%----------------------------------------------------------------------------- % Beginning of memo.let-e %----------------------------------------------------------------------------- Following this letter are four files (MEMO.STY, MEMO.TEX, MEMOREFS.TEX and MEMO.CHECKLIST) to be used when preparing a paper in AMS-TeX 2.1, for a volume in the Memoirs series. To make it easier to load these files separately on your system, they are separated by file delimiters. The .STY file is used to modify the AMS-TeX preprint style to the MEMO style. Instructions for using this file are listed at the top. The .TEX files are samples of the macros defined in the .STY file. The MEMO.TEX file is the main example 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 MEMOREFS.TEX file is a supplemental file that illustrates how references should be typed. The .CHECKLIST file should be printed and used to help you avoid the most common problems. Once your paper has been accepted for publication in MEMO, 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. %----------------------------------------------------------------------------- % End of memo.let-e %----------------------------------------------------------------------------- %----------------------------------------------------------------------------- % Beginning of memo.sty %----------------------------------------------------------------------------- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % This file is designed to work with AMS-TeX version 2.1. % % The TeX code defined here will modify the AMS-TeX 2.1 preprint style to % the Memoirs style. It sets up the correct page size, % puts a logo and a copyrightline on the first page, and formats the % top matter, headings and references appropriately. % % % Instructions: % % 1. Create a file named memo.sty containing the data in the lines % from %%% memo.sty %%% through \endinput . Install the file % in the same directory as amsppt.sty . % % 2. In a data file, include the line, \documentstyle{memo} % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % First input the preprint style \def\next{AMSPPT}\ifx\styname\next \else\input amsppt.sty\fi \catcode`\@=11 % Set the page size \pagewidth{29pc} \def\curraddr{\let\savedef@\curraddr \def\curraddr##1\endcurraddr{\let\curraddr\savedef@ \toks@\expandafter\expandafter\expandafter{% \csname address\number\addresscount@\endcsname}% \toks@@{##1}% \expandafter\xdef\csname address\number\addresscount@\endcsname {\the\toks@\endgraf\noexpand\nobreak \smallskip\indent\noexpand\eightpoint{\noexpand\rm \frills@{{\noexpand\it Current address\noexpand\/}:\space}% \def\noexpand\usualspace{\space}\the\toks@@\unskip}}}% \nofrillscheck\curraddr} \def\author#1\endauthor{\global\setbox\authorbox@ \vbox{\titless\baselineskip2\baselineskip\noindent\ignorespaces#1\endgraf} } \font\titless=cmss17 \font\smss=cmss12 \def\titlepage{\def\\{\hfill\break} \def\title##1\endtitle{\global\setbox\titlebox@\vtop{\titless \noindent\ignorespaces \baselineskip2\baselineskip{##1}\endgraf}}} \outer\def\endtitlepage{% {\smss Memoirs of the American Mathematical Society} \vskip1in \preauthor \ifvoid\authorbox@\else \vskip1pc plus1pc \unvbox\authorbox@\fi \vskip2pc \box\titlebox@ \vfill\end } \def\chapterno@{\the\chaptercount@} \def\thanks#1\endthanks{\vskip2pc\noindent\ignorespaces#1.\unskip} \def\keywords{\let\savedef@\keywords \def\keywords##1\endkeywords{\let\keywords\savedef@ {\vskip2pc\def\usualspace{{\it\enspace}}\eightpoint% \frills@{{\it Key words and phrases.\enspace}}% ##1\unskip.}}% \nofrillscheck\keywords} \def\subjclass{\let\savedef@\subjclass \def\subjclass##1\endsubjclass{\let\subjclass\savedef@ {\vskip2pc\def\usualspace{{\rm\enspace}}\eightpoint% \frills@{{\noexpand\rm1991 {\it Mathematics Subject Classification}.\enspace}}% ##1\unskip.}}% \nofrillscheck\subjclass} \outer\def\endtopmatter{\add@missing\endabstract \edef\next{\the\leftheadtoks}\ifx\next\empty \expandafter\leftheadtext\expandafter{\the\rightheadtoks}\fi \pretitle \box\titlebox@ \prepaper \vskip2pc plus1pc \topskip10pt% reset to normal value } {\def\title#1\endtitle{\relax} \def\chapter#1{\relax}\def\specialhead{\relax}\def\head#1\endhead{\relax} \def\subhead{\relax}\def\subsubhead{\relax} \gdef\newtocdefs{% \def \title##1\endtitle {\penaltyandskip@\z@\smallskipamount \hangindent\wd\tocheadbox@\noindent{##1}}% \def \chapter##1{% Chapter {##1.\unskip}\enspace}% \def \specialhead##1\endspecialhead {\par\hangindent\wd\tocheadbox@ \noindent##1\par}% \def \head##1 ##2\endhead {\par\hangindent\wd\tocheadbox@ \noindent \if\notempty{##1}\hbox to\wd\tocheadbox@{\hfil##1\enspace}\fi ##2\par}% \def \subhead##1 ##2\endsubhead {\par\vskip-\parskip {\normalbaselines \advance\leftskip\wd\tocheadbox@ \hangindent\wd\tocsubheadbox@ \noindent \if\notempty{##1}\hbox to\wd\tocsubheadbox@{##1\unskip\hfil}\fi ##2\par}}% \def \subsubhead##1 ##2\endsubsubhead {\par\vskip-\parskip {\normalbaselines \advance\leftskip\wd\tocheadbox@ \hangindent\wd\tocsubheadbox@ \noindent \if\notempty{##1}\hbox to\wd\tocsubheadbox@{##1\unskip\hfil}\fi ##2\par}}} } \let\subhead\relax \outer\def\subhead{% \add@missing\endroster \add@missing\enddefinition \add@missing\enddemo \add@missing\endexample \add@missing\endproclaim \let\savedef@\subhead \let\subhead\relax \def\subhead##1\endsubhead{\restoredef@\subhead \penaltyandskip@{-100}\subheadskip \varindent@{\def\usualspace{{\subheadfont@\enspace}}% \subheadfont@\ignorespaces##1\unskip\frills@{.