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Ammari H., Hyeonbae Kang — Reconstruction of Small Inhomogeneities from Boundary Measurements
Ammari H., Hyeonbae Kang — Reconstruction of Small Inhomogeneities from Boundary Measurements



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Название: Reconstruction of Small Inhomogeneities from Boundary Measurements

Авторы: Ammari H., Hyeonbae Kang

Аннотация:

This is the first book to provide a systematic exposition of promising techniques for the reconstruction of small inhomogeneities from boundary measurements. In particular, theoretical results and numerical procedures for the inverse problems for the conductivity equation, the Lamé system, as well as the Helmholtz equation are discussed in a readable and informative manner. The general approach developed in this book is based on layer potential techniques and modern asymptotic analysis of partial differential equations. The book is particularly suitable for graduate students in mathematics. TOC:Introduction.- Part I: Detection of Small Conductivity Inclusions; Transmission Problem; Generalized Polarization Tensors; Derivation of the Full Asymptotic Formula; Detection of Inclusions.- Part II: Detection of Small Elastic Inclusions; Transmission Problem for Elastostatics; Elastic Moment Tensor; Derivation of Small Asymptotic Expansions; Detections of Inclusions.- Part III: Detection of Small Electromagnetic Inclusions; Well-Posedness; Representation of Solutions; Derivation of Asymptotic Formulae; Reconstruction Algorithms.- Appendices.- References


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2004

Количество страниц: 231

Добавлена в каталог: 30.05.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Asymptotic formula      65 76 151 159 197 200
Closely spaced inclusions      56
Collectively compact operators      217
Conjecture of Polya — Szegoe      52
Constant current projection algorithm      80
Continuity method      22 216
Decomposition formula      34 65 188 197
Detection      79 83 85 159 164 166 211
Dipole approximation      65 66
Dirichlet-to-Neumann map      46
Eigenvalues of EMT's      138
Elastic moment tensors      123 129 155 159
Electric permittivity      177
Electrical impedance tomography      1 8
Energy identities      39
Fourier transform algorithm      89 209
Fundamental solution      14 110 185
Green's function      33 75 122 192 193
Green's identity      15 111
Hankel functions      186
Helmholtz equation      177 188 197
Injectivity      17
Inverse Fourier transform      90 211
Invertibility      17 28
Isoperimetric inequalities      3
Kelvin matrix      110
Korn's inequality      113 120
Lame system      105 109
Layer potentials      14 109 186
Least-squares algorithm      88
Linear sampling method      80 91
Lipschitz character      11
Lipschitz domain      11
Low-frequency scattering      41
Magnetic permeability      177
Moments estimation      100
MUSIC algorithm      91 213
Neumann function      30 33 66 154
Noise subspace      213
Partial Neumann-to-Dirichlet map      92
Plane wave      185
Poincare's inequality      12 13
Polarization tensor of Polya — Szegoe      42
Polarization tensors      41 66 202
Polarization tensors of ellipses      45
Positivity of EMT's      132
Positivity of the GPT's      47
Quadratic algorithm      85 166
Rellich identity      19 20 69 120
Representation by ellipses      63
Scattering amplitude      209
Shannon's sampling theorem      90 211
Size estimation      81
Sommerfeld radiation condition      185
Stability      86
Symmetry of EMT's      132
Symmetry of the GPT's      47
Transmission problem      11 116 118 185
Uniqueness      37 46 217
Variational algorithm      89
Variational Principle      52
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