⟦4a38650eb⟧

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Following this letter are three files (LAM.STY, LAM.TEX and LAM.CHECKLIST) to 
be used when preparing a paper in AMS-TeX 2.0, for a proceedings
volume in the Lectures in Applied Mathematics series.  To make it easier to 
load these files separately on your system, they are separated by a row of 
asterisks (***).


The .STY file is a modified, AMS-TeX preprint style file that adheres to the 
Lectures in Applied Mathematics form.  Instructions for using this file are 
listed at the top.

The .TEX file is a sample of the macros defined in the .STY file.  Before
preparing your paper you should TeX this file and print it to test the macros
and to get instructions for their use.

The .CHECKLIST file should be printed and used to help you avoid the most
common problems.

Reimbursement can be made to the typist or author according to the terms set
forth on the reimbursement form you received in your information package.  For
maximum reimbursement the instructions in the .TEX file must be followed.  The
cost of making any changes deemed necessary by the Editorial Department for
your .TEX file to conform to the style of the series will be calculated and
your reimbursement adjusted accordingly.  For reimbursement calculations the
page count used is that of the final, published form.

Once your paper has been input and proofread, please send the .TEX file to our
Internet address: PUB-SUBMIT@MATH.AMS.COM.  When you send the file please be
sure to include a message that identifies both the publication series and the
editor of the volume.

Should you have any technical questions, please contact our Technical Support
Group at 800-321-4AMS or 401-455-4080.  They can also be reached through
electronic mail at Internet: tech-support@math.ams.com.


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%-----------------------------------------------------------------------------
% BEGINNING OF FILE LAM.STY
%-----------------------------------------------------------------------------
%*********************************************************
% START OF LAM.STY
%%%%%%%%%%                        LAM.STY                   %%%%%
%                                                                8/90
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% This file is designed to work with AMS-TeX version 2.0.
%
% The TeX code defined here will input the AMS-TeX 2.0 preprint style
% and modify appropriate macros to conform to the Lectures in Applied 
% Mathematics style.  It sets the correct page size, puts a logo and a 
% copyrightline on the first page, formats the top matter, headings, and 
% references appropriately.
%
% Instructions:
%
%  1. Create a file named  lam.sty containing the data in the lines
%     from  %%% lam.sty %%%  through  \endinput .  Install the file
%     in the same directory as amsppt.sty .
%
%  2. In a data file, include  the line, \documentstyle{lam} 
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\catcode`\@=11

%  First input the preprint style

\def\next{AMSPPT}\ifx\styname\next \endinput
  \else\input amsppt.sty\fi


%  Set the page size and first-page sink appropriately

\pageheight{517pt}
\pagewidth{27pc}
\def\pretitle{\vskip6.5pc}

%  Switches to determine whether or not page numbers are wanted.

\newif\ifP@geNumbers	\P@geNumberstrue
\def\NoPageNumbers{\global\P@geNumbersfalse}

%  Switches to determine if running heads are to be used.
%  To select a style with running heads, include the command
%  \userunningheads  in the input file.

\newdimen\runheadskip  \runheadskip=3pt 	% 
\def\userunningheads{\global\runheads@true \NoPageNumbers}

%  In LAM, we do want running heads

\userunningheads

%  Define appropriate fonts

%  modify \title to use a larger font

\font@\titlebf=cmbx10 scaled \magstep2
\font@\titlei=cmmi10 scaled \magstep2
\font@\titlesy=cmsy10 scaled \magstep2
\def\titlefont{\normalbaselineskip18\p@
 \textonlyfont@\bf\titlebf
 \ifsyntax@\else
  \textfont\z@\titlebf  \scriptfont\z@\tenrm  \scriptscriptfont\z@\sevenrm
  \textfont\@ne\titlei  \scriptfont\@ne\teni  \scriptscriptfont\@ne\seveni
  \textfont\tw@\titlesy \scriptfont\tw@\tensy \scriptscriptfont\tw@\sevensy
  \textfont\thr@@\tenex \scriptfont\thr@@\tenex \scriptscriptfont\thr@@\tenex
 \fi
 \normalbaselines\titlebf}

\font@\titlebf=cmbx10 scaled\magstep2

\def\titlef@nt{\titlefont\bf}
\def\foliofont{\eightrm}    
\def\headlinefont@{\eightpoint}
\def\citefont@{\bf}

