# This is a shell archive. # Remove everything above and including the cut line. # Then run the remaining file through sh. On non-Unix # systems, unbundle this file with a text editor. #-----cut here------cut here------cut here------cut here-----# #! /bin/sh # This is a shell archive. Remove anything before this line, then unpack # it by saving it into a file and typing "sh file". To overwrite existing # files, type "sh file -c". You can also feed this as standard input via # unshar, or by typing "sh 'imappt.sty' <<'END_OF_FILE' X% This is the IMA preprint style file for amstex, imappt.sty. X% RCS information: $Revision: 1.7 $, $Date: 90/01/31 11:49:47 $. X% Authors: Bradley J. Lucier and Douglas N. Arnold. X% X% This is a style file for typesetting preprints and reports with AmSTeX, X% version 1.0 or later. It is used by the Institute of Mathematics and X% its Applications for its preprint series. There is a set of X% instructions for using this style file. To obtain a copy, send the X% message X% X% send imappt from siam X% X% to research!netlib or netlib@research.att.com or netlib@ornl.gov, X% or contact X% X% Prof. D. Arnold X% Department of Mathematics X% The Pennsylvania State University X% University Park, PA 16802 X% dna@math.psu.edu X% X% This style file is unsupported. 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\ifnum\pageno=\@ne\shipout\vbox{\vbox to\vsize X {\boxmaxdepth\maxdepth\pagecontents}\baselineskip2pc X \iflogo@\hbox to\hsize{\hfil\eightpoint Typeset by \AmSTeX} X \else\ifdraft@\footertext\fi\fi}\else X \shipout\vbox{\vbox to\vsize X {\boxmaxdepth\maxdepth\pagecontents}\baselineskip2pc X \footertext}% X \fi X \global\advance\pageno\@ne X \ifnum\outputpenalty>-\@MM\else\dosupereject\fi} X\tenpoint X\catcode`\@=\active X\def\styname{imappt}\def\styversion{1.2} END_OF_FILE if test 21581 -ne `wc -c <'imappt.sty'`; then echo shar: \"'imappt.sty'\" unpacked with wrong size! fi # end of 'imappt.sty' fi if test -f 'sample.tex' -a "${1}" != "-c" ; then echo shar: Will not clobber existing file \"'sample.tex'\" else echo shar: Extracting \"'sample.tex'\" \(6219 characters\) sed "s/^X//" >'sample.tex' <<'END_OF_FILE' X\magnification=\magstep1 X\input amstex X\documentstyle{imappt} X%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% X% Macros specific to this paper % X\define\BbbR{{\Bbb R}} % X\define\loner{{L^1(\BbbR)}} % X\define\linfr{{L^\infty(\BbbR)}} % X\define\bvr{{BV(\BbbR)}} % X\define\TV{{\roman {TV}}} % X\define\sdot{\,\cdot\,} % X%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% X\topmatter X\title XA SAMPLE PAPER TO ILLUSTRATE THE \\ XIMA PREPRINT STYLE\footnote"*"{Unlikely to appear.} X\endtitle X\author XBRADLEY J. LUCIER\footnote"\dag"{Department of Mathematics, Purdue University, XWest Lafayette, Indiana 47907. XThe work of the first author was not supported by the XWolf Foundation. X} and XDOUGLAS N. ARNOLD\footnote"\ddag"{Department of Mathematics, University Xof Maryland, College Park, Maryland 20742.} X\endauthor X\abstract{This nonsense paper exemplifies the IMA preprint style file for \AmSTeX\, Ximappt.sty. XThe IMA preprint style file, which Xis used by the Institute for Mathematics Xand its Applications for its preprints, Xis offered as a general purpose preprint style for mathematical papers. XIt is a modification of the amsppt style of XMichael Spivak. This paper also serves to illustrate many of the amstex Xmacros as used with the imappt style file.