M.A. Lifshits's Books

Gaussian Random Functions

By: M.A. Lifshits

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It is well known that the normal distribution is the most pleasant, one can even say, an exemplary object in the probability theory. It combines almost all conceivable nice properties that a distribution may ever have: symmetry, stability, indecomposability, a regular tail behavior, etc. Gaussian measures (the distributions of Gaussian random functions), as infinite-dimensional analogues of tht

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347

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Springer Science & Business Media

Published Date

ISBN 10

9401584745

ISBN 13

9789401584746

Local Properties of Distributions of Stochastic Functionals

By: Yu. A. Davydov, M. A. Lifshits, andN. V. Smorodina

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Local Properties of Distributions of Stochastic Functionals

By: Yu. A. Davydov, M. A. Lifshits, andN. V. Smorodina

This book investigates the distributions of functionals defined on the sample paths of stochastic processes. It contains systematic exposition and applications of three general research methods developed by the authors. (i) The method of stratifications is used to study the problem of absolute continuity of distribution for different classes of functionals under very mild smoothness assumptions. It can be used also for evaluation of the distribution density of the functional. (ii) The method of differential operators is based on the abstract formalism of differential calculus and proves to be a powerful tool for the investigation of the smoothness properties of the distributions. (iii) The superstructure method, which is a later modification of the method of stratifications, is used to derive strong limit theorems (in the variation metric) for the distributions of stochastic functionals under weak convergence of the processes. Various application examples concern the functionals of Gaussian, Poisson and diffusion processes as well as partial sum processes from the Donsker-Prokhorov scheme. The research methods and basic results in this book are presented here in monograph form for the first time. The text would be suitable for a graduate course in the theory of stochastic processes and related topics.

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208

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821897837

ISBN 13

9780821897836

Combinatorial Pattern Matching

18th Annual Symposium, CPM 2007, London, Canada, July 9-11, 2007, Proceedings

By: Bin Ma

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Combinatorial Pattern Matching

18th Annual Symposium, CPM 2007, London, Canada, July 9-11, 2007, Proceedings

By: Bin Ma

This volume features select refereed proceedings from the 18th Annual Symposium on Combinatorial Pattern Matching. Collectively, the papers provide great insights into the most recent advances in combinatorial pattern matching. They are organized into topical sections covering algorithmic techniques, approximate pattern matching, data compression, computational biology, pattern analysis, suffix arrays and trees, and algorithmic techniques.

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377

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Springer Science & Business Media

Published Date

ISBN 10

3540734368

ISBN 13

9783540734369

Electroinduced Drift of Neutral Charge Clusters in Salt Solutions

By: Li Hunda,M. A. Kazaryan,I.V. Shamanin

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Electroinduced Drift of Neutral Charge Clusters in Salt Solutions

By: Li Hunda,M. A. Kazaryan,I.V. Shamanin

Electroinduced Drift of Neutral Charge Clusters in Salt Solutions presents studies of the processes accompanying the effect of periodic electric and magnetic fields on salt solutions in polar dielectric liquids. The authors explain phenomena from a physical point of view, without theoretical constructions and mathematical calculations. This is done in order to make the book accessible to a wide audience and to help the reader navigate in a multilateral topic that is touched upon when studying processes that occur in liquid media under the external influence of an electromagnetic nature. Additional Features: Explores the phenomenon of selective drift of solvated ions in polar dielectric liquids Applies general principles of electricity and magnetism to describe experimental results Demonstrates how small perturbations of the equilibrium distribution determine not the corrections to the effects but the effects themselves Approaches nonequilibrium molecular physics as a science of physical and chemical processes This book will be useful to specialists, engineers and graduate students, especially those recording and transmitting information in liquid media.

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222

Publisher

CRC Press

Published Date

ISBN 10

1000246132

ISBN 13

9781000246131

Foundations of the Classical Theory of Partial Differential Equations

By: Yu.V. Egorov,M.A. Shubin

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Foundations of the Classical Theory of Partial Differential Equations

By: Yu.V. Egorov,M.A. Shubin

From the reviews: "...I think the volume is a great success ... a welcome addition to the literature ..." The Mathematical Intelligencer, 1993 "... It is comparable in scope with the great Courant-Hilbert Methods of Mathematical Physics, but it is much shorter, more up to date of course, and contains more elaborate analytical machinery...." The Mathematical Gazette, 1993

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264

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Springer Science & Business Media

Published Date

ISBN 10

3642580939

ISBN 13

9783642580932

Adsorption and Diffusion in Nanoporous Materials

By: Rolando M.A. Roque-Malherbe

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Adsorption and Diffusion in Nanoporous Materials

By: Rolando M.A. Roque-Malherbe

Offering a materials science point of view, the author covers the theory and practice of adsorption and diffusion applied to gases in microporous crystalline, mesoporous ordered, and micro/mesoporous amorphous materials. Examples used include microporous and mesoporous molecular sieves, amorphous silica, and alumina and active carbons, akaganeites, prussian blue analogues, metal organic frameworks and covalent organic frameworks. The use of single component adsorption, diffusion in the characterization of the adsorbent surface, pore volume, pore size distribution, and the study of the parameters characterizing single component transport processes in porous materials are detailed.

