03003nam 2200673Ia 450 991078580880332120230421054139.03-11-090009-210.1515/9783110900095(CKB)2670000000255897(EBL)934944(OCoLC)843635167(SSID)ssj0000559885(PQKBManifestationID)11373998(PQKBTitleCode)TC0000559885(PQKBWorkID)10568300(PQKB)10961853(MiAaPQ)EBC934944(DE-B1597)57152(OCoLC)979764774(DE-B1597)9783110900095(Au-PeEL)EBL934944(CaPaEBR)ebr10597629(EXLCZ)99267000000025589719950823d1994 uy 0engur|n|---|||||txtccrIntegral geometry of tensor fields[electronic resource] /V.A. SharafutdinovReprint 2010Utrecht, the Netherlands VSP19941 online resource (276 p.)Inverse and Ill-Posed Problems Series ;1Inverse and ill-posed problems seriesDescription based upon print version of record.3-11-062951-8 90-6764-165-0 Includes bibliographical references (p. 259-268) and index. Frontmatter -- 1 Introduction -- 2 The ray transform of symmetric tensor fields on Euclidean space -- 3 Some questions of tensor analysis -- 4 The ray transform on a Riemannian manifold -- 5 The transverse ray transform -- 6 The truncated transverse ray transform -- 7 The mixed ray transform -- 8 The exponential ray transform -- Bibliography -- IndexIntegral 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 mathematInverse and Ill-Posed Problems SeriesIntegral geometryCalculus of tensorsGeometry, DifferentialIntegral geometry.Calculus of tensors.Geometry, Differential.516.362SK 370rvkSharafutdinov V. A(Vladimir Alʹtafovich)1551006MiAaPQMiAaPQMiAaPQBOOK9910785808803321Integral geometry of tensor fields3810282UNINA