%	define  a logo for the upper left-hand corner
                      
\def\jourlogo{\hbox{\vbox to0pt{\vbox{\sevenrm \baselineskip8.0pt
	\parindent0pt \frenchspacing
	Lectures in Applied Mathematics\hfil\break
	Volume {\sevenbf\cvol@} (\cvolyear@)\par}\vss}}}

%  	macros to be put into the \topmatter for the logo

\def\cvol#1{\gdef\cvol@{\ignorespaces#1\unskip}}
\def\cvolyear#1{\gdef\cvolyear@{\ignorespaces#1\unskip}}
\def\cyear#1{\gdef\cyear@{\ignorespaces#1\unskip}\cyear@@#100000\end@}

\def\cyear@@#1#2#3#4#5\end@{\gdef\cyearmodc@{#3#4}%
	\gdef\cyearmodcHold@{#3#4}}

\cvol{00}
\cyear{0000}
\cvolyear{0000}

\font\sixsy=cmsy6

\def\copyrightline@{\rightline{%
	\vbox{\sixrm \textfont2=\sixsy \baselineskip 7pt
	    \halign{\hfil##\cr
		\copyright\cyear@\ American Mathematical Society\cr
		 0075-8485/\cyearmodc@\ \$1.00 + \$.25 per page\cr }}}}

\def\cyearmodc#1{\gdef\cyearmodc@{\ignorespaces#1\unskip}}


% Topmatter material

\def\title#1\endtitle{\global\setbox\titlebox@\vbox{\titlef@nt
   \raggedcenter@\ignorespaces\baselineskip=16pt{#1}\endgraf}
   \ifmonograph@\edef\next{\the\leftheadtoks}\ifx\next\empty
     \leftheadtext{#1}\fi\fi
   \edef\next{\the\rightheadtoks}\ifx\next\empty\rightheadtext{#1}\fi}

\def\author#1\endauthor{\global\setbox\authorbox@
   \vbox{\tenpoint\smc\raggedcenter@\ignorespaces
 \uppercase{#1}\endgraf}\relaxnext@ \edef\next{\the\leftheadtoks}%
 \ifx\next\empty\leftheadtext{#1}\fi}

\def\address#1\endaddress{\global\advance\addresscount@\@ne
 \expandafter\gdef\csname address\number\addresscount@\endcsname
 {\vskip6\p@ minus2\p@\eightpoint{\smc\ignorespaces#1}\par}}

\def\email{\nofrills@{\eightpoint{\it E-mail\/}:\enspace}\email@
  \DNii@##1\endemail{%
  \expandafter\gdef\csname email\number\addresscount@\endcsname
  {\def\usualspace{{\it\enspace}}\smallskip\eightpoint\email@
  \ignorespaces##1\par}}%
 \FN@\next@}

\def\curraddr{\nofrills@{\eightpoint{\it Current address\/}:\enspace}\curraddr@
  \DNii@##1\endcurraddr{%
  \expandafter\gdef\csname curraddr\number\addresscount@\endcsname
  {\def\usualspace{{\it\enspace}}\smallskip\eightpoint\curraddr@
  \ignorespaces##1\par}}%
 \FN@\next@}

%	abstract; abstract head is lightface, not \smc
\def\abstract{\nofrills@{{\eightpoint Abstract.\enspace}}\abstract@
	\DNii@{\setbox\abstractbox@\vbox\bgroup\noindent$$\vbox\bgroup
           \def\envir@{abstract}\advance\hsize-2\indenti
           \usualspace@{{\eightpoint\enspace}}\eightpoint
             \noindent\abstract@\ignorespaces}%
	\FN@\next@}


%	reformat the topmatter for the LAM style
    
\outer\def\endtopmatter{\runaway@{abstract}\hrule height\z@\vskip-\topskip
 \ifx\thesubjclass@\empty\else\makefootnote@{}{\thesubjclass@}\fi
  \ifx\thekeywords@\empty\else \makefootnote@{}{\thekeywords@}\fi
 \ifx\thethanks@\empty\else \makefootnote@{}{\thethanks@}\fi
 \jourlogo
 \pretitle
 \vskip36\p@ plus2\p@ minus2\p@
 \unvbox\titlebox@
 \preauthor
 \ifvoid\authorbox@\else\vskip14\p@ plus2\p@ minus2\p@\unvbox\authorbox@\fi
 \preabstract
 \ifvoid\abstractbox@\else\vskip30\p@ plus2\p@ minus2\p@\unvbox\abstractbox@\fi
 \prepaper
 \vskip18\p@ plus12\p@ minus6\p@\tenpoint}

%  Change from \noindent to \indent in a \proclaim and \demo.

