Singularity Theory and Some Problems of Functional Analysis

Singularity Theory and Some Problems of Functional Analysis PDF

Author: Semen Grigorʹevich Gindikin

Publisher: American Mathematical Soc.

Published: 1992

Total Pages: 212

ISBN-13: 9780821875025

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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.

New Developments in Singularity Theory

New Developments in Singularity Theory PDF

Author: Dirk Wiersma

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 470

ISBN-13: 9401008345

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Singularities arise naturally in a huge number of different areas of mathematics and science. As a consequence, singularity theory lies at the crossroads of paths that connect many of the most important areas of applications of mathematics with some of its most abstract regions. The main goal in most problems of singularity theory is to understand the dependence of some objects of analysis, geometry, physics, or other science (functions, varieties, mappings, vector or tensor fields, differential equations, models, etc.) on parameters. The articles collected here can be grouped under three headings. (A) Singularities of real maps; (B) Singular complex variables; and (C) Singularities of homomorphic maps.

Theory of Singularities and Its Applications

Theory of Singularities and Its Applications PDF

Author: Vladimir Igorevich Arnolʹd

Publisher:

Published: 1990

Total Pages: 346

ISBN-13: 9781470445485

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The theory of singularities lies at the crossroads between those branches of mathematics which are the most abstract and those which are the most applied. Algebraic and differential geometry and topology, commutative algebra and group theory are as intimately connected to singularity theory as are dynamical systems theory, control theory, differential equations, quantum mechanical and quasi-classical asymptotics, optics, and functional analysis. This collection of papers incorporates recent results of participants in the editor's ongoing seminar in singularity theory, held in the Mechanics and.

Applied Problems of Radon Transform

Applied Problems of Radon Transform PDF

Author: Semen Grigorʹevich Gindikin

Publisher: American Mathematical Soc.

Published: 1994

Total Pages: 276

ISBN-13: 9780821875087

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This collection is designed to acquaint readers with advances in Radon transforms carried out in the former Soviet Union. The papers focus on mathematical problems related to applications of Radon transforms. Some of the problems arose from practical tomography, while others are theoretical problems originating in tomography. The book should be of use to mathematicians working in integral geometry and mathematical problems of tomography, as well as scientists who work on inverse problems and their computer realization.

Wave propagation. Scattering theory

Wave propagation. Scattering theory PDF

Author: M. Sh Birman

Publisher: American Mathematical Soc.

Published: 1993-12-20

Total Pages: 274

ISBN-13: 9780821895917

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The papers in this collection were written primarily by members of the St. Petersburg seminar in mathematical physics. The seminar, now run by O. A. Ladyzhenskaya, was initiated in 1947 by V. I. Smirnov, to whose memory this volume is dedicated. The papers in the collection are devoted mainly to wave propagation processes, scattering theory, integrability of nonlinear equations, and related problems of spectral theory of differential and integral operators. The book is of interest to mathematicians working in mathematical physics and differential equations, as well as to physicists studying various wave propagation processes.

Some questions of differential geometry in the large

Some questions of differential geometry in the large PDF

Author: E. V. Shikin

Publisher: American Mathematical Soc.

Published: 1996-07-16

Total Pages: 208

ISBN-13: 9780821895979

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This collection contains articles that present recent results by geometers in Russia and the Ukraine. Papers in the collection deal with various questions related to the structure, symmetries, and embeddings of submanifolds in Euclidean and pseudo-Euclidian spaces. This collection offers a review of the challenges facing specialists in geometry in the large and features current research in the field.

Problems of reducing the exhaustive search

Problems of reducing the exhaustive search PDF

Author: G. E. Mints

Publisher: American Mathematical Soc.

Published: 1996-11-05

Total Pages: 206

ISBN-13: 9780821895986

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This collection contains translations of papers on propositional satisfiability and related logical problems which appeared in Problemy 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 inverse method in automated deduction, which was discovered at the same time as the resolution method of J. A. Robinson 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 proposititional satisfiability and related logical problems. The papers related to Maslov's iterative method of search reduction play a significant role.

Selected Papers on Analysis, Probability, and Statistics

Selected Papers on Analysis, Probability, and Statistics PDF

Author: Katsumi Nomizu

Publisher: American Mathematical Soc.

Published: 1994

Total Pages: 176

ISBN-13: 9780821875124

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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.

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