Update on Overleaf.

5 files changed, 519 insertions, 4 deletions

diff --git a/iopams.sty b/iopams.sty
index baf2b72..044dde9 100644
--- a/iopams.sty
+++ b/iopams.sty
@@ -1 +1,87 @@
-%% 
%% This is file `iopams.sty'
%% File to include AMS fonts and extra definitions for bold greek 
%% characters for use with iopart.cls
%%
\NeedsTeXFormat{LaTeX2e}
\ProvidesPackage{iopams}[1997/02/13 v1.0]
\RequirePackage{amsgen}[1995/01/01]
\RequirePackage{amsfonts}[1995/01/01]
\RequirePackage{amssymb}[1995/01/01]
\RequirePackage{amsbsy}[1995/01/01]
%
\iopamstrue   % \newif\ifiopams in iopart.cls & iopbk2e.cls
%             % allows optional text to be in author guidelines
%
% Bold lower case Greek letters
%
\newcommand{\balpha}{\boldsymbol{\alpha}}
\newcommand{\bbeta}{\boldsymbol{\beta}}
\newcommand{\bgamma}{\boldsymbol{\gamma}}
\newcommand{\bdelta}{\boldsymbol{\delta}}
\newcommand{\bepsilon}{\boldsymbol{\epsilon}}
\newcommand{\bzeta}{\boldsymbol{\zeta}}
\newcommand{\bfeta}{\boldsymbol{\eta}}
\newcommand{\btheta}{\boldsymbol{\theta}}
\newcommand{\biota}{\boldsymbol{\iota}}
\newcommand{\bkappa}{\boldsymbol{\kappa}}
\newcommand{\blambda}{\boldsymbol{\lambda}}
\newcommand{\bmu}{\boldsymbol{\mu}}
\newcommand{\bnu}{\boldsymbol{\nu}}
\newcommand{\bxi}{\boldsymbol{\xi}}
\newcommand{\bpi}{\boldsymbol{\pi}}
\newcommand{\brho}{\boldsymbol{\rho}}
\newcommand{\bsigma}{\boldsymbol{\sigma}}
\newcommand{\btau}{\boldsymbol{\tau}}
\newcommand{\bupsilon}{\boldsymbol{\upsilon}}
\newcommand{\bphi}{\boldsymbol{\phi}}
\newcommand{\bchi}{\boldsymbol{\chi}}
\newcommand{\bpsi}{\boldsymbol{\psi}}
\newcommand{\bomega}{\boldsymbol{\omega}}
\newcommand{\bvarepsilon}{\boldsymbol{\varepsilon}}
\newcommand{\bvartheta}{\boldsymbol{\vartheta}}
\newcommand{\bvaromega}{\boldsymbol{\varomega}}
\newcommand{\bvarrho}{\boldsymbol{\varrho}}
\newcommand{\bvarzeta}{\boldsymbol{\varsigma}}  %NB really sigma
\newcommand{\bvarsigma}{\boldsymbol{\varsigma}}
\newcommand{\bvarphi}{\boldsymbol{\varphi}}
%
% Bold upright capital Greek letters
%
\newcommand{\bGamma}{\boldsymbol{\Gamma}}
\newcommand{\bDelta}{\boldsymbol{\Delta}}
\newcommand{\bTheta}{\boldsymbol{\Theta}}
\newcommand{\bLambda}{\boldsymbol{\Lambda}}
\newcommand{\bXi}{\boldsymbol{\Xi}}
\newcommand{\bPi}{\boldsymbol{\Pi}}
\newcommand{\bSigma}{\boldsymbol{\Sigma}}
\newcommand{\bUpsilon}{\boldsymbol{\Upsilon}}
\newcommand{\bPhi}{\boldsymbol{\Phi}}
\newcommand{\bPsi}{\boldsymbol{\Psi}}
\newcommand{\bOmega}{\boldsymbol{\Omega}}
%
% Bold versions of miscellaneous symbols
%
\newcommand{\bpartial}{\boldsymbol{\partial}}
\newcommand{\bell}{\boldsymbol{\ell}}
\newcommand{\bimath}{\boldsymbol{\imath}}
\newcommand{\bjmath}{\boldsymbol{\jmath}}
\newcommand{\binfty}{\boldsymbol{\infty}}
\newcommand{\bnabla}{\boldsymbol{\nabla}}
\newcommand{\bdot}{\boldsymbol{\cdot}}
%
% Symbols for caption
%
\renewcommand{\opensquare}{\mbox{$\square$}}
\renewcommand{\opentriangle}{\mbox{$\vartriangle$}}
\renewcommand{\opentriangledown}{\mbox{$\triangledown$}}
\renewcommand{\opendiamond}{\mbox{$\lozenge$}}
\renewcommand{\fullsquare}{\mbox{$\blacksquare$}}
\newcommand{\fulldiamond}{\mbox{$\blacklozenge$}}
\newcommand{\fullstar}{\mbox{$\bigstar$}}
\newcommand{\fulltriangle}{\mbox{$\blacktriangle$}}
\newcommand{\fulltriangledown}{\mbox{$\blacktriangledown$}}

