S.P. Novikov's Books

Solitons and Geometry

By: S. P. Novikov

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This is an introduction to the geometry of Hamiltonian systems from the modern point of view where the basic structure is a Poisson bracket. Using this approach a mathematical analogue of the famous 'Dirac monopole' is obtained starting from the classical top in a gravity field. This approach is especially useful in physical applications in which a field theory appears; this is the subject of the second part of the lectures, which contains a theory of conservative hydrodynamic-type systems, based on Riemannian geometry, developed over the last decade. The theory has had success in solving problems in physics, such as ones associated with dispersive analogues of shock waves, and its development has led to the introduction of new notions in geometry. The book is based on lectures given by the author in Pisa and which were intended for a non-specialist audience. It provides an introduction from which to proceed to more advanced work in the area.

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Cambridge University Press

Published Date

ISBN 10

0521471966

ISBN 13

9780521471961

Topology I

General Survey

By: S.P. Novikov

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Topology I

General Survey

By: S.P. Novikov

This up-to-date survey of the whole field of topology is the flagship of the topology subseries of the Encyclopaedia. The book gives an overview of various subfields, beginning with the elements and proceeding right up to the present frontiers of research.

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326

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Springer Science & Business Media

Published Date

ISBN 10

3662105799

ISBN 13

9783662105795

Modern Geometry - Methods and Applications

Part I. The Geometry of Surfaces, Transformation Groups, and Fields

By: B.A. Dubrovin,A.T. Fomenko,S.P. Novikov

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Modern Geometry - Methods and Applications

Part I. The Geometry of Surfaces, Transformation Groups, and Fields

By: B.A. Dubrovin,A.T. Fomenko,S.P. Novikov

manifolds, transformation groups, and Lie algebras, as well as the basic concepts of visual topology. It was also agreed that the course should be given in as simple and concrete a language as possible, and that wherever practic able the terminology should be that used by physicists. Thus it was along these lines that the archetypal course was taught. It was given more permanent form as duplicated lecture notes published under the auspices of Moscow State University as: Differential Geometry, Parts I and II, by S. P. Novikov, Division of Mechanics, Moscow State University, 1972. Subsequently various parts of the course were altered, and new topics added. This supplementary material was published (also in duplicated form) as Differential Geometry, Part III, by S. P. Novikov and A. T. Fomenko, Division of Mechanics, Moscow State University, 1974. The present book is the outcome of a reworking, re-ordering, and ex tensive elaboration of the above-mentioned lecture notes. It is the authors' view that it will serve as a basic text from which the essentials for a course in modern geometry may be easily extracted. To S. P. Novikov are due the original conception and the overall plan of the book. The work of organizing the material contained in the duplicated lecture notes in accordance with this plan was carried out by B. A. Dubrovin.

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479

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Springer Science & Business Media

Published Date

ISBN 10

1468499467

ISBN 13

9781468499469

Basic Elements of Differential Geometry and Topology

By: S.P. Novikov,A.T. Fomenko

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Basic Elements of Differential Geometry and Topology

By: S.P. Novikov,A.T. Fomenko

One service mathematics has rendered the 'Et moi ..., si j'avait su comment en revenir, je n'y serais point aile.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded n- sense'. The series is divergent; therefore we may be able to do something with it. Eric T. Bell O. Heaviside Matht"natics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics seNe as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series

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500

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Springer Science & Business Media

Published Date

ISBN 10

9401578958

ISBN 13

9789401578950

Lasers with Nuclear Pumping

By: S.P. Melnikov,A.A. Sinyanskii,A.N. Sizov,George H. Miley

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Lasers with Nuclear Pumping

By: S.P. Melnikov,A.A. Sinyanskii,A.N. Sizov,George H. Miley

This book covers the history of lasers with nuclear pumping (Nuclear Pumped Lasers, NPLs). This book showcases the most important results and stages of NPL development in The Russian Federal Nuclear Center (VNIIEF) as well as other Russian and international laboratories, including laboratories in the United States. The basic science and technology behind NPLs along with potential applications are covered throughout the book. As the first comprehensive discussion of NPLs, students, researchers, and application engineers interested in high energy lasers will find this book to be an extremely valuable source of information about these unique lasers.

