% PRI2egui.tex
% v1.0, 13-mar-2002
% Copyright(C) 2002 Cambridge University Press

% Cambridge University Press will substitute Computer Modern fonts with
% Monotype fonts. Where you see \ifCUPmtlplainloaded, this is an internal
% font switch. You may define new CM fonts etc. but if you do, please indicate
% with a `replace fonts!' message. Please keep the font information together
% near the top of the file.

\documentclass{pri}

%%%%% Macros for the guide only %%%%%
% The following adds 6pt of space around verbatim environments.
\let\realverbatim=\verbatim
\let\realendverbatim=\endverbatim
\renewcommand\verbatim{\par\addvspace{6pt plus 2pt minus 1pt}\realverbatim}
\renewcommand\endverbatim{\realendverbatim\addvspace{6pt plus 2pt minus 1pt}}
\newcommand\lra{\ensuremath{\quad\longrightarrow\quad}}
%%%%% End of macros for the guide %%%%%


%%% USER-DEFINED MACROS HERE
%%% Keep your own macro definitions separate from the examples below.

%%% Some useful examples of macro definitions follow:

%%% For units of measure

\newcommand\dynpercm{\nobreak\mbox{$\;$dynes\,cm$^{-1}$}}
\newcommand\cmpermin{\nobreak\mbox{$\;$cm\,min$^{-1}$}}

%%% For dimensionless numbers

\newcommand\Real{\mbox{Re}}      % cf plain TeX's \Re and Reynolds number
\newcommand\Imag{\mbox{Im}}      % cf plain TeX's \Im
\newcommand\Rey{\mbox{\it Re}}   % Reynolds number
\newcommand\Pran{\mbox{\it Pr}}  % Prandtl number, cf plain TeX's \Pr product
\newcommand\Pen{\mbox{\it Pe}}   % Peclet number
\newcommand\Ai{\mbox{\rm Ai}}    % Airy function
\newcommand\Bi{\mbox{\rm Bi}}    % Airy function

% See if the author has AMS Euler fonts installed: If they have, attempt
% to use the 'upmath' package to provide upright math.

\ifCUPmtlplainloaded \else
  \checkfont{eurm10}
  \iffontfound
    \IfFileExists{upmath.sty}
      {\typeout{^^JFound AMS Euler Roman fonts on the system,
                   using the 'upmath' package.^^J}%
       \usepackage{upmath}}
      {\typeout{^^JFound AMS Euler Roman fonts on the system, but you
                   don't seem to have the}%
       \typeout{'upmath' package installed. jfm.cls can take advantage
                 of these fonts,^^Jif you use 'upmath' package.^^J}%
       \providecommand\mathup[1]{##1}%
       \providecommand\mathbup[1]{##1}%
       \providecommand\upi{\pi}%
       \providecommand\upartial{\partial}%
      }
  \else
    \providecommand\mathup[1]{#1}%
    \providecommand\mathbup[1]{#1}%
    \providecommand\upi{\pi}%
    \providecommand\upartial{\partial}%
  \fi
\fi

% See if the author has AMS symbol fonts installed: If they have, attempt
% to use the 'amssymb' package to provide the AMS symbol characters.

\ifCUPmtlplainloaded\else
  \checkfont{msam10}
  \iffontfound
    \IfFileExists{amssymb.sty}
      {\typeout{^^JFound AMS Symbol fonts on the system, using the
                'amssymb' package.^^J}%
       \usepackage{amssymb}%
      }{}
  \fi
\fi

% See if the author has the AMS 'amsbsy' package installed: If they have,
% use it to provide better bold math support (with \boldsymbol).

\ifCUPmtlplainloaded\else
  \IfFileExists{amsbsy.sty}
    {\typeout{^^JFound the 'amsbsy' package on the system, using it.^^J}%
     \usepackage{amsbsy}}
    {\providecommand\boldsymbol[1]{\mbox{\boldmath $##1$}}}
\fi


% For san-serif roman use \textsf and \mathsf as normal.
%
\newcommand\ssC{\mathsf{C}}    % for sans serif C
\newcommand\sfsP{\mathsfi{P}}  % for sans serif math P
\newcommand\sfbsX{\mathsfbi{X}} % for sans serif bold-math X

% Hat position

\newcommand\hatp{\skew3\hat{p}}         % p with hat
%\newcommand\hatR{\skew3\hat{R}}        % R with hat
%\newcommand\hatRR{\skew3\hat{\hatR}}   % R with 2 hats
%\newcommand\doubletildesigma{\skew2\tilde{\skew2\tilde{\Sigma}}}
%               italic Sigma with double tilde

% The use of \sbox, as shown here, is advised for frequently-occurring
% symbols, provided they always appear in the same font and point size.

\newsavebox{\thalfbox}
\sbox{\thalfbox}{$\textstyle\frac{1}{2}$}
\newcommand{\thalf}{\usebox{\thalfbox}}

\newsavebox{\shalfbox}
\sbox{\shalfbox}{$\scriptstyle\frac{1}{2}$}
\newcommand{\shalf}{\usebox{\shalfbox}}

\newsavebox{\squartbox}
\sbox{\squartbox}{$\frac{1}{4}$}
\newcommand{\squart}{\usebox{\squartbox}}

\newsavebox{\etbox}
\sbox{\etbox}{\boldmath $\eta$}
%\sbox{\etbox}{$\eta$}  % use this if your \boldmath doesn't work.
\newcommand{\etb}{\usebox{\etbox}}

\newsavebox{\biSbox}
\sbox{\biSbox}{\boldmath $S$}
\newcommand{\biS}{\usebox{\biSbox}}

% array strut to make delimiters come out right size both ends
\newsavebox{\astrutbox}
\sbox{\astrutbox}{\rule[-5pt]{0pt}{20pt}}
\newcommand{\astrut}{\usebox{\astrutbox}}

\ifCUPmtlplainloaded
  \else\newcommand{\bmath}[1] {\hbox{\mathversion{bold}${#1}$}}
\fi

