Alexander Mikhalev's Books

Combinatorial Methods

Free Groups, Polynomials, and Free Algebras

By: Vladimir Shpilrain,Alexander Mikhalev,Jie-tai Yu

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Combinatorial Methods

Free Groups, Polynomials, and Free Algebras

By: Vladimir Shpilrain,Alexander Mikhalev,Jie-tai Yu

The main purpose of this book is to show how ideas from combinatorial group theory have spread to two other areas of mathematics: the theory of Lie algebras and affine algebraic geometry. Some of these ideas, in turn, came to combinatorial group theory from low-dimensional topology in the beginning of the 20th Century.

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322

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Springer Science & Business Media

Published Date

ISBN 10

038721724X

ISBN 13

9780387217246

Fundamentals of Functions and Measure Theory

By: Valeriy K. Zakharov,Timofey V. Rodionov,Alexander V. Mikhalev

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Fundamentals of Functions and Measure Theory

By: Valeriy K. Zakharov,Timofey V. Rodionov,Alexander V. Mikhalev

This comprehensive two-volume work is devoted to the most general beginnings of mathematics. It goes back to Hausdorff’s classic Set Theory (2nd ed., 1927), where set theory and the theory of functions were expounded as the fundamental parts of mathematics in such a way that there was no need for references to other sources. Along the lines of Hausdorff’s initial work (1st ed., 1914), measure and integration theory is also included here as the third fundamental part of contemporary mathematics. The material about sets and numbers is placed in Volume 1 and the material about functions and measures is placed in Volume 2. Contents Historical foreword on the centenary after Felix Hausdorff’s classic Set Theory Fundamentals of the theory of functions Fundamentals of the measure theory Historical notes on the Riesz – Radon – Frechet problem of characterization of Radon integrals as linear functionals

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597

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Walter de Gruyter GmbH & Co KG

Published Date

ISBN 10

3110550229

ISBN 13

9783110550221

The Concise Handbook of Algebra

By: Alexander V. Mikhalev,G.F. Pilz

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The Concise Handbook of Algebra

By: Alexander V. Mikhalev,G.F. Pilz

It is by no means clear what comprises the "heart" or "core" of algebra, the part of algebra which every algebraist should know. Hence we feel that a book on "our heart" might be useful. We have tried to catch this heart in a collection of about 150 short sections, written by leading algebraists in these areas. These sections are organized in 9 chapters A, B, . . . , I. Of course, the selection is partly based on personal preferences, and we ask you for your understanding if some selections do not meet your taste (for unknown reasons, we only had problems in the chapter "Groups" to get enough articles in time). We hope that this book sets up a standard of what all algebraists are supposed to know in "their" chapters; interested people from other areas should be able to get a quick idea about the area. So the target group consists of anyone interested in algebra, from graduate students to established researchers, including those who want to obtain a quick overview or a better understanding of our selected topics. The prerequisites are something like the contents of standard textbooks on higher algebra. This book should also enable the reader to read the "big" Handbook (Hazewinkel 1999-) and other handbooks. In case of multiple authors, the authors are listed alphabetically; so their order has nothing to do with the amounts of their contributions.

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629

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Springer Science & Business Media

Published Date

ISBN 10

9401732671

ISBN 13

9789401732673

Monoids, Acts and Categories

With Applications to Wreath Products and Graphs. A Handbook for Students and Researchers

By: Mati Kilp,Ulrich Knauer,Alexander V. Mikhalev

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Monoids, Acts and Categories

With Applications to Wreath Products and Graphs. A Handbook for Students and Researchers

By: Mati Kilp,Ulrich Knauer,Alexander V. Mikhalev

The aim of the Expositions is to present new and important developments in pure and applied mathematics. Well established in the community over more than two decades, the series offers a large library of mathematical works, including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers interested in a thorough study of the subject. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany Katrin Wendland, University of Freiburg, Germany Honorary Editor Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Titles in planning include Yuri A. Bahturin, Identical Relations in Lie Algebras (2019) Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019) Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019) Volker Mayer, Mariusz Urbański, and Anna Zdunik, Random and Conformal Dynamical Systems (2021) Ioannis Diamantis, Boštjan Gabrovšek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)

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549

Publisher

Walter de Gruyter

Published Date

ISBN 10

3110812908

ISBN 13

9783110812909

Difference Algebra

By: Alexander Levin

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Difference Algebra

By: Alexander Levin

Difference algebra grew out of the study of algebraic difference equations with coefficients from functional fields. The first stage of this development of the theory is associated with its founder, J.F. Ritt (1893-1951), and R. Cohn, whose book Difference Algebra (1965) remained the only fundamental monograph on the subject for many years. Nowadays, difference algebra has overgrown the frame of the theory of ordinary algebraic difference equations and appears as a rich theory with applications to the study of equations in finite differences, functional equations, differential equations with delay, algebraic structures with operators, group and semigroup rings. The monograph is intended for graduate students and researchers in difference and differential algebra, commutative algebra, ring theory, and algebraic geometry. The book is self-contained; it requires no prerequisites other than the knowledge of basic algebraic concepts and a mathematical maturity of an advanced undergraduate.

