Nonlinear Stochastic Systems Theory and Applications to Physics
Nonlinear Stochastic Systems Theory and Applications to Physics

Author: G. Adomian

Publisher: Springer Science & Business Media

Published: 1988-12-31

Total Pages: 248

ISBN-13: 902772525X

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Approach your problems from the right end and begin with the answers. Then one day, perhaps you will find the final answer. "The Hermit Clad In Crane Feathers" In R. van Gullk's The Chinese Haze Hurders. It Isn't that they can't see the solution. It IS that they can't see the problem. G. K. Chesterton. The Scandal of Father Brown. "The POint of a Pin." Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of k now ledge of m athemat i cs and re I ated fie I ds does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, COding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And In addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely Integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the eXisting classificatIOn schemes.

Nonlinear Stochastic Systems Theory and Applications to Physics
Nonlinear Stochastic Systems Theory and Applications to Physics

Author: G. Adomian

Publisher: Springer

Published: 2001-12-14

Total Pages: 0

ISBN-13: 9789400925694

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Approach your problems from the right end and begin with the answers. Then one day, perhaps you will find the final answer. "The Hermit Clad In Crane Feathers" In R. van Gullk's The Chinese Haze Hurders. It Isn't that they can't see the solution. It IS that they can't see the problem. G. K. Chesterton. The Scandal of Father Brown. "The POint of a Pin." Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of k now ledge of m athemat i cs and re I ated fie I ds does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, COding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And In addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely Integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the eXisting classificatIOn schemes.

Stochastic Evolution Systems
Stochastic Evolution Systems

Author: Boris L. Rozovsky

Publisher: Springer

Published: 2018-10-03

Total Pages: 340

ISBN-13: 3319948938

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This monograph, now in a thoroughly revised second edition, develops the theory of stochastic calculus in Hilbert spaces and applies the results to the study of generalized solutions of stochastic parabolic equations. The emphasis lies on second-order stochastic parabolic equations and their connection to random dynamical systems. The authors further explore applications to the theory of optimal non-linear filtering, prediction, and smoothing of partially observed diffusion processes. The new edition now also includes a chapter on chaos expansion for linear stochastic evolution systems. This book will appeal to anyone working in disciplines that require tools from stochastic analysis and PDEs, including pure mathematics, financial mathematics, engineering and physics.

Stochastic Differential Systems Analysis and Filtering
Stochastic Differential Systems Analysis and Filtering

Author: V. S. Pugachev

Publisher:

Published: 1987-06-22

Total Pages: 584

ISBN-13:

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Gives applied methods for studying stochastic differential systems--in particular, the methods for finding the finite-dimensional distributions of the state vector and of the output of such systems, and also the estimation methods of the state and of the parameters of differential systems based on observations (filtering and extrapolation theory). Also studied are stochastic differential equations of general type with arbitrary processes and independent increments. The equations with Wiener processes are considered as a special case. The construction of stochastic differential systems in the book is based on Pugachev's equations for finite-dimensional characteristic functions of the processes determined by stochastic differential equations. Includes end-of-chapter problems.

Nonlinear Dynamics and Chaos
Nonlinear Dynamics and Chaos

Author: Steven H. Strogatz

Publisher: CRC Press

Published: 2018-05-04

Total Pages: 532

ISBN-13: 0429961111

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This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.

Stochastic Systems: Theory And Applications
Stochastic Systems: Theory And Applications

Author: V S Pugachev

Publisher: World Scientific Publishing Company

Published: 2002-01-02

Total Pages: 930

ISBN-13: 9813105887

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This book presents the general theory and basic methods of linear and nonlinear stochastic systems (StS) i.e. dynamical systems described by stochastic finite- and infinite-dimensional differential, integral, integrodifferential, difference etc equations. The general StS theory is based on the equations for characteristic functions and functionals. The book outlines StS structural theory, including direct numerical methods, methods of normalization, equivalent linearization and parametrization of one- and multi-dimensional distributions, based on moments, quasimoments, semi-invariants and orthogonal expansions. Special attention is paid to methods based on canonical expansions and integral canonical representations. About 500 exercises and problems are provided. The authors also consider applications in mathematics and mechanics, physics and biology, control and information processing, operations research and finance.