\let\varindent@\indent
\def\proclaimheadfont@{\smc}
\def\demoheadfont@{\smc}

%  Change \nofrills@ from .\enspace to .\quad in \proclaim

\outer\def\proclaim{\runaway@{proclaim}\def\envir@{proclaim}%
  \nofrills@{.\quad}\proclaim@
 \DNii@##1{\penaltyandskip@{-100}\medskipamount\varindent@
   \usualspace@{{\proclaimheadfont@\enspace}}\proclaimheadfont@
   \ignorespaces##1\unskip\proclaim@
  \sl\ignorespaces}% 
 \FN@\next@}

% Remove \smallskip before \demo

\def\demo{\runaway@{proclaim}\nofrills@{.\enspace}\demo@
 \DNii@##1{\par{\usualspace@{{\demoheadfont@\enspace}}%
  \varindent@\demoheadfont@\ignorespaces##1\unskip\demo@}\rm
  \ignorespaces}\FN@\next@}

%  Change \endremark to add a \medskip

\def\endremark{\par\penaltyandskip@{55}\medskipamount}

%  Change \nofrills@ from .\enspace to .\quad in \example

\def\example{\runaway@{proclaim}%
  \nofrills@{.\proclaimheadfont@\quad}\example@
        \DNii@##1{\penaltyandskip@{-100}\medskipamount
        {\usualspace@{{\proclaimheadfont@\enspace}}%
        \varindent@\proclaimheadfont@\ignorespaces##1\unskip\example@}%
        \rm \ignorespaces}\FN@\next@}

%  Roman type is needed within the statement of theorems for numerals,
%  fences, labels, etc.  This definition should ultimately be in amsppt.sty.

\def\rom#1{{\rm #1}}

\outer\def\specialhead{\runaway@{\string@\roster}\runaway@{proclaim}%
  \penaltyandskip@{-200}\aboveheadskip
  \begingroup\raggedcenter@\interlinepenalty\@M
  \specialheadfont@\ignorespaces}
\def\endspecialhead{\par\endgroup\nobreak\vskip\belowheadskip}

\def\head{\relaxnext@\nofrills@{.\enskip}\head@
   \DNii@##1\endhead{\bigbreak{\usualspace@{{\bf\enspace}}%
      \tenpoint\bf\ignorespaces##1\unskip\head@}\ignorespaces}%
   \FN@\next@}

\def\subheadfont@{\it}

\def\subsubhead{\relaxnext@\nofrills@{.\enspace}\subsubhead@
 \DNii@##1\endsubsubhead{\medbreak{\usualspace@{{\smc\enspace}}%
  \tenpoint\smc\ignorespaces##1\unskip\subsubhead@}\ignorespaces}%
 \FN@\next@}

% Captions should be in eight point caps and small caps

\def\captionfont@{\smc}
\def\topcaption#1#2\endcaption{%
  {\dimen@\hsize \advance\dimen@-\captionwidth@
   \eightpoint\rm\raggedcenter@ \advance\leftskip.5\dimen@ \rightskip\leftskip
  {\captionfont@#1}%
  \if\notempty{#2}.\enspace\ignorespaces#2\fi
  \endgraf}\nobreak\bigskip}
\def\botcaption#1#2\endcaption{%
  \nobreak\bigskip\eightpoint
  \setboxz@h{\captionfont@#1\if\notempty{#2}.\enspace\rm#2\fi}%
  {\dimen@\hsize \advance\dimen@-\captionwidth@
   \leftskip.5\dimen@ \rightskip\leftskip
   \noindent \ifdim\wdz@>\captionwidth@ 
   \else\hfil\fi 
  {\captionfont@#1}\if\notempty{#2}.\enspace\rm#2\fi\endgraf}}


%  Add current address to \enddocument

\outer\def\enddocument{%
 \runaway@{\string@\roster}\runaway@{proclaim}%
\ifmonograph@ % do nothing
\else
 \nobreak
 \count@\z@ \loop\ifnum\count@<\addresscount@\advance\count@\@ne
 \csname address\number\count@\endcsname
 \csname curraddr\number\count@\endcsname
 \csname email\number\count@\endcsname
 \repeat
\fi
 \vfill\supereject\end}

%  Modify the AMSPPT output routine to include (optional) running heads
%  and (optionally) exclude page numbers at the bottom.