\endinput
%% 
%% End of file `iopams.sty'.
\ No newline at end of file
+%% 
+%% This is file `iopams.sty'
+%% File to include AMS fonts and extra definitions for bold greek 
+%% characters for use with iopart.cls
+%%
+\NeedsTeXFormat{LaTeX2e}
+\ProvidesPackage{iopams}[1997/02/13 v1.0]
+\RequirePackage{amsgen}[1995/01/01]
+\RequirePackage{amsfonts}[1995/01/01]
+\RequirePackage{amssymb}[1995/01/01]
+\RequirePackage{amsbsy}[1995/01/01]
+%
+\iopamstrue   % \newif\ifiopams in iopart.cls & iopbk2e.cls
+%             % allows optional text to be in author guidelines
+%
+% Bold lower case Greek letters
+%
+\newcommand{\balpha}{\boldsymbol{\alpha}}
+\newcommand{\bbeta}{\boldsymbol{\beta}}
+\newcommand{\bgamma}{\boldsymbol{\gamma}}
+\newcommand{\bdelta}{\boldsymbol{\delta}}
+\newcommand{\bepsilon}{\boldsymbol{\epsilon}}
+\newcommand{\bzeta}{\boldsymbol{\zeta}}
+\newcommand{\bfeta}{\boldsymbol{\eta}}
+\newcommand{\btheta}{\boldsymbol{\theta}}
+\newcommand{\biota}{\boldsymbol{\iota}}
+\newcommand{\bkappa}{\boldsymbol{\kappa}}
+\newcommand{\blambda}{\boldsymbol{\lambda}}
+\newcommand{\bmu}{\boldsymbol{\mu}}
+\newcommand{\bnu}{\boldsymbol{\nu}}
+\newcommand{\bxi}{\boldsymbol{\xi}}
+\newcommand{\bpi}{\boldsymbol{\pi}}
+\newcommand{\brho}{\boldsymbol{\rho}}
+\newcommand{\bsigma}{\boldsymbol{\sigma}}
+\newcommand{\btau}{\boldsymbol{\tau}}
+\newcommand{\bupsilon}{\boldsymbol{\upsilon}}
+\newcommand{\bphi}{\boldsymbol{\phi}}
+\newcommand{\bchi}{\boldsymbol{\chi}}
+\newcommand{\bpsi}{\boldsymbol{\psi}}
+\newcommand{\bomega}{\boldsymbol{\omega}}
+\newcommand{\bvarepsilon}{\boldsymbol{\varepsilon}}
+\newcommand{\bvartheta}{\boldsymbol{\vartheta}}
+\newcommand{\bvaromega}{\boldsymbol{\varomega}}
+\newcommand{\bvarrho}{\boldsymbol{\varrho}}
+\newcommand{\bvarzeta}{\boldsymbol{\varsigma}}  %NB really sigma
+\newcommand{\bvarsigma}{\boldsymbol{\varsigma}}
+\newcommand{\bvarphi}{\boldsymbol{\varphi}}
+%
+% Bold upright capital Greek letters
+%
+\newcommand{\bGamma}{\boldsymbol{\Gamma}}
+\newcommand{\bDelta}{\boldsymbol{\Delta}}
+\newcommand{\bTheta}{\boldsymbol{\Theta}}
+\newcommand{\bLambda}{\boldsymbol{\Lambda}}
+\newcommand{\bXi}{\boldsymbol{\Xi}}
+\newcommand{\bPi}{\boldsymbol{\Pi}}
+\newcommand{\bSigma}{\boldsymbol{\Sigma}}
+\newcommand{\bUpsilon}{\boldsymbol{\Upsilon}}
+\newcommand{\bPhi}{\boldsymbol{\Phi}}
+\newcommand{\bPsi}{\boldsymbol{\Psi}}
+\newcommand{\bOmega}{\boldsymbol{\Omega}}
+%
+% Bold versions of miscellaneous symbols
+%
+\newcommand{\bpartial}{\boldsymbol{\partial}}
+\newcommand{\bell}{\boldsymbol{\ell}}
+\newcommand{\bimath}{\boldsymbol{\imath}}
+\newcommand{\bjmath}{\boldsymbol{\jmath}}
+\newcommand{\binfty}{\boldsymbol{\infty}}
+\newcommand{\bnabla}{\boldsymbol{\nabla}}
+\newcommand{\bdot}{\boldsymbol{\cdot}}
+%
+% Symbols for caption
+%
+\renewcommand{\opensquare}{\mbox{$\square$}}
+\renewcommand{\opentriangle}{\mbox{$\vartriangle$}}
+\renewcommand{\opentriangledown}{\mbox{$\triangledown$}}
+\renewcommand{\opendiamond}{\mbox{$\lozenge$}}
+\renewcommand{\fullsquare}{\mbox{$\blacksquare$}}
+\newcommand{\fulldiamond}{\mbox{$\blacklozenge$}}
+\newcommand{\fullstar}{\mbox{$\bigstar$}}
+\newcommand{\fulltriangle}{\mbox{$\blacktriangle$}}
+\newcommand{\fulltriangledown}{\mbox{$\blacktriangledown$}}
+
+\endinput
+%% 
+%% End of file `iopams.sty'.
diff --git a/iopart10.clo b/iopart10.clo
index 1805a0b..dec5747 100644
--- a/iopart10.clo
+++ b/iopart10.clo
@@ -1 +1,124 @@
-%% 
%% This is file `iopart10.clo'
%% 
%% This file is distributed in the hope that it will be useful, 
%% but WITHOUT ANY WARRANTY; without even the implied warranty of 
%% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. 
%% 
%% \CharacterTable
%%  {Upper-case    \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z
%%   Lower-case    \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z
%%   Digits        \0\1\2\3\4\5\6\7\8\9
%%   Exclamation   \!     Double quote  \"     Hash (number) \#
%%   Dollar        \$     Percent       \%     Ampersand     \&
%%   Acute accent  \'     Left paren    \(     Right paren   \)
%%   Asterisk      \*     Plus          \+     Comma         \,
%%   Minus         \-     Point         \.     Solidus       \/
%%   Colon         \:     Semicolon     \;     Less than     \<
%%   Equals        \=     Greater than  \>     Question mark \?
%%   Commercial at \@     Left bracket  \[     Backslash     \\
%%   Right bracket \]     Circumflex    \^     Underscore    \_
%%   Grave accent  \`     Left brace    \{     Vertical bar  \|
%%   Right brace   \}     Tilde         \~}
\ProvidesFile{iopart10.clo}[1997/01/13 v1.0 IOP Book file (size option)]
\renewcommand\normalsize{%
   \@setfontsize\normalsize\@xpt\@xiipt
   \abovedisplayskip 10\p@ \@plus2\p@ \@minus5\p@
   \abovedisplayshortskip \z@ \@plus3\p@
   \belowdisplayshortskip 6\p@ \@plus3\p@ \@minus3\p@
   \belowdisplayskip \abovedisplayskip
   \let\@listi\@listI}
\normalsize
\newcommand\small{%
   \@setfontsize\small\@ixpt{11}%
   \abovedisplayskip 8.5\p@ \@plus3\p@ \@minus4\p@
   \abovedisplayshortskip \z@ \@plus2\p@
   \belowdisplayshortskip 4\p@ \@plus2\p@ \@minus2\p@
   \def\@listi{\leftmargin\leftmargini
               \topsep 4\p@ \@plus2\p@ \@minus2\p@
               \parsep 2\p@ \@plus\p@ \@minus\p@
               \itemsep \parsep}%
   \belowdisplayskip \abovedisplayskip
}
\newcommand\footnotesize{%
   \@setfontsize\footnotesize\@viiipt{9.5}%
   \abovedisplayskip 6\p@ \@plus2\p@ \@minus4\p@
   \abovedisplayshortskip \z@ \@plus\p@
   \belowdisplayshortskip 3\p@ \@plus\p@ \@minus2\p@
   \def\@listi{\leftmargin\leftmargini