\enspace}}% \ignorespaces}% \nofrillscheck\subhead} \def\Monograph{\monograph@true% \let\varindent@\indent \def\headfont@{\bf}\def\proclaimheadfont@{\smc}% \def\demoheadfont@{\smc} \topskip7pc} % 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}} % Set the references font to be 10pt. \def\refsfont@{\tenpoint} % Turn off the "Typeset by \AmSTeX" logo \def\logo@{} \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 \nobreak \thetranslator@ \count@\z@ \loop\ifnum\count@<\addresscount@\advance\count@\@ne \csname address\number\count@\endcsname \csname email\number\count@\endcsname \repeat \vfill\supereject\end} \catcode`\@=13 \def\amsversion{2.1} \Monograph \endinput %----------------------------------------------------------------------------- % End of memo.sty %----------------------------------------------------------------------------- %----------------------------------------------------------------------------- % Beginning of memo.tex %----------------------------------------------------------------------------- % % AMS-TeX 2.1 sample file for memoirs volumes. % \input amstex \documentstyle{memo} \NoBlackBoxes % \def\ttmode{\begingroup \def\par{\leavevmode\endgraf}% \parskip0pt\parindent0pt\leftskip3pc \obeylines \def\{{\relax\char'173}\def\}{\relax\char'175} \def\\{\relax\char'134} \tt} \def\endttmode{\endgroup} % \rightheadtext{MAXIMAL IDEALS IN SUBALGEBRAS OF $C(X)$} \leftheadtext{John Q. Public} \topmatter \title\chapter{1} Sample Chapter for Memoirs,\\ On Maximal Ideals in Subalgebras of $C(X)$\endtitle \endtopmatter \document \head 1. Introduction % bold, centered; \endhead % don't type final punctuation This sample chapter illustrates the use of the \AmSTeX{} Version~2.1 preprint style with additional macros for the series {\bf Memoirs}. In this sample paper, brief instructions to authors will be 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}. A book for the {\bf Memoirs} series is generally comprised of a title page, contents page(s), an abstract page, and a varying number of chapters, including references. Each of these must be typed and \TeX ed as individual files. \subhead Title page\endsubhead The title page should follow a format similar to the following. \ttmode \\input amstex \\documentstyle\{memo\} \\titlepage \\title Title of the Book\\endtitle \\author Author One\\\\ and Author Two\\endauthor \\endtitlepage \endttmode This will provide a plain title page for preliminary purposes---the real title page will be produced at the AMS using different fonts. \subhead Top matter\endsubhead The input format and content of the top matter for each chapter is usually limited to the chapter number and title, and the text for the running heads, except for the contents and abstract pages which are explained below. The running head text should be input in all CAPS as {\tt\char`\\leftheadtext} and {\tt\char`\\rightheadtext} respectively. The title of the book should appear in the right running heads (odd-numbered pages) and the name(s) of the author(s) should appear in the left running heads (even-numbered pages). The full names and title should be used unless they require more than one line or would not leave space around the page number; in that event, abbreviated forms should be substituted. In the top matter, the title is input in caps and lowercase but will be set in all uppercase. \subhead Table of Contents\endsubhead The Table of Contents should be typed as a separate chapter and using the {\ttmode\\toc...\\endtoc\endttmode} structure as the body of the document. An example of a Table of Contents is given below.\eject \ttmode \\input amstex \\documentstyle\{memo\} \\topmatter \\title Contents\\endtitle \\endtopmatter \vskip-.5\baselineskip \\document \\toc \\title\\chapter\{{1}\} Matrix Algebras\\page\{{1}\}\\endtitle \\head Continuous complex-valued functions\\page\{{1}\}\\endhead ... \\title Bibliography\\page\{{307}\}\\endtitle \\endtoc \\enddocument \endttmode The chapter titles listed in the table of contents are typed in the same way as in actual use. To get page numbers in the table of contents, use {\tt\char`\\page} as shown, just before the ending of an element. This option is available for all levels of headings. \subhead Abstract page\endsubhead Like the contents page, the abstract page should also be handled as a separate chapter. The type of data that occurs on the abstract page of a {\bf Memoirs} publication is comparable to top matter material for other AMS journals or books; however, for the {\bf Memoirs} series, this information must be entered after the {\tt\char`\\document} command, {\it not} as part of the {\tt\char`\\topmatter}. The setup and available commands for a {\bf Memoirs} abstract page are as follows. \ttmode \\input amstex \\documentstyle\{memo\} \\topmatter \\title Abstract\\endtitle \\endtopmatter \vskip-.5\baselineskip \\document \qquad {\rm Text of abstract...} \vskip-.5\baselineskip \\keywords...\\endkeywords \\thanks...\\endthanks \\subjclass...\\endsubjclass \\enddocument \endttmode \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 these macros. 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 since no text follows the proclamation head before the list begins. 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 $00$, 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.