Advanced Studies In The Mathematical Theory Of Scattering Volume 3
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Advanced Studies In The Mathematical Theory Of Scattering Volume 3
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Author : Jean-Michel L. Bernard
language : en
Publisher: John Wiley & Sons
Release Date : 2024-10-11
Advanced Studies In The Mathematical Theory Of Scattering Volume 3 written by Jean-Michel L. Bernard and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-10-11 with Science categories.
This book presents a collection of independent mathematical studies, describing the analytical reduction of complex generic problems in the theory of scattering and propagation of electromagnetic waves in the presence of imperfectly conducting objects. Their subjects include: a global method for scattering by a multimode plane; diffraction by an impedance curved wedge; scattering by impedance polygons; advanced properties of spectral functions in frequency and time domains; bianisotropic media and related coupling expressions; and exact and asymptotic reductions of surface radiation integrals. The methods developed here can be qualified as analytical when they lead to exact explicit expressions, or semi-analytical when they drastically reduce the mathematical complexity of studied problems. Therefore, they can be used in mathematical physics and engineering to analyse and model, but also in applied mathematics to calculate the scattered fields in electromagnetism for a low computational cost.
Iii Scattering Theory
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Author : Michael Reed
language : en
Publisher: Academic Press
Release Date : 1979-04-28
Iii Scattering Theory written by Michael Reed and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979-04-28 with Mathematics categories.
Volume 3.
A Qualitative Approach To Inverse Scattering Theory
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Author : Fioralba Cakoni
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-10-28
A Qualitative Approach To Inverse Scattering Theory written by Fioralba Cakoni and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-28 with Mathematics categories.
Inverse scattering theory is an important area of applied mathematics due to its central role in such areas as medical imaging , nondestructive testing and geophysical exploration. Until recently all existing algorithms for solving inverse scattering problems were based on using either a weak scattering assumption or on the use of nonlinear optimization techniques. The limitations of these methods have led in recent years to an alternative approach to the inverse scattering problem which avoids the incorrect model assumptions inherent in the use of weak scattering approximations as well as the strong a priori information needed in order to implement nonlinear optimization techniques. These new methods come under the general title of qualitative methods in inverse scattering theory and seek to determine an approximation to the shape of the scattering object as well as estimates on its material properties without making any weak scattering assumption and using essentially no a priori information on the nature of the scattering object. This book is designed to be an introduction to this new approach in inverse scattering theory focusing on the use of sampling methods and transmission eigenvalues. In order to aid the reader coming from a discipline outside of mathematics we have included background material on functional analysis, Sobolev spaces, the theory of ill posed problems and certain topics in in the theory of entire functions of a complex variable. This book is an updated and expanded version of an earlier book by the authors published by Springer titled Qualitative Methods in Inverse Scattering Theory Review of Qualitative Methods in Inverse Scattering Theory All in all, the authors do exceptionally well in combining such a wide variety of mathematical material and in presenting it in a well-organized and easy-to-follow fashion. This text certainly complements the growing body of work in inverse scattering and should well suit both new researchers to the field as well as those who could benefit from such a nice codified collection of profitable results combined in one bound volume. SIAM Review, 2006
Introduction To Classical Electrodynamics Volume 1
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Author : Boucif Abdesselam
language : en
Publisher: John Wiley & Sons
Release Date : 2025-04-21
Introduction To Classical Electrodynamics Volume 1 written by Boucif Abdesselam and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-04-21 with Science categories.
Introduction to Classical Electrodynamics 1 introduces the fundamentals of electromagnetic field theory. This book begins with electrostatics, focusing on the concepts of point charges, electric fields, electric potential and Gauss’s theorem. It then examines conductors, influence phenomena and capacitors, before exploring electrokinetics, detailing the concepts of electric current, circuits and resistance, as well as Kirchhoff’s laws. Next, this book analyzes the notion of magnetic field, Lorentz and Laplace forces, Biot-Savart’s law, Ampère’s theorem, electric and magnetic moments, and multipole developments. Boundary problems for static potentials in vacuum are also studied. The book is aimed at students of physics and mathematics, as well as engineering students interested in electromagnetic theory, providing an overview of electromagnetic theory, with numerous practical applications.
Inside Out
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Author : Gunther Uhlmann
language : en
Publisher: Cambridge University Press
Release Date : 2003-11-10
Inside Out written by Gunther Uhlmann and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-11-10 with Mathematics categories.
In this book, leading experts in the theoretical and applied aspects of inverse problems offer extended surveys on several important topics.
