A.N. Tikhonov's Books

Numerical Methods for the Solution of Ill-Posed Problems

By: A.N. Tikhonov,A. Goncharsky,V.V. Stepanov,Anatoly G. Yagola

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Numerical Methods for the Solution of Ill-Posed Problems

By: A.N. Tikhonov,A. Goncharsky,V.V. Stepanov,Anatoly G. Yagola

Many problems in science, technology and engineering are posed in the form of operator equations of the first kind, with the operator and RHS approximately known. But such problems often turn out to be ill-posed, having no solution, or a non-unique solution, and/or an unstable solution. Non-existence and non-uniqueness can usually be overcome by settling for `generalised' solutions, leading to the need to develop regularising algorithms. The theory of ill-posed problems has advanced greatly since A. N. Tikhonov laid its foundations, the Russian original of this book (1990) rapidly becoming a classical monograph on the topic. The present edition has been completely updated to consider linear ill-posed problems with or without a priori constraints (non-negativity, monotonicity, convexity, etc.). Besides the theoretical material, the book also contains a FORTRAN program library. Audience: Postgraduate students of physics, mathematics, chemistry, economics, engineering. Engineers and scientists interested in data processing and the theory of ill-posed problems.

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257

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Springer Science & Business Media

Published Date

ISBN 10

940158480X

ISBN 13

9789401584807

A Collection of Problems on Mathematical Physics

International Series of Monographs in Pure and Applied Mathematics

By: B. M. Budak,A. A. Samarskii,A. N. Tikhonov

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A Collection of Problems on Mathematical Physics

International Series of Monographs in Pure and Applied Mathematics

By: B. M. Budak,A. A. Samarskii,A. N. Tikhonov

A Collection of Problems on Mathematical Physics is a translation from the Russian and deals with problems and equations of mathematical physics. The book contains problems and solutions. The book discusses problems on the derivation of equations and boundary condition. These Problems are arranged on the type and reduction to canonical form of equations in two or more independent variables. The equations of hyperbolic type concerns derive from problems on vibrations of continuous media and on electromagnetic oscillations. The book considers the statement and solutions of boundary value problems pertaining to equations of parabolic types when the physical processes are described by functions of two, three or four independent variables such as spatial coordinates or time. The book then discusses dynamic problems pertaining to the mechanics of continuous media and problems on electrodynamics. The text also discusses hyperbolic and elliptic types of equations. The book is intended for students in advanced mathematics and physics, as well as, for engineers and workers in research institutions.

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Page Count

783

Publisher

Elsevier

Published Date

ISBN 10

1483184862

ISBN 13

9781483184869

Equations of Mathematical Physics

By: A. N. Tikhonov,A. A. Samarskii

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Equations of Mathematical Physics

By: A. N. Tikhonov,A. A. Samarskii

Mathematical physics plays an important role in the study of many physical processes — hydrodynamics, elasticity, and electrodynamics, to name just a few. Because of the enormous range and variety of problems dealt with by mathematical physics, this thorough advanced undergraduate- or graduate-level text considers only those problems leading to partial differential equations. Contents: I. Classification of Partial Differential Equations II. Evaluations of the Hyperbolic Type III. Equations of the Parabolic Type IV. Equations of Elliptic Type V. Wave Propagation in Space VI. Heat Conduction in Space VII. Equations of Elliptic Type (Continuation) The authors — two well-known Russian mathematicians — have focused on typical physical processes and the principal types of equations dealing with them. Special attention is paid throughout to mathematical formulation, rigorous solutions, and physical interpretation of the results obtained. Carefully chosen problems designed to promote technical skills are contained in each chapter, along with extremely useful appendixes that supply applications of solution methods described in the main text. At the end of the book, a helpful supplement discusses special functions, including spherical and cylindrical functions.