               \topsep 3\p@ \@plus\p@ \@minus\p@
               \parsep 2\p@ \@plus\p@ \@minus\p@
               \itemsep \parsep}%
   \belowdisplayskip \abovedisplayskip
}
\newcommand\scriptsize{\@setfontsize\scriptsize\@viipt\@viiipt}
\newcommand\tiny{\@setfontsize\tiny\@vpt\@vipt}
\newcommand\large{\@setfontsize\large\@xiipt{14}}
\newcommand\Large{\@setfontsize\Large\@xivpt{18}}
\newcommand\LARGE{\@setfontsize\LARGE\@xviipt{22}}
\newcommand\huge{\@setfontsize\huge\@xxpt{25}}
\newcommand\Huge{\@setfontsize\Huge\@xxvpt{30}}
\if@twocolumn
  \setlength\parindent{12\p@}
\else
  \setlength\parindent{15\p@}
\fi
\setlength\headheight{12\p@}
\setlength\headsep   {12\p@}
\setlength\topskip   {10\p@}
\setlength\footskip{20\p@}
\setlength\maxdepth{.5\topskip}
\setlength\@maxdepth\maxdepth
\setlength\textwidth{31pc}
\setlength\textheight{49pc}
\setlength\oddsidemargin  {24\p@}
\setlength\evensidemargin {24\p@}
\setlength\marginparwidth {72\p@}
\setlength\marginparsep {10\p@}
\setlength\marginparpush{5\p@}
\setlength\topmargin{\z@}
\setlength\footnotesep{6.65\p@}
\setlength{\skip\footins}  {9\p@ \@plus 4\p@ \@minus 2\p@}
\setlength\floatsep       {12\p@ \@plus 2\p@ \@minus 2\p@}
\setlength\textfloatsep   {20\p@ \@plus 2\p@ \@minus 4\p@}
\setlength\intextsep      {12\p@ \@plus 2\p@ \@minus 2\p@}
\setlength\dblfloatsep    {12\p@ \@plus 2\p@ \@minus 2\p@}
\setlength\dbltextfloatsep{20\p@ \@plus 2\p@ \@minus 4\p@}
\setlength\@fptop{0\p@}
\setlength\@fpsep{8\p@ \@plus 2fil}
\setlength\@fpbot{0\p@}
\setlength\@dblfptop{0\p@}
\setlength\@dblfpsep{8\p@ \@plus 2fil}
\setlength\@dblfpbot{0\p@}
\setlength\partopsep{2\p@ \@plus 1\p@ \@minus 1\p@}
\def\@listI{\leftmargin\leftmargini
            \parsep=\z@ 
            \topsep=5\p@ \@plus3\p@ \@minus3\p@
            \itemsep=3\p@ \@plus2\p@ \@minus\p@}
\let\@listi\@listI
\@listi
\def\@listii {\leftmargin\leftmarginii
     \labelwidth\leftmarginii
     \advance\labelwidth-\labelsep
     \topsep=2\p@ \@plus2\p@ \@minus\p@
     \parsep=\z@
     \itemsep=\parsep}
\def\@listiii{\leftmargin\leftmarginiii
     \labelwidth\leftmarginiii
     \advance\labelwidth-\labelsep
     \topsep=\z@
     \parsep=\z@
     \partopsep=\z@
     \itemsep=\z@}
\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}
\endinput
%% 
%% End of file `iopart.clo'.
\ No newline at end of file
+%% 
+%% This is file `iopart10.clo'
+%% 
+%% This file is distributed in the hope that it will be useful, 
+%% but WITHOUT ANY WARRANTY; without even the implied warranty of 
+%% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. 
+%% 
+%% \CharacterTable
+%%  {Upper-case    \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z
+%%   Lower-case    \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z
+%%   Digits        \0\1\2\3\4\5\6\7\8\9
+%%   Exclamation   \!     Double quote  \"     Hash (number) \#
+%%   Dollar        \$     Percent       \%     Ampersand     \&
+%%   Acute accent  \'     Left paren    \(     Right paren   \)
+%%   Asterisk      \*     Plus          \+     Comma         \,
+%%   Minus         \-     Point         \.     Solidus       \/
+%%   Colon         \:     Semicolon     \;     Less than     \<
+%%   Equals        \=     Greater than  \>     Question mark \?
+%%   Commercial at \@     Left bracket  \[     Backslash     \\
+%%   Right bracket \]     Circumflex    \^     Underscore    \_
+%%   Grave accent  \`     Left brace    \{     Vertical bar  \|
+%%   Right brace   \}     Tilde         \~}
+\ProvidesFile{iopart10.clo}[1997/01/13 v1.0 IOP Book file (size option)]
+\renewcommand\normalsize{%
+   \@setfontsize\normalsize\@xpt\@xiipt
+   \abovedisplayskip 10\p@ \@plus2\p@ \@minus5\p@
+   \abovedisplayshortskip \z@ \@plus3\p@
+   \belowdisplayshortskip 6\p@ \@plus3\p@ \@minus3\p@
+   \belowdisplayskip \abovedisplayskip
+   \let\@listi\@listI}
+\normalsize
+\newcommand\small{%
+   \@setfontsize\small\@ixpt{11}%
+   \abovedisplayskip 8.5\p@ \@plus3\p@ \@minus4\p@
+   \abovedisplayshortskip \z@ \@plus2\p@
+   \belowdisplayshortskip 4\p@ \@plus2\p@ \@minus2\p@
+   \def\@listi{\leftmargin\leftmargini
+               \topsep 4\p@ \@plus2\p@ \@minus2\p@
+               \parsep 2\p@ \@plus\p@ \@minus\p@
+               \itemsep \parsep}%
+   \belowdisplayskip \abovedisplayskip
+}
+\newcommand\footnotesize{%
+   \@setfontsize\footnotesize\@viiipt{9.5}%
+   \abovedisplayskip 6\p@ \@plus2\p@ \@minus4\p@
+   \abovedisplayshortskip \z@ \@plus\p@
+   \belowdisplayshortskip 3\p@ \@plus\p@ \@minus2\p@
+   \def\@listi{\leftmargin\leftmargini
+               \topsep 3\p@ \@plus\p@ \@minus\p@
+               \parsep 2\p@ \@plus\p@ \@minus\p@
+               \itemsep \parsep}%
+   \belowdisplayskip \abovedisplayskip
+}
+\newcommand\scriptsize{\@setfontsize\scriptsize\@viipt\@viiipt}
+\newcommand\tiny{\@setfontsize\tiny\@vpt\@vipt}
+\newcommand\large{\@setfontsize\large\@xiipt{14}}
+\newcommand\Large{\@setfontsize\Large\@xivpt{18}}
+\newcommand\LARGE{\@setfontsize\LARGE\@xviipt{22}}
+\newcommand\huge{\@setfontsize\huge\@xxpt{25}}
+\newcommand\Huge{\@setfontsize\Huge\@xxvpt{30}}
+\if@twocolumn
+  \setlength\parindent{12\p@}
+\else
+  \setlength\parindent{15\p@}
+\fi
+\setlength\headheight{12\p@}
+\setlength\headsep   {12\p@}
+\setlength\topskip   {10\p@}
+\setlength\footskip{20\p@}
+\setlength\maxdepth{.5\topskip}
+\setlength\@maxdepth\maxdepth
+\setlength\textwidth{31pc}
+\setlength\textheight{49pc}
+\setlength\oddsidemargin  {24\p@}
+\setlength\evensidemargin {24\p@}
+\setlength\marginparwidth {72\p@}
+\setlength\marginparsep {10\p@}
+\setlength\marginparpush{5\p@}
+\setlength\topmargin{\z@}