\def\output@{\shipout\vbox{%
 \iffirstpage@ \global\firstpage@false
    \pagebody\baselineskip1.75pc\copyrightline@\baselineskip=1pc
    \centerline{\eightrm\folio}
 \else\ifrunheads@\makeheadline\vskip\runheadskip\fi
    \pagebody\baselineskip2pc\hbox to\hsize{\hfil\ifP@geNumbers\tenpoint
    \number\pageno\fi\hfil}%
 \fi}
 \global\advance\pageno\@ne
 \ifnum\outputpenalty>-\@MM\else\dosupereject\fi}

\catcode`\@=13

\def\amsversion{2.0}
\endinput                                 
***** END OF LAM.STY
%
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% END OF FILE LAM.STY
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\f


%-----------------------------------------------------------------------------
% BEGINNING OF FILE LAM.TEX
%-----------------------------------------------------------------------------
%*********************************************************
% START OF LAM.TEX
%%%%%%%%%%                        LAM.TEX                     %%%%
%                                                               8/90
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% AMS-TeX 2.0 style file for Lectures in Applied Mathematics volumes.
%
\input amstex
\documentstyle{lam}
\NoBlackBoxes
%
\leftheadtext{AUTHOR ONE AND AUTHOR TWO}
\rightheadtext{MAXIMAL IDEALS IN SUBALGEBRAS OF $C(X)$}

\topmatter
\title Sample Paper for Lectures in Applied Mathematics,\\
On Maximal Ideals in Subalgebras of $C(X)$\endtitle
\author Author One and Author Two\endauthor
\address Department of Mathematics, Northeastern University, Boston,
Mas\-sa\-chu\-setts 02115\endaddress  %Research address for author one
\curraddr Department of Mathematics and Statistics, Case Western Reserve
University, Cleveland, Ohio 43403\endcurraddr %Current address for author one
\email XYZ\@Math.AMS.com\endemail
\address Mathematical Research Section, School of Mathematical Sciences,
Australian National University, Canberra ACT 2601, Australia %address for 
%                                                             author two
\endaddress

%  The following items give publication information for the Lect. in Appl. Math. logo
\cvol{00}
\cvolyear{1990}
\cyear{1990}

%  Math Subject Classifications 
\subjclass Primary 54C40, 14E20; Secondary 46E25, 20C20\endsubjclass
\abstract This paper is a sample prepared to illustrate for authors
the use of the \AmSTeX{} Version~2.0 preprint style with additional
macros for the series {\bf Lectures in Applied Mathematics}.

The file used to prepare this sample is {\bf lam.tex}. Its coding 
should be used as a model when an author's paper is prepared.
\endabstract

%  \thanks will become a 1st page footnote.
%  Use \endgraf to indicate a new paragraph; a blank line or \par will
%  be recognized as an error.
%  Don't type a period at the end; it will be supplied.
\thanks The first author was supported in part by NSF
Grant \#000000.\endgraf
The final version of this paper will be submitted for
publication elsewhere\endthanks
\endtopmatter

\document

\head 1. Introduction                % bold, run in;
\endhead                             % don't type final punctuation
This sample paper illustrates the use of the \AmSTeX{} Version~2.0 preprint 
style with additional macros for the book series {\bf Lectures in Applied 
Mathematics}.  In this sample paper, brief instructions to authors are 
interspersed with mathematical text extracted from (purposely unidentified) 
published papers.  For instructions on preparing mathematical text, the author 
is referred to {\it The Joy of \TeX}, second edition, by Michael Spivak \cite{18}.

\subhead Top matter\endsubhead
The input format and content of the top matter can be best understood
by examining the first part of the sample file {\bf lam.tex}, up
through the {\tt\char`\\document} instruction.

