amsamp.tex 664 144 7 31672 6124605376 6131 % This is the sample paper for the AmSTeX SIAM style file, (amstex)siam.sty % for use with AmSTeX version 2.1 or later and amsppt.sty, version 2.1a. % RCS information: $Revision: 1.1 $, $Date: 93/01/25 15:33:19 $. \input amstex \documentstyle{amstexs1} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Macro definitions for running heads and first page % \accepted\SIMAF % \firstpageno{10} % \lastpageno{12} % \issuevolume{1} % \issuenumber{2} % \issuemonth{February} % \placenumber{002} % place of paper in this issue % \issueyear{1988} % \shortauthor{Bradley J. Lucier and Douglas N. Arnold} % \shorttitle{A Sample Paper} % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Macros specific to this paper % \define\loner{{L^1(\Bbb R)}} % \define\linfr{{L^\infty(\Bbb R)}} % \define\bvr{{\roman{BV}(\Bbb R)}} % \define\TV{{\roman {TV}}} % \define\sdot{\,\cdot\,} % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \topmatter \title A SAMPLE PAPER, WITH A RATHER LONG TITLE, TO ILLUSTRATE THE \AmSTeX\ SIAM STYLE\footnote[\boldkey*]{Unlikely to appear.} \endtitle \author BRADLEY J. LUCIER\footnote[\dag]{Department of Mathematics, Purdue University, West Lafayette, Indiana 47907. Present address, somewhere on the beach (lucier\@math.purdue.edu). The work of the first author was not supported by the Wolf Foundation.}\ and DOUGLAS N. ARNOLD\footnote[\ddag]{Department of Mathematics, Pennsylvania State University, University Park, Pennsylvania 16802.} \endauthor \abstract This sample paper illustrates many of the amstex macros as used with the \AmSTeX\ SIAM style file amstexsiam (version 2.0a). The \AmSTeX\ SIAM style file, which inputs and builds upon the amsppt style (version 2.1a or later) of Michael Spivak, gives authors easy access to most of the typographical constructions used in SIAM journals. It does not address the issues of the table of contents or tables, which must be set using more primitive \TeX\ macros. \endabstract \keywords porous medium, interface curves \endkeywords \subjclass 65N60 \endsubjclass \endtopmatter \document \subhead 1. Introduction\endsubhead We are concerned with numerical approximations to the so-called porous-medium equation \cite{6}, $$ \alignedat2 &u_t=\phi(u)_{xx},&&\qquad x\in\Bbb R,\quad t>0,\quad\phi(u)=u^m,\quad m>1, \\ &u(x,0)=u_0(x),&&\qquad x\in\Bbb R. \endalignedat \tag 1.1 $$ We assume that the initial data $u_0(x)$ has bounded support, that $0\leq u_0\leq M$, and that $\phi(u_0)_x\in\bvr$. It is well known that a unique solution $u(x,t)$ of (1.1) exists, and that $u$ satisfies $$ 0\leq u\leq M\text{ and }\TV\phi(u(\,\cdot\,,t))_x\leq\TV\phi(u_0)_x. \tag 1.2 $$ If the data has slightly more regularity, then this too is satisfied by the solution. Specifically, if $m$ is no greater than two and $u_0$ is Lipschitz continuous, then $u(\,\cdot\,,t)$ is also Lipschitz; if $m$ is greater than two and $(u_0^{m-1})_x\in\linfr$, then $(u(\,\cdot\,,t)^{m-1})_x\in\linfr$ (see [3]). (This will follow from results presented here, also.) We also use the fact that the solution $u$ is H\"older continuous in $t$. \subhead 2. $\linfr$ error bounds\endsubhead After a simple definition, we state a theorem that expresses the error of approximations $u^h$ in terms of the weak truncation error $E$. \definition{Definition 2.1}\rm A {\it definition} is the same as a theorem set in roman type. In version 2 of the \AmSTeX\ style file for the SIAM journals, definitions are set with their own command. \enddefinition \proclaim{Theorem 2.1} Let $\{u^h\}$ be a family of approximate solutions satisfying the following conditions for $0\leq t\leq T${\rm:} \roster \item For all $x\in\Bbb R$ and positive $t$, $0\leq u^h(x,t)\leq M${\rm;} \item Both $u$ and $u^h$ are H\"older--$\alpha$ in $x$ for some $\alpha\in(0,1\wedge 1/(m-1))${\rm;} $u^h$ is right continuous in $t${\rm;} and $u^h$ is H\"older continuous in $t$ on strips $\Bbb R\times(t^n,t^{n+1})$, with the set $\{t^n\}$ having no limit points\/{\rm;} and \item There exists a positive function $\omega(h,\epsilon)$ such that\/{\rm:} whenever $\{w^\epsilon\}_{0<\epsilon\leq\epsilon_0}$ is a family of functions in $\bold X$ for which {\roster \item"(a)" there is a sequence of positive numbers $\epsilon$ tending to zero, such that for these values of $\epsilon$, $\|w^\epsilon\|_\infty\leq 1/\epsilon$, \item"(b)" for all positive $\epsilon$, $\|w_x^\epsilon(\sdot,t)\|_\loner\leq 1/\epsilon^2$, and \item"(c)" for all $\epsilon>0$, $$ \sup\Sb x\in\Bbb R\\0\leq t_1,t_2\leq T\endSb \dfrac{|w^\epsilon(x,t_2)-w^\epsilon(x,t_1)|}{|t_2-t_1|^p}\leq 1/\epsilon^2, $$ where $p$ is some number not exceeding $1$, \endroster}% then\footnote{This is an obvious ploy, but we need a footnote.} $|E (u^h,w^\epsilon,T)|\leq\omega(h,\epsilon).$ \item This is the fourth item in the outer roster. \endroster Then, there is a constant $C=C(m,M,T)$ such that $$\multline \|u-u^h\|_{\infty,\Bbb R\times[0,T]}\leq C\biggl[ \sup \biggl |\int_\Bbb R(u_0(x)-u^h(x,0)) w(x,0) \,dx\biggr|\\ +\omega(h,\epsilon)+\epsilon^\alpha\biggr],\endmultline \tag 2.1 $$ where the supremum is taken over all $w\in\bold X$. \endproclaim \demo{Proof} We assume first that $Q$ is decreasing and consider the following cases: \case{Case\/ {\rm1:} $b'\geq 1/2$} We have $P(1/8)\geq\delta>0$ where $\delta$ depends only on $d$, for otherwise by (3.7) applied to $P$ and $p=\infty$, $P$ could not attain the value $1$ at $x=1$. Similarly, for $m=(a'+b')/2$, $Q(m)\geq\delta'>0$ for some $\delta'$ depending only on $d$ since otherwise $Q$ cannot attain the value $1$ at $x=a'$. Hence, for $\delta''=\min(\delta,\delta')$, $|A(y)|\geq|m-1/8|\geq b'/4\geq\frac18\max(b',1)$ for $y\in[0,\delta'']$. On the other hand, $|A(y)|\leq \max(b',1)$ for all $y\in[0,1]$, so (4.2) follows for all $1\leq p\leq\infty$. \endcase \case{Case\/ {\rm2:} $b'\leq 