+\setlength\footnotesep{6.65\p@}
+\setlength{\skip\footins}  {9\p@ \@plus 4\p@ \@minus 2\p@}
+\setlength\floatsep       {12\p@ \@plus 2\p@ \@minus 2\p@}
+\setlength\textfloatsep   {20\p@ \@plus 2\p@ \@minus 4\p@}
+\setlength\intextsep      {12\p@ \@plus 2\p@ \@minus 2\p@}
+\setlength\dblfloatsep    {12\p@ \@plus 2\p@ \@minus 2\p@}
+\setlength\dbltextfloatsep{20\p@ \@plus 2\p@ \@minus 4\p@}
+\setlength\@fptop{0\p@}
+\setlength\@fpsep{8\p@ \@plus 2fil}
+\setlength\@fpbot{0\p@}
+\setlength\@dblfptop{0\p@}
+\setlength\@dblfpsep{8\p@ \@plus 2fil}
+\setlength\@dblfpbot{0\p@}
+\setlength\partopsep{2\p@ \@plus 1\p@ \@minus 1\p@}
+\def\@listI{\leftmargin\leftmargini
+            \parsep=\z@ 
+            \topsep=5\p@ \@plus3\p@ \@minus3\p@
+            \itemsep=3\p@ \@plus2\p@ \@minus\p@}
+\let\@listi\@listI
+\@listi
+\def\@listii {\leftmargin\leftmarginii
+     \labelwidth\leftmarginii
+     \advance\labelwidth-\labelsep
+     \topsep=2\p@ \@plus2\p@ \@minus\p@
+     \parsep=\z@
+     \itemsep=\parsep}
+\def\@listiii{\leftmargin\leftmarginiii
+     \labelwidth\leftmarginiii
+     \advance\labelwidth-\labelsep
+     \topsep=\z@
+     \parsep=\z@
+     \partopsep=\z@
+     \itemsep=\z@}
+\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}
+\endinput
+%% 
+%% End of file `iopart.clo'.
diff --git a/iopart12.clo b/iopart12.clo
index 48ec5c1..d392bf9 100644
--- a/iopart12.clo
+++ b/iopart12.clo
@@ -1 +1,125 @@
-%% 
%% This is file `iopart12.clo'
%% 
%% This file is distributed in the hope that it will be useful, 
%% but WITHOUT ANY WARRANTY; without even the implied warranty of 
%% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. 
%% 
%% \CharacterTable
%%  {Upper-case    \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z
%%   Lower-case    \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z
%%   Digits        \0\1\2\3\4\5\6\7\8\9
%%   Exclamation   \!     Double quote  \"     Hash (number) \#
%%   Dollar        \$     Percent       \%     Ampersand     \&
%%   Acute accent  \'     Left paren    \(     Right paren   \)
%%   Asterisk      \*     Plus          \+     Comma         \,
%%   Minus         \-     Point         \.     Solidus       \/
%%   Colon         \:     Semicolon     \;     Less than     \<
%%   Equals        \=     Greater than  \>     Question mark \?
%%   Commercial at \@     Left bracket  \[     Backslash     \\
%%   Right bracket \]     Circumflex    \^     Underscore    \_
%%   Grave accent  \`     Left brace    \{     Vertical bar  \|
%%   Right brace   \}     Tilde         \~}
\ProvidesFile{iopart12.clo}[1997/01/15 v1.0 LaTeX2e file (size option)]
\renewcommand\normalsize{%
   \@setfontsize\normalsize\@xiipt{16}%
   \abovedisplayskip 12\p@ \@plus3\p@ \@minus7\p@
   \abovedisplayshortskip \z@ \@plus3\p@
   \belowdisplayshortskip 6.5\p@ \@plus3.5\p@ \@minus3\p@
   \belowdisplayskip \abovedisplayskip
   \let\@listi\@listI}
\normalsize
\newcommand\small{%
   \@setfontsize\small\@xipt{14}%
   \abovedisplayskip 11\p@ \@plus3\p@ \@minus6\p@
   \abovedisplayshortskip \z@ \@plus3\p@
   \belowdisplayshortskip 6.5\p@ \@plus3.5\p@ \@minus3\p@
   \def\@listi{\leftmargin\leftmargini
               \topsep 9\p@ \@plus3\p@ \@minus5\p@
               \parsep 4.5\p@ \@plus2\p@ \@minus\p@
               \itemsep \parsep}%
   \belowdisplayskip \abovedisplayskip
}
\newcommand\footnotesize{%
%   \@setfontsize\footnotesize\@xpt\@xiipt
   \@setfontsize\footnotesize\@xpt{13}%
   \abovedisplayskip 10\p@ \@plus2\p@ \@minus5\p@
   \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}%
   \belowdisplayskip \abovedisplayskip
}
\newcommand\scriptsize{\@setfontsize\scriptsize\@viiipt{9.5}}
\newcommand\tiny{\@setfontsize\tiny\@vipt\@viipt}
\newcommand\large{\@setfontsize\large\@xivpt{18}}
\newcommand\Large{\@setfontsize\Large\@xviipt{22}}
\newcommand\LARGE{\@setfontsize\LARGE\@xxpt{25}}
\newcommand\huge{\@setfontsize\huge\@xxvpt{30}}
\let\Huge=\huge
\if@twocolumn
  \setlength\parindent{14\p@}
\else
  \setlength\parindent{18\p@}
\fi
\setlength\headheight{14\p@}
\setlength\headsep{14\p@}
\setlength\topskip{12\p@}
\setlength\footskip{24\p@}
\setlength\maxdepth{.5\topskip}
\setlength\@maxdepth\maxdepth
\setlength\textwidth{37.2pc}
\setlength\textheight{56pc}
\setlength\oddsidemargin  {\z@}
\setlength\evensidemargin {\z@}
\setlength\marginparwidth {72\p@}
\setlength\marginparsep{10\p@}
\setlength\marginparpush{5\p@}
\setlength\topmargin{-12pt}
\setlength\footnotesep{8.4\p@}
\setlength{\skip\footins} {10.8\p@ \@plus 4\p@ \@minus 2\p@}
\setlength\floatsep       {14\p@ \@plus 2\p@ \@minus 4\p@}
\setlength\textfloatsep   {24\p@ \@plus 2\p@ \@minus 4\p@}
\setlength\intextsep      {16\p@ \@plus 4\p@ \@minus 4\p@}
\setlength\dblfloatsep    {16\p@ \@plus 2\p@ \@minus 4\p@}
\setlength\dbltextfloatsep{24\p@ \@plus 2\p@ \@minus 4\p@}
\setlength\@fptop{0\p@}
\setlength\@fpsep{10\p@ \@plus 1fil}
\setlength\@fpbot{0\p@}
\setlength\@dblfptop{0\p@}
\setlength\@dblfpsep{10\p@ \@plus 1fil}
\setlength\@dblfpbot{0\p@}
\setlength\partopsep{3\p@ \@plus 2\p@ \@minus 2\p@}
\def\@listI{\leftmargin\leftmargini
     \parsep=\z@
     \topsep=6\p@  \@plus3\p@ \@minus3\p@
     \itemsep=3\p@ \@plus2\p@ \@minus1\p@}
\let\@listi\@listI
\@listi
\def\@listii {\leftmargin\leftmarginii
     \labelwidth\leftmarginii
     \advance\labelwidth-\labelsep
     \topsep=3\p@ \@plus2\p@ \@minus\p@
     \parsep=\z@
     \itemsep=\parsep}
\def\@listiii{\leftmargin\leftmarginiii
     \labelwidth\leftmarginiii
     \advance\labelwidth-\labelsep
     \topsep=\z@
     \parsep=\z@
     \partopsep=\z@
     \itemsep=\z@}
\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}