The top matter includes both elements that must be input by the author and 
a few that are provided automatically.  In the top matter section, the title is 
input in caps and lowercase and will be set that way.  The author names should 
also be input in caps and lowercase; they will automatically be set in all caps.
The title and author names that are to appear in the running heads should be 
input in all UPPERCASE as {\tt\char`\\rightheadtext} and 
{\tt\char`\\leftheadtext} respectively. Full names and the complete title 
should be used unless they require too much space; in that event, abbreviated 
forms should be substituted.

An address should be input for each author.  If a current address is
different than the address where the research was carried out then both
addresses are given with the current address second and coded as indicated
in this sample file.  After these addresses, an address for electronic
mail should be given, if one exists. Note that no abbreviations are used in 
addresses, and complete addresses for each author must be entered in the order 
the names appear on the title page.  Although addresses are considered part of 
the top matter, they are set at the end of the paper, following the references.

Subject classifications ({\tt\char`\\subjclass}) and acknowledgments
({\tt\char`\\thanks}) are part of the top matter and will appear as
footnotes at the bottom of the first page.  Subject classifications
({\tt\char`\\subjclass}) are required. Use the 1980 Mathematics Subject
Classification (1985 Revision) that appears in annual indexes of
{\it Mathematical Reviews\/} beginning in 1984.  (The two-digit code from
the Contents is not sufficient.)

Use {\tt\char`\\thanks} for the footnotes that appear on the first page.  It is
generally desirable not to attach footnote numbers or symbols to titles or
author names used as headings.  If a footnote applies to only one author then
include this information in the footnote.  Only one instance of
{\tt\char`\\thanks} is permitted in a paper.  Multiple ``thanks'' footnotes may
be simulated by separating the appropriate parts from one another by
{\tt\char`\\endgraf}; this will begin a new paragraph in the footnote.

Papers published in proceedings of conferences are often abstracts or
preliminary versions.  In such a case, include the following in the
{\tt\char`\\thanks} to appear at the bottom of the first page: ``The final
[detailed] version of this paper will be [has been] submitted for
publication elsewhere.''  Papers that are to be considered for review
by {\it Mathematical Reviews\/} should include the following statement:
``This paper is in final form and no version of it will be submitted
for publication elsewhere.''

\subhead Fonts\endsubhead
The fonts used in this paper are from the Computer Modern family; they
should be available to all authors preparing papers with \AmSTeX\ 2.0.
However, the final copy may be set by the AMS using other fonts.  

\subhead A mathematical extract\endsubhead
The mathematical content of this sample paper has been extracted from
published papers, with no effort made to retain any mathematical sense.
It is intended only to illustrate the recommended manner of input.

Mathematical symbols in text should always be input in math mode as
illustrated in the following paragraph.

A function is invertible in $C(X)$ if it is never zero, and in $C^*(X)$ if
it is bounded away from zero. In an arbitrary $A(X)$, of course, there
is no such description of invertibility which is independent of the 
structure of the algebra. Thus in \S 2 we associate to each noninvertible
$f\in A(X)$ a $z$-filter $\Cal Z (f)$ that is a measure of where
$f$ is ``locally'' invertible in $A(X)$. This correspondence extends to
one between maximal ideals of $A(X)$ and $z$-ultrafilters on $X$.
In \S 3 we use the filters $\Cal Z (f)$ to describe the intersection of 
the free maximal ideals in any algebra $A(X)$. Finally, our main result
allows us to introduce the notion of $A(X)$-compactness of which 
compactness and realcompactness are special cases. In \S 4 we show how
the Banach-Stone theorem extends to $A(X)$-compact spaces.

\head 2. Theorems, lemmas, and other proclamations\endhead
Theorems and lemmas are varieties of proclamations.  Either may have a
proof, or a ``demonstration.''  The lemma and proof below illustrate
the use of a ``roster'' or itemized list; the first item in the proof
roster is run in.  Note that both proclamations and demonstrations
have their beginnings and ends marked in the file.

\proclaim{Lemma 1} Let $f, g\in  A(X)$ and let $E$, $F$ be cozero
sets in $X$.
\roster
\item"(a)" If $f$ is $E$-regular and $F\subseteq E$, then $f$ is $F$-regular.

\item"(b)" If $f$ is $E$-regular and $F$-regular, then $f$ is $E\cup F$-%
regular.

