Vladimir Turaev's Books

Homotopy Quantum Field Theory

By: Vladimir G. Turaev

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Homotopy Quantum Field Theory (HQFT) is a branch of Topological Quantum Field Theory founded by E. Witten and M. Atiyah. It applies ideas from theoretical physics to study principal bundles over manifolds and, more generally, homotopy classes of maps from manifolds to a fixed target space. This book is the first systematic exposition of Homotopy Quantum Field Theory. It starts with a formal definition of an HQFT and provides examples of HQFTs in all dimensions. The main body of the text is focused on $2$-dimensional and $3$-dimensional HQFTs. A study of these HQFTs leads to new algebraic objects: crossed Frobenius group-algebras, crossed ribbon group-categories, and Hopf group-coalgebras. These notions and their connections with HQFTs are discussed in detail. The text ends with several appendices including an outline of recent developments and a list of open problems. Three appendices by M. Muger and A. Virelizier summarize their work in this area. The book is addressed to mathematicians, theoretical physicists, and graduate students interested in topological aspects of quantum field theory. The exposition is self-contained and well suited for a one-semester graduate course. Prerequisites include only basics of algebra and topology.

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300

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European Mathematical Society

Published Date

ISBN 10

3037190868

ISBN 13

9783037190869

Quantum Invariants of Knots and 3-Manifolds

By: Vladimir G. Turaev

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Quantum Invariants of Knots and 3-Manifolds

By: Vladimir G. Turaev

Due to the strong appeal and wide use of this monograph, it is now available in its third revised edition. The monograph gives a systematic treatment of 3-dimensional topological quantum field theories (TQFTs) based on the work of the author with N. Reshetikhin and O. Viro. This subject was inspired by the discovery of the Jones polynomial of knots and the Witten-Chern-Simons field theory. On the algebraic side, the study of 3-dimensional TQFTs has been influenced by the theory of braided categories and the theory of quantum groups. The book is divided into three parts. Part I presents a construction of 3-dimensional TQFTs and 2-dimensional modular functors from so-called modular categories. This gives a vast class of knot invariants and 3-manifold invariants as well as a class of linear representations of the mapping class groups of surfaces. In Part II the technique of 6j-symbols is used to define state sum invariants of 3-manifolds. Their relation to the TQFTs constructed in Part I is established via the theory of shadows. Part III provides constructions of modular categories, based on quantum groups and skein modules of tangles in the 3-space. This fundamental contribution to topological quantum field theory is accessible to graduate students in mathematics and physics with knowledge of basic algebra and topology. It is an indispensable source for everyone who wishes to enter the forefront of this fascinating area at the borderline of mathematics and physics. Contents: Invariants of graphs in Euclidean 3-space and of closed 3-manifolds Foundations of topological quantum field theory Three-dimensional topological quantum field theory Two-dimensional modular functors 6j-symbols Simplicial state sums on 3-manifolds Shadows of manifolds and state sums on shadows Constructions of modular categories

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608

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Walter de Gruyter GmbH & Co KG

Published Date

ISBN 10

3110435225

ISBN 13

9783110435221

Stability, Structures And Chaos In Nonlinear Synchronization Networks

By: Valentin S Afraimovich,V I Nekorkin,G V Osipov,Vladimir D Shalfeev

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Stability, Structures And Chaos In Nonlinear Synchronization Networks

By: Valentin S Afraimovich,V I Nekorkin,G V Osipov,Vladimir D Shalfeev

The understanding of fields and media using discrete lattice models has been greatly aided by the advent of powerful computers. This has also led to the formulation of new and inspiring problems associated with the analysis of homogeneous discrete networks of interacting dynamical elements. This book investigates the nonlinear dynamics of peculiar discrete media made up of interconnected phase synchronization systems. After an introduction which sets out the nature of the problem, the book goes on to consider dynamic processes in chain and lattice networks, utilising both continuous and discrete synchronization systems as component elements. Computational studies aimed at oscillatory-wave phenomena will make the book valuable for specialists in radio engineering, biological excitable media and other branches of physics and biology as well as specialists in applied mathematics and nonlinear sciences.