} X X\keywords{porous medium, interface curves} X\subjclass{65N60} X\endtopmatter X\document X\subheading{1. Introduction} XWe are concerned with numerical approximations to the so-called Xporous-medium equation \cite{5}, X$$ X\alignedat2 X &u_t=\phi(u)_{xx},&&\qquad x\in\BbbR,\quad t>0,\quad\phi(u)=u^m,\quad m>1, X\\ X &u(x,0)=u_0(x),&&\qquad x\in\BbbR. X\endalignedat X\tag 1.1 X$$ XWe assume that the initial data $u_0(x)$ has bounded support, that X$0\leq u_0\leq M$, and that $\phi(u_0)_x\in\bvr$. XIt is well known that a unique solution $u(x,t)$ of (1.1) exists, Xand that $u$ satisfies X$$ X 0\leq u\leq M\text{ and }\TV\phi(u(\,\cdot\,,t))_x\leq\TV\phi(u_0)_x. X\tag 1.2 X$$ XIf the data has slightly more regularity, then this too is satisfied Xby the solution. Specifically, if $m$ is no greater than two and X$u_0$ is Lipschitz continuous, then $u(\,\cdot\,,t)$ is also Lipschitz; Xif $m$ is greater than two and $(u_0^{m-1})_x\in\linfr$, then X$(u(\,\cdot\,,t)^{m-1})_x\in\linfr$ X(see [3]). (This will follow from results presented here, also.) XWe also use the fact that the solution $u$ is H\"older continuous in $t$. X X\subheading{2. $\linfr$ error bounds} XAfter a simple definition, we state a theorem Xthat expresses the error of approximations $u^h$ in Xterms of the weak truncation error $E$. X\proclaim{Definition 2.1}\rm A {\it definition} Xis the same as a theorem set in roman Xtype. X\endproclaim X\proclaim{Theorem 2.1} XLet $\{u^h\}$ be a family of approximate solutions satisfying Xthe following conditions for $0\leq t\leq T$: X\roster X\item For all $x\in\BbbR$ and positive $t$, $0\leq u^h(x,t)\leq M$; X\item Both $u$ and $u^h$ are H\"older--$\alpha$ in $x$ Xfor some $\alpha\in(0,1\wedge 1/(m-1))$; $u^h$ is right continuous in $t$; Xand $u^h$ is H\"older continuous in $t$ on Xstrips $\BbbR\times(t^n,t^{n+1})$, with the set $\{t^n\}$ having no Xlimit points; and X\item There exists a positive function $\omega(h,\epsilon)$ such that: Xwhenever $\{w^\epsilon\}_{0<\epsilon\leq\epsilon_0}$ is a family of functions Xin $\bold X$ for which X{\roster X\item"(a)" there is a sequence of positive numbers $\epsilon$ tending Xto zero, such that for these values of X$\epsilon$, $\|w^\epsilon\|_\infty\leq 1/\epsilon$, X\item"(b)" for all positive X$\epsilon$, $\|w_x^\epsilon(\sdot,t)\|_\loner\leq 1/\epsilon^2$, and X\item"(c)" for all $\epsilon>0$, X$$ X\sup\Sb Xx\in\BbbR\\0\leq t_1,t_2\leq T\endSb X\dfrac{|w^\epsilon(x,t_2)-w^\epsilon(x,t_1)|}{|t_2-t_1|^p}\leq 1/\epsilon^2, X$$ Xwhere $p$ is some number not exceeding $1$, X\endroster} Xthen $|E (u^h,w^\epsilon,T)|\leq\omega(h,\epsilon).$ X\endroster XThen, there is a constant $C=C(m,M,T)$ such that X$$ X\|u-u^h\|_{\infty,\BbbR\times[0,T]}\leq XC\left[ X\sup \left |\int_\BbbR(u_0(x)-u^h(x,0)) w(x,0) \,dx\right|+ X\omega(h,\epsilon)+\epsilon^\alpha\right], X\tag 2.1 X$$ Xwhere the supremum is taken over all $w\in\bold X$. X\endproclaim X\demo{Proof}Let $z$ be in $\bold X$. Because $E(u,\sdot,\sdot)\equiv0$, XEquation (1.5) implies that X$$ X\int_\BbbR\Delta uz|^T_0dx=\int_0^T\int_\BbbR X\Delta u(z_t+\phi[u,u^h]z_{xx})\,dx\,dt- XE(u^h,z,t), X\tag 2.2 X$$ Xwhere $\Delta u=u-u^h$ and X$$ X\phi[u,u^h]=\dfrac{\phi(u)-\phi(u^h)}{u-u^h}. X$$ XExtend $\phi[u,u^h](\cdot,t)=\phi[u,u^h](\cdot,0)$ for negative $t$, and X$\phi[u,u^h](\cdot,t)=\phi[u,u^h](\cdot,T)$ Xfor $t>T$.\footnote{This is an obvious ploy, but we need a footnote.} XFix a point $x_0$ and a number $\epsilon>0$. Let $j_\epsilon$ Xbe a smooth function of $x$ with integral $1$ and support in X$[-\epsilon,\epsilon]$, Xand let $J_\delta$ be a smooth function of X$x$ and $t$ with integral $1$ and support in X$[-\delta,\delta]\times[-\delta,\delta]$; $\delta$ and $\epsilon$ are Xpositive numbers to be specified later. XWe choose $z=z^{\epsilon\delta}$ to satisfy X$$ X\aligned X &z_t+(\delta+J_\delta*\phi[u,u^h])z_{xx}=0,\qquad x\in\BbbR,\;0\leq t\leq T, X\\ X &z(x,T)=j_\epsilon(x-x_0). X\endaligned X\tag 2.3 X$$ XThe conclusion of the theorem now follows from (2.1) and the fact that X$$ X|j_\epsilon*\Delta u(x_0,t)-\Delta u(x_0,t)|\leq C\epsilon^\alpha, X$$ Xwhich follows from Assumption 2.