The emergence of singularity theory marks the return of mathematics to the study of the simplest analytical objects: functions, graphs, curves, surfaces. The modern singularity theory for smooth mappings, which is currently undergoing intensive developments, can be thought of as a crossroad where the most abstract topics (such as algebraic and differential geometry and topology, complex analysis, invariant theory, and Lie group theory) meet the most applied topics (such as dynamical systems, mathematical physics, geometrical optics, mathematical economics, and control theory). The papers in this volume include reviews of established areas as well as presentations of recent results in singularity theory. The authors have paid special attention to examples and discussion of results rather than burying the ideas in formalism, notation, and technical details. The aim is to introduce all mathematicians - as well as physicists, engineers, and other consumers of singularity theory - to the world of ideas and methods in this burgeoning area.

This collection contains translations of papers on propositional satisfiability and related logical problems which appeared in roblemy Sokrashcheniya Perebora, published in Russian in 1987 by the Scientific Council "Cybernetics" of the USSR Academy of Sciences. The problems form the nucleus of this intensively developing area. This translation is dedicated to the memory of two remarkable Russian mathematicians, Sergei Maslov and his wife Nina Maslova. Maslov is known as the originator of the universe method in automated deduction, which was discovered at the same time as the resolution method of J. A. Robison and has approximately the same range of applications. In 1981, Maslov proposed an iterative algorithm for propositional satisfiability based on some general ideas of search described in detail in his posthumously published book, Theory of Deductive Systems and Its Applications (1986; English 1987). This collection contains translations of papers on propositional satisfiability and related logical problems. The papers related to Maslov's iterative method of search reduction play a significant role.

This book presents papers that originally appeared in the Japanese journal Sugaku. The papers explore the relationship between number theory, algebraic geometry, and differential geometry.

This monograph is the first to develop a mathematical theory of gravitational lensing. The theory applies to any finite number of deflector planes and highlights the distinctions between single and multiple plane lensing. Introductory material in Parts I and II present historical highlights and the astrophysical aspects of the subject. Part III employs the ideas and results of singularity theory to put gravitational lensing on a rigorous mathematical foundation.

This book presents papers in the general area of mathematical analysis as it pertains to probability and statistics, dynamical systems, differential equations, and analytic function theory. Among the topics discussed are: stochastic differential equations, spectra of the Laplacian and Schrödinger operators, nonlinear partial differential equations which generate dissipative dynamical systems, fractal analysis on self-similar sets, and the global structure of analytic functions.

This is a collection of translations of a variety of papers on discrete mathematics by members of the Moscow Seminar on Discrete Mathematics. This seminar, begun in 1972, was marked by active participation and intellectual ferment. Mathematicians in the USSR often encountered difficulties in publishing, so many interesting results in discrete mathematics remained unknown in the West for some years, and some are unknown even to the present day. To help fill this communication gap, this collection offers papers that were obscurely published and very hard to find. Among the topics covered here are: graph theory, network flow and multicommodity flow, linear programming and combinatorial optimization, matroid theory and submodular systems, matrix theory and combinatorics, parallel computing, complexity of algorithms, random graphs and statistical mechanics, coding theory, and algebraic combinatorics and group theory.

This is the inaugural volume of a new book series published under the auspices of the St. Petersburg Mathematical Society. The book contains contributions by some of the leading mathematicians in St. Petersburg. Ranging over a wide array of topics, these papers testify to the diverse interests and productive mathematical life of the St. Petersburg Mathematical Society.

This book contains the doctoral dissertations of three students from Novosibirsk who participated in the seminar of L. A. Bokut'. The dissertation of Gerasimov focuses on Cohn's theory of noncommutative matrix localizations. Gerasimov presents a construction of matrix localization that is not directly related to (prime) matrix ideals of Cohn, but rather deals with localizations of arbitrary subsets of matrices over a ring. The work of Valitskas applies ideas and constructions of Gerasimov to embeddings of rings into radical rings (in the sense of Jacobson) to develop a theory essentially parallel to Cohn's theory of embeddings of rings into skew fields. Nesterenko's dissertation solves some important problems of Anan'in and Bergman about representations of (infinite-dimensional) algebras and categories in (triangular) matrices over commutative rings.

The five papers originally appeared in Japanese in the journal Sugaku and would ordinarily appear in the Society's translation of that journal, but are published separately here to expedite their dissemination. They explore such aspects as representation theory, differential geometry, invariant theory, and complex analysis. No index. Member prices are $47 for institutions and $35 for individual. Annotation copyrighted by Book News, Inc., Portland, OR.

This book contains papers on a wide range of topics, including diophantine equations, algebraic number theory, ring theory, theory of functions of a real variable, partial differential equations, approximation of functions, differential geometry, computing theory, and statistical mechanics. The last three papers present historical perspectives on mathematics in St. Petersburg.