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260

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World Scientific

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ISBN 10

9814501891

ISBN 13

9789814501897

Quantum Leap

From Dirac and Feynman, Across the Universe, to Human Body and Mind

By: Vladimir G. Ivancevic

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Quantum Leap

From Dirac and Feynman, Across the Universe, to Human Body and Mind

By: Vladimir G. Ivancevic

This is a unique 21st-century monograph that reveals a basic, yet deep understanding of the universe, as well as the human mind and body OCo all from the perspective of quantum mechanics and quantum field theory.This book starts with both non-mathematical and mathematical preliminaries. It presents the basics of both non-relativistic and relativistic quantum mechanics, and introduces Feynman path integrals and their application to quantum fields and string theory, as well as some non-quantum applications. It then describes the quantum universe in the form of loop quantum gravity and quantum cosmology. Lastly, the book turns to the human body and mind, applying quantum theory to electro-muscular stimulation and consciousness.It can be used as a graduate (or advanced undergraduate) textbook for a two-semester course in quantum physics and its modern applications. Some parts of the book can also be used by engineers, biologists, psychologists and computer scientists, as well as applied mathematicians, both in industry and academia.

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855

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World Scientific

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ISBN 10

9812819282

ISBN 13

9789812819284

Applied Differential Geometry

A Modern Introduction

By: Vladimir G. Ivancevic

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Applied Differential Geometry

A Modern Introduction

By: Vladimir G. Ivancevic

Introduction -- Technical preliminaries: tensors, actions and functors -- Applied manifold geometry -- Applied bundle geometry -- Applied jet geometry -- Geometrical path integrals and their applications

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1346

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World Scientific

Published Date

ISBN 10

9812770720

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9789812770721

Topological Methods in Hydrodynamics

By: Vladimir I. Arnold,Boris A. Khesin

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Topological Methods in Hydrodynamics

By: Vladimir I. Arnold,Boris A. Khesin

The first monograph to treat topological, group-theoretic, and geometric problems of ideal hydrodynamics and magnetohydrodynamics from a unified point of view. It describes the necessary preliminary notions both in hydrodynamics and pure mathematics with numerous examples and figures. The book is accessible to graduates as well as pure and applied mathematicians working in hydrodynamics, Lie groups, dynamical systems, and differential geometry.

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455

Publisher

Springer Nature

Published Date

ISBN 10

3030742784

ISBN 13

9783030742782

Further Insights into Oscillation Theory

By: Nikolai Verichev,Stanislav Verichev,Vladimir Erofeev

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Further Insights into Oscillation Theory

By: Nikolai Verichev,Stanislav Verichev,Vladimir Erofeev

The book is written for students of universities and postgraduate students specializing in the field of nonlinear dynamics, as well as specialists in various fields of mechanical engineering. It is devoted to the development of original methods, and outlines the results of analytical studies of dynamical chaos, synchronization, and dynamic structures in lattices of coupled rotators. It presents its findings within the context of the phase space of models and by involving methods of the qualitative theory of differential equations, the theory of bifurcations, and qualitative numerical methods.

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496

Publisher

Cambridge Scholars Publishing

Published Date

ISBN 10

1527572978

ISBN 13

9781527572973

Introduction to Nonlinear Oscillations

By: Vladimir I. Nekorkin

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Introduction to Nonlinear Oscillations

By: Vladimir I. Nekorkin

A systematic outline of the basic theory of oscillations, combining several tools in a single textbook. The author explains fundamental ideas and methods, while equally aiming to teach students the techniques of solving specific (practical) or more complex problems. Following an introduction to fundamental notions and concepts of modern nonlinear dynamics, the text goes on to set out the basics of stability theory, as well as bifurcation theory in one and two-dimensional cases. Foundations of asymptotic methods and the theory of relaxation oscillations are presented, with much attention paid to a method of mappings and its applications. With each chapter including exercises and solutions, including computer problems, this book can be used in courses on oscillation theory for physics and engineering students. It also serves as a good reference for students and scientists in computational neuroscience.