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298

Publisher

CRC Press

Published Date

ISBN 10

1351395769

ISBN 13

9781351395762

Equivariant Orthogonal Spectra and $S$-Modules

By: M. A. Mandell,J. Peter May

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Equivariant Orthogonal Spectra and $S$-Modules

By: M. A. Mandell,J. Peter May

The last few years have seen a revolution in our understanding of the foundations of stable homotopy theory. Many symmetric monoidal model categories of spectra whose homotopy categories are equivalent to the stable homotopy category are now known, whereas no such categories were known before 1993. The most well-known examples are the category of $S$-modules and the category of symmetric spectra. We focus on the category of orthogonal spectra, which enjoys some of the best features of $S$-modules and symmetric spectra and which is particularly well-suited to equivariant generalization. We first complete the nonequivariant theory by comparing orthogonal spectra to $S$-modules. We then develop the equivariant theory.For a compact Lie group $G$, we construct a symmetric monoidal model category of orthogonal $G$-spectra whose homotopy category is equivalent to the classical stable homotopy category of $G$-spectra. We also complete the theory of $S_G$-modules and compare the categories of orthogonal $G$-spectra and $S_G$-modules. A key feature is the analysis of change of universe, change of group, fixed point, and orbit functors in these two highly structured categories for the study of equivariant stable homotopy theory.

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Page Count

125

Publisher

American Mathematical Soc.

Published Date

ISBN 10

082182936X

ISBN 13

9780821829363

Approximate Solution of Operator Equations

By: M.A. Krasnosel'skii,G.M. Vainikko,R.P. Zabreyko,Ya.B. Ruticki,V.Va. Stet'senko

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Approximate Solution of Operator Equations

By: M.A. Krasnosel'skii,G.M. Vainikko,R.P. Zabreyko,Ya.B. Ruticki,V.Va. Stet'senko

One of the most important chapters in modern functional analysis is the theory of approximate methods for solution of various mathematical problems. Besides providing considerably simplified approaches to numerical methods, the ideas of functional analysis have also given rise to essentially new computation schemes in problems of linear algebra, differential and integral equations, nonlinear analysis, and so on. The general theory of approximate methods includes many known fundamental results. We refer to the classical work of Kantorovich; the investigations of projection methods by Bogolyubov, Krylov, Keldysh and Petrov, much furthered by Mikhlin and Pol'skii; Tikho nov's methods for approximate solution of ill-posed problems; the general theory of difference schemes; and so on. During the past decade, the Voronezh seminar on functional analysis has systematically discussed various questions related to numerical methods; several advanced courses have been held at Voronezh Uni versity on the application of functional analysis to numerical mathe matics. Some of this research is summarized in the present monograph. The authors' aim has not been to give an exhaustive account, even of the principal known results. The book consists of five chapters.

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495

Publisher

Springer Science & Business Media

Published Date

ISBN 10

9401027153

ISBN 13

9789401027151

Multiple Facets of Quantization and Supersymmetry

Michael Marinov Memorial Volume

By: M. A. Olshanetsky,Arkady Vainshtein

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Multiple Facets of Quantization and Supersymmetry

Michael Marinov Memorial Volume

By: M. A. Olshanetsky,Arkady Vainshtein

This book is dedicated to the memory of Michael Marinov, the theorist who together with Felix Berezin introduced the classical description of spin by anticommuting Grassmann variables. The Volume contains original papers and reviews of physicists and mathematicians written specifically for this book. These articles reflect the current status and recent developments in the areas of Marinov's research interests: quantum tunneling, quantization of constrained systems, supersymmetry and others. Included personal recollections portray a human face of Michael Marinov, a person of great knowledge and integrity.

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916

Publisher

World Scientific

Published Date

ISBN 10

9812380728

ISBN 13

9789812380722

Explosive Welding

Processes and Structures

By: B.A. Greenberg,M. A. Ivanov,S. V. Kuzmin,V. I. Lysak

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Explosive Welding

Processes and Structures

By: B.A. Greenberg,M. A. Ivanov,S. V. Kuzmin,V. I. Lysak

This reference explores explosion welding, a high intensity, transient impact that achieves metal compounds not obtainable otherwise. Electron microscopy images cover the structure of numerous welded joints including titanium–orthorhombic titanium aluminide, copper–tantalum, aluminum–tantalum, iron–silver, steel–steel, and copper–titanium. These weldable pairs have different solubility than their initial elements. The authors present various processes and structures including granulating fragmentation, cusps, splashes, and quasi-wave interface. Specific risk zones for chemical and petrochemical (coke chamber) reactors are probed and suggestions offered. Key Features: Offers new theories about explosion welding processes and structures Investigates dozens of weldable pairs with differing solubility from initial elements Studies both hetero- and homogeneous pairs Explores welded joints with flat, wavy and quasi-wavy separation boundaries Observes irregularities of the separation surface relief observing asperities and splashes and their transformation under intensified welding modes Unveils a new type of fragmentation under explosion welding Explosive Welding: Processes and Structures is a valuable resource for a wide range of experts involved in explosion welding, engineers, as well as graduate and postgraduate students.

