Random Fields Estimation Theory (Pitman Monographs & Surveys in Pure & Applied Mathematics.)

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Scattering of Acoustic and Electromagnetic Waves by Small Impedance Bodies of Arbitrary Shapes

(The behavior of acoustic or electromagnetic waves reflect...)

The behavior of acoustic or electromagnetic waves reflecting off, and scattering from, intercepted bodies of any size and kind can make determinations about the materials of those bodies and help in better understanding how to manipulate such materials for desired characteristics. This book offers analytical formulas which allow you to calculate acoustic and electromagnetic waves, scattered by one and many small bodies of an arbitrary shape under various boundary conditions. Equations for the effective (self-consistent) field in media consisting of many small bodies are derived. These results and formulas are new and not available in the works of other authors. In particular, the theory developed in this book is different from the classical work of Rayleigh on scattering by small bodies: not only analytical formulas are derived for the waves scattered by small bodies of an arbitrary shape, but the amplitude of the scattered waves is much larger, of the order O(a 2-k), than in Rayleigh scattering, where the order of the scattered waves is O(a3). Moreover, the many-body scattering theory is developed and equations for the effective field in the medium in which many small particles are embedded are derived. Applications, including meta- materials with a desired refraction coefficient, are discussed.

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Iterative Methods for Calculating Static Fields and Wave Scattering by Small Bodies

(Iterative methods for calculating static fields are prese...)

Iterative methods for calculating static fields are presented in this book. Static field boundary value problems are reduced to the boundary integral equations and these equations are solved by means of iterative processes. This is done for interior and exterior problems and for var­ ious boundary conditions. Most problems treated are three-dimensional, because for two-dimensional problems the specific and often powerful tool of conformal mapping is available. The iterative methods have some ad­ vantages over grid methods and, to a certain extent, variational methods: (1) they give analytic approximate formulas for the field and for some functionals of the field of practical importance (such as capacitance and polarizability tensor), (2) the formulas for the functionals can be used in a computer program for calculating these functionals for bodies of arbitrary shape, (3) iterative methods are convenient for computers. From a practical point of view the above methods reduce to the cal­ culation of multiple integrals. Of special interest is the case of inte­ grands with weak singularities. Some of the central results of the book are some analytic approximate formulas for scattering matrices for small bodies of arbitrary shape. These formulas answer many practical questions such as how does the scattering depend on the shape of the body or on the boundary conditions, how does one calculate the effective field in a medium consisting of many small particles, and many other questions.

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Random Fields Estimation

(This book contains a novel theory of random fields estima...)

This book contains a novel theory of random fields estimation of Wiener type, developed originally by the author and presented here. No assumption about the Gaussian or Markovian nature of the fields are made. The theory, constructed entirely within the framework of covariance theory, is based on a detailed analytical study of a new class of multidimensional integral equations basic in estimation theory. This book is suitable for graduate courses in random fields estimation. It can also be used in courses in functional analysis, numerical analysis, integral equations, and scattering theory.

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(Iterative Methods for Calculating Static Fields and Wave Scattering by Small Bodies * * ) Author: Alexander G. Ramm Jun-1982

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Wave Scattering By Small Bodies Of Arbitrary Shapes

(“This book is written as a guide for physicists and engin...)

“This book is written as a guide for physicists and engineers interested in atmospheric and ocean sciences, radiophysics, and colloidal chemistry.” Zentralblatt Math This book presents analytical formulas which allow one to calculate the S-matrix for the acoustic and electromagnetic wave scattering by small bodies or arbitrary shapes with arbitrary accuracy. Equations for the self-consistent field in media consisting of many small bodies are derived. Applications of these results to ultrasound mammography and electrical engineering are considered. The above formulas are not available in the works of other authors. Their derivation is based on a mathematical theory for solving integral equations of electrostatics, magnetostatics, and other static fields. These equations are at a simple characteristic value. Convergent iterative processes are constructed for stable solution of these equations. The theory completes the classical work of Rayleigh on scattering by small bodies by providing analytical formulas for polarizability tensors for bodies of arbitrary shapes.

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The Radon Transform and Local Tomography

(Over the past decade, the field of image processing has m...)

Over the past decade, the field of image processing has made tremendous advances. One type of image processing that is currently of particular interest is "tomographic imaging," a technique for computing the density function of a body, or discontinuity surfaces of this function. Today, tomography is widely used, and has applications in such fields as medicine, engineering, physics, geophysics, and security. The Radon Transform and Local Tomography clearly explains the theoretical, computational, and practical aspects of applied tomography. It includes sufficient background information to make it essentially self-contained for most readers.

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Scattering by Obstacles (Mathematics and Its Applications)

(Approach your problems from the right end It isn't that t...)

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.

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Theory and Applications of Some New Classes of Integral Equations

(This book is intended for &tudents, research engineers, a...)

This book is intended for &tudents, research engineers, and mathematicians interested in applications or numerical analysis. Pure analysts will also find some new problems to tackle. Most of the material can be understood by a reader with a relatively modest knowledge of differential and inte­ gral equations and functional analysis. Readers interested in stochastic optimization will find a new theory of prac­ tical . importance. Readers interested in problems of static and quasi-static electrodynamics, wave scattering by small bodies of arbitrary shape, and corresponding applications in geophysics, optics, and radiophysics will find explicit analytical formulas for the scattering matrix, polarizability tensor, electrical capacitance of bodies of an arbitrary shape; numerical examples showing the practical utility of these formulas; two-sided variational estimates for the pol­ arizability tensor; and some open problems such as working out a standard program for calculating the capacitance and polarizability of bodies of arbitrary shape and numerical calculation of multiple integrals with weak singularities. Readers interested in nonlinear vibration theory will find a new method for qualitative study of stationary regimes in the general one-loop passive nonlinear network, including stabil­ ity in the large, convergence, and an iterative process for calculation the stationary regime. No assumptions concerning the smallness of the nonlinearity or the filter property of the linear one-port are made. New results in the theory of nonlinear operator equations form the basis for the study.

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