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264

Publisher

John Wiley & Sons

Published Date

ISBN 10

352768543X

ISBN 13

9783527685431

Applied Differential Geometry: A Modern Introduction

By: Vladimir G Ivancevic,Tijana T Ivancevic

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Applied Differential Geometry: A Modern Introduction

By: Vladimir G Ivancevic,Tijana T Ivancevic

This graduate-level monographic textbook treats applied differential geometry from a modern scientific perspective. Co-authored by the originator of the world's leading human motion simulator — “Human Biodynamics Engine”, a complex, 264-DOF bio-mechanical system, modeled by differential-geometric tools — this is the first book that combines modern differential geometry with a wide spectrum of applications, from modern mechanics and physics, via nonlinear control, to biology and human sciences. The book is designed for a two-semester course, which gives mathematicians a variety of applications for their theory and physicists, as well as other scientists and engineers, a strong theory underlying their models.

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1346

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World Scientific

Published Date

ISBN 10

9814475645

ISBN 13

9789814475648

Introduction to Combinatorial Torsions

By: Vladimir Turaev

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Introduction to Combinatorial Torsions

By: Vladimir Turaev

This book is an introduction to combinatorial torsions of cellular spaces and manifolds with special emphasis on torsions of 3-dimensional manifolds. The first two chapters cover algebraic foundations of the theory of torsions and various topological constructions of torsions due to K. Reidemeister, J.H.C. Whitehead, J. Milnor and the author. We also discuss connections between the torsions and the Alexander polynomials of links and 3-manifolds. The third (and last) chapter of the book deals with so-called refined torsions and the related additional structures on manifolds, specifically homological orientations and Euler structures. As an application, we give a construction of the multivariable Conway polynomial of links in homology 3-spheres. At the end of the book, we briefly describe the recent results of G. Meng, C.H. Taubes and the author on the connections between the refined torsions and the Seiberg-Witten invariant of 3-manifolds. The exposition is aimed at students, professional mathematicians and physicists interested in combinatorial aspects of topology and/or in low dimensional topology. The necessary background for the reader includes the elementary basics of topology and homological algebra.

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140

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Springer Science & Business Media

Published Date

ISBN 10

3764364033

ISBN 13

9783764364038

Geometrical Dynamics of Complex Systems

A Unified Modelling Approach to Physics, Control, Biomechanics, Neurodynamics and Psycho-Socio-Economical Dynamics

By: Vladimir G. Ivancevic,Tijana T. Ivancevic

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Geometrical Dynamics of Complex Systems

A Unified Modelling Approach to Physics, Control, Biomechanics, Neurodynamics and Psycho-Socio-Economical Dynamics

By: Vladimir G. Ivancevic,Tijana T. Ivancevic

Geometrical Dynamics of Complex Systems is a graduate?level monographic textbook. Itrepresentsacomprehensiveintroductionintorigorousgeometrical dynamicsofcomplexsystemsofvariousnatures. By?complexsystems?,inthis book are meant high?dimensional nonlinear systems, which can be (but not necessarily are) adaptive. This monograph proposes a uni?ed geometrical - proachtodynamicsofcomplexsystemsofvariouskinds:engineering,physical, biophysical, psychophysical, sociophysical, econophysical, etc. As their names suggest, all these multi?input multi?output (MIMO) systems have something in common: the underlying physics. However, instead of dealing with the pop- 1 ular ?soft complexity philosophy?, we rather propose a rigorous geometrical and topological approach. We believe that our rigorous approach has much greater predictive power than the soft one. We argue that science and te- nology is all about prediction and control. Observation, understanding and explanation are important in education at undergraduate level, but after that it should be all prediction and control. The main objective of this book is to show that high?dimensional nonlinear systems and processes of ?real life? can be modelled and analyzed using rigorous mathematics, which enables their complete predictability and controllability, as if they were linear systems. It is well?known that linear systems, which are completely predictable and controllable by de?nition ? live only in Euclidean spaces (of various - mensions). They are as simple as possible, mathematically elegant and fully elaborated from either scienti?c or engineering side. However, in nature, no- ing is linear. In reality, everything has a certain degree of nonlinearity, which means: unpredictability, with subsequent uncontrollability.

