

%  *           CUP specials               *

%  ****************************************

%

%

%  The following code is taken from authordate.sty, by  David Rhead, of

%  the Cripps Computing Centre (February 1990), with some modifications

%  by ggw.  It is intended for documents

%  that use the author-date citation system.  When used in conjunction with

%  authordate1.bst, ... , authordate4.bst, it allows citations of the

%  form \shortcite{bloggs-60} as well as the usual \cite{bloggs-60}.

%  When

%       ... \cite{bloggs-60} ... \shortcite{bloggs-60} ...

%  appears in the input file,

%       ... (Bloggs, 1960) ... (1960) ...

%  appears in the final document.

%

%  Code taken from apalike.sty.

%

\def\@cite#1#2{(#1\if@tempswa , #2\fi)}

\def\@biblabel#1{}



% Set length of hanging indentation for bibliography entries

%

\newlength{\bibhang}

\setlength{\bibhang}{2em}



%  Define default title and page-head text.

%

\def\bibtitle{References}

\def\bibheadtitle{REFERENCES}



%  Code taken from aaai.sty.

%

% don't box citations, add space between multiple citations, separate with ;

\def\@citex[#1]#2{%

  \if@filesw\immediate\write\@auxout{\string\citation{#2}}\fi

  \def\@citea{}\@cite{\@for\@citeb:=#2\do

    {\@citea\def\@citea{; }\@ifundefined

       {b@\@citeb}{{\reset@font\bf ?}\@warning

       {Citation `\@citeb' on page \thepage \space undefined}}%

{\csname b@\@citeb\endcsname}}}{#1}}

% Allow short (name-less) citations, when used in

% conjunction with a bibliography style that creates labels like

%       \citename{<names>, }<year>

\let\@internalcite\cite

\def\cite{\def\citename##1{##1}\@internalcite}

\def\shortcite{\def\citename##1{}\@internalcite}



% RM for BSP note at end of article

\def\bsp{\medskip\reset@font\normalsize\noindent This paper has been

  produced using the Royal Astronomical Society/Blackwell Science

  \LaTeX\ style file.}





%  ****************************************

%  *                FLEQN                 *

%  ****************************************

%

% FLEQN DOCUMENT-STYLE OPTION - released 9 March 1987

%    for LaTeX version 2.09

% Copyright (C) 1987 by Leslie Lamport

%

% The following commands make the displayed math environments flush left,

% with an indentation of \mathindent from the prevailing left margin.



\def\[{\relax\ifmmode\@badmath\else\begin{trivlist}\item[]\leavevmode

  \hbox to\linewidth\bgroup$

  \displaystyle

  \hskip\mathindent\bgroup\fi}



\def\]{\relax\ifmmode \egroup $\hfil

       \egroup \end{trivlist}\else \@badmath \fi}



\def\equation{\refstepcounter{equation}\trivlist \item[]\leavevmode

  \hbox to\linewidth\bgroup $

  \displaystyle

\hskip\mathindent}





\def\endequation{$\hfil

           \displaywidth\linewidth\@eqnnum\egroup \endtrivlist}



\def\eqnarray{\stepcounter{equation}\let\@currentlabel=\theequation

\global\@eqnswtrue

\global\@eqcnt\z@\tabskip\mathindent\let\\=\@eqncr

\abovedisplayskip\topsep\ifvmode\advance\abovedisplayskip\partopsep\fi

\belowdisplayskip\abovedisplayskip

\belowdisplayshortskip\abovedisplayskip

\abovedisplayshortskip\abovedisplayskip

$$\halign

to \linewidth\bgroup\@eqnsel\hskip\@centering$\displaystyle\tabskip\z@

  {##}$&\global\@eqcnt\@ne \hskip 2\arraycolsep \hfil${##}$\hfil

  &\global\@eqcnt\tw@ \hskip 2\arraycolsep $\displaystyle{##}$\hfil

   \tabskip\@centering&\llap{##}\tabskip\z@\cr}



\def\endeqnarray{\@@eqncr\egroup

 \global\advance\c@equation\m@ne$$\global\@ignoretrue}



\newdimen\mathindent

\mathindent = \z@



%  ****************************************

%  *            MISCELLANEOUS             *

%  ****************************************

%

% DATE

\def\today{\number\day\ \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 \ \number\year}



%  ****************************************

%  *           INITIALIZATION             *

%  ****************************************

%

%

\newif\ifCUPmtlplainloaded

\ifx\CUP@mtlplain@loaded\undefined

\else

  \global\CUPmtlplainloadedtrue

  \input mnsym

\fi

%

\flushbottom

\ps@headings

\ifSFB@galley

 \raggedbottom

 \ps@empty

\fi

\ifSFB@referee

 \raggedbottom

\fi

\pagenumbering{arabic}

\if@twocolumn

 \twocolumn

 \sloppy

\else

 \onecolumn

\fi

\frenchspacing



% end of MN.sty