1/2$} We have $P(3/4)\leq\delta<1$ with $\delta$ depending only on $d$ for otherwise (3.7) applied to $1-P$ and $p=\infty$ would show that $P$ could not attain the value $0$ at $x=0$. It follows that $|A(y)|\geq 3/4-b'\geq 1/4$, $y\in[\delta,1]$, while $|A(y)|\leq 1$ for all $y\in[0,1]$. Hence (4.2) follows for all $1\leq p\leq\infty$. \endcase We consider now when $Q$ is increasing. We can assume that $Q$ is not a translate of $P$, i.e\., we do not have $P(x)=Q(x+\delta)$ for some $\delta$, for then (4.2) follows trivially. In what follows, $C$ and $\delta$ depend on $d$, and $C$ may depend on $p$. We consider the following cases: \case{Case\/ {\rm3:} $a'\geq 1/4$ and $b'\leq 100$} From (3.7) for $P$ and $p=\infty$, it follows that $P(1/8)\geq\delta$ since otherwise $P$ cannot attain the value $1$ at $x=1$. Hence $|A(y)|\geq a'-1/8\geq1/8$ on $[0,\delta]$. On the other hand $|A(y)|\leq b'$ for all $y\in[0,1]$ and hence (4.2) follows for all $1\leq p\leq\infty$. \endcase Let $z$ be in $\bold X$. Because $E(u,\sdot,\sdot)\equiv0$, Equation (1.5) implies that $$ \int_\Bbb R\Delta uz|^T_0dx=\int_0^T\int_\Bbb R \Delta u(z_t+\phi[u,u^h]z_{xx})\,dx\,dt- E(u^h,z,t), \tag 2.2 $$ where $\Delta u=u-u^h$ and $$ \phi[u,u^h]=\dfrac{\phi(u)-\phi(u^h)}{u-u^h}. $$ Extend $\phi[u,u^h](\cdot,t)=\phi[u,u^h](\cdot,0)$ for negative $t$, and $\phi[u,u^h](\cdot,t)=\phi[u,u^h](\cdot,T)$ for $t>T$. Fix a point $x_0$ and a number $\epsilon>0$. Let $j_\epsilon$ be a smooth function of $x$ with integral $1$ and support in $[-\epsilon,\epsilon]$, and let $J_\delta$ be a smooth function of $x$ and $t$ with integral $1$ and support in $[-\delta,\delta]\times[-\delta,\delta]$; $\delta$ and $\epsilon$ are positive numbers to be specified later. We choose $z=z^{\epsilon\delta}$ to satisfy $$ \aligned &z_t+(\delta+J_\delta*\phi[u,u^h])z_{xx}=0,\qquad x\in\Bbb R,\;0 \leq t\leq T,\\ &z(x,T)=j_\epsilon(x-x_0). \endaligned \tag 2.3 $$ The conclusion of the theorem now follows from (2.1) and the fact that $$ |j_\epsilon*\Delta u(x_0,t)-\Delta u(x_0,t)|\leq C\epsilon^\alpha, $$ which follows from Assumption 2. \qquad\qed \enddemo \example{Example\/ {\rm 1}} This is an example of an example. \endexample \remark{Remark\/ {\rm 1}} Examples are set the same as definitions in some styles, and the same as proofs in others. What convention does this style follow? \endremark Sometimes you want to include a figure, as in Fig.~1. \topinsert \def\Bif{{\bf if\/ }}\def\Bwhile{{\bf while\/ }}\def\Belse{{\bf else\/ }} \settabs\+\qquad&\qquad&\qquad&\qquad&\cr \+\smc Tree Partition Algorithm \{\cr \+&Let stack size denote the number of nodes in the\cr \+&&subtrees stored temporarily on the local stack\cr \+&pop I from global stack\cr \+&set stack size := 0\cr \+&\Bwhile (stack size $\leq$ max size and stack size + I$\rightarrow$tree size $>$ 3 (max size)) \{\cr \+&&process I as an interior node\cr \+&&let min tree be the smaller of the subtrees of the two children of I\cr \+&&let max tree be the larger of the subtrees of the two children of I\cr \+&&\Bif (min tree$\rightarrow$tree size + stack size $>$ 3 (max size)) \{\cr \+&&&push min tree onto the global stack\cr \+&&\} \Belse \{\cr \+&&&push min tree onto the local stack\cr \+&&&set stack size := stack size + min tree$\rightarrow$tree size\cr \+&&\}\cr \+&&set I := max tree\cr \+&\}\cr \+&\Bif (I$\rightarrow$tree size + stack size $>$ 3 (max size)) \{\cr \+&&push I onto the global stack\cr \+&\} \Belse \{\cr \+&&push I onto the local stack\cr \+&\}\cr \+&Process all subtrees on the local stack\cr \+\}\cr \botcaption{Fig.~1} Tree partition algorithm Tree partition algorithm Tree partition algorithm Tree partition algorithm Tree partition algorithm Tree partition algorithm Tree partition algorithm.\endcaption \endinsert We finish with a table of all SIAM journals. \midinsert \topcaption{Table 1}{SIAM journal acronyms and titles}\endcaption \settabs\+\indent&Acronym\indent&Title&\cr \hbox to \hsize{\hrulefill} \+&Acronym&Title&\cr \hbox to \hsize{\hrulefill} \+&SINUM&SIAM Journal on Numerical Analysis&\cr \+&SIREV&SIAM Review&\cr \+&SIMA&SIAM Journal on Mathematical Analysis&\cr \+&SIMAX&SIAM Journal on Matrix Analysis and Applications&\cr \+&SICOMP&SIAM Journal on Computing&\cr \+&SISC&SIAM Journal on Scientific Computing&\cr \+&SIOPT&SIAM Journal on Optimization&\cr \+&SIAP&SIAM Journal on Applied Mathematics&\cr \+&SICON&SIAM Journal on Control and Optimization&\cr \+&SIDMA&SIAM Journal on Discrete Mathematics&\cr \+&TVP&Theory of Probability and Its Applications&\cr \hbox to \hsize{\hrulefill} \endinsert \Refs \ref \no 1 \by L. A. Caffarelli and A. Friedman \paper Regularity of the free boundary of a gas flow in an $n$-dimensional porous medium \jour Indiana Math. J. \vol 29 \yr 1980 \pages 361--391 \endref \ref\no 2 \by R. DeVore and B. Lucier \paper High order regularity for solutions of the inviscid Burgers equation \inbook Nonlinear Hyperbolic Problems \procinfo Proceedings of an Advanced Research Workshop, Bordeaux, France, June 1988 \bookinfo Lecture Notes in Mathematics \vol 1402 \eds C. Carasso, P. Charrier, B. Hanouzet, and J.