\qed X\enddemo X\Refs X\ref X \no 1 X \by K. Hollig and M. Pilant X \paper Regularity of the free boundary for the porous medium equation X \paperinfo MRC Tech. Rep. 2742 X\endref X\ref X \no 2 X \by J. Jerome X \book Approximation of Nonlinear Evolution Systems X \publ Academic Press X \publaddr New York X \yr 1983 X\endref X\ref X \no 3 X \manyby R. J. LeVeque X \paper Convergence of a large time step generalization of Godunov's method X for conservation laws X \jour Comm. Pure Appl. Math. X \vol 37 X \yr 1984 X \pages 463--478 X\endref X\ref X \no 4 X \bysame X \paper A large time step generalization of Godunov's method for systems X of conservation laws X \jour X \toappear X\endref X\ref X \no 5 X \by B. J. Lucier X \paper On nonlocal monotone difference methods for scalar conservation laws X \jour Math. Comp. X \vol 47 X \yr 1986 X \pages 19--36 X\endref X\enddocument END_OF_FILE if test 6219 -ne `wc -c <'sample.tex'`; then echo shar: \"'sample.tex'\" unpacked with wrong size! fi # end of 'sample.tex' fi if test -f 'imapptdoc.tex' -a "${1}" != "-c" ; then echo shar: Will not clobber existing file \"'imapptdoc.tex'\" else echo shar: Extracting \"'imapptdoc.tex'\" \(9207 characters\) sed "s/^X//" >'imapptdoc.tex' <<'END_OF_FILE' X% This is the file imapptdoc.tex. Typeset with plain TeX. X\magnification=\magstephalf X\def\beginverbatim{\par\begingroup\setupverbatim\doverbatim} X{\catcode`\|=0 \catcode`\\=12 % | is temporary escape character X |obeylines|gdef|doverbatim^^M#1\endverbatim{#1|endgroup}} X\def\setupverbatim{\tentt \obeylines \uncatcodespecials \obeyspaces} X{\obeyspaces\global\let =\ } % let active space = control space X\def\uncatcodespecials{\def\do##1{\catcode`##1=12}\dospecials} X{\catcode`\^^M=13 \gdef\gobblecr{\ifnextchar X{\gobble}{\ignorespaces}}} X{\catcode`\ =\active\gdef\vobeyspaces{\catcode`\ \active \let \xobeysp}} X \def\xobeysp{\leavevmode{} } X\begingroup \catcode `|=0 \catcode `[= 1 X\catcode`]=2 \catcode `\{=12 \catcode `\}=12 X\catcode`\\=12 |gdef|@xverbatim#1\end{verbatim}[#1|end[verbatim]] X|gdef|@sxverbatim#1\end{verbatim*}[#1|end[verbatim*]] X|endgroup X\def\makeother#1{\catcode`#112\relax} X\def\verb{\begingroup \tt \uncatcodespecials X\averb} X\def\sverb#1{\def\tempa ##1#1{##1\endgroup}\tempa} X\def\averb{\obeyspaces \frenchspacing \sverb} X\font\textfontii = cmsy10 X\font\eightpt = cmr8 X\def\heading#1{\medskip\noindent{\bf #1.\ }} X\def\AmSTeX{{\textfontii A}\kern-.1667em\lower.5ex\hbox X {\textfontii M}\kern-.125em{\textfontii S}-\TeX} X\def\qed{\ifhmode\unskip\nobreak\fi\ifmmode\ifinner\else\hskip5pt\fi\fi X \hbox{\hskip5 pt \lower 1.5 pt\hbox{\vrule width .2 pt X \vbox{\hrule width 4 pt height .2 pt \vskip 7.1 pt X \hrule width 4 pt height .2 pt }\unskip\vrule width .2 pt}}} X\centerline{\bf USING THE IMA PREPRINT STYLE FILE} X\medskip X{\eightpt\centerline{DOUGLAS N. ARNOLD and BRADLEY J. LUCIER}} X\bigskip XThis document explains the use of the IMA preprint style file Xto typeset preprints and reports with X\AmSTeX. The IMA preprint style file, which is a Xmodification of the amsppt style of Michael Spivak, is Xintended as a general purpose preprint style for mathematical papers. XIt has been used by the Institute Xfor Mathematics and its Applications since 1987 for its preprint series. XIn these instructions we assume familiarity with \AmSTeX\ and amsppt, Xas documented in X{\it The Joy of \TeX\ } Xby Michael Spivak. X XMost