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Page Count

802

Publisher

Courier Corporation

Published Date

ISBN 10

0486173364

ISBN 13

9780486173368

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

Kinetic Models of Catalytic Reactions

By: G.S. Yablonskii,V.I. Bykov,V.I. Elokhin,A.N. Gorban

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Kinetic Models of Catalytic Reactions

By: G.S. Yablonskii,V.I. Bykov,V.I. Elokhin,A.N. Gorban

This book has been written by a group of mathematicians and chemists whose common interest is in the complex dynamics of catalytic reactions. Based on developments in mathematical chemistry, a general theory is described that allows the investigation of the relationships between the kinetic characteristics of complex reactions and their detailed reaction mechanism. Furthermore, a comprehensive analysis is made of some typical mechanism of catalytic reactions, in particular for the oxidation of carbon monoxide on platinum metals. In fact, the book presents three kinetics: (a) detailed, oriented to the elucidation of a detailed reaction mechanism according to its kinetic laws; (b) applied, with the aim of obtaining kinetic relationships for the further design of chemical reactors; and (c) mathematical kinetics whose purpose is the analysis of mathematical models for heterogeneous catalytic reactions taking place under steady- or unsteady-state conditions.

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Page Count

391

Publisher

Elsevier

Published Date

ISBN 10

0080868266

ISBN 13

9780080868264

Emergence of Dynamical Order

Synchronization Phenomena in Complex Systems

By: Susanna C. Manrubia,Alexander S. Mikhailov,Dam¡an H. Zannette

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Emergence of Dynamical Order

Synchronization Phenomena in Complex Systems

By: Susanna C. Manrubia,Alexander S. Mikhailov,Dam¡an H. Zannette

Large populations of interacting active elements, periodic or chaotic, can undergo spontaneous transitions to dynamically ordered states. These collective states are characterized by self-organized coherence revealed by full mutual synchronization of individual dynamics or the formation of multiple synchronous clusters. Such self-organization phenomena are essential for the functioning of complex systems of various origins, both natural and artificial. This book provides a detailed introduction to the theory of collective synchronization phenomena in large complex systems. Transitions to dynamical clustering and synchronized states are systematically discussed. Such concepts as dynamical order parameters, glass like behavior and hierarchical organization are presented.

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Page Count

359

Publisher

World Scientific

Published Date

ISBN 10

9812388036

ISBN 13

9789812388032

Modern Computational Aeroelasticity

By: Min Xu,Xiaomin An,Wei Kang,Guangning Li

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Modern Computational Aeroelasticity

By: Min Xu,Xiaomin An,Wei Kang,Guangning Li

The book provides a state-of-art overview of computational methods for nonlinear aeroelasticity and load analysis, focusing on key techniques and fundamental principles for CFD/CSD coupling in temporal domain. CFD/CSD coupling software design and applications of CFD/CSD coupling techniques are discussed in detail as well. It is an essential reference for researchers and students in mechanics and applied mathematics.

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Page Count

320

Publisher

Walter de Gruyter GmbH & Co KG

Published Date

ISBN 10

3110576627

ISBN 13

9783110576627

Multiparticle Dynamics

Proceedings of the XXXII International Symposium

By: A. N. Sissakian,Guennadi Kozlov,Elena Kolganova

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Multiparticle Dynamics

Proceedings of the XXXII International Symposium

By: A. N. Sissakian,Guennadi Kozlov,Elena Kolganova

Printbegrænsninger: Der kan printes 10 sider ad gangen og max. 40 sider pr. session.

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Page Count

469

Publisher

World Scientific

Published Date

ISBN 10

9812384030

ISBN 13

9789812384034

Self-Healing Nanotextured Vascular Engineering Materials

By: Alexander L. Yarin,Min Wook Lee,Seongpil An,Sam S. Yoon

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Self-Healing Nanotextured Vascular Engineering Materials

By: Alexander L. Yarin,Min Wook Lee,Seongpil An,Sam S. Yoon

This book gives an overview of the existing self-healing nanotextured vascular approaches. It describes the healing agents used in engineering self-healing materials as well as the fundamental physicochemical phenomena accompanying self-healing. This book also addresses the different fabrication methods used to form core–shell nanofiber mats. The fundamental theoretical aspects of fracture mechanics are outlined. A brief theoretical description of cracks in brittle elastic materials is given and the Griffith approach is introduced. The fracture toughness is described, including viscoelastic effects. Critical (catastrophic) and subcritical (fatigue) cracks and their growth are also described theoretically. The adhesion and cohesion energies are introduced as well, and the theory of the blister test for the two limiting cases of stiff and soft materials is developed. In addition, the effect of non-self-healing nanofiber mats on the toughening of ply surfaces in composites is discussed. The book also presents a brief description of the electrochemical theory of corrosion crack growth. All the above-mentioned phenomena are relevant in the context of self-healing materials.

