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Dynamical Systems VII
A collection of five surveys on dynamical systems, indispensable for graduate students and researchers in mathematics and theoretical physics. Written in the modern language of differential geometry, the book covers all the new differential geometric and Lie-algebraic methods currently used in the theory of integrable systems.
Mathematical Analysis
This volume contains three articles: "Asymptotic methods in the theory of ordinary differential equations" b'y V. F. Butuzov, A. B. Vasil'eva, and M. V. Fedoryuk, "The theory of best ap proximation in Dormed linear spaces" by A. L. Garkavi, and "Dy namical systems with invariant measure" by A. 'VI. Vershik and S. A. Yuzvinskii. The first article surveys the literature on linear and non linear singular asymptotic problems, in particular, differential equations with a small parameter. The period covered by the survey is primarily 1962-1967. The second article is devoted to the problem of existence, characterization, and uniqueness of best approximations in Banach spaces. One of the chapters al...
Probability and Statistical Physics in St. Petersburg
This book brings a reader to the cutting edge of several important directions of the contemporary probability theory, which in many cases are strongly motivated by problems in statistical physics. The authors of these articles are leading experts in the field and the reader will get an exceptional panorama of the field from the point of view of scientists who played, and continue to play, a pivotal role in the development of the new methods and ideas, interlinking it with geometry, complex analysis, conformal field theory, etc., making modern probability one of the most vibrant areas in mathematics.
Representations of the Infinite Symmetric Group
An introduction to the modern representation theory of big groups, exploring its connections to probability and algebraic combinatorics.
Functional Differential Equations
Together with the authors' Volume I. C*-Theory, the two parts comprising Functional Differential Equations: II. C*-Applications form a masterful work-the first thorough, up-to-date exposition of this field of modern analysis lying between differential equations and C*-algebras. The two parts of Volume II contain the applications of the C*-structures and theory developed in Volume I. They show the technique of using the C*-results in the study of the solvability conditions of non-local functional differential equations and demonstrate the fundamental principles underlying the interrelations between C* and functional differential objects. The authors focus on non-local pseudodifferential, sing...
Lipschitz Functions
The aim of this book is to present various facets of the theory and applications of Lipschitz functions, starting with classical and culminating with some recent results. Among the included topics we mention: characterizations of Lipschitz functions and relations with other classes of functions, extension results for Lipschitz functions and Lipschitz partitions of unity, Lipschitz free Banach spaces and their applications, compactness properties of Lipschitz operators, Bishop-Phelps type results for Lipschitz functionals, applications to best approximation in metric and in metric linear spaces, Kantorovich-Rubinstein norm and applications to duality in the optimal transport problem, Lipschitz mappings on geodesic spaces. The prerequisites are basic results in real analysis, functional analysis, measure theory (including vector measures) and topology, which, for reader's convenience, are surveyed in the first chapter of the book.
Felix Berezin: Life And Death Of The Mastermind Of Supermathematics
Felix Berezin was an outstanding Soviet mathematician who in the 1960s and 70s was the driving force behind the emergence of the branch of mathematics now known as supermathematics. The integral over the anticommuting Grassmann variables that he introduced in the 1960s laid the foundation for the path integral formulation of quantum field theory with fermions, the heart of modern supersymmetric field theories and superstrings. The Berezin integral is named for him, as is the closely related construction of the Berezinian, which may be regarded as the superanalog of the determinant.This book features a masterfully written memoir by Berezin's widow, Elena Karpel, who narrates a remarkable account of Berezin's life and his struggle for survival under the totalitarian Soviet regime. Supplemented with recollections by his close friends and colleagues, Berezin's accomplishments in mathematics, his novel ideas and breakthrough works, are reviewed in two articles written by Andrei Losev and Robert Minlos.
Problems of Reducing the Exhaustive Search
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.
Topics in Quantum Groups and Finite-Type Invariants
Presents the first collection of articles consisting entirely of work by the faculty and students at the Higher Mathematics College at the Independent University of Moscow. The 11 contributions cover symmetry groups of regular polyhedra over finite fields, vector bundles on an elliptical curve and Skylanin algebras, Tutte decomposition for graphs and symmetric matrices, and invarians and homology of spaces of knots in arbitrary manifolds. The focus of the text is on quantum groups and low-dimensional topology. No index. Annotation copyrighted by Book News, Inc., Portland, OR
Probability Measures on Groups X
The present volume contains the transactions of the lOth Oberwolfach Conference on "Probability Measures on Groups". The series of these meetings inaugurated in 1970 by L. Schmetterer and the editor is devoted to an intensive exchange of ideas on a subject which developed from the relations between various topics of mathematics: measure theory, probability theory, group theory, harmonic analysis, special functions, partial differential operators, quantum stochastics, just to name the most significant ones. Over the years the fruitful interplay broadened in various directions: new group-related structures such as convolution algebras, generalized translation spaces, hypercomplex systems, and ...