\endinput
%% 
%% End of file `iopart12.clo'.
\ No newline at end of file
+%% 
+%% This is file `iopart12.clo'
+%% 
+%% This file is distributed in the hope that it will be useful, 
+%% but WITHOUT ANY WARRANTY; without even the implied warranty of 
+%% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. 
+%% 
+%% \CharacterTable
+%%  {Upper-case    \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z
+%%   Lower-case    \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z
+%%   Digits        \0\1\2\3\4\5\6\7\8\9
+%%   Exclamation   \!     Double quote  \"     Hash (number) \#
+%%   Dollar        \$     Percent       \%     Ampersand     \&
+%%   Acute accent  \'     Left paren    \(     Right paren   \)
+%%   Asterisk      \*     Plus          \+     Comma         \,
+%%   Minus         \-     Point         \.     Solidus       \/
+%%   Colon         \:     Semicolon     \;     Less than     \<
+%%   Equals        \=     Greater than  \>     Question mark \?
+%%   Commercial at \@     Left bracket  \[     Backslash     \\
+%%   Right bracket \]     Circumflex    \^     Underscore    \_
+%%   Grave accent  \`     Left brace    \{     Vertical bar  \|
+%%   Right brace   \}     Tilde         \~}
+\ProvidesFile{iopart12.clo}[1997/01/15 v1.0 LaTeX2e file (size option)]
+\renewcommand\normalsize{%
+   \@setfontsize\normalsize\@xiipt{16}%
+   \abovedisplayskip 12\p@ \@plus3\p@ \@minus7\p@
+   \abovedisplayshortskip \z@ \@plus3\p@
+   \belowdisplayshortskip 6.5\p@ \@plus3.5\p@ \@minus3\p@
+   \belowdisplayskip \abovedisplayskip
+   \let\@listi\@listI}
+\normalsize
+\newcommand\small{%
+   \@setfontsize\small\@xipt{14}%
+   \abovedisplayskip 11\p@ \@plus3\p@ \@minus6\p@
+   \abovedisplayshortskip \z@ \@plus3\p@
+   \belowdisplayshortskip 6.5\p@ \@plus3.5\p@ \@minus3\p@
+   \def\@listi{\leftmargin\leftmargini
+               \topsep 9\p@ \@plus3\p@ \@minus5\p@
+               \parsep 4.5\p@ \@plus2\p@ \@minus\p@
+               \itemsep \parsep}%
+   \belowdisplayskip \abovedisplayskip
+}
+\newcommand\footnotesize{%
+%   \@setfontsize\footnotesize\@xpt\@xiipt
+   \@setfontsize\footnotesize\@xpt{13}%
+   \abovedisplayskip 10\p@ \@plus2\p@ \@minus5\p@
+   \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}%
+   \belowdisplayskip \abovedisplayskip
+}
+\newcommand\scriptsize{\@setfontsize\scriptsize\@viiipt{9.5}}
+\newcommand\tiny{\@setfontsize\tiny\@vipt\@viipt}
+\newcommand\large{\@setfontsize\large\@xivpt{18}}
+\newcommand\Large{\@setfontsize\Large\@xviipt{22}}
+\newcommand\LARGE{\@setfontsize\LARGE\@xxpt{25}}
+\newcommand\huge{\@setfontsize\huge\@xxvpt{30}}
+\let\Huge=\huge
+\if@twocolumn
+  \setlength\parindent{14\p@}
+\else
+  \setlength\parindent{18\p@}
+\fi
+\setlength\headheight{14\p@}
+\setlength\headsep{14\p@}
+\setlength\topskip{12\p@}
+\setlength\footskip{24\p@}
+\setlength\maxdepth{.5\topskip}
+\setlength\@maxdepth\maxdepth
+\setlength\textwidth{37.2pc}
+\setlength\textheight{56pc}
+\setlength\oddsidemargin  {\z@}
+\setlength\evensidemargin {\z@}
+\setlength\marginparwidth {72\p@}
+\setlength\marginparsep{10\p@}
+\setlength\marginparpush{5\p@}
+\setlength\topmargin{-12pt}
+\setlength\footnotesep{8.4\p@}
+\setlength{\skip\footins} {10.8\p@ \@plus 4\p@ \@minus 2\p@}
+\setlength\floatsep       {14\p@ \@plus 2\p@ \@minus 4\p@}
+\setlength\textfloatsep   {24\p@ \@plus 2\p@ \@minus 4\p@}
+\setlength\intextsep      {16\p@ \@plus 4\p@ \@minus 4\p@}
+\setlength\dblfloatsep    {16\p@ \@plus 2\p@ \@minus 4\p@}
+\setlength\dbltextfloatsep{24\p@ \@plus 2\p@ \@minus 4\p@}
+\setlength\@fptop{0\p@}
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+\setlength\@fpbot{0\p@}
+\setlength\@dblfptop{0\p@}
+\setlength\@dblfpsep{10\p@ \@plus 1fil}
+\setlength\@dblfpbot{0\p@}
+\setlength\partopsep{3\p@ \@plus 2\p@ \@minus 2\p@}
+\def\@listI{\leftmargin\leftmargini
+     \parsep=\z@
+     \topsep=6\p@  \@plus3\p@ \@minus3\p@
+     \itemsep=3\p@ \@plus2\p@ \@minus1\p@}
+\let\@listi\@listI
+\@listi
+\def\@listii {\leftmargin\leftmarginii
+     \labelwidth\leftmarginii
+     \advance\labelwidth-\labelsep
+     \topsep=3\p@ \@plus2\p@ \@minus\p@
+     \parsep=\z@
+     \itemsep=\parsep}
+\def\@listiii{\leftmargin\leftmarginiii
+     \labelwidth\leftmarginiii
+     \advance\labelwidth-\labelsep
+     \topsep=\z@
+     \parsep=\z@
+     \partopsep=\z@
+     \itemsep=\z@}
+\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}
+\endinput
+%% 
+%% End of file `iopart12.clo'.
diff --git a/setstack.sty b/setstack.sty
index 1d0130f..da428a6 100644
--- a/setstack.sty
+++ b/setstack.sty
@@ -1 +1,139 @@
-%%
%% This is file `setstack.sty', created by VIK 15 Dec 1998
%% Reproduces useful macros from amsmath.sty, thus avoiding the need to load the entire
%% amsmath.sty and run into conflicts
%% Adds definitions for \overset, \underset, \sideset, \substack, \boxed, \leftroot,
%% \uproot, \dddot, \ddddot, \varrow, \harrow (see The LateX Companion, pp 225-227)
\NeedsTeXFormat{LaTeX2e}% LaTeX 2.09 can't be used (nor non-LaTeX)
[1998/12/15]% LaTeX date must December 1998 or later
\ProvidesPackage{setstack}
\DeclareRobustCommand{\text}{%
  \ifmmode\expandafter\text@\else\expandafter\mbox\fi}
  \let\nfss@text\text
  \def\text@#1{\mathchoice
    {\textdef@\displaystyle\f@size{#1}}%
      {\textdef@\textstyle\tf@size{\firstchoice@false #1}}%
        {\textdef@\textstyle\sf@size{\firstchoice@false #1}}%
          {\textdef@\textstyle \ssf@size{\firstchoice@false #1}}%
            \check@mathfonts
}
\def\textdef@#1#2#3{\hbox{{%
             \everymath{#1}%
             \let\f@size#2\selectfont #3}}}