\newcommand{\GaPQ}  {G_a(P,Q)}
\newcommand{\Gat}   {\widetilde{G_a}}
\newcommand{\GsPQ}  {G_s(P,Q)}
\newcommand{\kgd}   {k\gamma d}
\newcommand{\ndq}   {\frac{\mbox{$\partial$}}{\mbox{$\partial$} n_q}}
\newcommand{\p}     {\mbox{$\partial$}}
\newcommand{\sh}    {^{\shalf}}
\newcommand{\smh}   {^{-\shalf}}
\newcommand{\sumjm} {\sum_{j=1}^{M}}
\newcommand{\tti}   {\rightarrow\infty}
\newcommand{\ttz}   {\rightarrow 0}
\mathchardef\varLambda="0103

\newcommand\eg{{e.g.\ }}
\newcommand\etc{{etc.\ }}
\newcommand\etal{\mbox{\it et al.}}
\newcommand\pri{Proceedings of the Royal Irish Academy}
\newcommand\pricls{\texttt{pri.cls}}

%-----title and author----------------------

  \title{\LaTeXe\ input guide for authors}

  \author[Woollatt, Chadwick and Wilson]{\newauthor A.J. Woollatt$^*$\\
    Cambridge University Press, Cambridge
    \newauthor P. Chadwick\\
    School of Mathematics, University of East Anglia, Norwich
    \and N.J. Wilson\\
    City College, Norwich
  }
  %\email{texline@cambridge.org}        %use for single-author papers
  \corresponding{texline@cambridge.org} %use for multi-author papers
  \titlefootnote{The subvention granted by City College, Norwich,
    towards the cost of publication of papers by members of its
    staff is gratefully acknowledged by the Royal Irish Academy.}
\communicated{T.D. Spearman, \textsc{m}.\textsc{r}.\textsc{i}.\textsc{a}}
\date{28 December 2000. Read 2 February 2001. Published 13 March 2002}
\pubyear{2002}
\volume{1}
\no{1}
\pagerange{\pageref{firstpage}--\pageref{lastpage}}

% -----------------------------

\begin{document}

\label{firstpage}
\maketitle

\begin{abstract}
This guide is for authors who are preparing papers for the
\emph{\pri} using the \LaTeXe\ document preparation system and the
Cambridge University Press PRI class file.
\end{abstract}

\section{Introduction}

The layout design for the \emph{\pri} has been implemented as a \LaTeXe\ class file.
The PRI class file (\pricls) is based on the ARTICLE class file as discussed in the \LaTeX\ %
manual.
Commands which differ from the standard \LaTeX\ interface, or which are
provided in addition to the standard interface, are explained in this
guide. This guide is not a substitute for the \LaTeX\ manual itself.

Note that the final printed version of papers will use a Monotype Times
font rather than the Computer Modern available to most authors. Also,
the measure in \pricls\ is different from the standard \LaTeXe\ article class. For
these reasons, line and page breaks will change and authors
should not insert hard breaks in their text.

\subsection{Introduction to \LaTeX}

The \LaTeX\ document preparation system is a special version of the
\TeX\ typesetting program.
 \LaTeX\ adds to \TeX\ a collection of commands which allow the author
to concentrate on the logical structure of the document rather than its
visual layout.

\LaTeX\ provides a consistent and comprehensive document preparation
interface.
\LaTeX\ can automatically number equations, figures,
tables, and list entries, as well as sections and
subsections.
Using this numbering system, bibliographic citations, page references
and cross-references to any other numbered entity (\eg
section, equation, figure, list entry) are quite straightforward.

\subsection{The PRI document class}

The use of document classes allows a simple change of style (or style option) to
transform the appearance of your document.
The CUP PRI class file preserves the standard \LaTeX\ interface such that any
document which can be produced using the standard \LaTeXe\ ARTICLE class file
can also be produced with the PRI class file.
However, the measure (or width of text) is slightly different from that
for ARTICLE; therefore line breaks will change and it is possible that
equations may need re-setting.


\section{Using the PRI class file}

First, copy the file \verb"pri.cls" into the correct subdirectory on your
system.
The PRI document class is implemented as a complete document class, \emph{not}
a document class option.
In order to use the PRI class file, replace \verb"article" by \verb"pri" in the
\verb"\documentclass" command at the beginning of your document:
%
\begin{verbatim}
  \documentclass{article}
\end{verbatim}
%
is replaced by
%
\begin{verbatim}
  \documentclass{pri}
\end{verbatim}
%
None of the standard document class options should be used.
Author-defined macros should be inserted before \verb"\begin{document}",
or in a separate file and should be included with the submission,
see \S\ref{secUser}. Authors must not change any of the macro definitions
or parameters in \verb"pri.cls".

\subsection{Document class options}

The standard document class options should \emph{not} be used with
the PRI class file:
\begin{itemize}
  \item \texttt{10pt}, \texttt{11pt}, \texttt{12pt} -- unavailable.
  \item \texttt{draft}, \texttt{twoside} (no associated style file) -- \texttt{twoside}
        is the default.
  \item \texttt{fleqn}, \texttt{leqno}, \texttt{titlepage}, \texttt{twocolumn} --
        unavailable.
  \item \texttt{proc}, \texttt{ifthen}, \texttt{bezier} -- can be used if necessary.
\end{itemize}

\section{Additional facilities}

In addition to all the standard \LaTeX\ design elements, the PRI class file
includes the following features:
\begin{itemize}
  \item Extended commands for specifying a short version
        of the title and author(s) for the running
        headlines.
  \item Title page details such as a `Communicated by\ldots' line.
  \item Abstract environment
  \item Control of enumerated lists.
  \item An extended \verb"theorem" environment.
  \item A \verb"definition" environment.
  \item A \verb"remark" environment.
  \item A \verb"proof" environment.
\end{itemize}
Once you have used these additional facilities in your document,
it can only be processed with \verb"pri.cls".

\subsection{Titles, authors' names and running headlines}

In the PRI style, the title of the article and the author's name (or authors'
names) are used both at the beginning of the article for the main title and
throughout the article as running headlines at the top of odd-numbered pages
(rectos). The \verb"\pagestyle" and \verb"\thispagestyle" commands should
\emph{not} be used.  Similarly, the commands \verb"\markright" and
\verb"\markboth" should not be necessary.

