Elliptic Boundary Value Problems with Indefinite Weights, Variational Formulations of the Principal Eigenvalue, and Applications PDF Download
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Author: Fethi Belgacem
Publisher: CRC Press
ISBN: 9780582315976
Category : Mathematics
Languages : en
Pages : 260
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Book Description
Elliptic Boundary Value Problems With Indefinite Weights presents a unified approach to the methodologies dealing with eigenvalue problems involving indefinite weights. The principal eigenvalue for such problems is characterized for various boundary conditions. Such characterizations are used, in particular, to formulate criteria for the persistence and extinctions of populations, and applications of the formulations obtained can be quite extensive.
Author: Fethi Belgacem
Publisher: CRC Press
ISBN: 9780582315976
Category : Mathematics
Languages : en
Pages : 260
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Book Description
Elliptic Boundary Value Problems With Indefinite Weights presents a unified approach to the methodologies dealing with eigenvalue problems involving indefinite weights. The principal eigenvalue for such problems is characterized for various boundary conditions. Such characterizations are used, in particular, to formulate criteria for the persistence and extinctions of populations, and applications of the formulations obtained can be quite extensive.
Author: T Li
Publisher: CRC Press
ISBN: 9780582276321
Category : Mathematics
Languages : en
Pages : 228
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Book Description
This first part of this book deals with the boundary value problem with equivalued surfaces, while the second part is concerned with the mathematical model and method, including the numerical method, of the resistivity well-logging for the three-lateral well-logging.
Author: John Roe
Publisher: CRC Press
ISBN: 9780582325029
Category : Mathematics
Languages : en
Pages : 222
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Book Description
Ten years after publication of the popular first edition of this volume, the index theorem continues to stand as a central result of modern mathematics-one of the most important foci for the interaction of topology, geometry, and analysis. Retaining its concise presentation but offering streamlined analyses and expanded coverage of important examples and applications, Elliptic Operators, Topology, and Asymptotic Methods, Second Edition introduces the ideas surrounding the heat equation proof of the Atiyah-Singer index theorem. The author builds towards proof of the Lefschetz formula and the full index theorem with four chapters of geometry, five chapters of analysis, and four chapters of topology. The topics addressed include Hodge theory, Weyl's theorem on the distribution of the eigenvalues of the Laplacian, the asymptotic expansion for the heat kernel, and the index theorem for Dirac-type operators using Getzler's direct method. As a "dessert," the final two chapters offer discussion of Witten's analytic approach to the Morse inequalities and the L2-index theorem of Atiyah for Galois coverings. The text assumes some background in differential geometry and functional analysis. With the partial differential equation theory developed within the text and the exercises in each chapter, Elliptic Operators, Topology, and Asymptotic Methods becomes the ideal vehicle for self-study or coursework. Mathematicians, researchers, and physicists working with index theory or supersymmetry will find it a concise but wide-ranging introduction to this important and intriguing field.
Author: Doina Cioranescu
Publisher: CRC Press
ISBN: 9780582369269
Category : Mathematics
Languages : en
Pages : 354
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Book Description
This book presents the texts of selected lectures on recent work in the field of nonlinear partial differential equations delivered by leading international experts at the well-established weekly seminar held at the Collège de France. Emphasis is on applications to numerous areas, including control theory, theoretical physics, fluid and continuum mechanics, free boundary problems, dynamical systems, scientific computing, numerical analysis, and engineering. Proceedings of this seminar will be of particular interest to postgraduate students and specialists in the area of nonlinear partial differential equations.
Author: Martin Brokate
Publisher: CRC Press
ISBN: 9780582312609
Category : Mathematics
Languages : en
Pages : 136
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Book Description
This volume constitutes the proceedings of a conference on functional analysis and its applications, which took place in India during December 1996. Topics include topological vector spaces, Banach algebras, meromorphic functions, partial differential equations, variational equations and inequalities, optimization, wavelets, elastroplasticity, numerical integration, fractal image compression, reservoir simulation, forest management, and industrial maths.
Author: T M Rassias
Publisher: CRC Press
ISBN: 9780582317116
Category : Mathematics
Languages : en
Pages : 284
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Book Description
In this volume, the contributing authors deal primarily with the interaction among problems of analysis and geometry in the context of inner product spaces. They present new and old characterizations of inner product spaces among normed linear spaces and the use of such spaces in various research problems of pure and applied mathematics. The methods employed are accessible to students familiar with normed linear spaces. Some of the theorems presented are at the same time simple and challenging.
Author: Saburou Saitoh
Publisher: CRC Press
ISBN: 1000158047
Category : Mathematics
Languages : en
Pages : 300
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Book Description
The general theories contained in the text will give rise to new ideas and methods for the natural inversion formulas for general linear mappings in the framework of Hilbert spaces containing the natural solutions for Fredholm integral equations of the first kind.
Author: K Farahmand
Publisher: CRC Press
ISBN: 9780582356221
Category : Mathematics
Languages : en
Pages : 180
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Book Description
Topics in Random Polynomials presents a rigorous and comprehensive treatment of the mathematical behavior of different types of random polynomials. These polynomials-the subject of extensive recent research-have many applications in physics, economics, and statistics. The main results are presented in such a fashion that they can be understood and used by readers whose knowledge of probability incorporates little more than basic probability theory and stochastic processes.
Author: John Ryan
Publisher: CRC Press
ISBN: 9780582356818
Category : Mathematics
Languages : en
Pages : 260
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Book Description
Clifford analysis has blossomed into an increasingly relevant and fashionable area of research in mathematical analysis-it fits conveniently at the crossroads of many fundamental areas of research, including classical harmonic analysis, operator theory, and boundary behavior. This book presents a state-of-the-art account of the most recent developments in the field of Clifford analysis with contributions by many of the field's leading researchers.
Author: Herbert Amann
Publisher: CRC Press
ISBN: 9780582317086
Category : Mathematics
Languages : en
Pages : 212
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Book Description
The numerous applications of partial differential equations to problems in physics, mechanics, and engineering keep the subject an extremely active and vital area of research. With the number of researchers working in the field, advances-large and small-come frequently. Therefore, it is essential that mathematicians working in partial differential equations and applied mathematics keep abreast of new developments. Progress in Partial Differential Equations, presents some of the latest research in this important field. Both volumes contain the lectures and papers of top international researchers contributed at the Third European Conference on Elliptic and Parabolic Problems. In addition to the general theory of elliptic and parabolic problems, the topics covered at the conference include: applications free boundary problems fluid mechanics general evolution problems ocalculus of variations homogenization modeling numerical analysis The research notes in these volumes offer a valuable update on the state-of-the-art in this important field of mathematics.