-L. Joly \yr 1989 \publ Springer-Verlag \publaddr New York \pages 147--154 \endref \ref \no 3 \bysame \paper Wavelets \jour Acta Numerica \yr 1992 \ed A. Iserles \publ Cambridge University Press \publaddr New York \pages 1--56 \endref \ref \no 4 \by R. A. DeVore and V. A. Popov \paper Interpolation spaces and non-linear approximation \inbook Function Spaces and Applications \bookinfo Lecture Notes in Mathematics \procinfo Proceedings of the US--Swedish Seminar held in Lund, Sweden, June 15--21, 1986 \vol 1302 \eds M. Cwikel, J. Peetre, Y. Sagher, and H. Wallin \publ Springer-Verlag \publaddr New York \yr 1988 \pages 191--205 \endref \ref \no 5 \by R. A. DeVore and X. M. Yu \paper Nonlinear $n$-widths in Besov spaces \inbook Approximation Theory VI: Vol. 1 \eds C. K. Chui, L. L. Schumaker, and J. D. Ward \publ Academic Press \publaddr New York \yr 1989 \pages 203--206 \lang In Russian \endref \ref \no 6 \by K. Hollig and M. Pilant \paper Regularity of the free boundary for the porous medium equation \paperinfo MRC Tech. Rep. 2742 \endref \ref \no 7 \by J. Jerome \book Approximation of Nonlinear Evolution Systems \publ Academic Press \publaddr New York \yr 1983 \endref \ref \no 8 \manyby R. J. LeVeque \paper Convergence of a large time step generalization of Godunov's method for conservation laws \jour Comm. Pure Appl. Math. \vol 37 \yr 1984 \pages 463--478 \endref \ref\no 9 \by O. Rioul and M. Vetterli \paper Wavelets and signal processing \jour IEEE Signal Processing Magazine \vol 8 \issue 4 \yr 1991 \toappear \endref \endRefs \enddocument nlinear Evolution Systems \publ Academic Press \publaddr New Yoramstexsi.sty 664 144 7 55671 6124605370 6526 %% This is amstexsiam.sty, the AmS-TeX SIAM style file. This file %% should be accompanied by the sample paper, siamsamp.tex, and the %% documentation file, siamdoc.tex. %% %% This is version 2.1 of November 1995. %% %% Authors: %% %% Prof. Bradley Lucier %% Department of Mathematics %% 1395 Mathematical Sciences Building %% Purdue University %% West Lafayette, IN 47907-1395 %% lucier@math.purdue.edu %% %% Prof. Douglas N. Arnold %% Department of Mathematics %% Penn State University %% University Park, PA 16802 %% dna@math.psu.edu %% %% Copyright 1988, 1990, 1993, 1995 by Bradley Lucier. All rights reserved. %% You have permission to copy this file, to use it as input to other TeX %% files, and to modify it as necessary to allow it to run at your site. %% In the interest of maintaining a consistent revision history, if you %% make changes, additions, or deletions to this file, you must indicate %% how the changes affected the original file, so that the original file %% can be reconstructed if necessary. %% %% This is an official SIAM style file for AmSTeX, version 2.1. It %% requires amsppt.sty, version 2.1a. Later versions are probably %% acceptable. This style file has been used to produce papers for %% SIAM journals that have been totally acceptable to SIAM production %% editors. %% %% This style file is unsupported. To report bugs, suggest changes, %% or make other comments, contact the first named author. %% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % RCS information: $Revision: 1.12 $, $Date: 95/11/20 13:11:59 $. \def\filename{amstexsiam.sty} \def\fileversion{2.1} \def\filedate{November 1995} \message{version \fileversion\space(\filedate):} \def\styname{AMSTEXSIAM}\def\styversion{2.1} % % We save the catcode of @ before we call amsppt.sty, since amsppt.sty % redefines \filename. % \expandafter\xdef\csname\filename\endcsname{% \catcode`\noexpand\@=\the\catcode`\@ \expandafter\gdef\csname\filename\endcsname{% \fileversion\space(\filedate)}} % \input amsppt.sty % \catcode`\@=11 % % Change the crucial dimensions. We use 20pt instead of 2 em for % the \parindent, because at one point we want to set it to the same thing % in \eightpoint, and 2 em in \eightrm is smaller than 2 em in \tenrm. % I removed every instance of em in this style file---it was used in the % setting of item numbers in rosters, and in the indentation of references. % I substituted 10 pts for it. % \def\pagewidth#1{\hsize#1\captionwidth@\hsize} \pagewidth{31 pc} \hcorrection{0.6666666 in} \pageheight{49.5 pc} \vcorrection{0.3333333 in} \topskip 12pt \parindent 20pt \parskip 0 pt % % change the space above and below displayed equations to 6 + 3 pts. % SIAM style is 6 pts. I also added a call to \rm to override the % call to \eightrm in \eightpoint in case anyone ever wants to redefine the % text fonts for \eightpt \addto\tenpoint{\abovedisplayskip 6\p@ plus 3\p@ \belowdisplayskip\abovedisplayskip \abovedisplayshortskip 0 \p@ plus 3\p@ \belowdisplayshortskip\belowdisplayskip} \addto\eightpoint{\abovedisplayskip 6\p@ plus 3\p@ \belowdisplayskip\abovedisplayskip \abovedisplayshortskip 0 \p@ plus 3\p@ \belowdisplayshortskip\belowdisplayskip\rm} % % various amsppt macros are not to be used in the amstexsiam style file % \def\taboo@#1{\def#1{% \errmessage{Do not use \string#1 in the amstexsiam style; see the instructions.}}} \taboo@\thanks\taboo@\endthanks % use the title footnote. \taboo@\preaffil\taboo@\affil\taboo@\endaffil % use the author footnotes \taboo@\address\taboo@\endaddress % use the author footnotes \taboo@\predate\taboo@\date\taboo@\enddate % use the title footnote. \taboo@\email\taboo@\endemail % use the author footnotes % % Changes to the topmatter. (Differences refer to amsppt.sty, version 2.1a) % % We don't increase the line spacing in the title, we don't uppercase, % we record the depth of the last line for use in \endtopmatter. % \newdimen\titledepth@ \def\title#1\endtitle{\global\setbox\titlebox@ \vtop{\bgroup\tenpoint\bf\raggedcenter@ #1\endgraf\global\titledepth@\prevdepth\egroup}\relaxnext@} % % \author uses small caps, otherwise is like title. % \newdimen\authordepth@ \def\author#1\endauthor{\global\setbox\authorbox@ \vtop{\bgroup\eightpoint\smc\raggedcenter@ #1\endgraf\global\authordepth@\prevdepth\egroup}\relaxnext@} % % Abstract: don't change the left and right skips, do indent, % don't put the thing in displayed math, change the % font from small cap to bold for "Abstract". Remember the depth of % the last line in abstract for \endtopmatter. % \newdimen\abstractdepth@ \def\abstract{\let\savedef@\abstract \def\abstract{\let\abstract\savedef@ \setbox\abstractbox@\vtop\bgroup \def\envir@end{\endabstract} \def\usualspace{\enspace}\eightpoint\indent \frills@{{\bf Abstract.