Although the main heading can run to several lines of text,
the running headline must be a single line.
Moreover, the main heading can also incorporate new line commands
(\eg \verb"\\") but these are not acceptable in a running headline.
To enable you to specify an alternative short title and author's name, the
standard \verb"\title" and \verb"\author" commands have been extended to take
an optional argument to be used as the running headline:
%
\begin{verbatim}
  \title[A short title]{The full title which can be as long
    as necessary}
  \author[Authors' surnames]{\newauthor The full name of the
    first author\\
    first author's affiliation, then \newauthor or \and as
    described below}
\end{verbatim}

An example will make all this clearer. To produce the title page
of this document, we have used:
%
\begin{verbatim}
  \title{\LaTeXe\ input guide for authors}

  \author[Woollatt, Chadwick and Wilson]{\newauthor A.J. Woollatt$^*$\\
    Cambridge University Press, Cambridge
    \newauthor P. Chadwick\\
    School of Mathematics, University of East Anglia, Norwich
    \and N.J. Wilson\\
    City College, Norwich
  }
  %\email{texline@cambridge.org}        %use for single-author papers
  \corresponding{texline@cambridge.org} %use for multi-author papers
\end{verbatim}

If there is only one author, substitute \verb"\ns" for \verb"\newauthor".
If you have more than one author, you use \verb"\newauthor" for
the first and subsequent authors (as above), and for the final
author, use \verb"\and".

Unless authors object, the Royal Irish Academy will be printing the
author's (or corresponding author's) e-mail address on the first page
of each article. These should be added using either \verb"\email"
or \verb"\corresponding", depending on the number of authors.
A raised asterisk ($^*$) also needs to inserted immediately after
the relevant author's name (see example above).

\subsection{Title page details}

You may wish to add an acknowledgement in the form of an unnumbered
footnote to the title page of your document using \verb"\titlefootnote",
and also a `Communicated by\ldots' line using \verb"\communicated". The details
in this guide were typeset using the following code:
%
\begin{verbatim}
  \titlefootnote{The subvention granted by City College, Norwich,
    towards the cost of publication of papers by members of its
    staff is gratefully acknowledged by the Royal Irish Academy.}
  \communicated{T.D. Spearman, \textsc{m}.\textsc{r}.\textsc{i}.\textsc{a}}
\end{verbatim}

The \LaTeX\ \verb"\thanks" command creates a footnote appearing at the bottom
of the title page.

\subsection{Abstract}

The PRI class file provides for an abstract, produced by
%
\begin{verbatim}
  \begin{abstract}
  ...
  \end{abstract}
\end{verbatim}

This should appear just \emph{before} the first \verb"\section" command.

\subsection{Lists}

The PRI class file provides the three standard list environments:
\begin{itemize}
  \item Numbered lists, created using the \verb"enumerate" environment.
  \item Bulleted lists, created using the \verb"itemize" environment.
  \item Labelled lists, created using the \verb"description" environment.
\end{itemize}
The \verb"enumerate" environment numbers each list item with an arabic
number in parentheses; alternative styles can be achieved by inserting a
redefinition of the number labelling command after the
\verb"\begin{enumerate}". For example, a list numbered with roman numerals
inside parentheses can be produced by the following commands:
%
\begin{verbatim}
  \begin{enumerate}
  \renewcommand{\theenumi}{\roman{enumi}}
  \item first item
         :
  \end{enumerate}
\end{verbatim}
%
This produces the following list:
\begin{enumerate}
  \renewcommand{\theenumi}{\roman{enumi}}
  \item first item
  \item second item
  \item etc.
\end{enumerate}

If your new label is so wide that it does not fit in the space available,
it is possible to increase the label width. You can do this by putting
the widest label as an optional argument, as you do in a bibliography
environment, e.g.\ \verb"\begin{enumerate}[99]".
Remember, once you have used the optional argument on the \verb"enumerate"
environment, you will not be able to process your document with a standard
\LaTeXe\ class file.

\subsection{Theorems}

The PRI class file has extended the standard \verb"\newtheorem" macro
to enable unnumbered theorems to be typeset with the use of the starred
version. For example, you would use:
%
\begin{verbatim}
  \newtheorem{theorem}{Theorem}[section]
  \begin{theorem}
  This gives me a normal numbered theorem.
  \end{theorem}
  \begin{theorem*}
  This gives me an unnumbered theorem.
  \end{theorem*}
\end{verbatim}
%
to typeset the following theorems:
%
  \newtheorem{theorem}{Theorem}[section]
  \begin{theorem}
  This gives me a normal numbered theorem.
  \end{theorem}
  \begin{theorem*}
  This gives me an unnumbered theorem.
  \end{theorem*}

The new macros which follow, \verb"\newdefinition" and
\verb"\newremark", have the same properties, namely numbered and
unnumbered versions. You can have a \verb"\newdefinition" or
a \verb"\newremark" using the same numbering system as theorems by
inserting the optional \verb"[theorem]", as illustrated in the following
examples.

\subsection{Definitions}

The \verb"\newdefinition" macro may be used for definitions. These
are typeset exactly the same as theorems, except the text is in roman
instead of italic. For example,
%
\begin{verbatim}
  \newdefinition{definition}[theorem]{Definition}
    \begin{definition}
       This is a definition.
    \end{definition}
    \begin{definition*}
       This is an unnumbered definition.
    \end{definition*}
\end{verbatim}
%
will typeset the following:
%
\newdefinition{definition}[theorem]{Definition}
  \begin{definition}
  This is a definition.
  \end{definition}
  \begin{definition*}
     This is an unnumbered definition.
  \end{definition*}

\subsection{Remarks}

The \verb"\newremark" macro may be used for remarks, examples,
and the like. You use it just as you would \verb"\newtheorem":
%
\begin{verbatim}
  \newremark{note}[theorem]{Note}
    \begin{note}
      This is a note.
    \end{note}
    \begin{note*}
      This is an unnumbered note.
    \end{note*}
\end{verbatim}
%
The output from the above code is as follows:
%
\newremark{note}[theorem]{Note}
%
  \begin{note}
    This is a note.
  \end{note}
  \begin{note*}
    This is an unnumbered note.
  \end{note*}

\subsection{Placing the number first}

If you would like your output to read, for example, \textbf{3.1.\enskip
Theorem.}, instead of \textbf{Theorem~3.1.}, you can use the
command \verb"\reversetheorems" in the preamble of your document. This will
affect the numbering of all the above three environments, \verb"\newtheorem", \verb"\newdefinition" and \verb"\newremark".