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842

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Springer Science & Business Media

Published Date

ISBN 10

140204545X

ISBN 13

9781402045455

Mathematical Problems and Methods of Hydrodynamic Weather Forecasting

By: Vladimir Gordin

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Mathematical Problems and Methods of Hydrodynamic Weather Forecasting

By: Vladimir Gordin

The material provides an historical background to forecasting developments as well as introducing recent advances. The book will be of interest to both mathematicians and physicians, the topics covered include equations of dynamical meteorology, first integrals, non-linear stability, well-posedness of boundary problems, non-smooth solutions, parameters and free oscillations, meteorological data processing, methods of approximation and interpolation and numerical methods for forecast modelling.

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846

Publisher

CRC Press

Published Date

ISBN 10

9056991647

ISBN 13

9789056991647

Methods of Noncommutative Analysis

Theory and Applications

By: Vladimir E. Nazaikinskii,Victor E. Shatalov,Boris Yu. Sternin

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Methods of Noncommutative Analysis

Theory and Applications

By: Vladimir E. Nazaikinskii,Victor E. Shatalov,Boris Yu. Sternin

The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 35 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob. Titles in planning include Mark M. Meerschaert, Alla Sikorskii, and Mohsen Zayernouri, Stochastic Models for Fractional Calculus, second edition (2018) Flavia Smarazzo and Alberto Tesei, Measure Theory: Radon Measures, Young Measures and Applications to Parabolic Problems (2019) Elena Cordero and Luigi Rodino, Time-Frequency Analysis of Operators (2019) Kezheng Li, Group Schemes and Their Actions (2019; together with Tsinghua University Press) Kai Liu, Ilpo Laine, and Lianzhong Yang, Complex Differential-Difference Equations (2021) Rajendra Vasant Gurjar, Kayo Masuda, and Masayoshi Miyanishi, Affine Space Fibrations (2022)

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385

Publisher

Walter de Gruyter

Published Date

ISBN 10

3110813548

ISBN 13

9783110813548

Geometry and Quantization of Moduli Spaces

By: Vladimir Fock,Andrey Marshakov,Florent Schaffhauser,Constantin Teleman,Richard Wentworth

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Geometry and Quantization of Moduli Spaces

By: Vladimir Fock,Andrey Marshakov,Florent Schaffhauser,Constantin Teleman,Richard Wentworth

This volume is based on four advanced courses held at the Centre de Recerca Matemàtica (CRM), Barcelona. It presents both background information and recent developments on selected topics that are experiencing extraordinary growth within the broad research area of geometry and quantization of moduli spaces. The lectures focus on the geometry of moduli spaces which are mostly associated to compact Riemann surfaces, and are presented from both classical and quantum perspectives.

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230

Publisher

Birkhäuser

Published Date

ISBN 10

3319335782

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9783319335780

Notes on Prosody and Abram Gannibal

By: Vladimir Nabokov

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Notes on Prosody and Abram Gannibal

By: Vladimir Nabokov

Two appendixes from Nabokov's famous edition of Eugene Onegin: his study of versification in English and Russian poetry, and his "term paper" on Pushkin’s Ethiopian ancestor. Originally published in 1965. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

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191

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Princeton University Press

Published Date

ISBN 10

1400875927

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9781400875924

Nonlinear Dynamics of Chaotic and Stochastic Systems

Tutorial and Modern Developments

By: Vadim S. Anishchenko,Vladimir Astakhov,Alexander Neiman,Tatjana Vadivasova,Lutz Schimansky-Geier

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Nonlinear Dynamics of Chaotic and Stochastic Systems

Tutorial and Modern Developments

By: Vadim S. Anishchenko,Vladimir Astakhov,Alexander Neiman,Tatjana Vadivasova,Lutz Schimansky-Geier

Contains both an exhaustive introduction to the subject as well as a detailed discussion of fundamental problems and research results. Despite the unified presentation of the subject, care has been taken to present the material in largely self-contained chapters.