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Page Count

271

Publisher

Springer

Published Date

ISBN 10

3030052672

ISBN 13

9783030052676

Problems Of Multiphase Fluid Filtration

By: A N Konovalov

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Problems Of Multiphase Fluid Filtration

By: A N Konovalov

This book deals with a spectrum of problems related to the mathematical modeling of multiphase filtration. Emphasis is placed on an inseparable triad: model — algorithm — computer code. An analysis of new and traditional filtration problems from the point of view of both their numerical implementation and the reproduction of one or another technological characteristics of the processes under consideration is given. The basic principles which underlie the construction of efficient numerical methods taking into account the filtration problems are discussed: non-evolutionary nature, degeneration, strongly varying coefficients, the (temporal) duration of the processes involved, etc. Also attention is paid to the splitting method in terms of the physical processes involved, the method of fictitious domains and the method of front separation in grid solution. A modular analysis is performed with computational algorithms, making it possible to set up simultaneously the structure of the algorithms themselves and the structure of programs to implement these algorithms on a computer. In conclusion, the author discusses issues concerning the possibility of constructing a model of an oil deposit on a computer.

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Page Count

190

Publisher

World Scientific

Published Date

ISBN 10

9814502138

ISBN 13

9789814502139

Statistics of Random Processes I

General Theory

By: R.S. Liptser,A.N. Shiryaev

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Statistics of Random Processes I

General Theory

By: R.S. Liptser,A.N. Shiryaev

A considerable number of problems in the statistics of random processes are formulated within the following scheme. On a certain probability space (Q, ff, P) a partially observable random process (lJ,~) = (lJ ~/), t :;::-: 0, is given with only the second component n ~ = (~/), t:;::-: 0, observed. At any time t it is required, based on ~h = g., ° s sst}, to estimate the unobservable state lJ/. This problem of estimating (in other words, the filtering problem) 0/ from ~h will be discussed in this book. It is well known that if M(lJ;)

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405

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1475716656

ISBN 13

9781475716658

Fractal Control and Its Applications

By: Shu Tang Liu,Yong Ping Zhang,Chang An Liu

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Fractal Control and Its Applications

By: Shu Tang Liu,Yong Ping Zhang,Chang An Liu

The book focuses on fractal control and applications in various fields. Fractal phenomena occur in nonlinear models, and since the behaviors depicted by fractals need to be controlled in practical applications, an understanding of fractal control is necessary. This book introduces readers to Julia set fractals and Mandelbrot set fractals in a range of models, such as physical systems, biological systems and SIRS models, and discusses controllers designed to control these fractals. Further, it demonstrates how the fractal dimension can be calculated in order to describe the complexity of various systems.Offering a comprehensive and systematic overview of the practical issues in fractal control, this book is a valuable resource for readers interested in practical solutions in fractal control. It will also appeal to researchers, engineers, and graduate students in fields of fractal control and applications, as well as chaos control and applications.

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Page Count

364

Publisher

Springer Nature

Published Date

ISBN 10

9811554595

ISBN 13

9789811554599

Limit Theorems for Functionals of Random Walks

By: A. N. Borodin,Ilʹdar Abdulovich Ibragimov

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Limit Theorems for Functionals of Random Walks

By: A. N. Borodin,Ilʹdar Abdulovich Ibragimov

This book examines traditional problems in the theory of random walks: limit theorems for additive and multiadditive functionals defined on a random walk. Although the problems are traditional, the methods presented here are new. The book is intended for experts in probability theory and its applications, as well as for undergraduate and graduate students specializing in these areas.