% adds underset, overset, sideset and 
% substack features from amsmath.sty (Companion p. 226)

\def\invalid@tag#1{\@amsmath@err{#1}{\the\tag@help}\gobble@tag}
\def\dft@tag{\invalid@tag{\string\tag\space not allowed here}}
\def\default@tag{\let\tag\dft@tag}

\def\Let@{\let\\\math@cr}
\def\restore@math@cr{\def\math@cr@@@{\cr}}

\def\overset#1#2{\binrel@{#2}%
\binrel@@{\mathop{\kern\z@#2}\limits^{#1}}}
\def\underset#1#2{\binrel@{#2}%
\binrel@@{\mathop{\kern\z@#2}\limits_{#1}}}
\def\sideset#1#2#3{%
\@mathmeasure\z@\displaystyle{#3}%
\global\setbox\@ne\vbox to\ht\z@{}\dp\@ne\dp\z@
 \setbox\tw@\box\@ne
\@mathmeasure4\displaystyle{\copy\tw@#1}%
\@mathmeasure6\displaystyle{#3\nolimits#2}%
\dimen@-\wd6 \advance\dimen@\wd4 \advance\dimen@\wd\z@
\hbox to\dimen@{}\mathop{\kern-\dimen@\box4\box6}%
}

\newenvironment{subarray}[1]{%
\vcenter\bgroup
\Let@ \restore@math@cr \default@tag
\baselineskip\fontdimen10 \scriptfont\tw@
\advance\baselineskip\fontdimen12 \scriptfont\tw@
\lineskip\thr@@\fontdimen8 \scriptfont\thr@@
\lineskiplimit\lineskip
\ialign\bgroup\ifx c#1\hfil\fi
$\m@th\scriptstyle##$\hfil\crcr
}{%
\crcr\egroup\egroup
}
\newcommand{\substack}[1]{\subarray{c}#1\endsubarray}

% definitions of dddot and ddddot(p. 225)

\def\dddot#1{{\mathop{#1}\limits^{\vbox to-1.4\ex@{\kern-\tw@\ex@
 \hbox{\normalfont ...}\vss}}}}
\def\ddddot#1{{\mathop{#1}\limits^{\vbox to-1.4\ex@{\kern-\tw@\ex@
 \hbox{\normalfont....}\vss}}}}

% definitions of leftroot, uproot (p.225)

\begingroup \catcode`\"=12
\gdef\@@sqrt#1{\radical"270370 {#1}}
\endgroup

\def\leftroot{\@amsmath@err{\Invalid@@\leftroot}\@eha}
\def\uproot{\@amsmath@err{\Invalid@@\uproot}\@eha}
\newcount\uproot@
\newcount\leftroot@
\def\root{\relaxnext@
  \DN@{\ifx\@let@token\uproot\let\next@\nextii@\else
   \ifx\@let@token\leftroot\let\next@\nextiii@\else
   \let\next@\plainroot@\fi\fi\next@}%
  \def\nextii@\uproot##1{\uproot@##1\relax\FN@\nextiv@}%
  \def\nextiv@{\ifx\@let@token\@sptoken\DN@. {\FN@\nextv@}\else
   \DN@.{\FN@\nextv@}\fi\next@.}%
  \def\nextv@{\ifx\@let@token\leftroot\let\next@\nextvi@\else
   \let\next@\plainroot@\fi\next@}%
  \def\nextvi@\leftroot##1{\leftroot@##1\relax\plainroot@}%
   \def\nextiii@\leftroot##1{\leftroot@##1\relax\FN@\nextvii@}%
  \def\nextvii@{\ifx\@let@token\@sptoken
   \DN@. {\FN@\nextviii@}\else
   \DN@.{\FN@\nextviii@}\fi\next@.}%
  \def\nextviii@{\ifx\@let@token\uproot\let\next@\nextix@\else
   \let\next@\plainroot@\fi\next@}%
  \def\nextix@\uproot##1{\uproot@##1\relax\plainroot@}%
  \bgroup\uproot@\z@\leftroot@\z@\FN@\next@}
\def\plainroot@#1\of#2{\setbox\rootbox\hbox{%
 $\m@th\scriptscriptstyle{#1}$}%
 \mathchoice{\r@@t\displaystyle{#2}}{\r@@t\textstyle{#2}}
 {\r@@t\scriptstyle{#2}}{\r@@t\scriptscriptstyle{#2}}\egroup}
\def\r@@t#1#2{\setboxz@h{$\m@th#1\@@sqrt{#2}$}%
 \dimen@\ht\z@\advance\dimen@-\dp\z@
 \setbox\@ne\hbox{$\m@th#1\mskip\uproot@ mu$}%
 \advance\dimen@ by1.667\wd\@ne
 \mkern-\leftroot@ mu\mkern5mu\raise.6\dimen@\copy\rootbox
 \mkern-10mu\mkern\leftroot@ mu\boxz@}
 
