Integral Geometry of Tensor Fields PDF Download
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Author: V. A. Sharafutdinov
Publisher: Walter de Gruyter
ISBN: 3110900092
Category : Mathematics
Languages : en
Pages : 277
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Book Description
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.
Author: V. A. Sharafutdinov
Publisher: Walter de Gruyter
ISBN: 3110900092
Category : Mathematics
Languages : en
Pages : 277
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Book Description
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.
Author: Lev Borisovich Vertgeim
Publisher:
ISBN:
Category : Integral geometry
Languages : en
Pages : 362
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Book Description
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 10
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Book Description
Author: Eva B. Vedel Jensen
Publisher: Springer
ISBN: 3319519514
Category : Mathematics
Languages : en
Pages : 469
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Book Description
The purpose of this volume is to give an up-to-date introduction to tensor valuations and their applications. Starting with classical results concerning scalar-valued valuations on the families of convex bodies and convex polytopes, it proceeds to the modern theory of tensor valuations. Product and Fourier-type transforms are introduced and various integral formulae are derived. New and well-known results are presented, together with generalizations in several directions, including extensions to the non-Euclidean setting and to non-convex sets. A variety of applications of tensor valuations to models in stochastic geometry, to local stereology and to imaging are also discussed.
Author: De-lin Ren
Publisher: World Scientific Publishing Company
ISBN: 9813103353
Category : Mathematics
Languages : en
Pages : 258
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Book Description
Essentials of integral geometry in a homogenous space are presented and the focus is on the basic results and applications. This book provides the readers with new findings, some being published for the first time and serves as an excellent graduate text.
Author: Joachim Weickert
Publisher: Springer Science & Business Media
ISBN: 3540312722
Category : Mathematics
Languages : en
Pages : 478
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Book Description
Matrix-valued data sets – so-called second order tensor fields – have gained significant importance in scientific visualization and image processing due to recent developments such as diffusion tensor imaging. This book is the first edited volume that presents the state of the art in the visualization and processing of tensor fields. It contains some longer chapters dedicated to surveys and tutorials of specific topics, as well as a great deal of original work by leading experts that has not been published before. It serves as an overview for the inquiring scientist, as a basic foundation for developers and practitioners, and as as a textbook for specialized classes and seminars for graduate and doctoral students.
Author: Sigurdur Helgason
Publisher: Springer Science & Business Media
ISBN: 9780817641092
Category : Mathematics
Languages : en
Pages : 214
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Book Description
The Radon transform is an important topic in integral geometry which deals with the problem of expressing a function on a manifold in terms of its integrals over certain submanifolds. Solutions to such problems have a wide range of applications, namely to partial differential equations, group representations, X-ray technology, nuclear magnetic resonance scanning, and tomography. This second edition, significantly expanded and updated, presents new material taking into account some of the progress made in the field since 1980. Aimed at beginning graduate students, this monograph will be useful in the classroom or as a resource for self-study. Readers will find here an accessible introduction to Radon transform theory, an elegant topic in integral geometry.
Author: Anvar Kh. Amirov
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110940949
Category : Mathematics
Languages : en
Pages : 212
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Book Description
In this monograph a method for proving the solvability of integral geometry problems and inverse problems for kinetic equations is presented. The application of this method has led to interesting problems of the Dirichlet type for third order differential equations, the solvability of which appears to depend on the geometry of the domain for which the problem is stated. Another considered subject is the problem of integral geometry on paraboloids, in particular the uniqueness of solutions to the Goursat problem for a differential inequality, which implies new theorems on the uniqueness of solutions to this problem for a class of quasilinear hyperbolic equations. A class of multidimensional inverse problems associated with problems of integral geometry and the inverse problem for the quantum kinetic equations are also included.
Author: T. Voronov
Publisher: CRC Press
ISBN: 9783718651993
Category : Mathematics
Languages : en
Pages : 152
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Book Description
The author presents the first detailed and original account of his theory of forms on supermanifolds-a correct and non-trivial analogue of Cartan-de Rham theory based on new concepts. The paper develops the apparatus of supermanifold differential topology necessary for the integration theory. A key feature is the identification of a class of proper morphisms intimately connected with Berezin integration, which are of fundamental importance in various problems. The work also contains a condensed introduction to superanalysis and supermanifolds, free from algebraic formalism, which sets out afresh such challenging problems as the Berezin intgegral on a bounded domain.
Author: Ke Yang
Publisher: Iiste
ISBN: 9781622659319
Category :
Languages : en
Pages :
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Book Description
This work is divided into Divergence Theorem at Manifold, Green Theorem at Manifold (Difference, corresponding to traditional Green Theorem) and Curl Theorem at Manifold (Difference, corresponding to traditional Stokes Theorem) three parts; From different perspectives of three new typical integral theorems, this work demonstrates that base on individualized geometric object (Manifold)coordinates, through matrixing operations, realize new formular conjunctions between different typical integrals; and provides corresponding numerical models; New integral formular demonstrations and numerical models indicate: Base on individualized geometric object coordinates, through unified standardized_concise_matrixing integral operations, science explorers can obtain analytic integral values or float integral values in discretional precision of discretional complicated geometric objects (Manifold; Especially point irregular, asymmetrical geometric shapes in 2-Dimensional and 3-Dimensional Euclidean space of real world); New typical numerical modelings possess vast mathematical, physical, engineering applicational field, involve that in 2-Dimensional and 3-Dimensional Euclidean space of real world, exact integral calculation of vector field and scalar field about discretional complicated geometric objects and their boundary regions, and then realize direct triple connection between calculus, topology and physical engineering calculation
