Linear And Nonlinear Perturbations Of The Operator Div
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Linear And Nonlinear Perturbations Of The Operator Div
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Author : Viktor Grigorʹevich Osmolovskiĭ
language : en
Publisher: American Mathematical Soc.
Release Date : 1997-01-01
Linear And Nonlinear Perturbations Of The Operator Div written by Viktor Grigorʹevich Osmolovskiĭ and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-01-01 with Mathematics categories.
This book presents results onboundary-value problems for L and the theory of nonlinear perturbations of L. Specifically, necessary and sufficient solvability conditions in explicit form are found for various boundary-value problems for the operator L. an analog of the Weyl decomposition is proved.
Linear And Nonlinear Perturbations Of The Operator Div
DOWNLOAD
Author : Viktor Grigorʹevich Osmolovskiĭ
language : en
Publisher: American Mathematical Soc.
Release Date : 1997
Linear And Nonlinear Perturbations Of The Operator Div written by Viktor Grigorʹevich Osmolovskiĭ and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.
The perturbation theory for the operator div is of particular interest in the study of boundary-value problems for the general nonlinear equation $F(\dot y,y,x)=0$. Taking as linearization the first order operator $Lu=C_{ij}u_{x_j}^i+C_iu^i$, one can, under certain conditions, regard the operator $L$ as a compact perturbation of the operator div. This book presents results on boundary-value problems for $L$ and the theory of nonlinear perturbations of $L$. Specifically, necessary and sufficient solvability conditions in explicit form are found for various boundary-value problems for the operator $L$. An analog of the Weyl decomposition is proved. The book also contains a local description of the set of all solutions (located in a small neighborhood of a known solution) to the boundary-value problems for the nonlinear equation $F(\dot y, y, x) = 0$ for which $L$ is a linearization. A classification of sets of all solutions to various boundary-value problems for the nonlinear equation $F(\dot y, y, x) = 0$ is given. The results are illustrated by various applications in geometry, the calculus of variations, physics, and continuum mechanics.
Linear And Nonlinear Perturbations Of The Operator Operatorname Div
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Author : Viktor Grigorʹevich Osmolovskiĭ
language : en
Publisher:
Release Date : 1997
Linear And Nonlinear Perturbations Of The Operator Operatorname Div written by Viktor Grigorʹevich Osmolovskiĭ and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Boundary value problems categories.
The perturbation theory for the operator div is of particular interest in the study of boundary-value problems for the general nonlinear equation F(\dot y, y, x)=0. Taking as linearization the first order operator Lu=C_{ij}u_{x_j}^i+C_iu^i, one can, under certain conditions, regard the operator L as a compact perturbation of the operator div. This book presents results on boundary-value problems for L and the theory of nonlinear perturbations of L. Specifically, necessary and sufficient solvability conditions in explicit form are found for various boundary-value problems for the operator L. An a.
Mathematics Of Information And Coding
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Author : Te Sun Han
language : en
Publisher: American Mathematical Soc.
Release Date : 2002
Mathematics Of Information And Coding written by Te Sun Han and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Computers categories.
This book is intended to provide engineering and/or statistics students, communications engineers, and mathematicians with the firm theoretic basis of source coding (or data compression) in information theory. Although information theory consists of two main areas, source coding and channel coding, the authors choose here to focus only on source coding. The reason is that, in a sense, it is more basic than channel coding, and also because of recent achievements in source coding and compression. An important feature of the book is that whenever possible, the authors describe universal coding methods, i.e., the methods that can be used without prior knowledge of the statistical properties of the data. The authors approach the subject of source coding from the very basics to the top frontiers in an intuitively transparent, but mathematically sound, manner. The book serves as a theoretical reference for communication professionals and statisticians specializing in information theory. It will also serve as an excellent introductory text for advanced-level and graduate students taking elementary or advanced courses in telecommunications, electrical engineering, statistics, mathematics, and computer science.
C Algebras And Elliptic Operators In Differential Topology
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Author : I_U_ri_ Petrovich Solov_v Evgeni_ Vadimovich Troit_s_ki_
language : en
Publisher: American Mathematical Soc.
Release Date : 2000-10-03
C Algebras And Elliptic Operators In Differential Topology written by I_U_ri_ Petrovich Solov_v Evgeni_ Vadimovich Troit_s_ki_ and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-10-03 with categories.
The aim of this book is to present some applications of functional analysis and the theory of differential operators to the investigation of topological invariants of manifolds. The main topological application discussed in the book concerns the problem of the description of homotopy-invariant rational Pontryagin numbers of non-simply connected manifolds and the Novikov conjecture of homotopy invariance of higher signatures. The definition of higher signatures and the formulation of the Novikov conjecture are given in Chapter 3. In this chapter, the authors also give an overview of different approaches to the proof of the Novikov conjecture. First, there is the Mishchenko symmetric signature and the generalized Hirzebruch formulae and the Mishchenko theorem of homotopy invariance of higher signatures for manifolds whose fundamental groups have a classifying space, being a complete Riemannian non-positive curvature manifold. Then the authors present Solovyov's proof of the Novikov conjecture for manifolds with fundamental group isomorphic to a discrete subgroup of a linear algebraic group over a local field, based on the notion of the Bruhat-Tits building. Finally, the authors discuss the approach due to Kasparov based on the operator $KK$-theory and another proof of the Mishchenko theorem. In Chapter 4, they outline the approach to the Novikov conjecture due to Connes and Moscovici involving cyclic homology. That allows one to prove the conjecture in the case when the fundamental group is a (Gromov) hyperbolic group. The text provides a concise exposition of some topics from functional analysis (for instance, $C^*$-Hilbert modules, $K$-theory or $C^*$-bundles, Hermitian $K$-theory, Fredholm representations, $KK$-theory, and functional integration) from the theory of differential operators (pseudodifferential calculus and Sobolev chains over $C^*$-algebras), and from differential topology (characteristic classes). The book explains basic ideas of the subject and can serve as a course text for an introduction to the study of original works and special monographs.