\item"(c)" If $f(x)\ge c>0$ for all $x\in E$, then $f$ is $E$-regular.

%\item"(d)" If $0<f(x)\le g(x)$ for all $x\in E$ and if $f$ is
%$E$-regular, then $g$ is $E$-regular.
%
%\item"(e)" If $f$ is $E$-regular and $g$ is $F$-regular, then $fg$ is 
%$E\cap F$-%
%regular and $f^2 +g^2$ is $E\cup F$-regular.
\endroster
\endproclaim

\demo{Proof}
\roster\runinitem "(a)" Obvious.

\item"(b)" Let $h, k\in A(X)$ satisfy $hf|_E=1$ and $kf|_F=1$. Let
$w=h+k-fhk$. Then $fw|_{E\cup F}=1$.

\item"(c)" Let $h=\max\{c,f\}$. Then $h|_E=f|_E$ and $h\ge c$. So $0<h^{-1}
\le c^{-1}$. Hence $h^{-1} \in C^*(X)\subseteq A(X)$, and 
$h^{-1} f|_E=1$. 

%\item"(d)" Let $h\in A(X)$ satisfy $hf|_E=1$. For $x\in E,\ h
%(x)>0$, so $h(x)g(x)\ge h(x)f(x)=1$. Thus by (c), there exists $k
%\in A(X)$ such that $khg|_E=1$.
%
%\item"(e)" If $hf|_E=1$ and $kg|_F=1$, then $hkgf|_{E\cap F}=1$. Now
%$f^2 +g^2\ge f^2$, so by (d), $f^2+g^2$ is $E$-regular. Similarly,
%it is $F$-regular, and so the result follows by (b).
\endroster
\enddemo

\definition{Definition}
For $f\in A(X)$, we define
$$
\Cal Z (f)=\{E\in Z[X]\: \text{$f$ is $E^c$-regular}\}.
\tag 2.1
$$
\enddefinition

\head 3. Roman type\endhead
Numbers, punctuation, (parentheses), [brackets], $\{$braces$\}$, and
symbols used as tags should always be set in roman type.  The following
sample theorem illustrates how to code for roman type within the
statement of a theorem.

\proclaim{3.1 Theorem}
Let $\Cal G$ be a free nilpotent-of-class-\rom{2} group of rank
$\ge 2$ with carrier $G$ and let
$$m : G\times G \to Z$$
satisfy \rom{(2.21)}, \rom{(2.22)}, and \rom{(2.24)}, and define
$\kappa$ by \rom{(2.23)}.  Then this kappa-group is kappa-nilpotent
of class \rom{2} and kappa-metabelian, that is to say, it satisfies
\rom{S2} and \rom{S3}, but it is kappa-abelian if, and only if,
$$m(x,y) = -1\quad\text{for all $x, y \notin G'$}.
\tag 3.1$$
\rom{(}Thus \rom{(3.1)} implies the trivial consequence
\rom{(2.1)}.\rom{)}  Assume now that \rom{(3.1)} does not hold,
so that the kappa-group is kappa-nonabelian.  Assume further that $m$
is not constant outside $G'$ \rom{(}inside $G'$ the values of $m$
clearly do not matter\rom{)}.  Then $\kappa$ is neither left nor right
linear, that is to say, neither \rom{S4} nor \rom{S5} holds:
\rom{I1} again holds, but none of \rom{I2--I5}.  As before,
\rom{I6} is equivalent to \rom{(2.25)}.  Now \rom{I7$'$}, however,
is equivalent to a condition similar to \rom{(2.25)}, namely
$$m(xz\sigma, yz\sigma) = m(x,y)\,.
\tag 3.2$$
%As before, each of \rom{I8--I11} is equivalent to \rom{(2.26)}.
%As before, \rom{J3} does not hold; but now \rom{J1}, \rom{J2}
%and \rom{J4} hold.
\endproclaim

Letters used as abbreviations rather than as variables or constants
are set in roman type.  Use the control sequences \cite{18\rm, p.\ 95}
for common mathematical functions and operators like $\log$ and $\lim$,
and use {\tt\char`\\cite} when citing a reference.  The reference tag
will be {\bf bold} automatically, but you will need to set any
additional information in roman type as illustrated by the coding of
the previous sentence.