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396

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3540424199

ISBN 13

9783540424192

Synergetic Phenomena in Active Lattices

Patterns, Waves, Solitons, Chaos

By: Vladimir I. Nekorkin,M. G. Velarde

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Synergetic Phenomena in Active Lattices

Patterns, Waves, Solitons, Chaos

By: Vladimir I. Nekorkin,M. G. Velarde

In this book, the authors deal with basic concepts and models, with methodologies for studying the existence and stability of motions, understanding the mechanisms of formation of patterns and waves, their propagation and interactions in active lattice systems, and about how much cooperation or competition between order and chaos is crucial for synergetic behavior and evolution.

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371

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Springer Science & Business Media

Published Date

ISBN 10

3642560539

ISBN 13

9783642560538

Quantum Groups

By: Vladimir K. Dobrev

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Quantum Groups

By: Vladimir K. Dobrev

With applications in quantum field theory, general relativity and elementary particle physics, this three-volume work studies the invariance of differential operators under Lie algebras, quantum groups and superalgebras. This second volume covers quantum groups in their two main manifestations: quantum algebras and matrix quantum groups. The exposition covers both the general aspects of these and a great variety of concrete explicitly presented examples. The invariant q-difference operators are introduced mainly using representations of quantum algebras on their dual matrix quantum groups as carrier spaces. This is the first book that covers the title matter applied to quantum groups. Contents Quantum Groups and Quantum Algebras Highest-Weight Modules over Quantum Algebras Positive-Energy Representations of Noncompact Quantum Algebras Duality for Quantum Groups Invariant q-Difference Operators Invariant q-Difference Operators Related to GLq(n) q-Maxwell Equations Hierarchies

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450

Publisher

Walter de Gruyter GmbH & Co KG

Published Date

ISBN 10

3110427788

ISBN 13

9783110427783

KAM Theory and Semiclassical Approximations to Eigenfunctions

By: Vladimir F. Lazutkin

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KAM Theory and Semiclassical Approximations to Eigenfunctions

By: Vladimir F. Lazutkin

It is a surprising fact that so far almost no books have been published on KAM theory. The first part of this book seems to be the first monographic exposition of this subject, despite the fact that the discussion of KAM theory started as early as 1954 (Kolmogorov) and was developed later in 1962 by Arnold and Moser. Today, this mathematical field is very popular and well known among physicists and mathematicians. In the first part of this Ergebnisse-Bericht, Lazutkin succeeds in giving a complete and self-contained exposition of the subject, including a part on Hamiltonian dynamics. The main results concern the existence and persistence of KAM theory, their smooth dependence on the frequency, and the estimate of the measure of the set filled by KAM theory. The second part is devoted to the construction of the semiclassical asymptotics to the eigenfunctions of the generalized Schrödinger operator. The main result is the asymptotic formulae for eigenfunctions and eigenvalues, using Maslov`s operator, for the set of eigenvalues of positive density in the set of all eigenvalues. An addendum by Prof. A.I. Shnirelman treats eigenfunctions corresponding to the "chaotic component" of the phase space.

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390

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Springer Science & Business Media

Published Date

ISBN 10

3642762476

ISBN 13

9783642762475

Algebras, Rings and Modules

Lie Algebras and Hopf Algebras

By: Michiel Hazewinkel,Nadezhda Mikhaĭlovna Gubareni,Vladimir V. Kirichenko

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Algebras, Rings and Modules

Lie Algebras and Hopf Algebras

By: Michiel Hazewinkel,Nadezhda Mikhaĭlovna Gubareni,Vladimir V. Kirichenko

Presenting an introduction to the theory of Hopf algebras, the authors also discuss some important aspects of the theory of Lie algebras. This book includes a chapters on the Hopf algebra of symmetric functions, the Hopf algebra of representations of the symmetric groups, the Hopf algebras of the nonsymmetric and quasisymmetric functions, and the Hopf algebra of permutations.