%   definition of \boxed (math in frame, no dollars) p 225

\def\boxed#1{\fbox{\m@th$\displaystyle#1$}}

% definition of \smash for top and bottom parts of expression in braces (p.227)
\renewcommand{\smash}[2][tb]{%
  \def\smash@{#1}%
  \ifmmode\@xp\mathpalette\@xp\mathsm@sh\else
        \@xp\makesm@sh\fi{#2}}

% additional difinitions for arrows 
% zero mm wide #2 mm long vertical arrow shifted 1 mm to left, 1 mm up
\newcommand{\varrow}[2]{%
\unitlength=1mm
  \begin{picture}(0,6) % (0,0)
  % - for #1 to point arrow down,+ to point arrow up
  \end{picture}%
  \put(0,6){\vector(0,#1 3){#2}}    % 6,- for down, 0, + for up
}
% 1 mm high #2 mm long horizontal arrow shifted 1 mm up (0,-1)
\newcommand{\harrow}[2]{%
\unitlength=1mm
  \begin{picture}(8,1)(0,-1) %
  % 1 mm distance between arrow and stackreled object over it (8,1)
  \put(0,0){\vector(#1 2,0){#2}}     % - to point arrow left, + right
  \end{picture}%
}

\endinput
%% end of setstack.sty
%% Corrections history:
%% 
\ No newline at end of file
+%%
+%% This is file `setstack.sty', created by VIK 15 Dec 1998
+%% Reproduces useful macros from amsmath.sty, thus avoiding the need to load the entire
+%% amsmath.sty and run into conflicts
+%% Adds definitions for \overset, \underset, \sideset, \substack, \boxed, \leftroot,
+%% \uproot, \dddot, \ddddot, \varrow, \harrow (see The LateX Companion, pp 225-227)
+\NeedsTeXFormat{LaTeX2e}% LaTeX 2.09 can't be used (nor non-LaTeX)
+[1998/12/15]% LaTeX date must December 1998 or later
+\ProvidesPackage{setstack}
+\DeclareRobustCommand{\text}{%
+  \ifmmode\expandafter\text@\else\expandafter\mbox\fi}
+  \let\nfss@text\text
+  \def\text@#1{\mathchoice
+    {\textdef@\displaystyle\f@size{#1}}%
+      {\textdef@\textstyle\tf@size{\firstchoice@false #1}}%
+        {\textdef@\textstyle\sf@size{\firstchoice@false #1}}%
+          {\textdef@\textstyle \ssf@size{\firstchoice@false #1}}%
+            \check@mathfonts
+}
+\def\textdef@#1#2#3{\hbox{{%
+             \everymath{#1}%
+             \let\f@size#2\selectfont #3}}}
+
+% adds underset, overset, sideset and 
+% substack features from amsmath.sty (Companion p. 226)
+
+\def\invalid@tag#1{\@amsmath@err{#1}{\the\tag@help}\gobble@tag}
+\def\dft@tag{\invalid@tag{\string\tag\space not allowed here}}
+\def\default@tag{\let\tag\dft@tag}
+
+\def\Let@{\let\\\math@cr}
+\def\restore@math@cr{\def\math@cr@@@{\cr}}
+
+\def\overset#1#2{\binrel@{#2}%
+\binrel@@{\mathop{\kern\z@#2}\limits^{#1}}}
+\def\underset#1#2{\binrel@{#2}%
+\binrel@@{\mathop{\kern\z@#2}\limits_{#1}}}
+\def\sideset#1#2#3{%
+\@mathmeasure\z@\displaystyle{#3}%
+\global\setbox\@ne\vbox to\ht\z@{}\dp\@ne\dp\z@
+ \setbox\tw@\box\@ne
+\@mathmeasure4\displaystyle{\copy\tw@#1}%
+\@mathmeasure6\displaystyle{#3\nolimits#2}%
+\dimen@-\wd6 \advance\dimen@\wd4 \advance\dimen@\wd\z@
+\hbox to\dimen@{}\mathop{\kern-\dimen@\box4\box6}%
+}
+
+\newenvironment{subarray}[1]{%
+\vcenter\bgroup
+\Let@ \restore@math@cr \default@tag
+\baselineskip\fontdimen10 \scriptfont\tw@
+\advance\baselineskip\fontdimen12 \scriptfont\tw@
+\lineskip\thr@@\fontdimen8 \scriptfont\thr@@
+\lineskiplimit\lineskip
+\ialign\bgroup\ifx c#1\hfil\fi
+$\m@th\scriptstyle##$\hfil\crcr
+}{%
+\crcr\egroup\egroup
+}
+\newcommand{\substack}[1]{\subarray{c}#1\endsubarray}
+
+% definitions of dddot and ddddot(p. 225)
+
+\def\dddot#1{{\mathop{#1}\limits^{\vbox to-1.4\ex@{\kern-\tw@\ex@
+ \hbox{\normalfont ...}\vss}}}}
+\def\ddddot#1{{\mathop{#1}\limits^{\vbox to-1.4\ex@{\kern-\tw@\ex@
+ \hbox{\normalfont....}\vss}}}}
+
+% definitions of leftroot, uproot (p.225)
+
+\begingroup \catcode`\"=12
+\gdef\@@sqrt#1{\radical"270370 {#1}}
+\endgroup
+
+\def\leftroot{\@amsmath@err{\Invalid@@\leftroot}\@eha}
+\def\uproot{\@amsmath@err{\Invalid@@\uproot}\@eha}
+\newcount\uproot@
+\newcount\leftroot@
+\def\root{\relaxnext@
+  \DN@{\ifx\@let@token\uproot\let\next@\nextii@\else
+   \ifx\@let@token\leftroot\let\next@\nextiii@\else
+   \let\next@\plainroot@\fi\fi\next@}%
+  \def\nextii@\uproot##1{\uproot@##1\relax\FN@\nextiv@}%
+  \def\nextiv@{\ifx\@let@token\@sptoken\DN@. {\FN@\nextv@}\else
+   \DN@.{\FN@\nextv@}\fi\next@.}%
+  \def\nextv@{\ifx\@let@token\leftroot\let\next@\nextvi@\else
+   \let\next@\plainroot@\fi\next@}%
+  \def\nextvi@\leftroot##1{\leftroot@##1\relax\plainroot@}%
+   \def\nextiii@\leftroot##1{\leftroot@##1\relax\FN@\nextvii@}%
+  \def\nextvii@{\ifx\@let@token\@sptoken
+   \DN@. {\FN@\nextviii@}\else
+   \DN@.{\FN@\nextviii@}\fi\next@.}%
+  \def\nextviii@{\ifx\@let@token\uproot\let\next@\nextix@\else
+   \let\next@\plainroot@\fi\next@}%
+  \def\nextix@\uproot##1{\uproot@##1\relax\plainroot@}%
+  \bgroup\uproot@\z@\leftroot@\z@\FN@\next@}
+\def\plainroot@#1\of#2{\setbox\rootbox\hbox{%
+ $\m@th\scriptscriptstyle{#1}$}%
+ \mathchoice{\r@@t\displaystyle{#2}}{\r@@t\textstyle{#2}}
+ {\r@@t\scriptstyle{#2}}{\r@@t\scriptscriptstyle{#2}}\egroup}
+\def\r@@t#1#2{\setboxz@h{$\m@th#1\@@sqrt{#2}$}%
+ \dimen@\ht\z@\advance\dimen@-\dp\z@
+ \setbox\@ne\hbox{$\m@th#1\mskip\uproot@ mu$}%
+ \advance\dimen@ by1.667\wd\@ne
+ \mkern-\leftroot@ mu\mkern5mu\raise.6\dimen@\copy\rootbox
+ \mkern-10mu\mkern\leftroot@ mu\boxz@}
+ 
+%   definition of \boxed (math in frame, no dollars) p 225
+
+\def\boxed#1{\fbox{\m@th$\displaystyle#1$}}
+
+% definition of \smash for top and bottom parts of expression in braces (p.227)
+\renewcommand{\smash}[2][tb]{%
+  \def\smash@{#1}%
+  \ifmmode\@xp\mathpalette\@xp\mathsm@sh\else
+        \@xp\makesm@sh\fi{#2}}
+
+% additional difinitions for arrows 
+% zero mm wide #2 mm long vertical arrow shifted 1 mm to left, 1 mm up
+\newcommand{\varrow}[2]{%
+\unitlength=1mm
+  \begin{picture}(0,6) % (0,0)
+  % - for #1 to point arrow down,+ to point arrow up
+  \end{picture}%
+  \put(0,6){\vector(0,#1 3){#2}}    % 6,- for down, 0, + for up
+}
+% 1 mm high #2 mm long horizontal arrow shifted 1 mm up (0,-1)
+\newcommand{\harrow}[2]{%
+\unitlength=1mm
+  \begin{picture}(8,1)(0,-1) %
+  % 1 mm distance between arrow and stackreled object over it (8,1)
+  \put(0,0){\vector(#1 2,0){#2}}     % - to point arrow left, + right
+  \end{picture}%
+}
+
+\endinput
+%% end of setstack.sty
+%% Corrections history:
+%% 
diff --git a/stokes.tex b/stokes.tex
index cfec1f2..06fea32 100644
--- a/stokes.tex
+++ b/stokes.tex
@@ -40,6 +40,50 @@
 