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528

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Springer Science & Business Media

Published Date

ISBN 10

1402069472

ISBN 13

9781402069475

The History of Research on Chemical Periodic Processes

By: Alexander Pechenkin

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The History of Research on Chemical Periodic Processes

By: Alexander Pechenkin

This book offers a survey of the historic development of selected areas of chemistry and chemical physics, discussing in detail the European, American and Russian approaches to the development of chemistry. Other key topics include the kinetics and non-linear thermodynamics of chemical reactions and mathematical modeling, which have found new applications in the theory of dynamical systems. The first observations of the periodicity of chemical reactions were lost in the mist of time. In the second half of the 19th century, the phenomenon of chemical periodicity was studied in relation to electrochemistry, solutions and colloids. Discovered in the late 19th century, Liesegang rings are still enigmatic and remain attractive for researchers. However, the discovery of the Belousov–Zhabotinsky reaction marked the successful culmination of the efforts to find a true chemical oscillatory reaction. The book investigates chemical phenomena that were neglected in the past, but have been rediscovered, placing them into a new conceptual framework. For example, it notes that William Bray, who discovered the first oscillatory homogeneous reaction in 1921, was influenced by the first bio-mathematicians who predicted chemical oscillations in homogeneous systems.

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105

Publisher

Springer

Published Date

ISBN 10

3319951084

ISBN 13

9783319951089

Graphs on Surfaces and Their Applications

By: Sergei K. Lando,Alexander K. Zvonkin

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Graphs on Surfaces and Their Applications

By: Sergei K. Lando,Alexander K. Zvonkin

Graphs drawn on two-dimensional surfaces have always attracted researchers by their beauty and by the variety of difficult questions to which they give rise. The theory of such embedded graphs, which long seemed rather isolated, has witnessed the appearance of entirely unexpected new applications in recent decades, ranging from Galois theory to quantum gravity models, and has become a kind of a focus of a vast field of research. The book provides an accessible introduction to this new domain, including such topics as coverings of Riemann surfaces, the Galois group action on embedded graphs (Grothendieck's theory of "dessins d'enfants"), the matrix integral method, moduli spaces of curves, the topology of meromorphic functions, and combinatorial aspects of Vassiliev's knot invariants and, in an appendix by Don Zagier, the use of finite group representation theory. The presentation is concrete throughout, with numerous figures, examples (including computer calculations) and exercises, and should appeal to both graduate students and researchers.

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463

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Springer Science & Business Media

Published Date

ISBN 10

3540383611

ISBN 13

9783540383611

Non-commutative Cryptography and Complexity of Group-theoretic Problems

By: Alexei G. Myasnikov,Vladimir Shpilrain,Alexander Ushakov

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Non-commutative Cryptography and Complexity of Group-theoretic Problems

By: Alexei G. Myasnikov,Vladimir Shpilrain,Alexander Ushakov

Examines the relationship between three different areas of mathematics and theoretical computer science: combinatorial group theory, cryptography, and complexity theory. It explores how non-commutative (infinite) groups can be used in public key cryptography. It also shows that there is remarkable feedback from cryptography to combinatorial group theory because some of the problems motivated by cryptography appear to be new to group theory.

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402

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821853600

ISBN 13

9780821853603

Complexity and Randomness in Group Theory

GAGTA BOOK 1

By: Frédérique Bassino,Ilya Kapovich,Markus Lohrey,Alexei Miasnikov,Cyril Nicaud,Andrey Nikolaev,Igor Rivin,Vladimir Shpilrain,Alexander Ushakov,Pascal Weil

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Complexity and Randomness in Group Theory

GAGTA BOOK 1

By: Frédérique Bassino,Ilya Kapovich,Markus Lohrey,Alexei Miasnikov,Cyril Nicaud,Andrey Nikolaev,Igor Rivin,Vladimir Shpilrain,Alexander Ushakov,Pascal Weil

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386

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Walter de Gruyter GmbH & Co KG

