Inverse Problems In The Theory Of Small Oscillations
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Inverse Problems In The Theory Of Small Oscillations
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Author : Vladimir Marchenko
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-12-12
Inverse Problems In The Theory Of Small Oscillations written by Vladimir Marchenko and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-12 with Frequencies of oscillating systems categories.
Inverse problems of spectral analysis deal with the reconstruction of operators of the specified form in Hilbert or Banach spaces from certain of their spectral characteristics. An interest in spectral problems was initially inspired by quantum mechanics. The main inverse spectral problems have been solved already for Schrödinger operators and for their finite-difference analogues, Jacobi matrices. This book treats inverse problems in the theory of small oscillations of systems with finitely many degrees of freedom, which requires finding the potential energy of a system from the observations of its oscillations. Since oscillations are small, the potential energy is given by a positive definite quadratic form whose matrix is called the matrix of potential energy. Hence, the problem is to find a matrix belonging to the class of all positive definite matrices. This is the main difference between inverse problems studied in this book and the inverse problems for discrete analogues of the Schrödinger operators, where only the class of tridiagonal Hermitian matrices are considered.
Inverse Problems In Quantum Scattering Theory
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Author : Khosrow Chadan
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Inverse Problems In Quantum Scattering Theory written by Khosrow Chadan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
The normal business of physicists may be schematically thought of as predic ting the motions of particles on the basis of known forces, or the propagation of radiation on the basis of a known constitution of matter. The inverse problem is to conclude what the forces or constitutions are on the basis of the observed motion. A large part of our sensory contact with the world around us depends on an intuitive solution of such an inverse problem: We infer the shape, size, and surface texture of external objects from their scattering and absorption of light as detected by our eyes. When we use scattering experiments to learn the size or shape of particles, or the forces they exert upon each other, the nature of the problem is similar, if more refined. The kinematics, the equations of motion, are usually assumed to be known. It is the forces that are sought, and how they vary from point to point. As with so many other physical ideas, the first one we know of to have touched upon the kind of inverse problem discussed in this book was Lord Rayleigh (1877). In the course of describing the vibrations of strings of variable density he briefly discusses the possibility of inferring the density distribution from the frequencies of vibration. This passage may be regarded as a precursor of the mathematical study of the inverse spectral problem some seventy years later.
Inverse Problems In Quantum Scattering Theory
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Author : K. Chadan
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-18
Inverse Problems In Quantum Scattering Theory written by K. Chadan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-18 with Science categories.
The Inverse Problem Of Scattering Theory
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Author : Z.S. Agranovich
language : en
Publisher: Courier Dover Publications
Release Date : 2020-05-21
The Inverse Problem Of Scattering Theory written by Z.S. Agranovich and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-21 with Mathematics categories.
This monograph by two Soviet experts in mathematical physics was a major contribution to inverse scattering theory. The two-part treatment examines the boundary-value problem with and without singularities. 1963 edition.
Spectral Analysis Differential Equations And Mathematical Physics A Festschrift In Honor Of Fritz Gesztesy S 60th Birthday
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Author : Helge Holden
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-07-08
Spectral Analysis Differential Equations And Mathematical Physics A Festschrift In Honor Of Fritz Gesztesy S 60th Birthday written by Helge Holden and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-08 with Mathematics categories.
This volume contains twenty contributions in the area of mathematical physics where Fritz Gesztesy made profound contributions. There are three survey papers in spectral theory, differential equations, and mathematical physics, which highlight, in particu
Inverse Problems In Vibration
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Author : G. M. L. Gladwell
language : en
Publisher: Martinus Nijhoff Publishing
Release Date : 1986
Inverse Problems In Vibration written by G. M. L. Gladwell and has been published by Martinus Nijhoff Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Mathematics categories.
Oscillation Matrices And Kernels And Small Vibrations Of Mechanical Systems
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Author : Feliks Ruvimovich Gantmakher
language : en
Publisher: American Mathematical Soc.
Release Date : 1961
Oscillation Matrices And Kernels And Small Vibrations Of Mechanical Systems written by Feliks Ruvimovich Gantmakher and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1961 with Technology & Engineering categories.
The exposition is self-contained. The first chapter presents all necessary results (with proofs) on the theory of matrices which are not included in a standard linear algebra course. The only prerequisite in addition to standard linear algebra is the theory of linear integral equations used in Chapter 5. The book is suitable for graduate students, research mathematicians and engineers interested in ordinary differential equations, integral equations, and theirapplications.
50 Years With Hardy Spaces
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Author : Anton Baranov
language : en
Publisher: Birkhäuser
Release Date : 2018-03-28
50 Years With Hardy Spaces written by Anton Baranov and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-28 with Mathematics categories.
Written in honor of Victor Havin (1933–2015), this volume presents a collection of surveys and original papers on harmonic and complex analysis, function spaces and related topics, authored by internationally recognized experts in the fields. It also features an illustrated scientific biography of Victor Havin, one of the leading analysts of the second half of the 20th century and founder of the Saint Petersburg Analysis Seminar. A complete list of his publications, as well as his public speech "Mathematics as a source of certainty and uncertainty", presented at the Doctor Honoris Causa ceremony at Linköping University, are also included.
Homogenization Theory For Multiscale Problems
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Author : Xavier Blanc
language : en
Publisher: Springer Nature
Release Date : 2023-04-29
Homogenization Theory For Multiscale Problems written by Xavier Blanc and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-04-29 with Mathematics categories.
The book provides a pedagogic and comprehensive introduction to homogenization theory with a special focus on problems set for non-periodic media. The presentation encompasses both deterministic and probabilistic settings. It also mixes the most abstract aspects with some more practical aspects regarding the numerical approaches necessary to simulate such multiscale problems. Based on lecture courses of the authors, the book is suitable for graduate students of mathematics and engineering.
Inverse Problems
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Author : Giovanni Alessandrini
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
Inverse Problems written by Giovanni Alessandrini and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
This volume presents the proceedings of a workshop on Inverse Problems and Applications and a special session on Inverse Boundary Problems and Applications. Inverse problems arise in practical situations, such as medical imaging, exploration geophysics, and non-destructive evaluation where measurements made in the exterior of a body are used to deduce properties of the hidden interior. A large class of inverse problems arise from a physical situation modeled by partial differential equations. The inverse problem is to determine some coefficients of the equation given some information about solutions. Analysis of such problems is a fertile area for interaction between pure and applied mathematics. This interplay is well represented in this volume where several theoretical and applied aspects of inverse problems are considered. The book includes articles on a broad range of inverse problems including the inverse conductivity problem, inverse problems for Maxwell's equations, time reversal mirrors, ultrasound using elastic pressure waves, inverse problems arising in the environment, inverse scattering for the three-body problem, and optical tomography. Also included are several articles on unique continuation and on the study of propagation of singularities for hyperbolic equations in anisotropic media. This volume is suitable for graduate students and research mathematicians interested in inverse problems and applications.