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 Mathematics 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.
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.
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
Methods Of Inverse Problems In Physics
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Author : Dilip N. Ghosh Roy
language : en
Publisher: CRC Press
Release Date : 1991-03-14
Methods Of Inverse Problems In Physics written by Dilip N. Ghosh Roy and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-03-14 with Science categories.
This interesting volume focuses on the second of the two broad categories into which problems of physical sciences fall-direct (or forward) and inverse (or backward) problems. It emphasizes one-dimensional problems because of their mathematical clarity. The unique feature of the monograph is its rigorous presentation of inverse problems (from quantum scattering to vibrational systems), transmission lines, and imaging sciences in a single volume. It includes exhaustive discussions on spectral function, inverse scattering integral equations of Gel'fand-Levitan and Marcenko, Povzner-Levitan and Levin transforms, Møller wave operators and Krein's functionals, S-matrix and scattering data, and inverse scattering transform for solving nonlinear evolution equations via inverse solving of a linear, isospectral Schrodinger equation and multisoliton solutions of the K-dV equation, which are of special interest to quantum physicists and mathematicians. The book also gives an exhaustive account of inverse problems in discrete systems, including inverting a Jacobi and a Toeplitz matrix, which can be applied to geophysics, electrical engineering, applied mechanics, and mathematics. A rigorous inverse problem for a continuous transmission line developed by Brown and Wilcox is included. The book concludes with inverse problems in integral geometry, specifically Radon's transform and its inversion, which is of particular interest to imaging scientists. This fascinating volume will interest anyone involved with quantum scattering, theoretical physics, linear and nonlinear optics, geosciences, mechanical, biomedical, and electrical engineering, and imaging research.
Inverse Problems Of Mathematical Physics
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Author : V. G. Romanov
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2018-11-05
Inverse Problems Of Mathematical Physics written by V. G. Romanov and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-05 with Mathematics categories.
No detailed description available for "Inverse Problems of Mathematical Physics".
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.
Inverse Problems Of Mathematical Physics
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Author : Mikhail M. Lavrent'ev
language : en
Publisher: Walter de Gruyter
Release Date : 2012-05-07
Inverse Problems Of Mathematical Physics written by Mikhail M. Lavrent'ev and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-07 with Mathematics categories.
This monograph deals with the theory of inverse problems of mathematical physics and applications of such problems. Besides it considers applications and numerical methods of solving the problems under study. Descriptions of particular numerical experiments 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.
Computational Methods For Inverse Problems
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Author : Curtis R. Vogel
language : en
Publisher: SIAM
Release Date : 2002-01-01
Computational Methods For Inverse Problems written by Curtis R. Vogel and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-01-01 with Mathematics categories.
Provides a basic understanding of both the underlying mathematics and the computational methods used to solve inverse problems.
Direct And Inverse Finite Dimensional Spectral Problems On Graphs
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Author : Manfred Möller
language : en
Publisher: Springer Nature
Release Date : 2020-10-30
Direct And Inverse Finite Dimensional Spectral Problems On Graphs written by Manfred Möller and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-30 with Mathematics categories.
Considering that the motion of strings with finitely many masses on them is described by difference equations, this book presents the spectral theory of such problems on finite graphs of strings. The direct problem of finding the eigenvalues as well as the inverse problem of finding strings with a prescribed spectrum are considered. This monograph gives a comprehensive and self-contained account on the subject, thereby also generalizing known results. The interplay between the representation of rational functions and their zeros and poles is at the center of the methods used. The book also unravels connections between finite dimensional and infinite dimensional spectral problems on graphs, and between self-adjoint and non-self-adjoint finite-dimensional problems. This book is addressed to researchers in spectral theory of differential and difference equations as well as physicists and engineers who may apply the presented results and methods to their research.