\subsection{Proof environment}

The standard \LaTeX\ constructs do not include a proof environment to
follow a theorem, lemma etc., and so one has been added in the PRI class file.
Note the use in the following examples of an optional argument in square
braces which may contain any information you may wish to add.
For example,
%
\begin{verbatim}
  \begin{theorem}[Miyajima]
  \label{miyajima}
  Let the scalar function $T(x,y,t,\bmath{\omega}) $ be a conserved
  density for solutions of \textrm{(9)}. Then the two-component
  function
  \begin{equation}
  {\bmath{P}} = {\mathsf J}{\mathcal E} T
  \end{equation}
  represents the infinitesimal generator of a symmetry group
  for \textrm{(9)}.
  \end{theorem}
%
  \begin{proof}[of Theorem~\ref{miyajima}]
  The assumption about $T$ means that
  \[
  0 \sim \frac{\upartial T}{\upartial t} +
  {\mathcal E}T \bmath{\omega}_t
  = \frac{\upartial T}{\upartial t} + \{ T, H\},
  \]
  where $\upartial T / \upartial t$ refers to
  explicit dependence on $t$. The skew symmetry of  ${\mathsf J}$
  hence implies
  \begin{equation}
  \frac{\upartial T}{\upartial t} \sim  \{ H, T\},
  \end{equation}
  whereupon the operation $\mathsf J \mathcal E$, which commutes
  with $\upartial_t$ in its present sense, gives
  \[
  \frac{\upartial {\bmath{P}}}{\upartial t} =
  {\mathsf J}{\mathcal E}\{ H, T\}.
  \]
  This equation reproduces the characterisation of symmetries that
  was expressed by (19), thus showing ${\mathrm P}$ to represent a
  symmetry group.
  \end{proof}
\end{verbatim}
%
will typeset the following:
%
  \begin{theorem}[Miyajima]
  \label{miyajima}
  Let the scalar function $T(x,y,t,\bmath{\omega}) $ be a conserved
  density for solutions of \textrm{(9)}. Then the two-component
  function
  \begin{equation}
  {\bmath{P}} = {\mathsf J}{\mathcal E} T
  \end{equation}
  represents the infinitesimal generator of a symmetry group
  for \textrm{(9)}.
  \end{theorem}
%
  \begin{proof}[of Theorem~\ref{miyajima}]
  The assumption about $T$ means that
  \[
  0 \sim \frac{\upartial T}{\upartial t} +
  {\mathcal E}T \bmath{\omega}_t
  = \frac{\upartial T}{\upartial t} + \{ T, H\},
  \]
  where $\upartial T / \upartial t$ refers to
  explicit dependence on $t$. The skew symmetry of  ${\mathsf J}$
  hence implies
  \begin{equation}
  \frac{\upartial T}{\upartial t} \sim  \{ H, T\},
  \end{equation}
  whereupon the operation $\mathsf J \mathcal E$, which commutes
  with $\upartial_t$ in its present sense, gives
  \[
  \frac{\upartial {\bmath{P}}}{\upartial t} =
  {\mathsf J}{\mathcal E}\{ H, T\}.
  \]
  This equation reproduces the characterisation of symmetries that
  was expressed by (19), thus showing ${\mathrm P}$ to represent a
  symmetry group.
  \end{proof}

The final \usebox{\proofbox} will not be included if the \verb"proof*"
environment is used.


\section{Mathematics and units}

The PRI class file will insert the correct space above and below
displayed maths if standard \LaTeX\ commands are used; for example use
\verb"\[ ... \]" and \emph{not} \verb"$$ ... $$". Do not leave blank
lines above and below displayed equations unless a new paragraph is
really intended.

\subsection{Numbering of equations}


The \verb"subequations" and \verb"subeqnarray" environments have been
incorporated into the PRI class file. Using these two environments, you can
number your equations (\ref{a1}), (\ref{a2}) \etc automatically. For
example, you can typeset
  \begin{subequations}
  \begin{equation}
    a_1 \equiv (2\Omega M^2/x)^{\frac{1}{4}} y^{\frac{1}{2}}
    \label{a1}
  \end{equation}
  and
  \begin{equation}
    a_2 \equiv (x/2\Omega)^{\frac{1}{2}}k_y/M.\label{a2}
  \end{equation}
  \end{subequations}
by using the \verb"subequations" environment as follows:
%
\begin{verbatim}
  \begin{subequations}
  \begin{equation}
    a_1 \equiv (2\Omega M^2/x)^{\frac{1}{4}} y^{\frac{1}{2}}
    \label{a1}
  \end{equation}
  and
  \begin{equation}
    a_2 \equiv (x/2\Omega)^{\frac{1}{2}}k_y/M.\label{a2}
  \end{equation}
  \end{subequations}
\end{verbatim}

You may also typeset an array such as:
  \begin{subeqnarray}
    \dot{X}    & = & \gamma X - \gamma\delta\eta ,\\
    \dot{\eta} & = & {\textstyle\frac{1}{2}} \delta + 2X\eta .
  \end{subeqnarray}
by using the \verb"subeqnarray" environment as follows:
%
  \begin{verbatim}
  \begin{subeqnarray}
    \dot{X}    & = & \gamma X - \gamma\delta\eta ,\\
    \dot{\eta} & = & {\textstyle\frac{1}{2}} \delta + 2X\eta .
  \end{subeqnarray}
  \end{verbatim}


\subsection{AMS fonts -- especially if you do not have them}

If you need symbols from the AMS font set but do not have them installed,
you can ensure that they will be correctly typeset by taking the following
steps.
Set up user-defined macros that can be redefined by the typesetter to use
the correct AMS macros. For example, the blackboard bold symbols,
sometimes called shell or outline characters, are obtained with the AMS
macro \verb"\mathbb{..}". Instead, use a macro definition such as:
%
\begin{verbatim}
  % replace font!
  \newcommand\BbbE{\ensuremath{\mathsf{E}}} % Blackboard bold E
\end{verbatim}
%
This substitutes a sans serif character where you want blackboard
bold. You can typeset the input file and the typesetter is alerted to do the
substitution.

The following example (which uses the \verb"\providecommand" macro) will work
without modification by the typesetter, because the \verb"\providecommand"
macro will not overwrite any existing \verb"\mathbb" definition.
%
\begin{verbatim}
  \providecommand\mathbb[1]{\ensuremath{\mathsf{#1}}}
  ...
  \newcommand\BbbE{\mathbb{E}} % Blackboard bold E
\end{verbatim}

If you wish to use AMS fonts with \LaTeXe\ you must be using at least
version 2.0. Earlier versions are not supported.