Sign Based Methods In Linear Statistical Models
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Author : M. V. Boldin
language : en
Publisher: American Mathematical Soc.
Release Date : 1997-04-22
Sign Based Methods In Linear Statistical Models written by M. V. Boldin and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-04-22 with Mathematics categories.
For nonparametric statistics, the last half of this century was the time when rank-based methods originated, were vigorously developed, reached maturity, and received wide recognition. The rank-based approach in statistics consists in ranking the observed values and using only the ranks rather than the original numerical data. In fitting relationships to observed data, the ranks of residuals from the fitted dependence are used. The signed-based approach is based on the assumption that random errors take positive or negative values with equal probabilities. Under this assumption, the sign procedures are distribution-free. These procedures are robust to violations of model assumptions, for instance, to even a considerable number of gross errors in observations. In addition, sign procedures have fairly high relative asymptotic efficiency, in spite of the obvious loss of information incurred by the use of signs instead of the corresponding numerical values. In this work, sign-based methods in the framework of linear models are developed. In the first part of the book, there are linear and factor models involving independent observations. In the second part, linear models of time series, primarily autoregressive models, are considered.
Characters Of Finite Groups Part 1
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Author : IA. G. Berkovich E. M. Zhmud'
language : en
Publisher: American Mathematical Soc.
Release Date : 1997-12-02
Characters Of Finite Groups Part 1 written by IA. G. Berkovich E. M. Zhmud' and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-12-02 with categories.
This book discusses character theory and its applications to finite groups. The work places the subject within the reach of people with a relatively modest mathematical background. The necessary background exceeds the standard algebra course with respect only to finite groups. Starting with basic notions and theorems in character theory, the authors present a variety of results on the properties of complex-valued characters and applications to finite groups. The main themes are degrees and kernels of irreducible characters, the class number and the number of nonlinear irreducible characters, values of irreducible characters, characterizations and generalizations of Frobenius groups, and generalizations and applications of monomial groups. The presentation is detailed, and many proofs of known results are new. Most of the results in the book are presented in monograph form for the first time. Numerous exercises offer additional information on the topics and help readers to understand the main concepts and results.
An Introduction To Algebraic Geometry
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Author : Kenji Ueno
language : en
Publisher: American Mathematical Soc.
Release Date : 1997
An Introduction To Algebraic Geometry written by Kenji Ueno and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.
This introduction to algebraic geometry allows readers to grasp the fundamentals of the subject with only linear algebra and calculus as prerequisites. After a brief history of the subject, the book introduces projective spaces and projective varieties, and explains plane curves and resolution of their singularities. The volume further develops the geometry of algebraic curves and treats congruence zeta functions of algebraic curves over a finite field. It concludes with a complex analytical discussion of algebraic curves. The author emphasizes computation of concrete examples rather than proofs, and these examples are discussed from various viewpoints. This approach allows readers to develop a deeper understanding of the theorems.
Calculus Of Variations And Optimal Control
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Author : N. P. Osmolovskii
language : en
Publisher: American Mathematical Soc.
Release Date : 1998-08-18
Calculus Of Variations And Optimal Control written by N. P. Osmolovskii and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-08-18 with Mathematics categories.
The theory of a Pontryagin minimum is developed for problems in the calculus of variations. The application of the notion of a Pontryagin minimum to the calculus of variations is a distinctive feature of this book. A new theory of quadratic conditions for a Pontryagin minimum, which covers broken extremals, is developed, and corresponding sufficient conditions for a strong minimum are obtained. Some classical theorems of the calculus of variations are generalized.
Optimal Control Of Distributed Systems Theory And Applications
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Author : A. V. Fursikov
language : en
Publisher: American Mathematical Soc.
Release Date : 1999-11-16
Optimal Control Of Distributed Systems Theory And Applications written by A. V. Fursikov and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-11-16 with Mathematics categories.
This volume presents the analysis of optimal control problems for systems described by partial differential equations. The book offers simple and clear exposition of main results in this area. The methods proposed by the author cover cases where the controlled system corresponds to well-posed or ill-posed boundary value problems, which can be linear or nonlinear. The uniqueness problem for the solution of nonlinear optimal control problems is analyzed in various settings. Solutions of several previously unsolved problems are given. In addition, general methods are applied to the study of two problems connected with optimal control of fluid flows described by the Navier-Stokes equations.