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Integral Geometry of Tensor Fields.
Integral geometry can be defined as determining some function or a more general quantity, which is defined on a manifold, given its integrals over submanifolds or a prescribed class. In this book, only integral geometry problems are considered for which the submanifolds are one-dimensional. The book...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Berlin :
De Gruyter,
1994.
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| Colección: | Inverse and ill-posed problems series.
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| Temas: | |
| Acceso en línea: | Texto completo |
MARC
| LEADER | 00000cam a2200000Mu 4500 | ||
|---|---|---|---|
| 001 | EBOOKCENTRAL_ocn843635167 | ||
| 003 | OCoLC | ||
| 005 | 20240329122006.0 | ||
| 006 | m o d | ||
| 007 | cr |n|---||||| | ||
| 008 | 130502s1994 gw o 000 0 eng d | ||
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| 020 | |a 9783110900095 | ||
| 020 | |a 3110900092 | ||
| 029 | 1 | |a AU@ |b 000055891648 | |
| 029 | 1 | |a AU@ |b 000068367900 | |
| 029 | 1 | |a DEBBG |b BV042353256 | |
| 035 | |a (OCoLC)843635167 | ||
| 050 | 4 | |a QA672 | |
| 082 | 0 | 4 | |a 516.3 |a 516.362 |
| 084 | |a SK 370 |2 rvk | ||
| 049 | |a UAMI | ||
| 100 | 1 | |a Sharafutdinov, V. A. | |
| 245 | 1 | 0 | |a Integral Geometry of Tensor Fields. |
| 260 | |a Berlin : |b De Gruyter, |c 1994. | ||
| 300 | |a 1 online resource (276 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a Inverse and Ill-Posed Problems Series ; |v v. 1 | |
| 588 | 0 | |a Print version record. | |
| 520 | |a Integral geometry can be defined as determining some function or a more general quantity, which is defined on a manifold, given its integrals over submanifolds or a prescribed class. In this book, only integral geometry problems are considered for which the submanifolds are one-dimensional. The book deals with integral geometry of symmetric tensor fields. This section of integral geometry can be considered as the mathematical basis for tomography or anisotropic media whose interaction with sounding radiation depends essentially on the direction in which the latter propagates. The main mathemat. | ||
| 505 | 0 | |a 1 Introduction -- 1.1 The problem of determining a metric by its hodograph and a linearization of the problem -- 1.2 The kinetic equation on a Riemannian manifold -- 1.3 Some remarks -- 2 The ray transform of symmetric tensor fields on Euclidean space -- 2.1 The ray transform and its relationship to the Fourier transform -- 2.2 Description of the kernel of the the ray transform in the smooth case -- 2.3 Equivalence of the first two statements of Theorem 2.2.1 in the case n = 2 -- 2.4 Proof of Theorem 2.2.2 -- 2.5 The ray transform of a field-distribution. | |
| 505 | 8 | |a 2.6 Decomposition of a tensor field into potential and solenoidal parts -- 2.7 A theorem on the tangent component -- 2.8 A theorem on conjugate tensor fields on the sphere -- 2.9 Primality of the ideal). | |
| 505 | 8 | |a 2.16 Application of the ray transform to an inverse problem of photoelasticity -- 2.17 Further results -- 3 Some questions of tensor analysis -- 3.1 Tensor fields -- 3.2 Covariant differentiation -- 3.3 Symmetric tensor fields -- 3.4 Semibasic tensor fields -- 3.5 The horizontal covariant derivative -- 3.6 Formulas of Gauss-Ostrogradskiĭ type for vertical and horizontal derivatives -- 4 The ray transform on a Riemannian manifold -- 4.1 Compact dissipative Riemannian manifolds -- 4.2 The ray transform on a CDRM -- 4.3 The problem of inverting the ray transform -- 4.4 Pestov's differential identity. | |
| 505 | 8 | |a 4.5 Poincaré's inequality for semibasic tensor fields -- 4.6 Reduction of Theorem 4.3.3 to an inverse problem for the kinetic equation -- 4.7 Proof of Theorem 4.3.3 -- 4.8 Consequences for the nonlinear problem of determining a metric from its hodograph -- 4.9 Bibliographical remarks -- 5 The transverse ray transform -- 5.1 Electromagnetic waves in quasi-isotropic media -- 5.2 The transverse ray transform on a CDRM -- 5.3 Reduction of Theorem 5.2.2 to an inverse problem for the kinetic equation -- 5.4 Estimation of the summand related to the right-hand side of the kinetic equation. | |
| 505 | 8 | |a 5.5 Estimation of the boundary integral and summands depending on curvature -- 5.6 Proof of Theorem 5.2.2 -- 5.7 Decomposition of the operators A0 and A1 -- 5.8 Proof of Lemma 5.6.1 -- 5.9 Final remarks -- 6 The truncated transverse ray transform -- 6.1 The polarization ellipse -- 6.2 The truncated transverse ray transform -- 6.3 Proof of Theorem 6.2.2 -- 6.4 Decomposition of the operator Qq -- 6.5 Proof of Lemma 6.3.1 -- 6.6 Inversion of the truncated transverse ray transform on Euclidean space -- 7 The mixed ray transform -- 7.1 Elastic waves in quasi-isotropic media. | |
| 590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
| 650 | 0 | |a Integral geometry. | |
| 650 | 0 | |a Calculus of tensors. | |
| 650 | 0 | |a Geometry, Differential. | |
| 650 | 6 | |a Géométrie intégrale. | |
| 650 | 6 | |a Calcul tensoriel. | |
| 650 | 6 | |a Géométrie différentielle. | |
| 650 | 7 | |a Calculus of tensors |2 fast | |
| 650 | 7 | |a Geometry, Differential |2 fast | |
| 650 | 7 | |a Integral geometry |2 fast | |
| 758 | |i has work: |a Integral geometry of tensor fields (Text) |1 https://id.oclc.org/worldcat/entity/E39PCGC7fkq8hXkh67XxTmwQv3 |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |z 9789067641654 |
| 830 | 0 | |a Inverse and ill-posed problems series. | |
| 856 | 4 | 0 | |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=934944 |z Texto completo |
| 938 | |a EBL - Ebook Library |b EBLB |n EBL934944 | ||
| 994 | |a 92 |b IZTAP | ||