\subsection{Typeface issues}

\subsubsection{Roman symbols.}\label{roman}
The mathematical operators and constants, such as sin, cos, log and exp,
are covered by plain \TeX\ macros which ensure that they are typeset in
roman text, even in math mode: \verb"\sin", \verb"\cos", \verb"\log",
\verb"\exp". Where single letters are concerned (\eg d, i, e) just use
the roman typeface in maths, i.e.\ \verb"$E=m{\mathrm c}^2$" which typesets as
$E=m{\mathrm c}^2$, giving the correct roman character but with maths spacing.
When the term involves more than one character (\eg \Real\ or \Imag )
text-character spacing is required:
%
\begin{verbatim}
  $\mbox{Re}\;x$
\end{verbatim}
%
which typesets as $\Real\;x$.

Where such expressions are used repeatedly, macro definitions can reduce
typing and editing. The following examples are included in the preamble
of the input files for this document, \verb"priguide.tex".
Authors are encouraged to use them and others like them.
%
\begin{verbatim}
  \newcommand\Real{\mbox{Re}}   % do not confuse with TeX's \Re
  \newcommand\Imag{\mbox{Im}}   % do not confuse with TeX's \Im
  \newcommand\Ai{\mbox{Ai}}     % Airy function
  \newcommand\Bi{\mbox{Bi}}     % Airy function
\end{verbatim}

\subsubsection{Multiletter italic symbols.}
If multiletter symbols are used in maths mode, for example Reynolds,
Prandtl numbers, \etc the standard maths mode spacing between them is
too large and text-character spacing is required. As described
in \S\ref{roman} (but here for italic letters) use for example
%
\begin{verbatim}
  \newcommand\Rey{\mbox{\it Re}}
  \newcommand\Pran{\mbox{\it Pr}}
\end{verbatim}

\subsubsection{Sans serif symbols.}

The \verb"\textsf" and \verb"\mathsf" commands change the typeface to
sans serif, giving upright characters. Occasionally, bold-sloping sans serif
is needed. You should use the following supplied
macros to obtain these fonts.\\[6pt]
%
\verb"  \textsf{text}  " \lra \textsf{text}
  \qquad \verb"\mathsf{math}  " \lra $\mathsf{math}$\\
\verb"  \textsfi{text} " \lra \textsfi{text}
  \qquad \verb"\mathsfi{math} " \lra $\mathsfi{math}$\\
\verb"  \textsfb{text} " \lra \textsfb{text}
  \qquad \verb"\mathsfb{math} " \lra $\mathsfb{math}$\\
\verb"  \textsfbi{text}" \lra \textsfbi{text}
  \qquad \verb"\mathsfbi{math}" \lra $\mathsfbi{math}$\\[6pt]
%
You can use them like this:
%
\begin{verbatim}
  \newcommand\ssC{\mathsf{C}}     % for sans serif C
  \newcommand\sfsP{\mathsfi{P}}   % for sans serif slanted P
  \newcommand\sfbsX{\mathsfbi{X}} % for sans serif bold slanted X
\end{verbatim}
%
Note that the bold-slanted macros \verb"\textsfbi" and
\verb"\mathsfbi" use the slanted sans serif font \verb"cmssi"
-- because there is no bold-slanted math sans serif font in available in
Computer Modern!  If you use the supplied sans-serif text and math commands
the typesetter will be able to substitute the fonts automatically.

\subsubsection{Script characters.}
Script characters should be typeset using plain \TeX 's \verb"\mathcal"
command. This produces the Computer Modern symbols such as {$\mathcal E\,$}
and {$\mathcal F\,$} in your hard copy but the the typesetter will substitute
the more florid script characters normally seen in the journal.

\subsection{Skewing of accents}
Accents such as hats, overbars and dots are normally centred over letters,
but when these are italic or sloping greek the accent may need to be moved
to the right so that it is centred over the top of the sloped letter. For
example, \verb"\newcommand\hatp{\skew3\hat{p}}" will produce $\hatp$.

\subsection{Units of measure}
Numbers and their units of measure should be typeset with fixed spaces
that will not break over two lines. This is easily done with user-defined
macros. For example,\linebreak \verb"52\dynpercm" typesets as
52\dynpercm , providing the following macro definition has been included
in the preamble.
%
\begin{verbatim}
  \newcommand\dynpercm{\nobreak\mbox{$\;$dynes\,cm$^{-1}$}}
\end{verbatim}

\section{User-defined macros}\label{secUser}
If you define your own macros you must ensure that their names do not
conflict with any existing macros in plain \TeX\ or \LaTeXe\ (or AMS\TeX\ %
if you are using this). You should also place them in the preamble to
your input file, between the \verb"\documentclass" and
\verb"\begin{document}" commands.

Apart from scanning the indexes of the relevant manuals, you can check
whether a macro name is already used in plain \TeX\ or \LaTeXe\ by using
the \TeX\ command \verb"show". For instance, run \LaTeXe\ interactively
and type \verb"\show\<macro_name>" at the \TeX\ prompt. (Alternatively,
insert the \verb"\show" command into the preamble of an input file and
\TeX\ it.)
%
\begin{verbatim}
  * \show\Re
\end{verbatim}
%
produces the following response from \TeX :
%
\begin{verbatim}
  > \Re=\mathchar"23C.
  <*> \show\Re
\end{verbatim}
%
By contrast \verb"\Real" is not part of plain \TeX\ or \LaTeXe\ and
\verb"\show\Real" generates:
%
\begin{verbatim}
  > \Real=undefined
  <*> \show\Real
\end{verbatim}
%
confirming that this name can be assigned to a user-defined macro.

Such macros must be in a place where they can easily be found and
modified by the journal's editors or typesetter. They must be gathered
together in the preamble of your input file, or in a separate
\verb"macros.tex" file with the command \verb"\input{macros}" in the
preamble. Macro definitions must not be scattered about your document
where they are likely to be completely overlooked by the typesetter.

The same applies to font definitions that are based on Computer Modern
fonts. These must be changed by the typesetter to use the journal's
\TeX\ typefaces Times and Helvetica. In this case, you should draw
attention to these font definitions on the hard copy that you submit for
publication and by placing a comment in your input file just before the
relevant definitions, for example \verb"% replace font!"