\enspace}}}% \nofrillscheck\abstract} \def\endabstract{\endgraf\global\abstractdepth@\prevdepth\unskip\egroup} % % Add keywords and subject classifications just like the abstract. % \def\prekeywords{} \newbox\keywordsbox@ \newdimen\keywordsdepth@ \def\keywords{\let\savedef@\keywords \def\keywords{\let\keywords\savedef@ \setbox\keywordsbox@\vtop\bgroup \def\envir@end{\endkeywords} \def\usualspace{\enspace}\eightpoint\indent \frills@{{\bf Key words.\enspace}}}% \nofrillscheck\keywords} \def\endkeywords{\endgraf\global\keywordsdepth@\prevdepth\unskip\egroup} \def\presubjclass{} \newbox\subjclassbox@ \newdimen\subjclassdepth@ \def\subjclass{\let\savedef@\subjclass \def\subjclass{\let\subjclass\savedef@ \setbox\subjclassbox@\vtop\bgroup \def\envir@end{\endsubjclass} \def\usualspace{\enspace}\eightpoint\indent \frills@{{\bf AMS subject classifications.\enspace}}}% \nofrillscheck\subjclass} \def\endsubjclass{\endgraf\global\subjclassdepth@\prevdepth\unskip\egroup} % % Amazingly enough, we get the spacing perfectly correct; however, if % any one part of the topmatter should need to cross a page boundary, % then we are in trouble, since we leave each part of the topmatter in a % \vbox, and things will have to be set by hand. (amsppt.sty has the same % problem if the abstract should cross a page boundary.) % After adding each part of the topmatter % we change \prevdepth to reflect the depth of the last line of each part. % \outer\def\endtopmatter{\add@missing\endabstract \add@missing\endkeywords\add@missing\endsubjclass \pretitle \begingroup % to localize variant topskip \topskip 3pc\advance\topskip by -\ht\titlebox@ \null\unvbox\titlebox@ \prevdepth\titledepth@ \endgroup \preauthor \ifvoid\authorbox@\else \baselineskip 18 pt\advance\baselineskip by -\ht\authorbox@ \null\unvbox\authorbox@\prevdepth\authordepth@\fi \preabstract \ifvoid\abstractbox@\else \baselineskip 24 pt\advance\baselineskip by -\ht\abstractbox@ \null\unvbox\abstractbox@\prevdepth\abstractdepth@\fi \prekeywords \ifvoid\keywordsbox@\else \baselineskip 20 pt\advance\baselineskip by -\ht\keywordsbox@ \null\unvbox\keywordsbox@\prevdepth\keywordsdepth@\fi \presubjclass \ifvoid\subjclassbox@\else \baselineskip 20 pt\advance\baselineskip by -\ht\subjclassbox@ \null\unvbox\subjclassbox@\prevdepth\subjclassdepth@\fi \ifvoid\tocbox@\else\vskip1.5pcplus.5pc\unvbox\tocbox@\fi \prepaper \vskip 8 pt % The first line of the paper body will be set with 12 pt % baselines, so this extra 8 points will make it 20 pts total. \tenpoint\relax } % % Simplify it, since we don't add a lot of things at the end of the % document like amsppt does. % \outer\def\enddocument{\par% \par will do a runaway check for \endref \add@missing\endRefs \add@missing\endroster \add@missing\endproclaim \add@missing\enddefinition \add@missing\enddemo \add@missing\endremark \add@missing\endexample \vfill\supereject\end} % % We add a thin space between the footnotemark and the footnotetext. % % We also undo \raggedcenter@ inside the foonote. % \def\undoraggedcenter@{\leftskip\z@\rightskip\z@\parfillskip0ptplus1fil% \parindent20pt\spaceskip0\p@\xspaceskip0\p@\pretolerance100% \tolerance200\exhyphenpenalty50\hyphenpenalty50} \def\makefootnote@#1#2{\insert\footins {\interlinepenalty\interfootnotelinepenalty \eightpoint\undoraggedcenter@\splittopskip\ht\strutbox\splitmaxdepth\dp\strutbox \floatingpenalty\@MM\leavevmode{#1}\,\footstrut \ignorespaces#2\unskip\lower\dp\strutbox \vbox to\dp\strutbox{}}} % % The skip before a heading is 6 pts, no stretchiness % \subheadskip 6 pt % % % the amsppt monograph style has the same indentation rules as the SIAM % style. % \let\varindent@\indent % % Proclaims use small caps. % \def\proclaimheadfont@{\smc} % % Now we have to change a lot of things because Spivak put \medskipamounts % before and after proclaims, etc. Perhaps he should have defined and used % \varskipamount@ like varindent@ and then we would have had to change only % one line. (Hint, hint!) To keep things simple, I just changed the % \medskipamounts to 0pt in the following, even though it doesn't make % total sense to do so. % % Next line needed since it was previously defined outer. % \let\proclaim\relax \outer\def\proclaim{% \let\savedef@\proclaim \let\proclaim\relax \add@missing\endroster \add@missing\enddefinition \add@missing\endproclaim \envir@stack\endproclaim \def\proclaim##1{\restoredef@\proclaim \penaltyandskip@{-100}{0pt}\varindent@ \def\usualspace{{\proclaimheadfont@\enspace}}\proclaimheadfont@ \ignorespaces##1\unskip\frills@{.\enspace}% \it\ignorespaces}% \nofrillscheck\proclaim} \def\endproclaim{\revert@envir\endproclaim \par\rm \penaltyandskip@{55}{0pt}} \def\remark{\let\savedef@\remark \let\remark\relax \add@missing\endroster \add@missing\endproclaim \envir@stack\endremark \def\remark##1{\restoredef@\remark \penaltyandskip@\z@{0pt} {\def\usualspace{{\remarkheadfont@\enspace}}% \varindent@\remarkheadfont@\ignorespaces##1\unskip \frills@{.\enspace}}\rm \ignorespaces}\nofrillscheck\remark} \def\definition{\let\savedef@\definition \let\definition\relax \add@missing\endproclaim \add@missing\endroster \add@missing\enddefinition \envir@stack\enddefinition \def\definition##1{\restoredef@\definition \penaltyandskip@{-100}{0pt} {\def\usualspace{{\proclaimheadfont@\enspace}}% \varindent@\proclaimheadfont@\ignorespaces##1\unskip \frills@{.