Scattering Theory Some Old And New Problems
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Author : Dmitri R. Yafaev
language : en
Publisher: Springer
Release Date : 2007-05-06
Scattering Theory Some Old And New Problems written by Dmitri R. Yafaev and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-06 with Mathematics categories.
Scattering theory is, roughly speaking, perturbation theory of self-adjoint operators on the (absolutely) continuous spectrum. It has its origin in mathematical problems of quantum mechanics and is intimately related to the theory of partial differential equations. Some recently solved problems, such as asymptotic completeness for the Schrödinger operator with long-range and multiparticle potentials, as well as open problems, are discussed. Potentials for which asymptotic completeness is violated are also constructed. This corresponds to a new class of asymptotic solutions of the time-dependent Schrödinger equation. Special attention is paid to the properties of the scattering matrix, which is the main observable of the theory. The book is addressed to readers interested in a deeper study of the subject.
Recent Advances In Inverse Scattering Schur Analysis And Stochastic Processes
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Author : Daniel Alpay
language : en
Publisher: Birkhäuser
Release Date : 2015-04-30
Recent Advances In Inverse Scattering Schur Analysis And Stochastic Processes written by Daniel Alpay and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-04-30 with Mathematics categories.
The volume is dedicated to Lev Sakhnovich, who made fundamental contributions in operator theory and related topics. Besides bibliographic material, it includes a number of selected papers related to Lev Sakhnovich's research interests. The papers are related to operator identities, moment problems, random matrices and linear stochastic systems.
Semigroups Of Linear Operators And Applications
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Author : Jerome A. Goldstein
language : en
Publisher: Courier Dover Publications
Release Date : 2017-05-17
Semigroups Of Linear Operators And Applications written by Jerome A. Goldstein and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-05-17 with Mathematics categories.
Advanced graduate-level treatment of semigroup theory explores semigroups of linear operators and linear Cauchy problems. The text features challenging exercises and emphasizes motivation, heuristics, and further applications. 1985 edition.
Evolution Equations
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Author : David Ellwood
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-06-26
Evolution Equations written by David Ellwood 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 2013-06-26 with Mathematics categories.
This volume is a collection of notes from lectures given at the 2008 Clay Mathematics Institute Summer School, held in Zürich, Switzerland. The lectures were designed for graduate students and mathematicians within five years of the Ph.D., and the main focus of the program was on recent progress in the theory of evolution equations. Such equations lie at the heart of many areas of mathematical physics and arise not only in situations with a manifest time evolution (such as linear and nonlinear wave and Schrödinger equations) but also in the high energy or semi-classical limits of elliptic problems. The three main courses focused primarily on microlocal analysis and spectral and scattering theory, the theory of the nonlinear Schrödinger and wave equations, and evolution problems in general relativity. These major topics were supplemented by several mini-courses reporting on the derivation of effective evolution equations from microscopic quantum dynamics; on wave maps with and without symmetries; on quantum N-body scattering, diffraction of waves, and symmetric spaces; and on nonlinear Schrödinger equations at critical regularity. Although highly detailed treatments of some of these topics are now available in the published literature, in this collection the reader can learn the fundamental ideas and tools with a minimum of technical machinery. Moreover, the treatment in this volume emphasizes common themes and techniques in the field, including exact and approximate conservation laws, energy methods, and positive commutator arguments. Titles in this series are co-published with the Clay Mathematics Institute (Cambridge, MA).
Function Spaces And Partial Differential Equations
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Author : Ali Taheri
language : en
Publisher: OUP Oxford
Release Date : 2015-07-30
Function Spaces And Partial Differential Equations written by Ali Taheri and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-30 with Mathematics categories.
This is a book written primarily for graduate students and early researchers in the fields of Analysis and Partial Differential Equations (PDEs). Coverage of the material is essentially self-contained, extensive and novel with great attention to details and rigour. The strength of the book primarily lies in its clear and detailed explanations, scope and coverage, highlighting and presenting deep and profound inter-connections between different related and seemingly unrelated disciplines within classical and modern mathematics and above all the extensive collection of examples, worked-out and hinted exercises. There are well over 700 exercises of varying level leading the reader from the basics to the most advanced levels and frontiers of research. The book can be used either for independent study or for a year-long graduate level course. In fact it has its origin in a year-long graduate course taught by the author in Oxford in 2004-5 and various parts of it in other institutions later on. A good number of distinguished researchers and faculty in mathematics worldwide have started their research career from the course that formed the basis for this book.