\section{Some guidelines for using standard facilities}

The following notes may help you achieve the best effects with the
standard \LaTeX\ facilities that remain in the PRI class file.

\subsection{Sections}

Only the first three \LaTeX\ section levels are defined in the PRI class
file:
\begin{itemize}
  \item[] Heading A -- \verb"\begin{section}"
  \item[] Heading B -- \verb"\begin{subsection}"
  \item[] Heading C -- \verb"\begin{subsubsection}"
\end{itemize}
There is no \verb"paragraph" or \verb"subparagraph" in the PRI class file.

To obtain non-bold in a bold heading use the usual plain \TeX\ commands for
changing typeface; for example \verb"\section{Fluctuations in Ca\textsc{ii}}".


\subsection{Tables}

The \texttt{table} environment is implemented as described in
the \LaTeX\ manual to provide consecutively numbered floating
inserts for tables.

The PRI class file will cope with most table positioning problems and you
should not normally use the optional positional qualifiers \verb"t",
\verb"b", \verb"h" on the \verb"table" environment, as this would override
these decisions.

The PRI class file dictates that vertical rules should never be used within the
body of the table. Extra space can be inserted to distinguish
groups of rows (using \verb"\tabcolsep") or columns (using \verb"\jot").
Table captions must be above the table itself, so the \verb"\caption"
command should appear immediately after \verb"\begin{table}".
%
  \begin{table}
  \caption{An example table.} \label{sample-table}
  \begin{minipage}{\textwidth}
    \tabcolsep=8pt
    \begin{tabular}{cccc}
    \hline
      {Figure} & {$hA$} & {$hB$}\footnote{A table must be
       inside a minipage environment if it includes
       table footnotes.}
       & {$hC$}\\
    \hline
      2 & $\exp\;(\upi \mathrm{i} x)$
        & $\exp\;(\upi \mathrm{i} y)$ & $0$\\
      3 & $-1$    & $\exp\;(\upi \mathrm{i} x)$ & $1$\\
      4 & $-4+3{\mathrm i}$ & $-4+3 \mathrm{i}$ & 1.6\\
      5 & $-2$    & $-2$    & $1.2 \mathrm{i}$\\
    \hline
    \end{tabular}
  \end{minipage}
  \end{table}

As an example, table~\ref{sample-table} is produced using the following
commands:
%
\begin{verbatim}
  \begin{table}
  \caption{An example table.} \label{sample-table}
  \begin{minipage}{\textwidth}
    \tabcolsep=8pt
    \begin{tabular}{cccc}
    \hline
      {Figure} & {$hA$} & {$hB$}\footnote{A table must be
       inside a minipage environment if it includes
       table footnotes.}
       & {$hC$}\\
    \hline
      2 & $\exp\;(\upi \mathrm{i} x)$
        & $\exp\;(\upi \mathrm{i} y)$ & $0$\\
      3 & $-1$    & $\exp\;(\upi \mathrm{i} x)$ & $1$\\
      4 & $-4+3{\mathrm i}$ & $-4+3 \mathrm{i}$ & 1.6\\
      5 & $-2$    & $-2$    & $1.2 \mathrm{i}$\\
    \hline
    \end{tabular}
  \end{minipage}
  \end{table}
\end{verbatim}

The \verb"tabular" environment has been modified for the PRI class file in the
following ways:
\begin{enumerate}
  \item Additional vertical space is inserted above and below a horizontal
        rule produced by \verb"\hline"
  \item Tables are centred, and will span the full width of the page; that is,
        they are similar to the tables that will be produced by using the
        command \verb"\begin{minipage}{\textwidth}".
\end{enumerate}
Commands to redefine quantities such as \verb"\arraystretch" should be omitted.

\subsection*{Illustrations}

Figures must be supplied electronically,  in a form that can be directly included by \LaTeX. If they are
supplied as encapsulated PostScript files, they must have tight bounding boxes.

The PRI class file will cope with most figure positioning problems and you should not normally use the
optional positional qualifiers \verb"t", \verb"b", \verb"h" on the \verb"figure" environment, as this
would override these decisions. Figure captions should be below the figure itself, therefore the
\verb"\caption" command should appear after the space left for the illustration within the \verb"figure"
environment. For example, figure~\ref{sample-figure} is produced using the following commands:
\begin{figure}
  \vspace{50pt}
  \caption{An example figure with space for artwork}
  \label{sample-figure}
\end{figure}

\begin{verbatim}
  \begin{figure}
    \vspace{50pt}
    \caption{An example figure with space for artwork}
    \label{sample-figure}
  \end{figure}
\end{verbatim}

\subsection{Acknowledegments}
Acknowledgments should appear at the close of your paper, just before
the list of references and any appendices.  You should use either the
\verb"acknowledgement" or \verb"acknowledgements" environment, which
will give you the \hbox{\textsc{Acknowledgement}} or
\hbox{\textsc{Acknowledgements}} headings respectively.

\subsection{Appendices}

You should use the standard \LaTeX\ \verb"\appendix" command to place any
Appendices, normally, just before the references. This numbers
appendices as A, B etc., equations as (A1), (B1) etc., and figures and
tables as A1, B1 \etc

\subsection{References}

As with standard \LaTeX, there are two ways of producing a list of references; either by compiling a list
(using a \verb"thebibliography" environment), or by using BibTeX with a suitable bibliographic database.

\subsubsection{References in the text.}

References in the text are given by author in the form \cite{Heuser} and for multiple citations,
\cite{Mack, Buck}. Each entry has a key, which is assigned by the author and used to refer to that entry
in the text. It is essential to add the number of bibliography entries into the curly braces, in this
example we have 6 entries, so we say \verb"\begin{thebibliography}{6}". If you forget to do this, the
labels will fall into the margin.

\subsubsection{The list of references.}

The following listing shows some references prepared in the style of the journal; the code produces the
references at the end of this guide.
%
\begin{verbatim}
  \begin{thebibliography}{6}

  \bibitem{Heuser}
  H. Heuser, \textit{Funtional analysis}, Wiley, Chichester, 1982.




  \bibitem{YuBan}
  S. Yu and G. Ban, A theorem about LA-groups,
  \textit{Journal of Guangxi University} \textbf{19} (1) (1994), 10--18.