\proclaimheadfont@\enspace}}% \rm \ignorespaces}% \nofrillscheck\definition} \def\enddefinition{\revert@envir\enddefinition\par} \def\enddemo{\par\revert@envir\enddemo \endremark} % % Examples are set the same as remarks in the SIAM style. % \def\example{\DN@{\ifx\next\nofrills \DN@####1####2{\remark####1{####2}\envir@stack\endexample \ignorespaces}% \else \DN@####1{\remark{####1}\envir@stack\endexample\ignorespaces}% \fi \next@}% \FN@\next@} \def\endexample{\par\revert@envir\endexample \endremark} % % We will add a \case ... \endcase macro % \def\case{\DN@{\ifx\next\nofrills \DN@####1####2{\remark####1{####2}\envir@stack\endcase \ignorespaces}% \else \DN@####1{\remark{####1}\envir@stack\endcase\ignorespaces}% \fi \next@}% \FN@\next@} \def\endcase{\par\revert@envir\endcase \endremark} % % Remarks, proofs, etc. have the first word in italic. % \def\remarkheadfont@{\it} % % Redefine \qed % \def\qed{\ifhmode\unskip\nobreak\fi\ifmmode\ifinner\else\hskip5\p@\fi\fi \hbox{\hskip25\p@ minus 10 \p@\hbox{\vrule width .6\p@\vbox{\hrule width 4\p@ height .6\p@\vskip 6.2\p@\hrule width 4\p@ height .6\p@}\unskip\vrule width .6\p@}\hskip\p@}} % % We should deal somewhat with table and figure legends. Unfortunately, % they differ in several key respects from the amsppt style. Tables have % "Table 1" in small caps centered on first line of caption, table % description centered in italics on following lines. Legend has "Fig. 1." % in smc followed by description in italic. % \def\topcaption#1#2\endcaption{% \eightpoint{\dimen@\hsize \advance\dimen@-\captionwidth@ \it\raggedcenter@ \advance\leftskip.5\dimen@ \rightskip\leftskip {\captionfont@#1}% \if\notempty{#2}\\\ignorespaces#2\fi \endgraf}\nobreak\smallskip} \def\botcaption#1#2\endcaption{% \nobreak\medskip \eightpoint\setboxz@h{\captionfont@#1\if\notempty{#2}.\enspace\it#2\fi}% {\dimen@\hsize \advance\dimen@-\captionwidth@ \leftskip.5\dimen@ \rightskip\leftskip \noindent \ifdim\wdz@<\captionwidth@ \hfil{\captionfont@#1}\if\notempty{#2}.\enspace\it#2\fi\hfil \else \par{\captionfont@#1}% \if\notempty{#2}.\enspace\it#2\fi\endgraf\fi}} \def\@ins{\par\begingroup\def\vspace##1{\vskip##1\relax}% \def\captionwidth##1{\captionwidth@##1\relax}% \setbox\z@\vbox\bgroup} % start a \vbox % % We remove the smallskip before rosters and change them to not use hang % indents. % \rosteritemwd20pt \newdimen\rosteritemindent@ \rosteritemindent@-20pt \def\roster{% \envir@stack\endroster \global\advance\rosteritemindent@ by 20 pt \edef\leftskip@{\leftskip\the\leftskip}% \relaxnext@ \rostercount@\z@ \def\item{\FN@\rosteritem@}% \DN@{\ifx\next\runinitem\let\next@\nextii@\else \let\next@\nextiii@\fi\next@}% \DNii@\runinitem% {\unskip% \DN@{\ifx\next[\let\next@\nextii@\else \ifx\next"\let\next@\nextiii@\else\let\next@\nextiv@\fi\fi\next@}% \DNii@[####1]{\rostercount@####1\relax \enspace\therosteritem{\number\rostercount@}~\ignorespaces}% \def\nextiii@"####1"{\enspace{\rm####1}~\ignorespaces}% \def\nextiv@{\enspace\therosteritem1\rostercount@\@ne~}% \par@\firstitem@false% \FN@\next@}% \def\nextiii@{\par\par@ \penalty\@m \firstitem@true} \FN@\next@} \def\rosteritem@{\iffirstitem@\firstitem@false \else\par\vskip-\parskip\fi \leftskip\rosteritemindent@\noindent \DNii@[##1]{\rostercount@##1\relax\itembox@}% \def\nextiii@"##1"{\def\therosteritem@{\rm##1}\itembox@}% \def\nextiv@{\advance\rostercount@\@ne\itembox@}% \def\therosteritem@{\therosteritem{\number\rostercount@}}% \ifx\next[\let\next@\nextii@\else\ifx\next"\let\next@\nextiii@\else \let\next@\nextiv@\fi\fi\next@} % % We change itembox to do what it should % \def\itembox@{\hskip\parindent\hbox to \rosteritemwd{\hss\kern\z@\therosteritem@\enspace}\ignorespaces} % % We change the default roster indent to 20 pt (from 16), and remove the % "\global\rosteritemwd16pt" from \endroster. This allows us to use % nested rosters in an easy way. % \def\endroster{\relaxnext@\revert@envir\endroster\par \global\advance\rosteritemindent@ by -20 pt \leftskip@\penalty-50 \DN@{\ifx\next\Runinitem\let\next@\relax\else\nextRunin@false \let\item\plainitem@\ifx\next\par\DN@\par{\everypar \expandafter{\the\everypartoks@}}\else\DN@{\noindent\everypar \expandafter{\the\everypartoks@}}\fi\fi\next@}\FN@\next@} % % References: % % We change the word "REFERENCES" to 8 pt roman, and add 28 pt skip % and a \goodbreak above "REFERENCES" and 8 pt skip and \nobreak below. % \let\Refs\relax \outer\def\Refs{\add@missing\endroster \add@missing\endproclaim \let\savedef@\Refs \let\Refs\relax % because of \outer-ness \def\Refs##1{\restoredef@\Refs \goodbreak\vskip 28 pt \hbox to\hsize{\hfil\refsfont@\rm \ignorespaces##1\unskip\hfil}\nobreak \vskip 8pt \begingroup\def\envir@end{\endRefs}\refsfont@\sfcode`\.\@m }% \nofrillscheck{\csname Refs\expandafter\endcsname \frills@{{REFERENCES}}}} % % Author names are in small caps. % \def\by{\makerefbox\by\bybox@\smc} % % When we redefine \by, we have to re`let' \manyby. % \let\manyby\by % % Removed the \thinspace between the rule and the comma, raised % it by a point, and made it .2 pts thick. % \def\bysame{\by\hbox to 30pt{\leaders\hrule height 1.2pt depth -1pt\hfill}} % % \ed and \eds are kind of funny; the \edbox@ is used as the \bybox@ % if there is no \bybox@; the instructions will have to say to use % \ed or \eds after \by in each reference. % \def\ed{\makerefbox\ed\edbox@{\ifvoid\bybox@\smc\fi}} \def\eds{\gdef\edtext{eds.}\makerefbox\eds\edbox@{\ifvoid\bybox@\smc\fi}} % % Paper names are in italics. % \def\paper{\makerefbox\paper\paperbox@\it} % % The volume number is always roman in the SIAM style. % \def\vol{\makerefbox\vol\volbox@\empty} % % The SIAM style does not use "no." before the issue, or v. before % the volume, even in a book. % \def\defaultreftexts{\gdef\edtext{ed.}\gdef\pagestext{pp.