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Page Count

276

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821804383

ISBN 13

9780821804384

At His Side

The Last Years of Isaac Babel

By: A.N. Pirozhkova

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At His Side

The Last Years of Isaac Babel

By: A.N. Pirozhkova

I WISH TO RESTORE to public memory certain features of a man endowed with great goodness of spirit, a passionate interest in people, and a miraculous gift for depicting them." So begins A. N. Pirozhkova's moving memoir of her life with Isaac Babel, perhaps the Soviet Union's greatest writer, and one of the literary world's most lively and endearing characters. Pirozhkova was the only female engineer working on Stalin's grand Moscow subway project when she met Babel in 1932 and they spent the next eight years as husband and wife. At His Side is populated with Babel's wide circle of friends - among them Maxim Gorky, Sergey Eisenstein, and André Malraux - and includes some wonderful vignettes, as when Babel accompanies a cantankerous Boris Pasternak on a long train ride to Germany to receive a literary prize. But it is Babel himself, the affable and always witty writer, who is given vivid life on this pages. And then, in 1940, Stalin's secret police arrive at the door to take Babel away, and there begins the long and sorrowful aftermath to the story. After a mock trial, Babel was summarily executed, but his fate was kept from Pirozhkova and for years she was led to believe he was alive - and writing - in a Siberian prison camp. It was not until 1952 that she learned that Babel was dead, but even then the authorities played with the truth, claiming he'd died of a heart attack. It was only after the collapse of the Soviet Union that Pirozhkova learned the true circumstances of Babel's murder. "Babel lives in his wife’s lucid yet adoring prose. We are with her, at his side"--New York Times Book Review "This glimpse into Babel’s last few years on earth, written by the person closest to him, will be a treasured possession" --Richard Bernstein The New York Times

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Page Count

212

Publisher

Steerforth

Published Date

ISBN 10

1883642981

ISBN 13

9781883642983

Equations of Mathematical Physics

By: A. N. Tikhonov,A. A. Samarskii

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Equations of Mathematical Physics

By: A. N. Tikhonov,A. A. Samarskii

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Page Count

802

Publisher

Courier Corporation

Published Date

ISBN 10

0486173364

ISBN 13

9780486173368

A Collection of Problems on Mathematical Physics

International Series of Monographs in Pure and Applied Mathematics

By: B. M. Budak,A. A. Samarskii,A. N. Tikhonov

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A Collection of Problems on Mathematical Physics

International Series of Monographs in Pure and Applied Mathematics

By: B. M. Budak,A. A. Samarskii,A. N. Tikhonov

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Page Count

783

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Elsevier

Published Date

ISBN 10

1483184862

ISBN 13

9781483184869

Book's by A.N. Tikhonov

Numerical Methods for the Solution of Ill-Posed Problems

Numerical Methods for the Solution of Ill-Posed Problems

A Collection of Problems on Mathematical Physics

A Collection of Problems on Mathematical Physics

Equations of Mathematical Physics

Equations of Mathematical Physics

Lasers with Nuclear Pumping

Lasers with Nuclear Pumping

Kinetic Models of Catalytic Reactions

Kinetic Models of Catalytic Reactions

Emergence of Dynamical Order

Emergence of Dynamical Order

Modern Computational Aeroelasticity

Modern Computational Aeroelasticity

Multiparticle Dynamics

Multiparticle Dynamics

Self-Healing Nanotextured Vascular Engineering Materials

Self-Healing Nanotextured Vascular Engineering Materials

Problems Of Multiphase Fluid Filtration

Problems Of Multiphase Fluid Filtration

Statistics of Random Processes I

Statistics of Random Processes I

Fractal Control and Its Applications

Fractal Control and Its Applications

Limit Theorems for Functionals of Random Walks

Limit Theorems for Functionals of Random Walks

At His Side

At His Side

Equations of Mathematical Physics

Equations of Mathematical Physics

A Collection of Problems on Mathematical Physics

A Collection of Problems on Mathematical Physics

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