Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

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.

Random fields. --- Estimation theory. --- Estimating techniques --- Least squares --- Mathematical statistics --- Stochastic processes --- Fields, Random

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Inverse problems are the problems that consist of finding an unknown property of an object or a medium from the observation or a response of this object or a medium to a probing signal. Thus the theory of inverse problems yields a theoretical basis for remote sensing and non-destructive evaluation. For example, if an acoustic plane wave is scattered by an obstacle, and one observes the scattered field from the obstacle, or in some exterior region, then the inverse problem is to find the shape and material properties of the obstacle. Such problems are important in the identification of flying objects (airplanes, missiles etc.) objects immersed in water (submarines, fish) and in many other situations. This book presents the theory of inverse spectral and scattering problems and of many other inverse problems for differential equations in an essentially self-contained way. An outline of the theory of ill-posed problems is given, because inverse problems are often ill-posed. There are many novel features in this book. The concept of property C, introduced by the author, is developed and used as the basic tool for a study of a wide variety of one- and multi-dimensional inverse problems, making the theory easier and shorter. New results include recovery of a potential from I-function and applications to classical and new inverse scattering and spectral problems, study of inverse problems with"incomplete data", study of some new inverse problems for parabolic and hyperbolic equations, discussion of some non-overdetermined inverse problems, a study of inverse problems arising in the theory of ground-penetrating radars, development of DSM (dynamical systems method) for solving ill-posed nonlinear operator equations, comparison of the Ramm's inversion method for solving fixed-energy inverse scattering problem with the method based on the Dirichlet-to-Neumann map, derivation of the range of applicability and error estimates for Born's inversion, a study of some integral geometry problems, including tomography, inversion formulas for the spherical means, proof of the invertibility of the steps in the Gel'fand-Levitan and Marchenko inversion procedures, derivation of the inversion formulas and stability estimates for the multidimensional inverse scattering problems with fixed-energy noisy discrete data, new uniqueness and stability results in obstacle inverse scattering, formulation and a solution of an inverse problem of radiomeasurements, methods for finding small inhomogeneities from surface scattering data.

Engineering mathematics. --- Engineering mathematics --- Inverse problems (Differential equations) --- Engineering & Applied Sciences --- Civil & Environmental Engineering --- Applied Mathematics --- Civil Engineering --- Engineering --- Engineering analysis --- Mathematics --- Engineering. --- Image processing. --- Differential equations. --- Applied mathematics. --- Physics. --- Appl.Mathematics/Computational Methods of Engineering. --- Applications of Mathematics. --- Theoretical, Mathematical and Computational Physics. --- Image Processing and Computer Vision. --- Ordinary Differential Equations. --- Mathematical analysis --- Differential equations --- Mathematics. --- Computer vision. --- Differential Equations. --- Mathematical and Computational Engineering. --- 517.91 Differential equations --- Machine vision --- Vision, Computer --- Artificial intelligence --- Image processing --- Pattern recognition systems --- Math --- Science --- Mathematical physics. --- Optical data processing. --- Optical computing --- Visual data processing --- Bionics --- Electronic data processing --- Integrated optics --- Photonics --- Computers --- Physical mathematics --- Physics --- Optical equipment

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

In this book, mathematicians, engineers, physicists, and materials scientists will learn how to create material with a desired refraction coefficient. For example, how to create material with negative refraction or with desired wave-focusing properties. The methods for creating these materials are based on the many-body wave scattering theory developed by the author. The book offers new analytical formulas that allow one to calculate acoustic and electromagnetic waves, scattered by one and many small impedance bodies of an arbitrary shape under various boundary conditions. Equations for the effective (self-consistent) field in media consisting of many small impedance particles are derived. Numerical methods for solving many-body wave scattering problems are developed for small impedance scatterers.

Wave-motion, Theory of. --- Undulatory theory --- Mechanics

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

The book is of interest to graduate students in functional analysis, numerical analysis, and ill-posed and inverse problems especially. The book presents a general method for solving operator equations, especially nonlinear and ill-posed. It requires a fairly modest background and is essentially self-contained. All the results are proved in the book, and some of the background material is also included. The results presented are mostly obtained by the author. Contains a systematic development of a novel general method, the dynamical systems method, DSM for solving operator equations, especially nonlinear and ill-posed. Self-contained, suitable for wide audience. Can be used for various courses for graduate students and partly for undergraduates (especially for RUE classes).

Differential geometry. Global analysis

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)