}} % % second and following lines in references are indented 20 pt more than first. % \def\ref{\par \begingroup \def\envir@end{\endref}% \advance\refindentwd 20 pt\noindent\hangindent\refindentwd \advance\refindentwd-20 pt \def\par{\add@missing\endref}% \global\let\nofrills@list\empty \refbreaks \procpaper@false \book@false \def\curbox{\z@}\setbox\z@\vbox\bgroup } % % We change the reference styles for keys and numbers to be the same; % the number contained in square brackets followed by an enspace. % \def\refstyle#1{\uppercase{% \if#1A\relax \def\keyformat##1{\hfil[##1]\enspace}% \else\if#1B\relax \def\keyformat##1{\aftergroup\kern \aftergroup-\aftergroup\refindentwd}% \refindentwd\parindent \else\if#1C\relax \def\keyformat##1{\hfil[##1]\enspace}% \fi\fi\fi}% end of \uppercase } % % Here I am at a loss. The early, inscrutable part of endref@ is, of % course, from amsppt 2.1a, so see amsppt.doc for the documentation. % The latter part (Case 1: etc.), just tries to put things into % their correct place with their correct spacing and surrounding punctuation % and words (ed., etc.). The changes from amsppt to siam are too numerous to % list; again, compare this code to amsppt.doc % \def\endref@{% \keyhook@ \def\nofrillscheck##1{% \def\do####1{\ifx##1####1\let\frills@\eat@\fi}% \let\frills@\identity@ \nofrills@list}% \ifvoid\bybox@ \ifvoid\edbox@ \else\setbox\bybox@\hbox{\unhbox\edbox@\breakcheck \nofrillscheck\edbox@\frills@{\smc, \edtext}\refbreak@}\fi \fi \ifvoid\keybox@\else\hbox to\refindentwd{% \keyformat{\unhbox\keybox@}}\fi \commaunbox@\morerefbox@ \ppunbox@\empty\empty\bybox@\empty \ifbook@ % Case 1: \book etc. \commaunbox@\bookbox@ \commaunbox@\procinfobox@ \commaunbox@\bookinfobox@ \ppunbox@\empty\space\volbox@\empty \ppunbox@,\space\edbox@{, \edtext}% \commaunbox@\publbox@ \commaunbox@\publaddrbox@ \commaunbox@\yrbox@ \else \commaunbox@\paperbox@ \commaunbox@\paperinfobox@ \ifprocpaper@ % Case 2: \paper ... \inbook \ppunbox@,{ in }\bookbox@\empty \commaunbox@\procinfobox@ \commaunbox@\bookinfobox@ \ppunbox@\empty\space\volbox@\empty \ppunbox@,\space\edbox@{, \edtext}% \commaunbox@\publbox@ \commaunbox@\publaddrbox@ \commaunbox@\yrbox@ \else % Case 3: \paper ... \jour \commaunbox@\jourbox@ \commaunbox@\volbox@ \commaunbox@\issuebox@ \ppunbox@\empty{ (}\yrbox@)% \commaunbox@\publbox@ \commaunbox@\publaddrbox@ \fi \fi \ppunbox@,{ \pagestext~}\pagesbox@\empty \commaunbox@\finalinfobox@ \commaunbox@\miscnotebox@ \finalpunct\ppunbox@\empty{ (}\langbox@)% \defaultreftexts } % % \iffirstpage@ is defined in amsppt; we make sure it is true. % \firstpage@true % % We want to avoid people setting papers with the SIAM slug by default. % We introduce a new macro \accepted that will set a flag to do this. % \newif\ifaccepted@ \def\firstpageno#1{\gdef\firstpageno@{#1}} \def\lastpageno#1{\gdef\lastpageno@{#1}} \def\journalname#1{\gdef\journalname@{#1}} \def\issuevolume#1{\gdef\issuevolume@{#1}} \def\issuenumber#1{\gdef\issuenumber@{#1}} \def\issuemonth#1{\gdef\issuemonth@{#1}} \def\placenumber#1{\gdef\placenumber@{#1}} \def\issueyear#1{\gdef\issueyear@{#1}} \def\shorttitle#1{\gdef\shorttitle@{\lowercase{#1}}} \def\shortauthor#1{\gdef\shortauthor@{\lowercase{#1}}} \def\accepted{\accepted@true \journalname{XXXXXXXXXXXXXXXXXX}% \firstpageno{1}% \lastpageno{XX}% \issuevolume{0}% \issuenumber{0}% \issuemonth{XXXXXXX}% \placenumber{000}% \issueyear{19XX}% } \shortauthor{} \shorttitle{} \accepted@false \output={\output@} % % The new output@, taken almost verbatim from amstexsiam, version 1.*; % I changed \oddhead and \evenhead to \shorttitle and \shortauthor---users % shouldn't really have to check whether the title is on odd or even pages. % \def\output@{% \iffirstpage@\global\firstpage@false\shipout \vbox{\ifaccepted@\global\pageno=\firstpageno@\vbox to 2 pc {\baselineskip=8pt\vss \hbox to \hsize{\sixrm\journalname@\hfill{\textfont\tw@\sixsy \copyright}\ \issueyear@\ Society for Industrial and Applied Mathematics} \hbox to \hsize{\sixrm Vol.~\issuevolume@, No.~\issuenumber@, pp.~\firstpageno@--\lastpageno@, \issuemonth@\ \issueyear@\hfill \placenumber@}\vskip-\prevdepth\vskip 8 pt}\else\vbox {\vrule height 2 pc width 0 pt}\fi\nointerlineskip \vbox to\vsize {\boxmaxdepth=\maxdepth \pagecontents}\nointerlineskip\vbox to 16 pt{\vss \hbox to \hsize{\eightpoint\hfill\number\pageno\hfill}}}% \else \shipout\vbox{\vbox to 2 pc{\baselineskip=12pt \vss\ifodd\pageno \hbox to \hsize{\tenpoint\relaxnext@\phantom{\number\pageno}\hfil {\smc\frenchspacing{\shorttitle@}}\hfil\number\pageno} \else \hbox to \hsize{\tenpoint\number\pageno\hfil{\smc\frenchspacing{\shortauthor@}}\hfil\relaxnext@ \phantom{\number\pageno}}\fi\vskip-\prevdepth\vskip 12 pt}\nointerlineskip% \vbox to\vsize {\boxmaxdepth=\maxdepth \pagecontents}}% changed to resemble TeXBook, p255 PCD \fi \global\advance\pageno\@ne \ifnum\outputpenalty>-\@MM\else\dosupereject\fi} \def\SIMAF{\journalname{{\sixrm SIAM J. M{\fiverm ATH.} F{\fiverm OOL.}}}}% for sample paper \def\SIAP{\journalname{{\sixrm SIAM J. A{\fiverm PPL.} M{\fiverm ATH.}}}} \def\SICOMP{\journalname{{\sixrm SIAM J. C{\fiverm OMPUT.}}}} \def\SICON{\journalname{{\sixrm SIAM J. C{\fiverm ONTROL} {\fiverm AND} O{\fiverm PTIMIZATION}}}} \def\SIDMA{\journalname{{\sixrm SIAM J. D{\fiverm ISC.} M{\fiverm ATH.}}}} \def\SIMA{\journalname{{\sixrm SIAM J. M{\fiverm ATH.} A{\fiverm NAL.}}}} \def\SIMAX{\journalname{{\sixrm SIAM J. M{\fiverm ATRIX} A{\fiverm NAL.} A{\fiverm PPL.}}}} \def\SINUM{\journalname{{\sixrm SIAM J. N{\fiverm UMER.} A{\fiverm NAL.}}}} \def\SIOPT{\journalname{{\sixrm SIAM J. O{\fiverm PTIMIZATION}}}} \def\SISC{\journalname{{\sixrm SIAM J. S{\fiverm CI.} C{\fiverm OMPUT.}}}} \def\SIREV{\journalname{{\sixrm SIAM R{\fiverm EVIEW}}}} %\def\TVP{\journalname{{Theory of Probability and its Applications}}} % but the slug is so different for this journal that I won't include it. % % From amstexsiam version 1.