Scattering by Obstacles / by Alexander G. Ramm
(Mathematics and Its Applications ; 21)
| データ種別 | 電子ブック |
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| 出版情報 | Dordrecht : Springer Netherlands , 1986 |
| 本文言語 | 英語 |
| 大きさ | 444p : online resource |
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| 内容注記 | I. Scattering by an Obstacle 1. Statement of the Problem. Basic Integral Equations 2. Existence and Uniqueness of the Solution to the Scattering Problem 3. Eigenfunction Expansion Theorem 4. Properties of the Scattering Amplitude 5. The S-Matrix and Wave Operators 6. Inequalities for Solutions to Helmholtz’s Equation for Large frequencies 7. Representations of solutions to Helmholtz’s Equation II. The Inverse Scattering (Diffraction) Problem 1. Statement of the Problem and Uniqueness Theorems 2. Reconstruction of Obstacles from the Scattering Data at High Frequencies 3. Stability of the Surface with Respect to Small Perturbations of the Data III. Time Dependent Problem 1. Statement of the Problems 2. The Limiting Amplitude Principle (Abstract Results) 3. The Limiting Amplitude Principle for the Laplacian in Exterior Domains 4. Decay of Energy 5. Singularity and Eigenmode Expansion Methods IV. T-Matrix Scheme and Other Numerical Schemes 1. Statement of the Problem 2. Justification of the T-Matrix Scheme 3. Numerical Results 4. Other Schemes V. Scattering by Small Bodies 1. Scattering by a Single Small Body 2. Scattering by Many Small Bodies 3. Electromagnetic Wave Scattering by Small Bodies 4. Behavior of the Solutions to Exterior Boundary Value Problems at Low Frequencies VI. Some Inverse Scattering Problems of Geophysics 1. Inverse Scattering for Geophysical Problems 2. Two Parameter Inversion 3. An Inversion Formula in Scattering Theory 4. A Model Inverse Problem of Induction Logging VII. Scattering by Obstacles with Infinite Boundaries 1. Statement of the Problem 2. Spectral Properties of the Laplacians 3. Spectral Properties of the Dirichlet Laplacian in Semi-Infinite Tubes 4. Absence of Positive Eigenvalues for the Dirichlet Laplacian Under Local Assumptions at Infinity 5. The Limiting Absorption Principle and Compact Perturbations of the Boundary 6. Eigenfunction Expansions in Canonical Domains Appendix 1. Summary of some Results in Potential Theory and Embedding Theorems Appendix 2. Summary of some Results in Operator Theory Appendix 4. Stable Numerical Differentiation Appendix 5. Limit of the Spectra of the Interior Neumann Problems when a Solid Domain Shrinks to a Plane One Appendix 6. Construction of a Surface from its Principal Curvatures Appendix 7. Resonances Research Problems Bibliographical Notes List of Symbols |
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| 一般注記 | Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. 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; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics |
| 著者標目 | *Ramm, Alexander G. author SpringerLink (Online service) |
| 件 名 | LCSH:Mathematics LCSH:Integral equations LCSH:Physics FREE:Mathematics FREE:Integral Equations FREE:Physics, general |
| 分 類 | DC23:515.45 |
| 巻冊次 | ISBN:9789400945449 
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| ISBN | 9789400945449 |
| URL | http://dx.doi.org/10.1007/978-94-009-4544-9 |
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