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Page Count

472

Publisher

Springer

Published Date

ISBN 10

3319088823

ISBN 13

9783319088822

Fixed Point Theory and Best Approximation: The KKM-map Principle

By: S.P. Singh,B. Watson,P. Srivastava

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Fixed Point Theory and Best Approximation: The KKM-map Principle

By: S.P. Singh,B. Watson,P. Srivastava

The aim of this volume is to make available to a large audience recent material in nonlinear functional analysis that has not been covered in book format before. Here, several topics of current and growing interest are systematically presented, such as fixed point theory, best approximation, the KKM-map principle, and results related to optimization theory, variational inequalities and complementarity problems. Illustrations of suitable applications are given, the links between results in various fields of research are highlighted, and an up-to-date bibliography is included to assist readers in further studies. Audience: This book will be of interest to graduate students, researchers and applied mathematicians working in nonlinear functional analysis, operator theory, approximations and expansions, convex sets and related geometric topics and game theory.

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231

Publisher

Springer Science & Business Media

Published Date

ISBN 10

9401588228

ISBN 13

9789401588225

Bubbles in Polymeric Liquids

Dynamics and Heat-Mass Transfer

By: S.P. Levitsky,Z.P. Shulman

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Bubbles in Polymeric Liquids

Dynamics and Heat-Mass Transfer

By: S.P. Levitsky,Z.P. Shulman

From the Authors' Preface The advancements of technology . . . and chemical engineering have brought about extensive use of a wide range of rheologically complex materials, e.g., polymeric solutions and melts, suspensions, mixtures, oil products, fibre-forming substances, etc. that are characterized by diverse and, every so often, significant deviations from classical Newtonian behavior. Such materials are often used in conditions where the formation of vapor-gas bubbles or two-phase flow regimes is possible. This necessitates deep investigations into the thermo-hydrodynamic problems of liquids with bubbles for the case of a continuous phase with anomalous rheological properties. These conditions are typical of a number of applications and manufacturing processes, e.g., gas removal from polymeric solutions or melts in production of film, chemical fibres and other polymeric materials. . . . The bubbles containing gas or vapor-gas mixtures are often present in polymeric systems. This is because of a number of reasons, e.g., a low wettability of solid surfaces by polymers, the use of volatile solvents, abundance of vapor-gas nuclei, the capture of gas by porous or fibre-like polymeric particles during the polymer dissolution or melting, etc. Spontaneous evacuation of bubbles in polymeric media is usually complicated by a high viscosity of the liquid; therefore two-phase polymeric systems possess a higher sedimentation and aggregation stability than bubble mixtures in low-molecular-weight liquids. One of the main problems in the dynamics of vapor-liquid and gas-liquid systems is the investigation of heat and mass transfer and phase interactions in a liquid with bubbles. The decisive importance of this problem in the analysis of various aspects of the bubbly fluid behavior under diverse conditions, in particular, during a sound wave propagation, has given impetus to numerous researches. The current state of art in the investigation of Newtonian liquids with bubbles is described in voluminous literature. However, these problems have been much less studied for non-Newtonian systems. Behavior of bubbles in polymeric liquids is of great interest because of wide application in chemical technology. . . . In a number of processes connected with the application of polymeric fluids, the dynamic interaction of bubbles with liquid phase plays the key role. Such interaction in the case of a polymeric liquid phase are essentially influenced by the specific properties of macromolecular fluids, including primarily the rheological effects. These effects in the bubble dynamics combined with heat and mass transfer between the bubble content and the ambient liquid constitute the main subject of the analysis presented in this book. Macrokinetics Laboratory, and Full Professor at the Byelorussian Polytechnic Institute, Department of Heat and Power Engineering. Dr. Schulman is recognized as a leading authority in his field of investigation. Extensive Bibliography: A valuable feature of this new book is its extensive international bibliography, with 393 references.

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Page Count

316

Publisher

CRC Press

Published Date

ISBN 10

1566762472

ISBN 13

9781566762472

Periodic Differential Operators

By: B. Malcolm Brown,Michael S.P. Eastham,Karl Michael Schmidt

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Periodic Differential Operators

By: B. Malcolm Brown,Michael S.P. Eastham,Karl Michael Schmidt

Periodic differential operators have a rich mathematical theory as well as important physical applications. They have been the subject of intensive development for over a century and remain a fertile research area. This book lays out the theoretical foundations and then moves on to give a coherent account of more recent results, relating in particular to the eigenvalue and spectral theory of the Hill and Dirac equations. The book will be valuable to advanced students and academics both for general reference and as an introduction to active research topics.