 \maketitle
 
+\section{Preamble}
+
+Complex landscapes are basically functions of many variables having many minima and, inevitably,
+many saddles of all indices, i.e. the number of unstable directions. Optimization problems 
+require us to find the deepest minima, often a difficult task.
+For example, particles with a repulsive mutual potential enclosed in a box will have many stable
+configurations, and we are asked to find the one with lowest energy.
+
+An aim of complexity theory is to be able to classify these landscapes in families having
+common properties. Two simplifications make the task potentially tractable. The first is to consider
+the limit of many variables. In the example of the particles, the limit of many particles (i.e. the thermodynamic limit)
+may be expected to bring about simplifications.
+The second simplification is of more technical nature:  we consider  functions that contain some random element to them, and we
+study the average of an ensemble. The paradigm of this is the spin-glass, where the interactions are random, and we are asked to find the
+ground state energy {\em on average over randomness}.
+
+Spin glass theory gave a surprise: random   landscapes come in two kinds:  those that
+have a `threshold level' of energy, below which there are many minima but no saddles, 
+separated by high barriers, and those that have all sorts of saddles all the way down to the lowest 
+energy levels, and local minima are separated by relatively small barriers.
+The latter are still complex, but good solutions are easier to find.
+This classification is closely related to the structure of their Replica Trick solutions.
+Armed with this solvable (random) example, it was easy to find non-random examples 
+that behave, at least approximately,  in these two ways (e.g. sphere packings and the Travelling salesman Problem,
+belong to first and second classes, respectively).
+
+What about systems whose variables are not real, but rather complex? 
+Recalling the Cauchy-Riemann conditions, we immediately see a difficulty: if our cost is, say, the real part of a function of
+$N$ complex variables, in terms of the corresponding $2N$ real variables it has only saddles of index $N$!
+Even worse: often not all saddles are equally interesting, so simply finding the lowest is not usually what we
+need to do (more about this below).
+As it turns out, there is a set of interesting questions to ask, as we describe below. For each saddle, there is a `thimble' 
+spanned by the
+lines along which the cost function decreases. The way in which these thimbles fill the complex space is crucial for many
+problems of analytic continuation, and is thus what we need to study. The central role played by saddles
+in a real landscape, the `barriers', is now played by the Stokes lines, where thimbles exchange their properties. 
+Perhaps not surprisingly, the two classes of real landscapes described above retain their role in the complex case, but now  
+the distinction is that while in the first class the Stokes lines are rare, in the second class they proliferate.
+
+In  this paper we shall start from a many-variable integral of a real function, and deform it in the many variable complex space.
+The landscape one faces is the full one in this space, and we shall see that this is an example where the proliferation -- or lack of it -- 
+of Stokes lines is the interesting quantity  in this context.
+
+
 \section{Introduction}
 
 Analytic continuation of physical theories is sometimes useful. Some theories