\head 4. References\endhead
When you are ready to begin the bibliography, type {\tt\char`\\Refs}
before the first reference.  This produces the heading for the
bibliography and changes the type to a smaller size.  Input each reference
using the \AmSTeX{} control sequences given in Appendix C of \cite{18}.
Arrange the references in alphabetical order by the last name of the first
named author.  The references at the end of this sample file have been
chosen to illustrate the coding of the most common types of references.
Use the abbreviations of names of journals as given in annual indexes of
{\it Mathematical Reviews}.

The sample references have been labeled with numbers, as
{\tt\char`\\no 10}, etc.  To use letters instead of numbers for labels,
you can use, for example, {\tt\char`\\key C1}.

References are set with hanging indentation, The amount of indentation
is preset to accommodate the most common case, two-digit numbers.
It can be increased (or decreased) by specifying the widest number or
key used in the references. For example,
{\tt\char`\\widestnumber\char`\\no\{999\}} and
{\tt\char`\\widestnumber\char`\\key\{GHMaR\}}
will increase the indentation to accommodate a three-digit number or the key
\hbox{[GHMaR]} respectively.  Note that the parts of the formatting that
depend on the current journal style are taken into account automatically
(the period after a number or the [\dots]\ around a key, plus the usual
space).

After the last reference, type {\tt\char`\\endRefs} to mark the end of the
bibliography.

General instructions for tagging references are given in Appendix C of
\cite{18}.  Some changes have been made in the upgrade to \AmSTeX{}
Version~2.0.  Except for the simplification of the {\tt\char`\\key},
the new conventions are illustrated in the bibliography at the end of
this sample.

\head 5. Figures\endhead
Figures should be handled as inserts.  The amount of space left should equal
the exact height of the figure.  Extra space around the figure will be
provided automatically.  The positioning of figures may need to be changed
to obtain the best possible page layout.  Thus, it is important to label
your figures and use the labels in the text when referring to figures.
The figure caption should be positioned below the figure.

\example{Example 5}
For the link in Figure 5a, the Massey product $\langle u_1$, $u_2$, $u_3$,
$u_4$, $u_5\rangle$ in $S^3-L$ is defined and consists of all
integer multiples of $\gamma_{1,5}$.  For the link in Figure 5b,
the Massey product $\langle u_1, u_2, u_3, u_4, u_5\rangle$ in
$S^3-L$ contains the single element $\gamma_{1,5}$.  Since the links
in Figures 5a and 5b are homotopic, the example indicates that Massey
products in $S^3-L$ with distinct $u_j$'s do not, in general,
determine homotopy invariants of the link.  For the link in Figure 5a
and the link in Figure 5b, the Massey product $\langle u_1, u_2, \dots,
u_5\rangle$ in $\{S^3-L_i\}_{i=1}^5$ contains the single element
$\gamma_{1,5}$.

%  art work measures 15pc for figure 5a, 11pc for figure 5b

\midinsert
\vskip 15pc
\botcaption{Figure 5{\rm a}}\endcaption
\endinsert
\midinsert
\vskip 11pc
\botcaption{Figure 5{\rm b}}\endcaption
\endinsert


In most cases, figures will be rendered for consistency of style within a
book.  Please provide figure manuscript drawn in black ink with clean,
unbroken lines on nonabsorbent paper.

\specialhead 6. Other headings\endspecialhead
\subhead A subheading\endsubhead % bold, run-in; do not type ending punctuation
We conclude by noting that another characterization of $A$-compactness
follows from Mandelker \cite 5. We call a family $\Cal S$ of closed sets in
$X\ A$-stable if every $f\in A(X)$ is bounded on some member of $\Cal S$.
Then one can show (as in \cite 5) that a space is $A$-compact if and only if 
every $A$-stable family of closed sets with the finite intersection property
has nonempty intersection.

\subsubhead A second-level subheading\endsubsubhead
This paragraph is included only to illustrate the appearance of a
sub-subheading.

