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Scattering Theory for dissipative and time-dependent systems has been intensively studied in the last fifteen years. The results in this field, based on various tools and techniques, may be found in many published papers. This monograph presents an approach which can be applied to spaces of both even and odd dimension. The ideas on which the approach is based are connected with the RAGE type theorem, with Enss' decomposition of the phase space and with a time-dependent proof of the existence of the operator W which exploits the decay of the local energy of the perturbed and free systems. Som

Boundary value problems. --- Scattering operator. --- Wave equation.

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This volume consists of the papers presented at the 6th International Workshop on Scattering Theory and Biomedical Engineering. Organized every two years, this workshop provides an overview of the hot topics in scattering theory and biomedical technology, and brings together young researchers and senior scientists, creating a forum for the exchange of new scientific ideas. At the sixth meeting, all the invited speakers, who are recognized as being eminent in their field and, more important, as being stimulating speakers, presented their latest achievements.

Biomedical engineering --- Scattering (Mathematics) --- Clinical engineering --- Medical engineering --- Bioengineering --- Biophysics --- Engineering --- Medicine --- Scattering theory (Mathematics) --- Boundary value problems --- Differential equations, Partial --- Scattering operator --- Mathematical models

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This volume deals with scattering theory, applied mathematics, modeling and biomedical engineering. Most of the papers describe mathematical methods, numerical solutions and models for well-known problems in those areas.The proceedings have been selected for coverage in: Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)

Biomedical Engineering --- Scattering (Mathematics) --- Scattering theory (Mathematics) --- Boundary value problems --- Differential equations, Partial --- Scattering operator --- Clinical engineering --- Medical engineering --- Bioengineering --- Biophysics --- Engineering --- Medicine

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Solitons have been of considerable interest to mathematicians since their discovery by Kruskal and Zabusky. This book brings together several aspects of soliton theory currently only available in research papers. Emphasis is given to the multi-dimensional problems arising and includes inverse scattering in multi-dimensions, integrable nonlinear evolution equations in multi-dimensions and the ∂ method. Thus, this book will be a valuable addition to the growing literature in the area and essential reading for all researchers in the field of soliton theory.

Solitons. --- Evolution equations, Nonlinear. --- Inverse problems (Differential equations) --- Scattering (Mathematics) --- Scattering theory (Mathematics) --- Boundary value problems --- Differential equations, Partial --- Scattering operator --- Differential equations --- Nonlinear equations of evolution --- Nonlinear evolution equations --- Differential equations, Nonlinear --- Pulses, Solitary wave --- Solitary wave pulses --- Wave pulses, Solitary --- Connections (Mathematics) --- Nonlinear theories --- Wave-motion, Theory of --- Inverse scattering transform. --- Scattering transform, Inverse --- Transform, Inverse scattering --- Transformations (Mathematics)

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The use of various types of wave energy is an increasingly promising, non-destructive means of detecting objects and of diagnosing the properties of quite complicated materials. An analysis of this technique requires an understanding of how waves evolve in the medium of interest and how they are scattered by inhomogeneities in the medium. These scattering phenomena can be thought of as arising from some perturbation of a given, known system and they are analysed by developing a scattering theory. This monograph provides an introductory account of scattering phenomena and a guide to the technical requirements for investigating wave scattering problems. It gathers together the principal mathematical topics which are required when dealing with wave propagation and scattering problems, and indicates how to use the material to develop the required solutions. Both potential and target scattering phenomena are investigated and extensions of the theory to the electromagnetic and elastic fields are provided. Throughout, the emphasis is on concepts and results rather than on the fine detail of proof; a bibliography at the end of each chapter points the interested reader to more detailed proofs of the theorems and suggests directions for further reading. Aimed at graduate and postgraduate students and researchers in mathematics and the applied sciences, this book aims to provide the newcomer to the field with a unified, and reasonably self-contained, introduction to an exciting research area and, for the more experienced reader, a source of information and techniques.

Mathematics. --- Functional Analysis. --- Operator Theory. --- Partial Differential Equations. --- Functional analysis. --- Operator theory. --- Differential equations, partial. --- Mathématiques --- Analyse fonctionnelle --- Théorie des opérateurs --- Scattering (Mathematics). --- Scattering (Physics) -- Mathematics. --- Waves -- Mathematics. --- Scattering (Physics) --- Scattering (Mathematics) --- Waves --- Scattering theory (Mathematics) --- Atomic scattering --- Atoms --- Nuclear scattering --- Particles (Nuclear physics) --- Scattering of particles --- Wave scattering --- Scattering --- Physics. --- Partial differential equations. --- Optics. --- Electrodynamics. --- Optics and Electrodynamics. --- Dynamics --- Physics --- Light --- Partial differential equations --- Functional analysis --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Cycles --- Hydrodynamics --- Benjamin-Feir instability --- Boundary value problems --- Differential equations, Partial --- Scattering operator --- Collisions (Nuclear physics) --- Particles --- Collisions (Physics) --- Classical Electrodynamics.