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Investigation Methods for Inverse Problems. (Record no. 65232)

MARC details
000 -LEADER
fixed length control field 05767nam a22004813i 4500
001 - CONTROL NUMBER
control field EBC3049581
003 - CONTROL NUMBER IDENTIFIER
control field MiAaPQ
005 - DATE AND TIME OF LATEST TRANSACTION
control field 20240729124348.0
006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS
fixed length control field m o d |
007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION
fixed length control field cr cnu||||||||
008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION
fixed length control field 240724s2002 xx o ||||0 eng d
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 9783110943849
Qualifying information (electronic bk.)
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
Canceled/invalid ISBN 9789067643610
035 ## - SYSTEM CONTROL NUMBER
System control number (MiAaPQ)EBC3049581
035 ## - SYSTEM CONTROL NUMBER
System control number (Au-PeEL)EBL3049581
035 ## - SYSTEM CONTROL NUMBER
System control number (CaPaEBR)ebr11008961
035 ## - SYSTEM CONTROL NUMBER
System control number (CaONFJC)MIL807324
035 ## - SYSTEM CONTROL NUMBER
System control number (OCoLC)922950405
040 ## - CATALOGING SOURCE
Original cataloging agency MiAaPQ
Language of cataloging eng
Description conventions rda
-- pn
Transcribing agency MiAaPQ
Modifying agency MiAaPQ
050 #4 - LIBRARY OF CONGRESS CALL NUMBER
Classification number QC20.7.D5 -- R64 2002eb
100 1# - MAIN ENTRY--PERSONAL NAME
Personal name Romanov, Vladimir G.
245 10 - TITLE STATEMENT
Title Investigation Methods for Inverse Problems.
250 ## - EDITION STATEMENT
Edition statement 1st ed.
264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE
Place of production, publication, distribution, manufacture Berlin/Boston :
Name of producer, publisher, distributor, manufacturer De Gruyter, Inc.,
Date of production, publication, distribution, manufacture, or copyright notice 2002.
264 #4 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE
Date of production, publication, distribution, manufacture, or copyright notice ©2002.
300 ## - PHYSICAL DESCRIPTION
Extent 1 online resource (292 pages)
336 ## - CONTENT TYPE
Content type term text
Content type code txt
Source rdacontent
337 ## - MEDIA TYPE
Media type term computer
Media type code c
Source rdamedia
338 ## - CARRIER TYPE
Carrier type term online resource
Carrier type code cr
Source rdacarrier
490 1# - SERIES STATEMENT
Series statement Inverse and Ill-Posed Problems Series ;
Volume/sequential designation v.34
505 0# - FORMATTED CONTENTS NOTE
Formatted contents note Intro -- Preface -- 1 Introduction -- 1.1 One-dimensional inverse kinematics problem -- 1.2 Inverse dynamical problem for a string -- 1.3 Inverse problems for a layered medium -- 2 Ray statements of inverse problems -- 2.1 Posing of the inverse problems -- 2.2 Asymptotic expansion -- 2.2.1 Asymptotic expansion of the solution -- 2.2.2 Reduction of the inverse problem -- 2.2.3 Construction of τ(x, y) -- 2.2.4 Proof of the expansion in the odd-dimensional case -- 2.2.5 Proof of the expansion in the even-dimensional case -- 2.2.6 Proof of the auxiliary lemma -- 2.3 Uniqueness theorems for the inverse problem -- 2.3.1 A proof of the stability estimate for the integral geometry problem -- 2.3.2 Uniqueness theorem for the integral geometry problem related to a vector field -- 2.3.3 Proof of the uniqueness theorem for inverse kinematics problem -- 2.3.4 The wave equation with an attenuation -- 2.3.5 Concluding remarks -- 2.4 Inverse problems related to a local heterogeneity -- 3 Local solvability of some inverse problems -- 3.1 Banach's spaces of analytic functions -- 3.2 Determining coefficients of the lower terms -- 3.2.1 Determining a coefficient of the lower term -- 3.2.2 Determining an attenuation coefficient -- 3.3 Determining the speed of the sound -- 3.4 A regularization method for solving an inverse problem -- 3.4.1 Theorems related to the system of integro-differential equations -- 3.4.2 Estimates of a solution to the algebraic equations -- 3.4.3 Convergence the approximate solution to the exact one -- 4 Inverse problems with single measurements -- 4.1 Determining coefficient of the lowest term -- 4.1.1 Statement of the problem and stability estimates -- 4.1.2 Proof of the stability theorems -- 4.1.3 Proof of Lemma 4.1.3 -- 4.1.4 Proof of Lemma 4.1.4 -- 4.2 Determining coefficients under first derivatives.