\Refs

\ref\no 1
\by     V. L. Arnol$'$d, A. N. Varchenko, and S. M. Gusein-Zade
\book   Singularities of differentiable maps.~{\rm I}
\publ   ``Nauka'' \publaddr Moscow \yr 1982 \lang Russian
\transl English transl. \publ Birkh\"auser \yr 1985
\endref
\ref\no 2 \bysame
\book   Singularities of differentiable maps.~{\rm II}
\publ   ``Nauka'' \publaddr Moscow \yr 1984
\transl English transl. \publ Birkh\"auser \yr 1988
\endref
\ref\no 3
\by     H. Bass, E. H. Connell, and D. Wright
\paper  The Jacobian conjecture
\jour   Bull. Amer. Math. Soc.
\vol    7 \yr 1982 \pages 287--330
\endref
\ref\no 4
\by     H. Bass and G. H. Meisters
\paper  Polynomial flows in the plane
\jour   Adv. in Math. \vol 55 \yr 1985 \pages 173--203
\endref
\ref\no 5
\by     E. A. Coddington and N. Levinson
\book   Theory of ordinary differential equations
\ed     Editor Name
\bookinfo extra book info
\publ   McGraw-Hill \publaddr New York
\yr     1955
\endref
\ref\no 6
\by     B. Coomes
\book   Polynomial flows, symmetry groups, and conditions sufficient for 
        injectivity of maps
\bookinfo Ph.D. thesis, Univ. Nebraska-Lincoln
\yr     1988
\endref
\ref\no 7 \bysame % B. Coomes
\paper  The Lorenz system does not have a polynomial flow
\jour   J. Differential Equations
\toappear
\endref
\ref\no 8
\by     E. Formanek
\paper  Generating the ring of matrix invariants
\inbook Lecture Notes in Math. vol. 1197
\publ   Springer-Verlag \publaddr Berlin and New York
\yr     1986 \pages 73--82
\endref
\ref\no 9
\by     P. Gabriel
\paper  Unzerlegbare Darstellungen. {\rm II}
\jour   Manuscripta Math. \vol 6 \yr 1972 \pages 71--103
\endref
\ref\no 10
\by     J. Guckenheimer, P. Holmes, M. Martineau, and L. P. Robinson
\book   Nonlinear oscillations, dynamical systems, and bifurcations of vector
        fields
\publ   Springer-Verlag \publaddr New York
\yr     1983
\endref
\ref\no 11
\by     J. K. Hunter and J. Scheurie
\paper  Perturbed solitary wave solutions of a model equation for water waves
\jour   Physica D 
\toappear
\endref
\ref\no 12
\by     G. H. Meisters
\paper  Jacobian problems in differential equations and algebraic geometry
\jour   Rocky Mountain J. Math. \vol 12 \yr 1982 \pages 679--705
\endref
\ref\no 13 \bysame  % Meisters
\paper  Polynomial flows on $\bold R^n$
\inbook Proc. Semester on Dynamical Systems (Warsaw, Autumn 1986)
\publ   Springer-Verlag
\publaddr Berlin, Heidelberg, and New York
\toappear
\endref
\ref\no 14
\by     G. H. Meisters and C. Olech
\paper  A poly-flow formulation of the Jacobian conjecture
\jour   Bull. Acad. Polon. Sci. S\'er. Sci. Math.
\vol    35
\yr     1987
\pages  725--731
\endref
\ref\no 15
\by     S. Osher
\paper  Shock capturing algorithms for equations of mixed type
\inbook  Numerical Methods for Partial Differential Equations
\eds    S. I. Hariharan and T. H. Moulton
\publ   Longman
\publaddr New York
\yr     1986
\pages  305--322
\endref
\ref\no 16
\by     L. A. Ostrovsky
\paper  Nonlinear internal waves in a rotating ocean
\paperinfo Part 2
\jour   Oceanology 
\vol    18
\yr     1978
\pages  181--191
\endref
\ref \no 17
\by     G. S. Petrov 
\paper  Elliptic integrals and their nonoscillatory behavior
\jour   Funktsional. Anal. i Pri\-lo\-zhen.
\vol    20
\yr     1986
\pages  46--49
\transl\nofrills English transl. in
\jour   Functional Anal. Appl. \vol 20 \yr 1986
\endref

\ref\no 18
\by     M. D. Spivak \book The Joy of \TeX{}, \rm second edition
\publ   Amer. Math. Soc., Providence, R.~I. \yr 1986\endref

\endRefs

\enddocument

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		     Check List for Electronic Manuscripts

		    Lectures in Applied Mathematics Volumes


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