Inverse Problems in the Theory of Small Oscillations PDF Download
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Author: Vladimir Marchenko
Publisher: American Mathematical Soc.
ISBN: 1470448904
Category : Mathematics
Languages : en
Pages : 170
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Book Description
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.
Author: Vladimir Marchenko
Publisher: American Mathematical Soc.
ISBN: 1470448904
Category : Mathematics
Languages : en
Pages : 170
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Book Description
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.
Author: Mohsen Razavy
Publisher: World Scientific Publishing Company
ISBN: 9789811221668
Category : Science
Languages : en
Pages : 380
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Book Description
This book is a compilation of different methods of formulating and solving inverse problems in physics from classical mechanics to the potentials and nucleus-nucleus scattering. Mathematical proofs are omitted since excellent monographs already exist dealing with these aspects of the inverse problems. The emphasis here is on finding numerical solutions to complicated equations. A detailed discussion is presented on the use of continued fractional expansion, its power and its limitation as applied to various physical problems. In particular, the inverse problem for discrete form of the wave equation is given a detailed exposition and applied to atomic and nuclear scattering, in the latter for elastic as well as inelastic collision. This technique is also used for inverse problem of geomagnetic induction and one-dimensional electrical conductivity. Among other topics covered are the inverse problem of torsional vibration, and also a chapter on the determination of the motion of a body with reflecting surface from its reflection coefficient.
Author: Curtis R. Vogel
Publisher: SIAM
ISBN: 0898717574
Category : Mathematics
Languages : en
Pages : 195
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Book Description
Provides a basic understanding of both the underlying mathematics and the computational methods used to solve inverse problems.
Author: Feliks Ruvimovich Gantmakher
Publisher: American Mathematical Soc.
ISBN:
Category : Technology & Engineering
Languages : en
Pages : 424
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Book Description
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.
Author: Anton Baranov
Publisher: Birkhäuser
ISBN: 3319590782
Category : Mathematics
Languages : en
Pages : 477
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Book Description
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.
Author: Helge Holden
Publisher: American Mathematical Soc.
ISBN: 0821875744
Category : Mathematics
Languages : en
Pages : 409
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Book Description
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
Author: V. G. Romanov
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110926016
Category : Mathematics
Languages : en
Pages : 248
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Book Description
No detailed description available for "Inverse Problems of Mathematical Physics".
Author: Xavier Blanc
Publisher: Springer Nature
ISBN: 3031218337
Category : Mathematics
Languages : en
Pages : 469
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Book Description
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.
Author: Arieh Iserles
Publisher: Cambridge University Press
ISBN: 9780521818766
Category : Mathematics
Languages : en
Pages : 600
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Book Description
An annual volume presenting substantive survey articles in numerical mathematics and scientific computing.
Author: Isaac Elishakoff
Publisher: CRC Press
ISBN: 1000611000
Category : Science
Languages : en
Pages : 464
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Book Description
The engineering community generally accepts that there exists only a small set of closed-form solutions for simple cases of bars, beams, columns, and plates. Despite the advances in powerful computing and advanced numerical techniques, closed-form solutions remain important for engineering; these include uses for preliminary design, for evaluation
