The inverse obstacle scattering problem consists of finding the unknown surface of a body (obstacle) from the scattering (;;), where (;;) is the scattering amplitude; is the direction of the scattered, incident wave, respectively, is the unit sphere in the ℝ3 and k > 0 is the modulus of the wave vector.
The scattering data is called non-over-determined if its dimensionality is the same as the one of the unknown object. By the dimensionality one understands the minimal number of variables of a function describing the data or an object. In an inverse obstacle scattering problem this number is 2, and an example of non-over-determined data is (): = (;₀;₀). By sub-index 0 a fixed value of a variable is denoted.
It is proved in this book that the data (), known for all in an open subset of , determines uniquely the surface and the boundary condition on . This condition can be the Dirichlet, or the Neumann, or the impedance type.
The above uniqueness theorem is of principal importance because the non-over-determined data are the minimal data determining uniquely the unknown . There were no such results in the literature, therefore the need for this book arose. This book contains a self-contained proof of the existence and uniqueness of the scattering solution for rough surfaces.
Автор: Alexander G. Ramm Название: Spectral and Scattering Theory ISBN: 1489915540 ISBN-13(EAN): 9781489915542 Издательство: Springer Рейтинг: Цена: 93160.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Proceedings of Sessions from the First Congress of the International Society for Analysis, Applications and Computing held in Newark, Delaware, June, 2-, 1997
Автор: Donald G. Truhlar; Barry Simon Название: Multiparticle Quantum Scattering with Applications to Nuclear, Atomic and Molecular Physics ISBN: 1461273188 ISBN-13(EAN): 9781461273189 Издательство: Springer Рейтинг: Цена: 46570.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This IMA Volume in Mathematics and its Applications MULTIPARTICLE QUANTUM SCATTERING WITH APPLICATIONS TO NUCLEAR, ATOMIC AND MOLECULAR PHYSICS is based on the proceedings of a workshop with the same title, which was an integral part of the 1994-1995 IMA program on "Waves and Scattering." We would like to thank Donald G. Truhlar and Barry Simon for their ex- cellent work as organizers of this meeting and as editors of the proceedings. We also take this opportunity to thank the National Science Foundation (NSF), the Army Research Office (ARO), and the Office of Naval Research (ONR), whose financial support made the workshop possible. A vner Friedman Robert Gulliver v PREFACE The workshop on Multiparticle Quantum Scattering with Applications to Nuclear, Atomic, and Molecular Physics was held June 12-16, 1995 at the Institute for Mathematics and Its Applications in the University of Min- nesota Twin Cities campus as part of the 1994-95 Program on Waves and Scattering. There were about seventy participants including the plenary lecturers whose contributions are included in this volume. The workshop was preceded by a two-day tutorial featuring lectures by Donald J. Kouri and Gian Michele Graf, and we are pleased that both Professors Graf and Kouri were able to write up their tutorials as opening chapters of this volume.
Автор: Dyatlov, Semyon Zworski, Maciej Название: Mathematical theory of scattering resonances ISBN: 147044366X ISBN-13(EAN): 9781470443665 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 112860.00 T Наличие на складе: Невозможна поставка. Описание: Scattering resonances generalize bound states/eigenvalues for systems in which energy can scatter to infinity. A typical resonance has a rate of oscillation (just as a bound state does) and a rate of decay. Although the notion is intrinsically dynamical, an elegant mathematical formulation comes from considering meromorphic continuations of Green's functions. The poles of these meromorphic continuations capture physical information by identifying the rate of oscillation with the real part of a pole and the rate of decay with its imaginary part. An example from mathematics is given by the zeros of the Riemann zeta function: they are, essentially, the resonances of the Laplacian on the modular surface. The Riemann hypothesis then states that the decay rates for the modular surface are all either $0$ or $\frac14$. An example from physics is given by quasi-normal modes of black holes which appear in long-time asymptotics of gravitational waves.This book concentrates mostly on the simplest case of scattering by compactly supported potentials but provides pointers to modern literature where more general cases are studied. It also presents a recent approach to the study of resonances on asymptotically hyperbolic manifolds. The last two chapters are devoted to semiclassical methods in the study of resonances.