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220

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Springer Science & Business Media

Published Date

ISBN 10

3034805284

ISBN 13

9783034805285

Modern Geometry - Methods and Applications

Part I. The Geometry of Surfaces, Transformation Groups, and Fields

By: B.A. Dubrovin,A.T. Fomenko,S.P. Novikov

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Modern Geometry - Methods and Applications

Part I. The Geometry of Surfaces, Transformation Groups, and Fields

By: B.A. Dubrovin,A.T. Fomenko,S.P. Novikov

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479

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1468499467

ISBN 13

9781468499469

Solitons and Geometry

By: S. P. Novikov

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Solitons and Geometry

By: S. P. Novikov

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Cambridge University Press

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ISBN 10

0521471966

ISBN 13

9780521471961

Topology I

General Survey

By: S.P. Novikov

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Topology I

General Survey

By: S.P. Novikov

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326

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Springer Science & Business Media

Published Date

ISBN 10

3662105799

ISBN 13

9783662105795

Modern Geometry - Methods and Applications

Part I. The Geometry of Surfaces, Transformation Groups, and Fields

By: B.A. Dubrovin,A.T. Fomenko,S.P. Novikov

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Modern Geometry - Methods and Applications

Part I. The Geometry of Surfaces, Transformation Groups, and Fields

By: B.A. Dubrovin,A.T. Fomenko,S.P. Novikov

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464

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Springer

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ISBN 10

1468499475

ISBN 13

9781468499476

Modern Geometry— Methods and Applications

Part II: The Geometry and Topology of Manifolds

By: B.A. Dubrovin,A.T. Fomenko,S.P. Novikov

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Modern Geometry— Methods and Applications

Part II: The Geometry and Topology of Manifolds

By: B.A. Dubrovin,A.T. Fomenko,S.P. Novikov

Up until recently, Riemannian geometry and basic topology were not included, even by departments or faculties of mathematics, as compulsory subjects in a university-level mathematical education. The standard courses in the classical differential geometry of curves and surfaces which were given instead (and still are given in some places) have come gradually to be viewed as anachronisms. However, there has been hitherto no unanimous agreement as to exactly how such courses should be brought up to date, that is to say, which parts of modern geometry should be regarded as absolutely essential to a modern mathematical education, and what might be the appropriate level of abstractness of their exposition. The task of designing a modernized course in geometry was begun in 1971 in the mechanics division of the Faculty of Mechanics and Mathematics of Moscow State University. The subject-matter and level of abstractness of its exposition were dictated by the view that, in addition to the geometry of curves and surfaces, the following topics are certainly useful in the various areas of application of mathematics (especially in elasticity and relativity, to name but two), and are therefore essential: the theory of tensors (including covariant differentiation of them); Riemannian curvature; geodesics and the calculus of variations (including the conservation laws and Hamiltonian formalism); the particular case of skew-symmetric tensors (i. e.

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447

Publisher

Springer Science & Business Media

Published Date

ISBN 10

146121100X

ISBN 13

9781461211006

Topology II

Homotopy and Homology. Classical Manifolds

By: D.B. Fuchs,O.Ya. Viro

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Topology II

Homotopy and Homology. Classical Manifolds

By: D.B. Fuchs,O.Ya. Viro

Two top experts in topology, O.Ya. Viro and D.B. Fuchs, give an up-to-date account of research in central areas of topology and the theory of Lie groups. They cover homotopy, homology and cohomology as well as the theory of manifolds, Lie groups, Grassmanians and low-dimensional manifolds. Their book will be used by graduate students and researchers in mathematics and mathematical physics.

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276

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Springer Science & Business Media

Published Date

ISBN 10

3540519963

ISBN 13

9783540519966

Basic Elements of Differential Geometry and Topology

By: S.P. Novikov,A.T. Fomenko

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Basic Elements of Differential Geometry and Topology

By: S.P. Novikov,A.T. Fomenko

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9401578958

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9789401578950

Book's by S.P. Novikov

Solitons and Geometry

Solitons and Geometry

Topology I

Topology I

Modern Geometry - Methods and Applications

Modern Geometry - Methods and Applications

Basic Elements of Differential Geometry and Topology

Basic Elements of Differential Geometry and Topology

Lasers with Nuclear Pumping

Lasers with Nuclear Pumping

Fixed Point Theory and Best Approximation: The KKM-map Principle

Fixed Point Theory and Best Approximation: The KKM-map Principle

Bubbles in Polymeric Liquids

Bubbles in Polymeric Liquids

Periodic Differential Operators

Periodic Differential Operators

Modern Geometry - Methods and Applications

Modern Geometry - Methods and Applications

Solitons and Geometry

Solitons and Geometry

Topology I

Topology I

Modern Geometry - Methods and Applications

Modern Geometry - Methods and Applications

Modern Geometry— Methods and Applications

Modern Geometry— Methods and Applications

Topology II

Topology II

Basic Elements of Differential Geometry and Topology

Basic Elements of Differential Geometry and Topology

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