\ 99} for common mathematical functions and operators like $\log$ and $\lim$, and use {\tt\char`\\cite} when citing a reference. \head 4. References\endhead References start a new chapter and should be typed as such with {\tt References} entered as the {\tt\char`\\title}. 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. There are sample references included in the file named {\tt memorefs.tex}. These examples have been chosen to illustrate the coding of the most common types of references. Use the abbreviations of names of journals and book series 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). General instructions for tagging references are given in Appendix C of \cite{18}. Some changes have been made in the upgrade to \AmSTeX{} Version~2.1. Except for the simplification of the {\tt\char`\\key}, the new conventions are illustrated in the bibliography at the end of this sample. Even though the author's address is not part of the references, if the following information is present, it should be entered in the topmatter section of the {\bf References} chapter. \ttmode \\address...\\endaddress \\curraddr...\\endcurraddr \\email...\\endemail \endttmode \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 necessary to label your figures and use the labels in text when referring to figures. The figure caption should be positioned below the figure. Please provide camera-ready figures drawn in black ink with clean, unbroken lines on nonabsorbent paper. \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 $\gamma_{1,5}$. \endexample % art work measures 9.75pc for figure 5a, 7pc for figure 5b \topinsert \vskip 9.75pc \botcaption{Figure 5{\rm a}}\endcaption \endinsert \topinsert \vskip 7pc \botcaption{Figure 5{\rm b}}\endcaption \endinsert \head 6. Other headings\endhead \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. \enddocument %----------------------------------------------------------------------------- % End of memo.tex %----------------------------------------------------------------------------- %----------------------------------------------------------------------------- % Beginning of memo.checklist %----------------------------------------------------------------------------- Check List for Electronic Manuscripts Memoirs Volumes - The final version of a manuscript must be approved by an editor before it is received by the AMS. The author should proofread the paper before submitting to the AMS. - Even though the title on the first page of each chapter is printed in upper- case, it should be typed with only the first letter of major words and any proper names in uppercase (CAPS); other words should be lowercase. - The running heads for the right-hand (odd-numbered pages) should have the title (shortened if necessary) all in CAPS. - The author(s) name(s) on the title page should be in CAPS and lowercase. - The running heads for the left-hand (even-numbered pages) should have the author(s) name(s) all in CAPS. Names in running heads should match names as given on the first page (shorten to fit only if necessary). - Grant information and final publication information should be listed on the abstract page. - Citations in the manuscript should be coded using ``\cite''. - References should be typed as a separate chapter and coded using the AMS-TeX codes and should include all available information. - The address, current address (if different), and e-mail address of each author, if included, should be entered in the \topmatter section of the references chapter. - Each chapter should be a separate TeX file. - The title page, table of contents, abstract page, and references should each be a separate TeX file, as explained in the instructions. - The .tex files should include NO ``input'' files other than amstex. - All definitions should be at the top of the file and none of them should redefine any TeX or AMS-TeX commands. - Definitions should be used consistently throughout the paper. - No definitions should be used for formatting text; only the AMS-TeX formatting commands should be used. - A covering letter should be included with the electronic submission. The letter should clearly identify the author, title, and intended publication series. It should also tell us where the author can be reached throughout the publication process. %----------------------------------------------------------------------------- % End of memo.checklist %----------------------------------------------------------------------------- %----------------------------------------------------------------------------- % Beginning of memorefs.tex %----------------------------------------------------------------------------- \input amstex \documentstyle{memo} \overfullrule=0pt \topmatter \title References\endtitle \address Department of Mathematics, Northeastern University, Boston, Massachusetts 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 \endtopmatter \document \widestnumber\no{10} \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-\break 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{}\bookinfo 2nd ed. \publ Amer. Math. Soc., Providence, RI \yr 1986\endref \enddocument %----------------------------------------------------------------------------- % End of memorefs.tex %-----------------------------------------------------------------------------