of the points introduced below are illustrated in Xthe nonsense paper {\it A sample paper to illustrate the XIMA preprint style}. X X\heading{Document style} Include the commands \verb"\input amstex" Xand \verb"\documentstyle{imappt}" near the top of your document. X X\heading{Magnification} To obtain reasonable results, you {\it must} set X\verb"\magnification=\magstep 1" {\it before} the command \verb"\input Xamstex". X X\heading{Title} Use \verb"\title" and \verb"\endtitle". XType the title in all caps. XAttach any footnotes (see below) that apply to the paper Xas a whole to the title. X X\heading{Author} Use \verb"\author" and \verb"\endauthor". XType the author's name in all caps. For multiple authors type the word X``and'' in lowercase. X X\heading{Author's affiliation} Give the affiliation of each author Xin a footnote (see below) attached to each author's name. Statements Xacknowledging support should be contained in the same footnote. XDo {\it not} use the \verb"\affil" or \verb"\address" macros. X X\heading{Abstract} If there is an abstract, use \verb"\abstract". X X\heading{Keywords} If there are keywords, Xuse \verb"\keywords" with commas between keywords Xbut without ending punctuation. X X\heading{Subject classifications} If there are AMS Xsubject classifications, use \verb"\subjclass" Xwith commas between classifications Xbut without ending punctuation. X X\heading{Footnotes} Use \verb"\footnote". XFor the topmatter, use footnote symbols. XIn the rest of the paper Xuse numbered footnotes. XThe order of footnote symbols is star (*\thinspace=\thinspace\verb"*"), Xdagger (\dag\thinspace=\thinspace\verb"\dag"), double-dagger X(\ddag\thinspace=\thinspace\verb"\ddag"), Xsection-marker (\S\thinspace=\thinspace\verb"\S"). X X\heading{Headings} Use \verb"\heading" without ending punctuation. XThe argument consists of the section number followed by a period Xand then the section name with only the first word capitalized. XVery long papers could use \verb"\heading" and \verb"\endheading" Xfor major headings and \verb"\heading" for minor headings. If X\verb"\heading" is used start heading name with a section mark X(\S\thinspace=\thinspace\verb"\S") and the section number followed by a period and the Xsection title with the first letter of each major word capitalized. X X\heading{Equation numbers} Use \verb"\tag". X X\heading{Theorems, etc} Use \verb"\proclaim" and \verb"\endproclaim" Xfor theorems, lemmas, corollaries, claims, propositions, etc. The Xargument to \verb"\proclaim" takes no ending punctuation. X X\heading{Definitions} Use \verb"\proclaim" and \verb"\endproclaim", Xbut use \verb"\rm" to set the body of the definition in roman. X X\heading{Proofs, etc} Use \verb"\demo" and \verb"\enddemo" Xfor proofs, examples, remarks, cases, etc. The Xargument to \verb"\demo" takes no ending punctuation. The Xend-of-proof mark is an open box (\qed\ =\thinspace\verb"\qed"). X X\heading{Lists and sublists} Use \verb"\roster" and \verb"\endroster". XRosters use default labels of the form (1), (2), etc. XSubrosters are permitted. Each subroster {\it must} be enclosed Xin a separate pair of braces. Note that subrosters are {\it not} Xstandard \AmSTeX. X X\heading{References} These can be done exactly as in {\it The Joy Xof \TeX} using \verb"\Refs" and \verb"\ref". X X\heading{Table of contents} There are no special macros provided to set Xa table of contents. If a table of contents is desired, follow these Xguidelines. Switch to eight point type (\verb"\eightpoint"). XCenter the word ``CONTENTS'' in caps. Capitalize only the first word Xof entries. Runover lines align with the start of entries. XPlace the section number