# ePub Integral Geometry of Tensor Fields (Inverse and Ill-Posed Problems) download

# by V. a. Sharafutdinov

The Inverse and Ill-Posed Problems Series is a series of monographs publishing postgraduate level information on inverse and ill-posed .

The series aims to publish works which involve both theory and applications in, . physics, medicine, geophysics, acoustics, electrodynamics, tomography, and ecology.

Please see ww. egruyter. com for more information. 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 of 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.

Integral geometry of tensor elds, Vladimir A. Sharafutdinov. of the posed problem settled by the above mentioned construction? In other words: is it. Utrecht: VSP With index, ref. ISBN 90–6764–165–0 bound NUGI 811 Subject headings: tensor elds, integral geometry. Integral geometry is well known to be closely related to inverse problems for kinetic and transport equations. In Section . we introduce the kinetic equation on a Riemannian manifold and show that the integral geometry problem for a tensor eld is equivalent to an inverse problem of determining the source, in the kinetic equation, which depends polynomially on a direction.

Computer Centre of USSR Academy of Sciences, Siberian Branch, Novosibirsk. Full text: PDF file (383 kB). Bibliographic databases: UDC: 51. +513. 516 Presented: М. М. Лаврентьев Received: 0. 2. Bibitem{Sha86} by . A.

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We consider the integral geometry problem of finding a symmetric 2-tensor field in a unit . Method of ridge functions, J. Inverse Ill-Posed Probl. V. Sharafutdinov, Integral Geometry for Tensor Fields, Nauka, Novosibirsk (1993); English transl.

We consider the integral geometry problem of finding a symmetric 2-tensor field in a unit disk provided that the ray transforms of this field are known. 15, No. 1, 1–38 (2007).

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The line complex we consider consists of all lines passing through a fixed curve $gamma subset mathbb{R}^n$. Subjects: Analysis of PDEs (math.

The book deals with integral geometry of symmetric tensor fields. THE RAY TRANSFORM OF SYMMETRIC TENSOR FIELDS ON EUCLIDEAN SPACE The ray transform and its relationship to the Fourier transform. This section of integral geometry can be considered as the mathematical basis for tomography of anisotropic media whose interaction with sounding radiation depends essentially on the direction in which the latter propagates. The main mathematical objects tackled have been given the term ''ray transform'' which refers mainly to optical and seismic rays rather than to X-rays. Description of the kernel of the ray transform in the smooth case.

Integral geometry of tensor fields on a manifold of negative curvature. LN Pestov, VA Sharafutdinov. On reconstruction of the speed of sound from a part of boundary. Journal of inverse and ill-posed problems 7 (5), 481-486, 1999. Siberian Mathematical Journal 29 (3), 427-441, 1988. On characterization of the range and inversion formulas for the geodesic X-ray transform. An inverse kinematic problem with internal sources. L Pestov, G Uhlmann, H Zhou. Inverse problems 31 (5), 055006, 2015.

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.

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