Автор: Alexander G. Ramm Название: Scattering by Obstacles ISBN: 9027721033 ISBN-13(EAN): 9789027721037 Издательство: Springer Рейтинг: Цена: 102480.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: 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;
Автор: Necasova Название: Navier-Stokes Flow Around a Rotating Obstacle ISBN: 9462392307 ISBN-13(EAN): 9789462392304 Издательство: Springer Рейтинг: Цена: 51230.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание:
The book provides a comprehensive, detailed and self-contained treatment of the fundamental mathematical properties of problems arising from the motion of viscous incompressible fluids around rotating obstacles. It offers a new approach to this type of problems. We derive the fundamental solution of the steady case and we give pointwise estimates of velocity and its gradient (first and second one). Each chapter is preceded by a thorough discussion of the investigated problems, along with their motivation and the strategy used to solve them.
The book will be useful to researchers and graduate students in mathematics, in particular mathematical fluid mechanics and differential equations.
Автор: Arshak Petrosyan, Henrik Shahgholian, Nina Uraltseva Название: Regularity of Free Boundaries in Obstacle-Type Problems ISBN: 0821887947 ISBN-13(EAN): 9780821887943 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 54510.00 T Наличие на складе: Невозможна поставка. Описание: The regularity theory of free boundaries flourished during the late 1970s and early 1980s and had a major impact in several areas of mathematics, mathematical physics, and industrial mathematics, as well as in applications. Since then the theory continued to evolve. Numerous new ideas, techniques, and methods have been developed, and challenging new problems in applications have arisen. The main intention of the authors of this book is to give a coherent introduction to the study of the regularity properties of free boundaries for a particular type of problems, known as obstacle-type problems. The emphasis is on the methods developed in the past two decades. The topics include optimal regularity, nondegeneracy, rescalings and blowups, classification of global solutions, several types of monotonicity formulas, Lipschitz, $C^1$, as well as higher regularity of the free boundary, structure of the singular set, touch of the free and fixed boundaries, and more. The book is based on lecture notes for the courses and mini-courses given by the authors at various locations and should be accessible to advanced graduate students and researchers in analysis and partial differential equations.
Автор: David Colton; Rainer Kress Название: Inverse Acoustic and Electromagnetic Scattering Theory ISBN: 3030303500 ISBN-13(EAN): 9783030303501 Издательство: Springer Рейтинг: Цена: 130430.00 T Наличие на складе: Поставка под заказ. Описание: The inverse scattering problem is central to many areas of science and technology such as radar, sonar, medical imaging, geophysical exploration and nondestructive testing. This book is devoted to the mathematical and numerical analysis of the inverse scattering problem for acoustic and electromagnetic waves. In this fourth edition, a number of significant additions have been made including a new chapter on transmission eigenvalues and a new section on the impedance boundary condition where particular attention has been made to the generalized impedance boundary condition and to nonlocal impedance boundary conditions. Brief discussions on the generalized linear sampling method, the method of recursive linearization, anisotropic media and the use of target signatures in inverse scattering theory have also been added.
Автор: Peter D. Miller; Peter A. Perry; Jean-Claude Saut; Название: Nonlinear Dispersive Partial Differential Equations and Inverse Scattering ISBN: 1493998056 ISBN-13(EAN): 9781493998050 Издательство: Springer Рейтинг: Цена: 93160.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This volume contains lectures and invited papers from the Focus Program on 'Nonlinear Dispersive Partial Differential Equations and Inverse Scattering' held at the Fields Institute from July 31-August 18, 2017. The conference brought together researchers in completely integrable systems and PDE with the goal of advancing the understanding of qualitative and long-time behavior in dispersive nonlinear equations. The program included Percy Deift’s Coxeter lectures, which appear in this volume together with tutorial lectures given during the first week of the focus program. The research papers collected here include new results on the focusing ?nonlinear Schr?dinger (NLS) equation, the massive Thirring model, and the Benjamin-Bona-Mahoney equation as dispersive PDE in one space dimension, as well as the Kadomtsev-Petviashvili II equation, the Zakharov-Kuznetsov equation, and the Gross-Pitaevskii equation as dispersive PDE in two space dimensions.The Focus Program coincided with the fiftieth anniversary of the discovery by Gardner, Greene, Kruskal and Miura that the Korteweg-de Vries (KdV) equation could be integrated by exploiting a remarkable connection between KdV and the spectral theory of Schrodinger's equation in one space dimension. This led to the discovery of a number of completely integrable models of dispersive wave propagation, including the cubic NLS equation, and the derivative NLS equation in one space dimension and the Davey-Stewartson, Kadomtsev-Petviashvili and Novikov-Veselov equations in two space dimensions. These models have been extensively studied and, in some cases, the inverse scattering theory has been put on rigorous footing. It has been used as a powerful analytical tool to study global well-posedness and elucidate asymptotic behavior of the solutions, including dispersion, soliton resolution, and semiclassical limits.