Published Date

ISBN 10

3110667029

ISBN 13

9783110667028

The Classical Groups and K-Theory

By: Alexander J. Hahn,O.Timothy O'Meara

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The Classical Groups and K-Theory

By: Alexander J. Hahn,O.Timothy O'Meara

It is a great satisfaction for a mathematician to witness the growth and expansion of a theory in which he has taken some part during its early years. When H. Weyl coined the words "classical groups", foremost in his mind were their connections with invariant theory, which his famous book helped to revive. Although his approach in that book was deliberately algebraic, his interest in these groups directly derived from his pioneering study of the special case in which the scalars are real or complex numbers, where for the first time he injected Topology into Lie theory. But ever since the definition of Lie groups, the analogy between simple classical groups over finite fields and simple classical groups over IR or C had been observed, even if the concept of "simplicity" was not quite the same in both cases. With the discovery of the exceptional simple complex Lie algebras by Killing and E. Cartan, it was natural to look for corresponding groups over finite fields, and already around 1900 this was done by Dickson for the exceptional Lie algebras G and E • However, a deep reason for this 2 6 parallelism was missing, and it is only Chevalley who, in 1955 and 1961, discovered that to each complex simple Lie algebra corresponds, by a uniform process, a group scheme (fj over the ring Z of integers, from which, for any field K, could be derived a group (fj(K).

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589

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Springer Science & Business Media

Published Date

ISBN 10

3662131528

ISBN 13

9783662131527

The Restricted 3-Body Problem: Plane Periodic Orbits

By: Alexander D. Bruno

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The Restricted 3-Body Problem: Plane Periodic Orbits

By: Alexander D. Bruno

The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany

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377

Publisher

Walter de Gruyter

Published Date

ISBN 10

3110901730

ISBN 13

9783110901733

Branching Solutions to One-dimensional Variational Problems

By: Alexander O. Ivanov,A. A. Tuzhilin

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Branching Solutions to One-dimensional Variational Problems

By: Alexander O. Ivanov,A. A. Tuzhilin

This book deals with the new class of one-dimensional variational problems OCo the problems with branching solutions. Instead of extreme curves (mappings of a segment to a manifold) we investigate extreme networks, which are mappings of graphs (one-dimensional cell complexes) to a manifold. Various applications of the approach are presented, such as several generalizations of the famous Steiner problem of finding the shortest network spanning given points of the plane. Contents: Preliminary Results; Networks Extremality Criteria; Linear Networks in R N; Extremals of Length Type Functionals: The Case of Parametric Networks; Extremals of Functionals Generated by Norms. Readership: Researchers in differential geometry and topology.

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Page Count

365

Publisher

World Scientific

Published Date

ISBN 10

9812810714

ISBN 13

9789812810717

Impact Spectropolarimetric Sensing

By: Sergi Kazantsev,Natalia M. Firstova,Alexander G. Petrashen

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Impact Spectropolarimetric Sensing

By: Sergi Kazantsev,Natalia M. Firstova,Alexander G. Petrashen

The first presentation of the novel interdisciplinary optical remote sensing technique for various ionized diluted media, based on the collisional polarization of the spectoral emission. The book provides a methodology of the impact spectropolarimetic sensing of many solutions to many practical diagnostic problems.

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365

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Springer Science & Business Media

Published Date

ISBN 10

146154839X

ISBN 13

9781461548393

Light Scattering Reviews 10

Light Scattering and Radiative Transfer

By: Alexander A. Kokhanovsky

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Light Scattering Reviews 10

Light Scattering and Radiative Transfer

By: Alexander A. Kokhanovsky

The work is aimed at the review of hot topics in modern light scattering and radiative transfer. A special attention will be given to the description of the methods of integro-differential radiative transfer equation solution. In particular, the asymptotic radiative transfer and the method of discrete ordinates will be considered. A comprehensive review of light absorption in the terrestrial atmosphere will be given as well. The inverse problem solution will be reviewed as well.

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355

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Springer

Published Date

ISBN 10

3662467623

ISBN 13

9783662467626

Handbook of Mathematics for Engineers and Scientists

By: Andrei D. Polyanin,Alexander V. Manzhirov

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Handbook of Mathematics for Engineers and Scientists

By: Andrei D. Polyanin,Alexander V. Manzhirov

Covering the main fields of mathematics, this handbook focuses on the methods used for obtaining solutions of various classes of mathematical equations that underlie the mathematical modeling of numerous phenomena and processes in science and technology. The authors describe formulas, methods, equations, and solutions that are frequently used in scientific and engineering applications and present classical as well as newer solution methods for various mathematical equations. The book supplies numerous examples, graphs, figures, and diagrams and contains many results in tabular form, including finite sums and series and exact solutions of differential, integral, and functional equations.