* % \def\footnoterule{\hrule width 36 pt height .2 pt\vskip 2.8\p@} \skip\footins=12 pt plus 18 pt minus 6 pt % % We use \key in references by default, with a two digit key width. % \refstyle{A} \widestnumber\key{00} % % Centered tags on splits seems to be the default. % \CenteredTagsOnSplits % % The multlinegap@ is 0pt for the SIAM style. % \multlinegap@0pt % % Every paper will have at least one bold footnotemark (in the title), % so we load bold. \loadbold % % Start in 10 pt text. % \tenpoint % % Reset the catcode of @ and reset amstexsiam.sty to be the version number. % \csname amstexsiam.sty\endcsname % % Make sure that we endinput here so following lines are not interpreted % by TeX % \endinput %% %% End of file `amstexsiam.sty' plits seems to be the default. % \CenteredTagsOnSplits % % The multlinsiamdoc.tex 664 144 7 26075 6124605406 6265 %% This is siamdoc.tex, the documentation file for the AmSTeX SIAM %% style file. This file should be accompanied by the style file %% itself, amstexsiam.sty, and the sample paper, siamsample.tex. %% %% This is version 2.1 of March 1995. %% %% Authors: %% %% Prof. Bradley Lucier %% Department of Mathematics %% 1395 Mathematical Sciences Building %% Purdue University %% West Lafayette, IN 47907-1395 %% lucier@math.purdue.edu %% %% Prof. Douglas N. Arnold %% Department of Mathematics %% Penn State University %% University Park, PA 16802 %% dna@math.psu.edu %% %% This file should be typeset with Plain TeX, not AmS-TeX or LaTeX. %% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % RCS information: $Revision: 1.5 $ $Date: 95/03/03 13:00:26 $ \catcode`\@=11 \ifx\amstexloaded@\undefined\relax\else \W@{^^JTypeset this file with plain TeX, not AmSTeX.^^J}\end\fi \catcode`\@=\active \magnification=\magstephalf \tolerance=1000 \def\beginverbatim{\par\begingroup\setupverbatim\doverbatim} {\catcode`\|=0 \catcode`\\=12 % | is temporary escape character |obeylines|gdef|doverbatim^^M#1\endverbatim{#1|endgroup}} \def\setupverbatim{\tentt \obeylines \uncatcodespecials \obeyspaces} {\obeyspaces\global\let =\ } % let active space = control space \def\uncatcodespecials{\def\do##1{\catcode`##1=12}\dospecials} {\catcode`\^^M=13 \gdef\gobblecr{\ifnextchar {\gobble}{\ignorespaces}}} {\catcode`\ =\active\gdef\vobeyspaces{\catcode`\ \active \let \xobeysp}} \def\xobeysp{\leavevmode{} } \begingroup \catcode `|=0 \catcode `[= 1 \catcode`]=2 \catcode `\{=12 \catcode `\}=12 \catcode`\\=12 |gdef|@xverbatim#1\end{verbatim}[#1|end[verbatim]] |gdef|@sxverbatim#1\end{verbatim*}[#1|end[verbatim*]] |endgroup \def\makeother#1{\catcode`#112\relax} \def\v{\begingroup \tt \uncatcodespecials \averb} \def\sverb#1{\def\tempa ##1#1{##1\endgroup}\tempa} \def\averb{\obeyspaces \frenchspacing \sverb} \font\textfontii = cmsy10 \font\eightpt = cmr8 \def\heading#1{\medskip\noindent{\bf #1.\ }} \def\AmSTeX{{\textfontii A}\kern-.1667em\lower.5ex\hbox {\textfontii M}\kern-.125em{\textfontii S}-\TeX} \def\qed{\ifhmode\unskip\nobreak\fi\ifmmode\ifinner\else\hskip5 pt \fi\fi \hbox{\hskip25 pt \hbox{\vrule width .2 pt \vbox{\hrule width 4 pt height .2 pt \vskip 6.2 pt \hrule width 4 pt height .2 pt }\unskip\vrule width .2 pt }\hskip 0pt }} \centerline{\bf USING THE \AmSTeX\ SIAM STYLE FILE} \medskip {\eightpt\centerline{BRADLEY J. LUCIER and DOUGLAS N. ARNOLD}} \bigskip The \AmSTeX\ SIAM style file, amstexsiam.sty, is intended to help authors to produce a paper that is typographically acceptable for publication in a SIAM journal. Beginning with version 2, amstexsiam.sty inputs amsppt.sty and then makes modifications as necessary. Version 2 of amstexsiam.sty works with version 2.1 of \AmSTeX\ and version 2.1a of amsppt.sty, and should work with latter versions. This brief guide assumes familiarity with \AmSTeX\ and amsppt, as documented in {\it The Joy of \TeX\ } by Michael Spivak. Most of the points introduced below are illustrated in the nonsense paper {\it A sample paper, with a rather long title, to illustrate the \AmSTeX\ SIAM style}. \heading{Publication information} When the paper has been accepted, 10 lines similar to these should be place immediately after the \v"documentsyle" line: \medskip \beginverbatim \accepted\SINUM \firstpageno{10} \lastpageno{12} \issuevolume{1} \issuenumber{2} \issuemonth{February} \placenumber{002} \issueyear{1988} \shortauthor{Bradley J. Lucier and Douglas N. Arnold} \shorttitle{A Sample Paper} \endverbatim \medskip\noindent The \v"\accepted" macro should be followed by a control sequence taken from the following table indicating the specific journal. \medskip \settabs\+\indent&Acronym\indent&Title&\cr \+& \v"\SINUM"&SIAM Journal on Numerical Analysis&\cr \+& \v"\SIREV"&SIAM Review&\cr \+& \v"\SIMA"&SIAM Journal on Mathematical Analysis&\cr \+& \v"\SIMAX"&SIAM Journal on Matrix Analysis and Applications&\cr \+& \v"\SICOMP"&SIAM Journal on Computing&\cr \+& \v"\SISC"&SIAM Journal on Scientific Computing&\cr \+& \v"\SIOPT"&SIAM Journal on Optimization&\cr \+& \v"\SIAP"&SIAM Journal on Applied Mathematics&\cr \+& \v"\SICON"&SIAM Journal on Control and Optimization&\cr \+& \v"\SIDMA"&SIAM Journal on Discrete Mathematics&\cr \medskip\noindent The next lines give information for the publication data printed at the top of the first page of the paper and for the running heads. This information consists of the first page number of the article, the last page number of the article, the journal name, the issue volume, the issue number, the month of appearance, the year of appearance, the place of the paper in the issue, the head for even pages (the author(s)'s name(s) shortened if necessary to fit on the headline), and the head for odd pages (the title shortened if necessary). If the \v"\accepted" macro is not present, the publication information will be ignored except for \v"\shortauthor" and \v"\shorttitle", which may be used for page headers. \heading{Top matter} The {\it only}\/ constructions allowed between \v"\topmatter" and \v"\endtopmatter" are, in order, \v"\title" $\dots$ \v"\endtitle", \v"\author" $\dots$ \v"\endauthor", \v"\abstract" $\dots$ \v"\endabstract", \v"\keywords" $\dots$ \v"\endkeywords", and \v"\subjclass" $\dots$ \v"\endsubjclass". (For special situations, \v"\pretitle", \v"\preauthor", \v"\preabstract", \v"\prekeywords", \v"\presubjclass", and \v"\prepaper" can also be defined; see {\it The Joy of \TeX\/}). \heading{Title} Use \v"\title" and \v"\endtitle". Type the title in all caps. The title may have a footnote (at final publication time there will be a footnote indicating when the paper was received). The footnote mark should be a bold asterisk obtained with \v"\footnote[\boldkey*]{Text of footnote.