  \bibitem{Kim}
  Y.K. Kim and A Rhemtulla, on locally graded groups, in D.L. Johnson
  and A.C. Kim (eds), \textit{Proceedings of the Third International
  Conference on Group Theory, Pusan, Korea, 1994,}  Springer,
  Berlin--Heidelberg--New York, 1995, pp 191--7.


  \bibitem{Arve}
  W. Arveson, \textit{Continuous analogues of Fock space}, Memoirs of the
  American Mathematical Society 409, Cambridge, Mass., 1989.


  \bibitem{Mack}
  M. Mackey, JB*-triples and the quasi-invertible manifold, unpublished PhD
  thesis, University College Dublin, 1999.

  \bibitem{Buck}
  S. Buckley, Relative solidity for spaces of analytic functions, preprint
  (electronic), National University of Ireland, Maynooth, posted May 1999 (see
  http://www.maths.may.ie/staff/sbuckley/download.html).

\end{verbatim}
%
Each entry takes the form
%
\begin{verbatim}
  \bibitem{cross-reference tag}
    Bibliography entry
\end{verbatim}

  \begin{thebibliography}{6}

  \bibitem{Heuser}
  H. Heuser, \textit{Funtional analysis}, Wiley, Chichester, 1982.


  \bibitem{YuBan}
  S. Yu and G. Ban, A theorem about LA-groups,
  \textit{Journal of Guangxi University} \textbf{19} (1) (1994), 10--18.


  \bibitem{Kim}
  Y.K. Kim and A Rhemtulla, on locally graded groups, in D.L. Johnson
  and A.C. Kim (eds), \textit{Proceedings of the Third International
  Conference on Group Theory, Pusan, Korea, 1994,}  Springer,
  Berlin--Heidelberg--New York, 1995, pp 191--7.


  \bibitem{Arve}
  W. Arveson, \textit{Continuous analogues of Fock space}, Memoirs of the
  American Mathematical Society 409, Cambridge, Mass., 1989.


  \bibitem{Mack}
  M. Mackey, JB*-triples and the quasi-invertible manifold, unpublished PhD
  thesis, University College Dublin, 1999.

  \bibitem{Buck}
  S. Buckley, Relative solidity for spaces of analytic functions, preprint
  (electronic), National University of Ireland, Maynooth, posted May 1999 (see
  http://www.maths.may.ie/staff/sbuckley/download.html).
  \end{thebibliography}

\newpage

\appendix
\section{Special commands in \texttt{pri.cls}}

The following is a summary of the new commands, optional
arguments and environments which have been added to the
standard \LaTeX\ user-interface in creating the PRI class file.

\vspace{6pt}
\newcommand\bgtabular{\begin{tabular}{p{0.35\textwidth}p{0.65\textwidth}}}
\noindent{\tabcolsep=0pt
\bgtabular
\emph{New commands}      & \\
\verb"\author"          & use \verb"\\" to start the affiliation\\
\verb"\ns"              & to add a name space after `By' when there
                           is only one author.\\
\verb"\newauthor"       & to start first author's name if there is more
                           than one author, and for all author's names
                           except the last.\\
\verb"\and"             & to start the last author's name.\\
\verb"\email"           & produces `$^*$E-mail:' -- use for single-author papers\\
\verb"\corresponding"   & produces `$^*$Corresponding author, e-mail:' -- use for multi-author papers\\
\verb"\titlefootnote"   & for acknowledgements at the foot of the title page.\\
\verb"\communicated"    & for a `Communicated by\ldots' line.\\
\verb"\removebrackets"  & removes the `(\ )' brackets from the optional
                          argument of environments created by the
                          \verb"\newtheorem", \verb"\newdefinition" and
                          \verb"\newremark" commands. Should be placed
                          just before the appropriate environment.\\
\verb"\reversetheorems" & to put theorem/definition/remark numbers first,
                          e.g.\ \textbf{3.1.\enskip Theorem.}\\
\verb"\newremark"       & used as \verb"\newtheorem" to define environments.
                           For remarks, examples, etc.\\
\verb"\newdefinition"   & for definitions.\\
\verb"\nosectioneqnreset" & stops \verb"\section" commands resetting the
                            \verb"equation" counter. It also redefines
                            \verb"\theequation" to give output in the
                            form (1) (equation) and not (1.1) (section.equation).\\[6.5pt]
\emph{New optional arguments} & \\
\verb"[<short title>]"  & in the \verb"\title" command: to define a shorter
                           title to be used in the running head.\\
\verb"[<short author>]" & in the \verb"\author" command: to define authors'
                           surnames to be used in the running head.\\
\verb"[<widest label>]" & in \verb"\begin{enumerate}": to ensure the correct
                           alignment of numbered lists with wide
                           labels.\\[6.5pt]
\emph{New environments}  & \\
\verb"newtheorem*"      & an unnumbered version of newtheorem.\\
\verb"newdefinition"    & this environment works like the \verb"theorem"
                           environment; it typesets a bold heading but
                           differs from a theorem by using roman text.\\
\verb"newdefinition*"   & as above, but unnumbered.\\
\verb"newremark"        & this environment works like the \verb"theorem"
                           environment; but typesets an italic heading
                           followed by roman text.\\
\verb"newremark*"       & as above, but unnumbered.\\
\verb"proof"            & to typeset mathematical proofs.
\end{tabular}
\par\vskip 6pt
\bgtabular
\emph{New environments continued} & \\
\verb"proof*"           & to typeset mathematical proofs without the
                           terminating proofbox.\\
\verb"subeqnarray"      & enables equation numbers in an array to be
                           numbered as (6.1a), (6.2b), etc.\\
\verb"subequation"      & enables consecutive equations to be numbered
                           (6.1a), (6.1b), etc.\\
\verb"tabular"          & has been modified to insert additional space above
                           and below an \verb"\hrule" and the table caption
                           and body is centred with rules full out across the
                           text measure.\\
\verb"acknowledgement"  & to typeset an \textsc{Acknowledgement} heading.\\
\verb"acknowledgements" & to typeset an \textsc{Acknowledgements} heading.
\end{tabular}
}% end of tabcolsep=0pt

\section{Notes for editors}
\setcounter{subsubsection}{0}

This appendix contains additional information which may be useful to
those who are involved with the final production stages of an article.
Authors, who are generally not typesetting the final pages in the
journal's typeface (Monotype Times), do not need this information.