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1542

Publisher

CRC Press

Published Date

ISBN 10

1420010514

ISBN 13

9781420010510

Combinatorial Methods

Free Groups, Polynomials, and Free Algebras

By: Vladimir Shpilrain,Alexander Mikhalev,Jie-tai Yu

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Combinatorial Methods

Free Groups, Polynomials, and Free Algebras

By: Vladimir Shpilrain,Alexander Mikhalev,Jie-tai Yu

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322

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Springer Science & Business Media

Published Date

ISBN 10

038721724X

ISBN 13

9780387217246

Fundamentals of Functions and Measure Theory

By: Valeriy K. Zakharov,Timofey V. Rodionov,Alexander V. Mikhalev

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Fundamentals of Functions and Measure Theory

By: Valeriy K. Zakharov,Timofey V. Rodionov,Alexander V. Mikhalev

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480

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Walter de Gruyter GmbH & Co KG

Published Date

ISBN 10

3110550962

ISBN 13

9783110550962

The Concise Handbook of Algebra

By: Alexander V. Mikhalev,G.F. Pilz

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The Concise Handbook of Algebra

By: Alexander V. Mikhalev,G.F. Pilz

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629

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Springer Science & Business Media

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ISBN 10

9401732671

ISBN 13

9789401732673

Endomorphism Rings of Abelian Groups

By: P.A. Krylov,Alexander V. Mikhalev,A.A. Tuganbaev

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Endomorphism Rings of Abelian Groups

By: P.A. Krylov,Alexander V. Mikhalev,A.A. Tuganbaev

Every Abelian group can be related to an associative ring with an identity element, the ring of all its endomorphisms. Recently the theory of endomor phism rings of Abelian groups has become a rapidly developing area of algebra. On the one hand, it can be considered as a part of the theory of Abelian groups; on the other hand, the theory can be considered as a branch of the theory of endomorphism rings of modules and the representation theory of rings. There are several reasons for studying endomorphism rings of Abelian groups: first, it makes it possible to acquire additional information about Abelian groups themselves, to introduce new concepts and methods, and to find new interesting classes of groups; second, it stimulates further develop ment of the theory of modules and their endomorphism rings. The theory of endomorphism rings can also be useful for studies of the structure of additive groups of rings, E-modules, and homological properties of Abelian groups. The books of Baer [52] and Kaplansky [245] have played an important role in the early development of the theory of endomorphism rings of Abelian groups and modules. Endomorphism rings of Abelian groups are much stu died in monographs of Fuchs [170], [172], and [173]. Endomorphism rings are also studied in the works of Kurosh [287], Arnold [31], and Benabdallah [63].

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456

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Springer Science & Business Media

Published Date

ISBN 10

9401703450

ISBN 13

9789401703451

Differential and Difference Dimension Polynomials

By: Alexander V. Mikhalev,A.B. Levin,E.V. Pankratiev,M.V. Kondratieva

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Differential and Difference Dimension Polynomials

By: Alexander V. Mikhalev,A.B. Levin,E.V. Pankratiev,M.V. Kondratieva

The role of Hilbert polynomials in commutative and homological algebra as well as in algebraic geometry and combinatorics is well known. A similar role in differential algebra is played by the differential dimension polynomials. The notion of differential dimension polynomial was introduced by E. Kolchin in 1964 [KoI64]' but the problems and ideas that had led to this notion (and that are reflected in this book) have essentially more long history. Actually, one can say that the differential dimension polynomial describes in exact terms the freedom degree of a dynamic system as well as the number of arbitrary constants in the general solution of a system of algebraic differential equations. The first attempts of such description were made at the end of 19th century by Jacobi [Ja890] who estimated the number of algebraically independent constants in the general solution of a system of linear ordinary differential equations. Later on, Jacobi's results were extended to some cases of nonlinear systems, but in general case the problem of such estimation (that is known as the problem of Jacobi's bound) remains open. There are some generalization of the problem of Jacobi's bound to the partial differential equations, but the results in this area are just appearing. At the beginning of the 20th century algebraic methods in the theory of differen tial equations were actively developed by F. Riquier [RiqlO] and M.

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Page Count

434

Publisher

Springer Science & Business Media

Published Date

ISBN 10

9401712573

ISBN 13

9789401712576

Book's by Alexander Mikhalev

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