Автор: Fioralba Cakoni; David Colton Название: A Qualitative Approach to Inverse Scattering Theory ISBN: 1461488265 ISBN-13(EAN): 9781461488262 Издательство: Springer Рейтинг: Цена: 79190.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: 1. Functional Analysis and Sobolev Spaces.- 2. Ill-Posed Problems.- 3. Scattering by Imperfect Conductors.- 4. Inverse Scattering Problems for Imperfect Conductors.- 5. Scattering by Orthotropic Media.- 6. Inverse Scattering Problems for Orthotropic Media.- 7. Factorization Methods.- 8. Mixed Boundary Value Problems.- 9. Inverse Spectral Problems for Transmission Eigenvalues.- 10. A Glimpse at Maxwell's Equations.
Автор: Vu, Pham Loi Название: Inverse scattering problems and their application to nonlinear integrable equations ISBN: 0367334895 ISBN-13(EAN): 9780367334895 Издательство: Taylor&Francis Рейтинг: Цена: 153120.00 T Наличие на складе: Нет в наличии. Описание: El paquete Courseware consiste de dos publicaciones , VeriSM - Fundamentos Courseware y Fundamentos guia de estudio.Este material de entrenamiento cubre el plan de estudios para la calificacion VeriSM fundamentos. El entrenamiento puede ser entregado durante dos dias. Este Courseware esta acreditado para preparar al estudiante para la certificacion VeriSM. VeriSM Fundamentos consiste de dos partes: VeriSM Essentials y VeriSM Plus, cada uno cubriendo un dia de entrenamiento.Los estudiantes que ya tienen un certificado en Gestion de Servicios (TI) pueden beneficiarse del conocimiento que ya tienen. Son el publico objetivo para el entrenamiento VeriSM Plus unicamente. Cuando aprueben el examen VeriSM Plus, recibiran el certificado de VeriSM fundamentos. Proveedores de entrenamiento que quieran ofrecer un dia de capacitacion sobre principios de gestion de servicios podrian decidir ofrecer unicamente el entrenamiento de VeriSM Essentials. Los estudiantes que aprueben el examen VeriSM Essentials, recibiran el certificado de VeriSM Essentials. Si posteriormente ellos aprueban el examen VeriSM plus, recibiran automaticamente el certificado VeriSM Fundamentos.El courseware cubre los siguientes temas:¢ La organizacion del servicio (Essentials)¢ Cultura del servicio (Essentials)¢ Personas y cultura organizacional (Essentials)¢ El modelo VeriSM (Ambas)¢ Practicas progresivas (Plus)¢ Tecnologias innovadoras (Plus)VeriSM es un enfoque holistico y orientado a la empresa, que le ayuda a comprender el creciente panorama de las mejores practicas y como integrarlas para ofrecer valor al consumidor.Esto es una evolucion en el pensamiento de la Gestion de Servicios y ofrece un enfoque actualizado, incluyendo las ultimas practicas y desarrollos tecnologicos, para ayudar a las organizaciones a transformar su negocio en la nueva realidad de la era digital.VeriSM es un enfoque de Gestion de Servicios que esta Dirigido por el valor, Evolutivo, Responsivo (Adaptado) e Integrado VeriSM es una marca registrada y propiedad del IFDC, la Fundacion Internacional de Habilidades Digitales
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