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This book presents important recent developments in mathematical and computational methods used in impedance imaging and the theory of composite materials. The methods involved come from various areas of pure and applied mathematics, such as potential theory, PDEs, complex analysis, and numerical methods. The unifying thread in this book is the use of generalized polarization and moment tensors. The main approach is based on modern layer potential techniques. By augmenting the theory with interesting practical examples and numerical illustrations, the exposition brings simplicity to the advanced material. An introductory chapter covers the necessary basics. With its extensive list of references and open problems, the book should enhance accessibility to specialized literature and stimulate progress in the fields of impedance imaging and composite materials. Graduate students and researchers in applied mathematics will benefit from this book. Researchers in engineering and physics might also find this book helpful.
Electric conductivity  Polarization (Electricity)  Tensor algebra.  Inverse problems (Differential equations)  Mathematics.  Algebra, Tensor  Algebras, Linear  Tensor products  Dielectric relaxation  Differential equations  Conductivity, Electric  Free electron theory of metals  Transport theory  Biomedical engineering.  Potential theory (Mathematics).  Differential equations, partial.  Radiology, Medical.  Applications of Mathematics.  Biomedical Engineering and Bioengineering.  Potential Theory.  Partial Differential Equations.  Imaging / Radiology.  Clinical radiology  Radiology, Medical  Radiology (Medicine)  Medical physics  Partial differential equations  Green's operators  Green's theorem  Potential functions (Mathematics)  Potential, Theory of  Mathematical analysis  Mechanics  Clinical engineering  Medical engineering  Bioengineering  Biophysics  Engineering  Medicine  Math  Science  Applied mathematics.  Engineering mathematics.  Partial differential equations.  Radiology.  Radiological physics  Physics  Radiation  Engineering analysis  Mathematics
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Partial differential equations  Differential equations  Mathematics  Human biochemistry  Physical methods for diagnosis  differentiaalvergelijkingen  medische biochemie  Laplacetransformatie  toegepaste wiskunde  biochemie  radiologie  medische beeldvorming  fysicochemie
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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.
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This book presents important recent developments in mathematical and computational methods used in impedance imaging and the theory of composite materials. The methods involved come from various areas of pure and applied mathematics, such as potential theory, PDEs, complex analysis, and numerical methods. The unifying thread in this book is the use of generalized polarization and moment tensors. The main approach is based on modern layer potential techniques. By augmenting the theory with interesting practical examples and numerical illustrations, the exposition brings simplicity to the advanced material. An introductory chapter covers the necessary basics. With its extensive list of references and open problems, the book should enhance accessibility to specialized literature and stimulate progress in the fields of impedance imaging and composite materials. Graduate students and researchers in applied mathematics will benefit from this book. Researchers in engineering and physics might also find this book helpful.
Partial differential equations  Differential equations  Mathematics  Human biochemistry  Physical methods for diagnosis  differentiaalvergelijkingen  medische biochemie  Laplacetransformatie  toegepaste wiskunde  biochemie  radiologie  medische beeldvorming  fysicochemie
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Mathematics  Mathematics  akoestiek  Matlab (informatica)  wiskunde  wiskunde
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This book covers recent mathematical, numerical, and statistical approaches for multistatic imaging of targets with waves at single or multiple frequencies. The waves can be acoustic, elastic or electromagnetic. They are generated by point sources on a transmitter array and measured on a receiver array. An important problem in multistatic imaging is to quantify and understand the tradeoffs between data size, computational complexity, signaltonoise ratio, and resolution. Another fundamental problem is to have a shape representation well suited to solving target imaging problems from multistatic data. In this book the tradeoff between resolution and stability when the data are noisy is addressed. Efficient imaging algorithms are provided and their resolution and stability with respect to noise in the measurements analyzed. It also shows that highorder polarization tensors provide an accurate representation of the target. Moreover, a dictionarymatching technique based on new invariants for the generalized polarization tensors is introduced. Matlab codes for the main algorithms described in this book are provided. Numerical illustrations using these codes in order to highlight the performance and show the limitations of numerical approaches for multistatic imaging are presented.
Engineering & Applied Sciences  Applied Physics  Mathematics.  Mathematical physics.  Mathematical Applications in the Physical Sciences.  Image processing  Mathematical statistics.  Mathematics  Statistical inference  Statistics, Mathematical  Statistics  Probabilities  Sampling (Statistics)  Statistical methods  Physical mathematics  Physics  Math  Science
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