Superanalysis
Superanalysis

Author: Andrei Y. Khrennikov

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 359

ISBN-13: 9401146098

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defined as elements of Grassmann algebra (an algebra with anticom muting generators). The derivatives of these elements with respect to anticommuting generators were defined according to algebraic laws, and nothing like Newton's analysis arose when Martin's approach was used. Later, during the next twenty years, the algebraic apparatus de veloped by Martin was used in all mathematical works. We must point out here the considerable contribution made by F. A. Berezin, G 1. Kac, D. A. Leites, B. Kostant. In their works, they constructed a new division of mathematics which can naturally be called an algebraic superanalysis. Following the example of physicists, researchers called the investigations carried out with the use of commuting and anticom muting coordinates supermathematics; all mathematical objects that appeared in supermathematics were called superobjects, although, of course, there is nothing "super" in supermathematics. However, despite the great achievements in algebraic superanaly sis, this formalism could not be regarded as a generalization to the case of commuting and anticommuting variables from the ordinary Newton analysis. What is more, Schwinger's formalism was still used in practically all physical works, on an intuitive level, and physicists regarded functions of anticommuting variables as "real functions" == maps of sets and not as elements of Grassmann algebras. In 1974, Salam and Strathdee proposed a very apt name for a set of super points. They called this set a superspace.

Convex and Starlike Mappings in Several Complex Variables
Convex and Starlike Mappings in Several Complex Variables

Author: Sheng Gong

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 220

ISBN-13: 9401152063

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This book deals with the theory of convex and starlike biholomorphic mappings in several complex variables. The underlying theme is the extension to several complex variables of geometric aspects of the classical theory of univalent functions. This is the first book which systematically studies this topic. It gathers together, and presents in a unified manner, the current state of affairs for convex and starlike biholomorphic mappings in several complex variables. The majority of the results presented are due to the author, his co-workers and his students. Audience: This volume will be of interest to research mathematicians whose work involves several complex variables and one complex variable.

Representation of Lie Groups and Special Functions
Representation of Lie Groups and Special Functions

Author: N.Ja. Vilenkin

Publisher: Springer Science & Business Media

Published: 2013-04-17

Total Pages: 518

ISBN-13: 9401728852

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In 1991-1993 our three-volume book "Representation of Lie Groups and Spe cial Functions" was published. When we started to write that book (in 1983), editors of "Kluwer Academic Publishers" expressed their wish for the book to be of encyclopaedic type on the subject. Interrelations between representations of Lie groups and special functions are very wide. This width can be explained by existence of different types of Lie groups and by richness of the theory of their rep resentations. This is why the book, mentioned above, spread to three big volumes. Influence of representations of Lie groups and Lie algebras upon the theory of special functions is lasting. This theory is developing further and methods of the representation theory are of great importance in this development. When the book "Representation of Lie Groups and Special Functions" ,vol. 1-3, was under preparation, new directions of the theory of special functions, connected with group representations, appeared. New important results were discovered in the traditional directions. This impelled us to write a continuation of our three-volume book on relationship between representations and special functions. The result of our further work is the present book. The three-volume book, published before, was devoted mainly to studying classical special functions and orthogonal polynomials by means of matrix elements, Clebsch-Gordan and Racah coefficients of group representations and to generaliza tions of classical special functions that were dictated by matrix elements of repre sentations.

Trigonometric Fourier Series and Their Conjugates
Trigonometric Fourier Series and Their Conjugates

Author: L. Zhizhiashvili

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 314

ISBN-13: 9400902832

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Research in the theory of trigonometric series has been carried out for over two centuries. The results obtained have greatly influenced various fields of mathematics, mechanics, and physics. Nowadays, the theory of simple trigonometric series has been developed fully enough (we will only mention the monographs by Zygmund [15, 16] and Bari [2]). The achievements in the theory of multiple trigonometric series look rather modest as compared to those in the one-dimensional case though multiple trigonometric series seem to be a natural, interesting and promising object of investigation. We should say, however, that the past few decades have seen a more intensive development of the theory in this field. To form an idea about the theory of multiple trigonometric series, the reader can refer to the surveys by Shapiro [1], Zhizhiashvili [16], [46], Golubov [1], D'yachenko [3]. As to monographs on this topic, only that ofYanushauskas [1] is known to me. This book covers several aspects of the theory of multiple trigonometric Fourier series: the existence and properties of the conjugates and Hilbert transforms of integrable functions; convergence (pointwise and in the LP-norm, p > 0) of Fourier series and their conjugates, as well as their summability by the Cesaro (C,a), a> -1, and Abel-Poisson methods; approximating properties of Cesaro means of Fourier series and their conjugates.