31 Ergebnisse - Zeige 1 von 20.

This book revises and expands upon the prior edition, The Navier-Stokes Problem. The focus of this book is to provide a mathematical analysis of the Navier-Stokes Problem (NSP) in R^3 without boundaries. Before delving into analysis, the author begins by explaining the background and history of the Navier-Stokes Problem. This edition includes new analysis and an a priori estimate of the solution. The estimate proves the contradictory nature of...

The main result of this book is a proof of the contradictory nature of the Navier¿Stokes problem (NSP). It is proved that the NSP is physically wrong, and the solution to the NSP does not exist on ¿+ (except for the case when the initial velocity and the exterior force are both equal to zero, in this case, the solution ¿¿¿¿(¿¿¿¿, ¿¿¿¿) to the NSP exists for all ¿¿¿¿ ¿ 0 and ¿¿¿¿(¿¿¿¿, ¿¿¿¿) = 0). It is shown that if the initial data ¿¿¿¿0(¿¿¿...

This book gives a necessary and sufficient condition in terms of the scattering amplitude for a scatterer to be spherically symmetric. By a scatterer we mean a potential or an obstacle. It also gives necessary and sufficient conditions for a domain to be a ball if an overdetermined boundary problem for the Helmholtz equation in this domain is solvable. This includes a proof of Schiffer's conjecture, the solution to the Pompeiu problem, and oth...

The inverse obstacle scattering problem consists of finding the unknown surface of a body (obstacle) from the scattering ¿¿¿¿(¿¿¿¿, ¿¿¿¿, ¿¿¿¿), where ¿¿¿¿(¿¿¿¿, ¿¿¿¿, ¿¿¿¿) is the scattering amplitude, ¿¿¿¿, ¿¿¿¿ ¿¿¿¿ ¿¿¿¿² is the direction of the scattered, incident wave, respectively, ¿¿¿¿² is the unit sphere in the ¿³ and k > 0 is the modulus of the wave vector. The scattering data is called non-over-determined if its dimensionality is the...

Keine Beschreibung.

Keine Beschreibung.

The main result of this book is a proof of the contradictory nature of the Navier‒Stokes problem (NSP). It is proved that the NSP is physically wrong, and the solution to the NSP does not exist on ℝ+ (except for the case when the initial velocity and the exterior force are both equal to zero, in this case, the solution 𝑣(𝑥, 𝑡) to the NSP exists for all 𝑡 ≥ 0 and 𝑣(𝑥, 𝑡) = 0).It is shown that if the initial data 𝑣0(𝑥) ≢ 0, 𝑓(𝑥, 𝑡) = 0 and the s...

The main result of this book is a proof of the contradictory nature of the Navier‒Stokes problem (NSP). It is proved that the NSP is physically wrong, and the solution to the NSP does not exist on ℝ+ (except for the case when the initial velocity and the exterior force are both equal to zero, in this case, the solution 𝑣(𝑥, 𝑡) to the NSP exists for all 𝑡 ≥ 0 and 𝑣(𝑥, 𝑡) = 0).It is shown that if the initial data 𝑣0(𝑥) ≢ 0, 𝑓(𝑥, 𝑡) = 0 and the s...

Radon Transform and Local Tomography presents new theories and computational methods that cannot be found in any other book. New material, aimed at solving important problems in tomographic imaging and image processing in general, as well as detailed descriptions of the new algorithms and the results of their testing, are expertly covered. The theory described in this book solves the important problem of finding discontinuities of function fro...

The inverse obstacle scattering problem consists of finding the unknown surface of a body (obstacle) from the scattering ¿¿¿¿(¿¿¿¿, ¿¿¿¿, ¿¿¿¿), where ¿¿¿¿(¿¿¿¿, ¿¿¿¿, ¿¿¿¿) is the scattering amplitude, ¿¿¿¿, ¿¿¿¿ ¿¿¿¿ ¿¿¿¿² is the direction of the scattered, incident wave, respectively, ¿¿¿¿² is the unit sphere in the R³ and k > 0 is the modulus of the wave vector. The scattering data is called non-over-determined if its dimensionality is the...

The inverse obstacle scattering problem consists of finding the unknown surface of a body (obstacle) from the scattering ¿¿¿¿(¿¿¿¿, ¿¿¿¿, ¿¿¿¿), where ¿¿¿¿(¿¿¿¿, ¿¿¿¿, ¿¿¿¿) is the scattering amplitude, ¿¿¿¿, ¿¿¿¿ ¿¿¿¿ ¿¿¿¿² is the direction of the scattered, incident wave, respectively, ¿¿¿¿² is the unit sphere in the R³ and k > 0 is the modulus of the wave vector. The scattering data is called non-over-determined if its dimensionality is the...

This book gives a necessary and sufficient condition in terms of the scattering amplitude for a scatterer to be spherically symmetric. By a scatterer we mean a potential or an obstacle. It also gives necessary and sufficient conditions for a domain to be a ball if an overdetermined boundary problem for the Helmholtz equation in this domain is solvable. This includes a proof of Schiffer's conjecture, the solution to the Pompeiu problem, and oth...

This book gives a necessary and sufficient condition in terms of the scattering amplitude for a scatterer to be spherically symmetric. By a scatterer we mean a potential or an obstacle. It also gives necessary and sufficient conditions for a domain to be a ball if an overdetermined boundary problem for the Helmholtz equation in this domain is solvable. This includes a proof of Schiffer's conjecture, the solution to the Pompeiu problem, and oth...

Creating Materials with a Desired Refraction Coefficient' provides a recipe for creating materials with a desired refraction coefficient, and the many-body wave scattering problem for many small impedance bodies is solved. The physical assumptions make the multiple scattering effects essential. On the basis of this theory, a recipe for creating materials with a desired refraction coefficient is given. Technological problems are formulated whic...

Keine Beschreibung.

The book is important as it contains results many of which are not available in the literature, except in the author's papers. Among other things, it gives uniqueness theorems for inverse scattering problems when the data are non-over-determined, numerical method for solving inverse scattering problems, a method (MRC) for solving direct scattering problem.

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 ...

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 reg...

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 ...

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 reg...