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425

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821852620

ISBN 13

9780821852620

Lermontov's Narratives of Heroism

By: Vladimir Golstein

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Lermontov's Narratives of Heroism

By: Vladimir Golstein

This is the first study of Russian writer Mikhail Lermontov (1814-41) that attempts to integrate the in-depth interpretations of all his major texts--including his famous A Hero of Our Time, the novel that laid the foundation for the Russian psychological novel. Lermontov's explorations of the virtues and limitations of heroic, self-reliant conduct have subsequently become obscured or misread. This new book focuses upon the peculiar, disturbing, and arguably most central feature of Russian culture: its suspicion of and hostility toward individual achievement and self-assertion. The analysis and interpretation of Lermontov's texts enables Golstein to address broader cultural issues by exploring the reasons behind the persistent misreading of Lermontov's major works and by investigating the cultural attitudes that shaped Russia's reaction to the challenges of modernity.

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266

Publisher

Northwestern University Press

Published Date

ISBN 10

0810116111

ISBN 13

9780810116115

The Struggle Between Life and Death in Proto-Bactrian Culture

Ritual and Conflict

By: Vladimir I. Ionesov

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The Struggle Between Life and Death in Proto-Bactrian Culture

Ritual and Conflict

By: Vladimir I. Ionesov

A systematic analysis of the Bactrian archaeological record. The author's assessments of excavated findings aim to provide a better sense of how urban (or fortress-city) life developed out of small-scale traditional societies.

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320

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Edwin Mellen Press

Published Date

ISBN 10

0773472908

ISBN 13

9780773472907

Chaos, Synchronization and Structures in Dynamics of Systems with Cylindrical Phase Space

By: Nikolai Verichev,Stanislav Verichev,Vladimir Erofeev

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Chaos, Synchronization and Structures in Dynamics of Systems with Cylindrical Phase Space

By: Nikolai Verichev,Stanislav Verichev,Vladimir Erofeev

This book develops analytical methods for studying the dynamical chaos, synchronization, and dynamics of structures in various models of coupled rotators. Rotators and their systems are defined in a cylindrical phase space, and, unlike oscillators, which are defined in Rn, they have a wider “range” of motion: There are vibrational and rotational types for cyclic variables, as well as their combinations (rotational-vibrational) if the number of cyclic variables is more than one. The specificity of rotator phase space poses serious challenges in terms of selecting methods for studying the dynamics of related systems. The book chiefly focuses on developing a modified form of the method of averaging, which can be used to study the dynamics of rotators. In general, the book uses the “language” of the qualitative theory of differential equations, point mappings, and the theory of bifurcations, which helps authors to obtain new results on dynamical chaos in systems with few degrees of freedom. In addition, a special section is devoted to the study and classification of dynamic structures that can occur in systems with a large number of interconnected objects, i.e. in lattices of rotators and/or oscillators. Given its scope and format, the book can be used both in lectures and courses on nonlinear dynamics, and in specialized courses on the development and operation of relevant systems that can be represented by a large number of various practical systems: interconnected grids of various mechanical systems, various types of networks including not only mechanical but also biological systems, etc.

