\documentclass[a4paper,11pt,numreferences,mathsec,kaplist]{isueps} \usepackage{isu} \begin{document} \setcounter{aqwe}{2} % If the article is in English, the value aqwe counter set to 2 \begin{article} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{opening} %УДК \udk{518.517} \msc{123} %MSC codes see http://www.ams.org/msc/ % The title of the article \title{Multilinear integral \\ Volterra equation of the first kind:\\ elements of the theory and numerical methods\thanks {This work was supported by RFBR grant 00 - 00 -00000.}} %авторы \author{I. I.~\surname{Ivanov}} %affiliation \institute{Irkutsk State University} \author{P. P.~\surname{Petrov}} \institute{Novosibirsk State University} % running title \runningtitle{MULTILINEAR VOLTERRA INTEDGRAL EQUATIONS} \runningauthor{{I. I. IVANOV, P. P. PETROV}} % The abstract (200-250 слов) \begin{abstract} In this paper the author gives an overview of the recent results in the theory and numerical methods for solving multilinear Volterra integral equations of the first kind...\end{abstract} %\keywords{Key words (up to 5 words or expressions)} \keywords{majorant equation; Lambert function; nonlinear integral inequalities; Sharp estimates, numerical methods.} \end{opening} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %Contents %in the language of the article \avtogl{I. Ivanov, P. Petrov} {Multilinear Volterra integral equations of type I elements of the theory and numerical methods} %in english \avtogle{I. Ivanov, P. Petrov}{Polilinear integral Volterra equations of the first kind: the elements of the theory and numeric methods} %The content \section{Specificity of multilinear Volterra equations of the first kind } In (4) $ N = 1,2 , $ 3, we write the series %definition \begin{definition}The text of the definition \end{definition} $\bar{x}$ 123456789 %theorem \begin{theorem} The statement of the theorem \ilabel{vipeq3} %lable \end{theorem} %proof \begin{proof} The text of the proof \end{proof} Based on the theorem \iref {vipeq3} we obtain \begin{theorem} The statement of the theorem \ilabel{vipeq4} \end{theorem} Based on the theorem \iref {vipeq4} we obtain %%%%%%%%%%%%%% unnumbered theorem \begin{theorem*} The text of the unnumbered theorem \end{theorem*} \begin{equation} x+y^2=\ln x\ilabel{vipeq1} \end{equation} Substituting in the \iref {vipeq1} instead of $ x $ variable $ y $ we obtain \begin{equation} y+y^2=\ln y\ilabel{vipeq2} \end{equation} By the formula \iref {vipeq2} %\lemma \begin{lemma} The text of the lemma \end{lemma} %\unnumbered lemma \begin{lemma*} unnumbered lemma \end{lemma*} \begin{state} The text of the statement \end{state} \begin{proposition} The text of the proposition \end{proposition} \begin{corollary} The text of the corollary \end{corollary} % remark \begin{remark} The text of the remark \ilabel{vipre1} \end{remark} Given the remark \iref{vipre1} Thus, even in the case of constant kernels continuous solution of the bilinear equation exists ... \section{Majorant equation (bilinear case)} Using the notation of ~ \cite{T1975,aYa1952} ... \bigskip We recommend using the following samples for references. The list of references should be in alphabetical order. \begin{thebibliography}{999} \bibitem{Kr1965} Krni\'c L. Types of Bases in the Algebra of Logic. \textit{Glasnik Matematicko-Fizicki i Astronomski}, ser 2, 1965, vol. 20, pp. 23-32. \bibitem{M1989} Miyakawa M., Stojmenovi\'c I., Lau D., Rosenberg I. Classification and basis enumerations of the algebras for partial functions. \textit{Proc. 19th International Symposium on Multi-Valued logic}, Rostock, 1989, pp. 8-13. \bibitem{T1975}Tarasov V.V. Completeness Criterion for Partial Logic Functions (in Russian). \textit{Problemy Kibernetiki}, Moscow, Nauka,1975, vol. 30, pp.~319-325. \bibitem{aYa1952}Yablonskij S.V. On the Superpositions of Logic Functions (in Russian). \textit{Mat. Sbornik}, 1952, vol. 30, no. 2(72), pp. 329-348. \bibitem{S1984} Stojmenovi\'c I. Classification of $P_3$ and the enumeration of base of $P_3$, \textit{Rev. of Res. 14, Fat. Of Sci., Math. Ser}., Novi Sad, 1984, p. 73-80. \end{thebibliography} \bigskip %in english \textbf{Ivanov Ivan Ivanovich}, Doctor of Science (Physics and Mathematicks), Professor, Institute of mathematics, economics and informatics, Irkutsk State University, 664000, Irkutsk, K. Marks str., 1, tel.: (3952)242210\\ \email{avtor@math.isu.ru} \textbf{Petrov Petr Petrovich}, Candidate of Science (Physics and Mathematicks), Asso\-ciate Professor, Institute of mathematics, economics and informatics, Novo\-si\-birsk State University, 664000, Novo\-si\-birsk, K. Marks str., 1,\\ tel.: (3952)242210 tel.: (3952)242210 \email{petrov@math1.isu.ru} % Making version of the article in Russian %authors \avtore{И. И. Иванов, П. П. Петров} %название \naze{Полилинейные интегральные уравнения Вольтерра I рода: элементы теории и численные методы} %аннотация, \begin{abstracte} В статье дан обзор результатов, полученных авторами в последние годы в области теории и численных методов решения полилинейных интегральных уравнений Вольтерра I рода... \end{abstracte} %ключевые слова \keywordse{мажорантные уравнения; функция Ламберта; нелинейные интегральные неравенства; неулучшаемые оценки; численные методы.} \selectlanguage{russian} %Сведения об авторах \textbf{Иванов Иван Иванович}, доктор физико-математических наук, профессор, Иркутский государственный университет, 1, K. Mаркса ул., Иркутск, 664003 тел.: (3952)242210 \email{avtor@math.isu.ru} \textbf{Петров Петр Петрович}, кандидат физико-математических наук, Новосибирский государcтвенный университет, 1, K. Mаркса ул., Новосибирск, 664003 тел.: (3952)242210 \email{avtor@math.isu.ru} \end{article} \end{document}