505 8# - FORMATTED CONTENTS NOTE
Formatted contents note 4.3 Determining the speed of sound in the wave equation -- 4.3.1 Formulation of the problem and a stability estimate of the solution -- 4.3.2 Proof of Theorem 4.3.1 -- 4.3.3 Proof of Lemma 4.3.5 -- 4.3.4 Proof of Lemma 4.3.6 -- 4.3.5 Proof of the inequality (4.3.24) -- 4.4 Case of a point source -- 4.4.1 Formulations of the problem and results -- 4.4.2 Proofs of the stability theorems -- 4.4.3 Properties of a solution to problem (4.4.1) -- 4.4.4 Proof of Lemma 4.4.3 -- 4.4.5 Proof of Lemma 4.4.4 -- 5 Stability estimates related to inverse problems for the transport equation -- 5.1 The problem of determining the relaxation and a density of inner sources -- 5.1.1 Statement of basic and auxiliary problems -- 5.1.2 The basic results -- 5.1.3 Proof of Theorem 5.1.1 -- 5.1.4 Proof of the auxiliary lemmas -- 5.2 A stability estimate in the problem of determining the dispersion index and relaxation in 2D -- 5.2.1 Statement of the problem and the basic results -- 5.2.2 Proof of Lemma 5.2.1 -- 5.2.3 A priori estimates -- 5.2.4 Proof of Theorem 5.2.3 -- 5.3 The problem of determining the dispersion index and relaxation in 3D -- 5.3.1 Statement of the problem and the main results -- 5.3.2 Proof of Lemma 5.3.1 -- 5.3.3 A priori estimates for function ω(x, v) -- 5.3.4 Estimates for functions ώ(x, v) and σ̃(x) -- 5.3.5 A priori estimates and differential properties of function u¯(x,v,v°) -- 5.3.6 A priori estimates and properties of function v(x, v,v°) -- 5.3.7 Equations for the derivatives of function ṽ(x, u, v°) -- 5.3.8 Proof of inequality (5.3.24) -- 5.3.9 Proof of inequality (5.3.25) -- 5.3.10 Proof of inequality (5.3.26) -- 5.3.11 Auxiliary formulae -- Bibliography.
520 ## - SUMMARY, ETC.
Summary, etc. The Inverse and Ill-Posed Problems Series is a series of monographs publishing postgraduate level information on inverse and ill-posed problems for an international readership of professional scientists and researchers. The series aims to publish works which involve both theory and applications in, e.g., physics, medicine, geophysics, acoustics, electrodynamics, tomography, and ecology.
588 ## - SOURCE OF DESCRIPTION NOTE
Source of description note Description based on publisher supplied metadata and other sources.
590 ## - LOCAL NOTE (RLIN)
Local note Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name entry element Inverse problems (Differential equations) -- Numerical solutions.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name entry element Mathematical physics.
655 #4 - INDEX TERM--GENRE/FORM
Genre/form data or focus term Electronic books.
776 08 - ADDITIONAL PHYSICAL FORM ENTRY
Relationship information Print version:
Main entry heading Romanov, Vladimir G.
Title Investigation Methods for Inverse Problems
Place, publisher, and date of publication Berlin/Boston : De Gruyter, Inc.,c2002
International Standard Book Number 9789067643610
797 2# - LOCAL ADDED ENTRY--CORPORATE NAME (RLIN)
Corporate name or jurisdiction name as entry element ProQuest (Firm)
830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE
Uniform title Inverse and Ill-Posed Problems Series
856 40 - ELECTRONIC LOCATION AND ACCESS
Uniform Resource Identifier <a href="https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=3049581">https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=3049581</a>
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