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207

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Springer Nature

Published Date

ISBN 10

3030361039

ISBN 13

9783030361037

Complex Nonlinearity

Chaos, Phase Transitions, Topology Change and Path Integrals

By: Vladimir G. Ivancevic,Tijana T. Ivancevic

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Complex Nonlinearity

Chaos, Phase Transitions, Topology Change and Path Integrals

By: Vladimir G. Ivancevic,Tijana T. Ivancevic

Complex Nonlinearity: Chaos, Phase Transitions, Topology Change and Path Integrals is a book about prediction & control of general nonlinear and chaotic dynamics of high-dimensional complex systems of various physical and non-physical nature and their underpinning geometro-topological change. The book starts with a textbook-like expose on nonlinear dynamics, attractors and chaos, both temporal and spatio-temporal, including modern techniques of chaos–control. Chapter 2 turns to the edge of chaos, in the form of phase transitions (equilibrium and non-equilibrium, oscillatory, fractal and noise-induced), as well as the related field of synergetics. While the natural stage for linear dynamics comprises of flat, Euclidean geometry (with the corresponding calculation tools from linear algebra and analysis), the natural stage for nonlinear dynamics is curved, Riemannian geometry (with the corresponding tools from nonlinear, tensor algebra and analysis). The extreme nonlinearity – chaos – corresponds to the topology change of this curved geometrical stage, usually called configuration manifold. Chapter 3 elaborates on geometry and topology change in relation with complex nonlinearity and chaos. Chapter 4 develops general nonlinear dynamics, continuous and discrete, deterministic and stochastic, in the unique form of path integrals and their action-amplitude formalism. This most natural framework for representing both phase transitions and topology change starts with Feynman’s sum over histories, to be quickly generalized into the sum over geometries and topologies. The last Chapter puts all the previously developed techniques together and presents the unified form of complex nonlinearity. Here we have chaos, phase transitions, geometrical dynamics and topology change, all working together in the form of path integrals. The objective of this book is to provide a serious reader with a serious scientific tool that will enable them to actually perform a competitive research in modern complex nonlinearity. It includes a comprehensive bibliography on the subject and a detailed index. Target readership includes all researchers and students of complex nonlinear systems (in physics, mathematics, engineering, chemistry, biology, psychology, sociology, economics, medicine, etc.), working both in industry/clinics and academia.

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855

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Springer Science & Business Media

Published Date

ISBN 10

3540793577

ISBN 13

9783540793571

The Arnoldfest

Proceedings of a Conference in Honour of V.I. Arnold for His Sixtieth Birthday

By: Vladimir Igorevich Arnolʹd

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The Arnoldfest

Proceedings of a Conference in Honour of V.I. Arnold for His Sixtieth Birthday

By: Vladimir Igorevich Arnolʹd

This volume presents articles originating from invited talks at an exciting international conference held at The Fields Institute in Toronto celebrating the sixtieth birthday of the renowned mathematician, Vladimir Arnold. Experts from the world over--including several from "Arnold's school"--gave illuminating talks and lively poster sessions. The presentations focused on Arnold's main areas of interest: singularity theory, the theory of curves, symmetry groups, dynamical systems, mechanics, and related areas of mathematics. The book begins with notes of three lectures by V. Arnold given in the framework of the Institute's Distinguished Lecturer program. The topics of the lectures are: (1) From Hilbert's Superposition Problem to Dynamical Systems (2) Symplectization, Complexification, and Mathematical Trinities (3) Topological Problems in Wave Propagation Theory and Topological Economy Principle in Algebraic Geometry. Arnold's three articles include insightful comments on Russian and Western mathematics and science. Complementing the first is Jurgen Moser's "Recollections", concerning some of the history of KAM theory.

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575

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American Mathematical Soc.

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ISBN 10

0821809458

ISBN 13

9780821809457

The Culture and Social Institutions of Ancient Iran

By: Muhammad A. Dandamaev,Vladimir G. Lukonin

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The Culture and Social Institutions of Ancient Iran

By: Muhammad A. Dandamaev,Vladimir G. Lukonin

The authors look in detail at the highly developed social institutions of the Achaemenid Empire.

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486

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Cambridge University Press

Published Date

ISBN 10

0521611911

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9780521611916

Computer Modeling and Simulation of Dynamic Systems Using Wolfram SystemModeler

By: Kirill Rozhdestvensky,Vladimir Ryzhov,Tatiana Fedorova,Kirill Safronov,Nikita Tryaskin,Shaharin Anwar Sulaiman,Mark Ovinis,Suhaimi Hassan

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Computer Modeling and Simulation of Dynamic Systems Using Wolfram SystemModeler

By: Kirill Rozhdestvensky,Vladimir Ryzhov,Tatiana Fedorova,Kirill Safronov,Nikita Tryaskin,Shaharin Anwar Sulaiman,Mark Ovinis,Suhaimi Hassan

This book briefly discusses the main provisions of the theory of modeling. It also describes in detail the methodology for constructing computer models of dynamic systems using the Wolfram visual modeling environment, SystemModeler, and provides illustrative examples of solving problems of mechanics and hydraulics. Intended for students and professionals in the field, the book also serves as a supplement to university courses in modeling and simulation of dynamic systems.