}". All math should be typed using \v"\boldkey" and \v"\boldsymbol" to get bold italic Roman and Greek letters and symbols; see {\it The Joy of \TeX\/}. \heading{Author} Use \v"\author" and \v"\endauthor". Type the author's name in all caps. For multiple authors include the word ``and'' in lowercase before the name of the last author. For three or more authors follow each author's names except the last with a comma. Give the affiliation of each author in a footnote attached to the author's name (before the following comma, if any). (Do {\it not} use the \v"\affil" or \v"\address" macros.) Statements acknowledging support should be contained in the same footnote. The order of footnote symbols in these footnotes is dagger (\dag\thinspace =\thinspace \v"\dag"), double-dagger (\ddag\thinspace =\thinspace \v"\ddag"), section-marker (\S\thinspace = \thinspace\v"\S"), paragraph-marker (\P\thinspace = \thinspace\v"\P"). \heading{Abstract} Use \v"\abstract" and \v"\endabstract". \heading{Keywords} Use \v"\keywords" and \v"\endkeywords". Keywords are separated with commas but not followed by any punctuation. \heading{Subject classifications} Use \v"\subjclass" and \v"\endsubjclass". Subject classifications are separated with commas but not followed by any punctuation. \heading{Footnotes} Use \v"\footnote". Except for the topmatter, discussed above, use numbered footnotes. \heading{Headings} Use \v"\subheading" without ending punctuation. The argument usually begins with the section number followed by a period and then the section name with only the first word capitalized. Very long papers could use \v"\heading" and \v"\subheading". If \v"\heading" is used, start heading name with a section mark (\S\thinspace =\thinspace\v"\S") and the section number followed by a period and the section title with the first letter of each major word capitalized. All math should be typed using \v"\boldkey" and \v"\boldsymbol" to get bold italic Roman and Greek letters and symbols; see {\it The Joy of \TeX\/}. \heading{Equation numbers} Use \v"\tag". \heading{Proclamations} Use \v"\proclaim" $\dots$ \v"\endproclaim" for theorems, lemmas, corollaries, claims, propositions, etc. Use \v"\demo" $\dots$ \v"\enddemo" for proofs, \v"\remark" $\dots$ \v"\endremark" for remarks, \v"\definition" $\dots$ \v"\enddefinition" for definitions, \v"\example" $\dots$ \v"\endexample" for examples, and \v"\case" $\dots$ \v"\endcase" for cases. In each construction the opening control sequence (\v"\proclaim", \v"\demo", $\dots$ ) takes a single argument with no closing punctuation as in \v"\proclaim{Theorem 2.3}" or \v"\demo{Proof}". If remarks, examples, or cases are to be numbered, you must explicitly change to roman type for the number: \v"\remark{Remark \rom{3}}". \heading{Punctuation} All vertical punctuation symbols, i.e.,~), (, :, ;, ?, !, ], and [, and numbers are to be set on roman type, even if in italic text (e.g.,~in proclaims or in the headings of demos, remarks, etc.). One can do this with, for example, the \v"\rom" macro, as \v"{\it Assume that \rom{(1.1)} holds.}" or \v"{\it Fermat's Last Theorem is true \rom(this is new\rom).}", which yield {\it Assume that {\rm (1.1)} holds.} and {\it Fermat's Last Theorem is true {\rm(}this is new\/{\rm)}.} \heading{End-of-proof mark}The symbol signalling the end of a proof is an open box, shown at the end of this paragraph. It is obtained with \v"\qed". Appropriate white space will be supplied automatically.\qed \heading{Lists and sublists} Use \v"\roster" $\dots$ \v"\endroster". Rosters use default labels of the form (1), (2), etc. Subrosters are permitted. Each subroster {\it must}\/ be enclosed in a separate pair of braces. \heading{References} Enclose the reference section with \v"\Refs" $\dots$ \v"\endRefs". References are set just as described in {\it The Joy of \TeX.} Authors' names must be entered as first and possibly middle initial, each followed by a period and a space, followed by the last name. Only the first letter of the last name is capitalized. Use \v"\by" before either \v"\ed" or \v"\eds". \heading{Figures and tables} There is only rudimentary support for figures and tables in the style file. Use \v"\topinsert" $\dots$ \v"\endinsert" or \v"\midinsert" $\dots$ \v"\endinsert" to surround a figure, including the caption at the end as, for example, \v"\botcaption{Fig.~1} This is a figure caption.\endcaption". Use \v"\topinsert" $\dots$ \v"\endinsert" or \v"\midinsert" $\dots$ \v"\endinsert"to surround the table, including the caption at the start as, for example, \v"\topcaption{Table 1}This line describes the table\endcaption". Place rules above and below column headings and at the end of the table using \v"\hbox to \hsize{\hrulefill}". \heading{Table of contents} No special macros are provided to set a table of contents. You can try the macros described in {\it The Joy of \TeX\/}. Otherwise, follow these guidelines. Switch to eight point type (\v"\eightpoint"). Center the word ``CONTENTS'' in caps. Capitalize only the first word of entries. Runover lines align with the start of entries. Place the section number flush left with one em to section title, spaced dots from end of entry to page number, and two ems between the dots and page number. Leave 18--20 points of vertical space, baseline to baseline, to the text above and below. \bye ros described in {\it The Joy of \TeX\/}. Otherwise, follow these guidelines. Switch to eight point type (\v"\eightpoint"). Center the word ``CONTENTS'' in caps. Capitalize only the first word of entries. Runover lines align with the start of entries. Place the section number flush left with one em to section title, spaced dots from end of entry to page number, and two ems between the dots and page number. Leave 18--20 points of vertical spac