flush left with one em to section title, Xspaced dots from end of entry to page number, and two ems between the Xdots and page number. Leave 18--20 points Xof vertical space, (baseline Xto baseline, before magnification) to the text above and below. X X\heading{Tables} There are no special macros provided to set Xtables. Follow these guidelines. XSwitch to eight point type (\verb"\eightpoint"). XCenter the table on the page width. Put a minimum Xof 18 points Xspace (baseline to baseline, before magnification) above and/or below the table. XCenter the label over the table. The label Xshould be of the form \verb"{\smc Table~1.}" The title of the table should Xbe in slanted roman centered over the table with only the first word capitalized. XColumn headings may be in set in six point type if necessary to fit properly Xover the columns. Place standard \TeX\ rules (0.4 point thick, before Xmagnification) Xabove and below the column headings, and at the end of the table. X X\heading{Figure legends} Use \verb"\topspace" or \verb"\midspace". XSet the caption as, for example, X\verb"\topspace{3 in}\caption{\eightpoint{\smc Fig\. 1.\enspace}\it Type caption here.}". X X\heading{New control sequences available in the IMA preprint style} XThe amount that each roster is indented is controlled by the value of X\verb"\rosterindent". For most lists the default value need not Xbe changed. XTo get a footer that indicates Xthat the paper is a draft, give the command \verb"\draft" immediately Xafter the \verb"\documentstyle" command. This will also print the Xdate and the file name in the footer. XShould you ever want to set the footer text explicitly, Xyou may redefine \verb"\footertext". X X\heading{Control sequences available Xin the amsppt style but not the IMA preprint style} XDo not use the commands X\verb"\affil", \verb"\endaffil", \verb"\address", \verb"\date", and X\verb"\thanks". They have been redefined in the IMA preprint style file Xto give error messages when used, because Xtheir function has been taken over by other constructions, mainly footnotes Xto the title of the paper and the authors' names. X X\heading{Fonts} The font \verb"cmcsc10" is Xused at 8 point (\verb"cmcsc10 at 8 pt") so there is a Xcaps-and-small-caps font for use in references, etc. You must Xhave the appropriate \verb"pxl", \verb"pk" or \verb"gf" file for Xyour printer driver. (See your local \TeX\ guru. He or she may Xbe able to generate the font in the right size using Metafont.) XAlternatively, you can redefine the font \verb"\eightsmc" Xto be another font which you have available. XIf you have no eight point caps-and-small-caps font, then Xgive the command \verb"\font\eightsmc=cmr8" to substitute Xeight point roman. X XThe file uses the newer \verb"cm" (computer modern) family of fonts X(\verb"cmr9", \verb"cmr8", \verb"cmr6", \verb"cmmi9", \verb"cmmi8", X\verb"cmmi6", \verb"cmsy9", \verb"cmsy8", \verb"cmsy6", \verb"cmbx9", X\verb"cmbx8", \verb"cmbx6", \verb"cmti9", \verb"cmti8", \verb"cmsl9", X\verb"cmsl8", \verb"cmcsc10", and \verb"cmcsc10 at 8 pt"), so you will Xhave to change these references to the appropriate \verb"am" (almost Xmodern) fonts if that is all you have available at your site. The Xstyle file also assumes the existence of the American Mathematical XSociety fonts \verb"msxm9", \verb"msxm8", \verb"msxm6", \verb"msym9", X\verb"msym8", and \verb"msym6". If you do not have these fonts, then Xcomment out the lines in imappt.sty that reference them. X X\bye END_OF_FILE if test 9207 -ne `wc -c <'imapptdoc.tex'`; then echo shar: \"'imapptdoc.tex'\" unpacked with wrong size! fi # end of 'imapptdoc.tex' fi echo shar: End of shell archive. exit 0