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166

Publisher

CRC Press

Published Date

ISBN 10

1000712974

ISBN 13

9781000712971

Random Processes by Example

By: Mikhail Lifshits,Mikhail Anatolʹevich Lifshit︠s︡

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Random Processes by Example

By: Mikhail Lifshits,Mikhail Anatolʹevich Lifshit︠s︡

This volume first introduces the mathematical tools necessary for understanding and working with a broad class of applied stochastic models. The toolbox includes Gaussian processes, independently scattered measures such as Gaussian white noise and Poisson random measures, stochastic integrals, compound Poisson, infinitely divisible and stable distributions and processes.Next, it illustrates general concepts by handling a transparent but rich example of a “teletraffic model”. A minor tuning of a few parameters of the model leads to different workload regimes, including Wiener process, fractional Brownian motion and stable Lévy process. The simplicity of the dependence mechanism used in the model enables us to get a clear understanding of long and short range dependence phenomena. The model also shows how light or heavy distribution tails lead to continuous Gaussian processes or to processes with jumps in the limiting regime. Finally, in this volume, readers will find discussions on the multivariate extensions that admit a variety of completely different applied interpretations.The reader will quickly become familiar with key concepts that form a language for many major probabilistic models of real world phenomena but are often neglected in more traditional courses of stochastic processes.

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219

Publisher

World Scientific Publishing Company Incorporated

Published Date

ISBN 10

9814522287

ISBN 13

9789814522281

Local Properties of Distributions of Stochastic Functionals

By: Yu. A. Davydov, M. A. Lifshits, andN. V. Smorodina

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Local Properties of Distributions of Stochastic Functionals

By: Yu. A. Davydov, M. A. Lifshits, andN. V. Smorodina

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Page Count

208

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821897837

ISBN 13

9780821897836

Spatial Deterministic Epidemics

By: M A Lifshits,World Bank

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Spatial Deterministic Epidemics

By: M A Lifshits,World Bank

The study of epidemic models is one of the central topics of mathematical biology. This volume presents in monograph form the rigorous mathematical theory developed to analyze the asymptotic behaviour of certain types of epidemic models. The main model discussed is the so-called spatial deterministic epidemic in which infected individuals are not allowed to again become susceptible, and infection is spread by means of contact distributions. Results concern the existence of travelling wave solutions, the asymptotic speed of propagation and the spatial final size. A central result for radially symmetric contact distributions is that the speed of propagation is the minimum wave speed. Further results are obtained using a saddle point method, suggesting that this result also holds for more general situations. Methodology, used to extend the analysis from one-type to multi-type models, is likely to prove useful when analyzing other multi-type systems in mathematical biology. This methodology is applied to two other areas in the monograph, namely epidemics with return to the susceptible state and contact branching processes.

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Page Count

273

Publisher

American Mathematical Society(RI)

Published Date

ISBN 10

1470413299

ISBN 13

9781470413293

Book's by M.A. Lifshits

Gaussian Random Functions

Gaussian Random Functions

Local Properties of Distributions of Stochastic Functionals

Local Properties of Distributions of Stochastic Functionals

Combinatorial Pattern Matching

Combinatorial Pattern Matching

Electroinduced Drift of Neutral Charge Clusters in Salt Solutions

Electroinduced Drift of Neutral Charge Clusters in Salt Solutions

Foundations of the Classical Theory of Partial Differential Equations

Foundations of the Classical Theory of Partial Differential Equations

Adsorption and Diffusion in Nanoporous Materials

Adsorption and Diffusion in Nanoporous Materials

Equivariant Orthogonal Spectra and $S$-Modules

Equivariant Orthogonal Spectra and $S$-Modules

Approximate Solution of Operator Equations

Approximate Solution of Operator Equations

Multiple Facets of Quantization and Supersymmetry

Multiple Facets of Quantization and Supersymmetry

Explosive Welding

Explosive Welding

Random Processes by Example

Random Processes by Example

Local Properties of Distributions of Stochastic Functionals

Local Properties of Distributions of Stochastic Functionals

Spatial Deterministic Epidemics

Spatial Deterministic Epidemics

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