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274

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Springer Nature

Published Date

ISBN 10

9811528039

ISBN 13

9789811528033

Quantum Neural Computation

By: Vladimir G. Ivancevic,Tijana T. Ivancevic

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Quantum Neural Computation

By: Vladimir G. Ivancevic,Tijana T. Ivancevic

Quantum Neural Computation is a graduate–level monographic textbook. It presents a comprehensive introduction, both non-technical and technical, into modern quantum neural computation, the science behind the fiction movie Stealth. Classical computing systems perform classical computations (i.e., Boolean operations, such as AND, OR, NOT gates) using devices that can be described classically (e.g., MOSFETs). On the other hand, quantum computing systems perform classical computations using quantum devices (quantum dots), that is devices that can be described only using quantum mechanics. Any information transfer between such computing systems involves a state measurement. This book describes this information transfer at the edge of classical and quantum chaos and turbulence, where mysterious quantum-mechanical linearity meets even more mysterious brain’s nonlinear complexity, in order to perform a super–high–speed and error–free computations. This monograph describes a crossroad between quantum field theory, brain science and computational intelligence.

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938

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Springer Science & Business Media

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ISBN 10

9048133505

ISBN 13

9789048133505

Neuro-Fuzzy Associative Machinery for Comprehensive Brain and Cognition Modelling

By: Vladimir G. Ivancevic,Tijana T. Ivancevic

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Neuro-Fuzzy Associative Machinery for Comprehensive Brain and Cognition Modelling

By: Vladimir G. Ivancevic,Tijana T. Ivancevic

This book represents a comprehensive introduction into both conceptual and rigorous brain and cognition modelling. It is devoted to understanding, prediction and control of the fundamental mechanisms of brain functioning. The reader will be provided with a scientific tool enabling him or her to perform a competitive research in brain and cognition modelling. This is a graduate–level monographic textbook.

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738

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Springer

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ISBN 10

3540483969

ISBN 13

9783540483960

Torsions of 3-dimensional Manifolds

By: Vladimir Turaev

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Torsions of 3-dimensional Manifolds

By: Vladimir Turaev

From the reviews: "This is an excellent exposition about abelian Reidemeister torsions for three-manifolds." —Zentralblatt Math "This monograph contains a wealth of information many topologists will find very handy. ...Many of the new points of view pioneered by Turaev are gradually becoming mainstream and are spreading beyond the pure topology world. This monograph is a timely and very useful addition to the scientific literature." —Mathematical Reviews

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218

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Springer Science & Business Media

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ISBN 10

3764369116

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9783764369118

Monoidal Categories and Topological Field Theory

By: Vladimir Turaev,Alexis Virelizier

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Monoidal Categories and Topological Field Theory

By: Vladimir Turaev,Alexis Virelizier

This monograph is devoted to monoidal categories and their connections with 3-dimensional topological field theories. Starting with basic definitions, it proceeds to the forefront of current research. Part 1 introduces monoidal categories and several of their classes, including rigid, pivotal, spherical, fusion, braided, and modular categories. It then presents deep theorems of Müger on the center of a pivotal fusion category. These theorems are proved in Part 2 using the theory of Hopf monads. In Part 3 the authors define the notion of a topological quantum field theory (TQFT) and construct a Turaev-Viro-type 3-dimensional state sum TQFT from a spherical fusion category. Lastly, in Part 4 this construction is extended to 3-manifolds with colored ribbon graphs, yielding a so-called graph TQFT (and, consequently, a 3-2-1 extended TQFT). The authors then prove the main result of the monograph: the state sum graph TQFT derived from any spherical fusion category is isomorphic to the Reshetikhin-Turaev surgery graph TQFT derived from the center of that category. The book is of interest to researchers and students studying topological field theory, monoidal categories, Hopf algebras and Hopf monads.

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