\subsubsection{Catchline commands.}
To be placed in the preamble:
\begin{itemize}
  \item \verb"\date{}"
  \item \verb"\pubyear{}"
  \item \verb"\volume{}"
  \item \verb"\no{}"
  \item \verb"\pagerange{}"
\ifCUPmtlplainloaded
  \item \verb"\firstarticle" (for first article in a part, must be used
        before \verb"\maketitle")
\fi
\end{itemize}

\subsubsection{Footnotes.}
If a footnote falls at the bottom of a page, it is possible for the
footnote to appear on the following page (a feature of \TeX ). Check
for this.

\subsubsection{Font substitution.}
Check for use of AMS fonts, bold slanted sans serifs, and bold math italic
and alter preamble definitions to use the appropriate AMS / CUP and Monotype
fonts for phototypesetter output.

\subsubsection{Font sizes.}
The PRI class file defines all the standard \LaTeX\ font sizes. For example:
\begin{itemize}
  \item \verb"\tiny" -- {\tiny This is tiny text.}
  \item \verb"\scriptsize" -- {\scriptsize This is scriptsize text.}
  \item \verb"\footnotesize" -- {\footnotesize This is footnotesize text.}
  \item \verb"\indexsize" -- {\indexsize This is indexsize text.}
  \item \verb"\small" -- {\small This is small text.}
  \item \verb"\tablebody" -- This is tablebody text.
  \item \verb"\abstractsize" -- This is abstractsize text.
  \item \verb"\normalsize" -- This is normalsize text (default).
  \item \verb"\large" -- {\large This is large text.}
  \item \verb"\Large" -- {\Large This is Large text.}
  \item \verb"\LARGE" -- {\LARGE This is LARGE text.}
\end{itemize}

\smallskip
All these sizes are summarized in Table~\ref{tab:fontsizes}.
%
  \begin{table}
  % trick to make a ? the width of a number
  \catcode`\?=\active \gdef?{\setbox0=\hbox{0}\hbox to\wd0{}}
  \caption{Type sizes for \LaTeX\ size-changing commands.}
  \label{tab:fontsizes}
  \tabcolsep=7pt
  \begin{tabular}{llp{6cm}}
  \hline
  Name                 & Size(pt)       & Usage\\
  \hline
  \verb"\tiny"         &     ?5/6     & -- \\
  \verb"\scriptsize"   &     ?7/8     & -- \\
  \verb"\footnotesize" &     ?8/10    & index, footnotes,
                                        references\\
  \verb"\indexsize"    &     ?8/9     & received line, catchline. \\
  \verb"\small"        &     ?9/10    & quote, quotations, figure
                                        captions.\\
  \verb"\tablebody"    &     ?9/11    & table body size.\\
  \verb"\abstractsize" &     10/10    & abstracts.\\
  \verb"\normalsize"   &     10/12    & main text size, title, author,
                                        A,~B and~C heads, table
                                        captions.\\
  \verb"\large"        &     11/13    & A head, part no. \\
  \verb"\Large"        &     14/18    & -- \\
  \verb"\LARGE"        &     17/19    & -- \\
  \verb"\huge"         &     20/25    & -- \\
  \verb"\Huge"         &     25/30    & -- \\
  \hline
  \end{tabular}
  \end{table}

\ifCUPmtlplainloaded

\section{Macros provided by \texttt{pri2esym.sty}}

\subsection{Additional fonts.}

\begin{itemize}\itemsep=6pt
\item The complete (v2) AMS symbols are available using the normal names:
\[
\hbox{\verb"\boxdot \boxplus \boxtimes"} \lra
  \boxdot \boxplus \boxtimes
\]

\item Blackboard bold:
\[
\hbox{\verb"$\mathbb{ABC}$"} \lra \mathbb{ABC}
\]

\item Fraktur/Gothic:
\[
   \hbox{\verb"$\mathfrak{ABC}$"} \lra \mathfrak{ABC}
\]

\item The $\lessmuch$ (\verb"\lessmuch") and $\greatermuch$ (\verb"\greatermuch")
symbols are provided.

\item Bold math italic/symbols are provided by the \verb"\bmath" macro.
The \verb"PRI2esym" style also defines most of the
symbols from Appendix F of the \TeX book. These can be obtained by using
their normal (unbold) symbol name prefixed with a `b'. \eg \verb|\nabla|
becomes \verb|\bnabla|. The only exception to this rule is \verb|\eta|,
which whould lead to a clash with \verb|\beta|. In this case use
\verb|\boldeta| for bold eta.

\item Upright math and upright bold math:
An upright version of any symbol from the math italic font(s)
(\verb|mtmi|, \verb|mtmib|) can be produced as follows:
\[
  \hbox{\verb|$\mathup{\pi} \ge \mathbup{\pi}$|}
    \quad\lra\quad \mathup{\pi} \ge \mathbup{\pi}
\]
The following upright (and bold upright) symbols are pre-defined:
\verb"\upi", \verb"\upartial", \verb"\umu", \verb"\ubpi", \verb"\ubpartial"
and \verb"\ubmu".

\item Sans serif text and math fonts:\\
\hspace*{-32pt}%
\begin{tabular}{@{}llll@{}}
\hline\hline
Macro name         & \TeX\ font      & Sample     & Description\\
\hline
\verb| \textsfi{..}|  & \verb|mtssi10|  & \textsfi{ABC}   & (text) sans-serif italic\\[3pt]
\verb|$\mathsfi{..}$| & \verb|mtmiss10| & $\mathsfi{ABC}$ & (math) sans-serif italic\\[3pt]

\verb| \textsfb{..}|  & \verb|mtssbx10| & \textsfb{ABC}   & (text) sans-serif bold\\[3pt]
\verb|$\mathsfb{..}$| & \verb|mtmssb10| & $\mathsfb{ABC}$ & (math) sans-serif bold\\[3pt]

\verb| \textsfbi{..}|  & \verb|mtssbi10| & \textsfbi{ABC} & (text) sans-serif bold italic\\[3pt]
\verb|$\mathsfbi{..}$| & \verb|mtmisb10| & $\mathsfbi{ABC}$ & (math) sans-serif bold italic\\
\hline\hline
\end{tabular}

\subsection{Other useful macros.}

\item The \verb"\tfrac" and \verb"dfrac" macros are defined to give
text style and display style fractions. These commands work in the
same way as \verb"\frac".

\end{itemize}

\fi

\label{lastpage}

\end{document}