Investigation Methods for Inverse Problems. (Record no. 65232)
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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> |
Public note | Click to View |
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