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Author : Luis A. Santaló
Publisher : Cambridge University Press
Page : 426 pages
File Size : 48,5 Mb
Release : 2004-10-28
Category : Mathematics
ISBN : 9780521523448
Classic text on integral geometry now available in paperback in the Cambridge Mathematical Library.
Author : Luis Antonio Santaló
Publisher : Unknown
Page : 454 pages
File Size : 54,9 Mb
Release : 1976
Category : Geometric probabilities
ISBN : UCAL:B3990445
Author : Daniel A. Klain,Gian-Carlo Rota
Publisher : Cambridge University Press
Page : 196 pages
File Size : 48,5 Mb
Release : 1997-12-11
Category : Mathematics
ISBN : 0521596548
The purpose of this book is to present the three basic ideas of geometrical probability, also known as integral geometry, in their natural framework. In this way, the relationship between the subject and enumerative combinatorics is more transparent, and the analogies can be more productively understood. The first of the three ideas is invariant measures on polyconvex sets. The authors then prove the fundamental lemma of integral geometry, namely the kinematic formula. Finally the analogues between invariant measures and finite partially ordered sets are investigated, yielding insights into Hecke algebras, Schubert varieties and the quantum world, as viewed by mathematicians. Geometers and combinatorialists will find this a most stimulating and fruitful story.
Author : De-lin Ren
Publisher : World Scientific
Page : 260 pages
File Size : 52,6 Mb
Release : 1994
Category : Mathematics
ISBN : 9810211074
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 : Rolf Schneider,Wolfgang Weil
Publisher : Springer Science & Business Media
Page : 692 pages
File Size : 50,7 Mb
Release : 2008-09-08
Category : Mathematics
ISBN : 9783540788591
Stochastic geometry deals with models for random geometric structures. Its early beginnings are found in playful geometric probability questions, and it has vigorously developed during recent decades, when an increasing number of real-world applications in various sciences required solid mathematical foundations. Integral geometry studies geometric mean values with respect to invariant measures and is, therefore, the appropriate tool for the investigation of random geometric structures that exhibit invariance under translations or motions. Stochastic and Integral Geometry provides the mathematically oriented reader with a rigorous and detailed introduction to the basic stationary models used in stochastic geometry – random sets, point processes, random mosaics – and to the integral geometry that is needed for their investigation. The interplay between both disciplines is demonstrated by various fundamental results. A chapter on selected problems about geometric probabilities and an outlook to non-stationary models are included, and much additional information is given in the section notes.
Author : Herbert Solomon
Publisher : SIAM
Page : 180 pages
File Size : 41,8 Mb
Release : 1978-06-01
Category : Mathematics
ISBN : 9780898710250
Topics include: ways modern statistical procedures can yield estimates of pi more precisely than the original Buffon procedure traditionally used; the question of density and measure for random geometric elements that leave probability and expectation statements invariant under translation and rotation; and much more.
Author : Luis A. Santalo
Publisher : Cambridge University Press
Page : 421 pages
File Size : 49,7 Mb
Release : 1984-12-28
Category : Mathematics
ISBN : 0521302218
Integral geometry originated with problems on geometrical probability and convex bodies. Its later developments, however, have proved to be useful in several fields ranging from pure mathematics (measure theory, continuous groups) to technical and applied disciplines (pattern recognition, stereology). This book is a systematic exposition of the theory and a compilation of the main results in the field. The volume can be used for a one-semester undergraduate course in probability and differential geometry or as a complement to classical courses on differential geometry, Lie groups, or probability.
Author : Georges Matheron
Publisher : John Wiley & Sons
Page : 294 pages
File Size : 40,8 Mb
Release : 1974
Category : Mathematics
ISBN : UOM:39015038937648
Author : R. V. Ambartzumian
Publisher : Cambridge University Press
Page : 312 pages
File Size : 44,9 Mb
Release : 1990-09-28
Category : Mathematics
ISBN : 0521345359
The classical subjects of geometric probability and integral geometry, and the more modern one of stochastic geometry, are developed here in a novel way to provide a framework in which they can be studied. The author focuses on factorization properties of measures and probabilities implied by the assumption of their invariance with respect to a group, in order to investigate nontrivial factors. The study of these properties is the central theme of the book. Basic facts about integral geometry and random point process theory are developed in a simple geometric way, so that the whole approach is suitable for a nonspecialist audience. Even in the later chapters, where the factorization principles are applied to geometrical processes, the only prerequisites are standard courses on probability and analysis. The main ideas presented have application to such areas as stereology and geometrical statistics and this book will be a useful reference book for university students studying probability theory and stochastic geometry, and research mathematicians interested in this area.
Author : A.M. Mathai
Publisher : CRC Press
Page : 580 pages
File Size : 51,6 Mb
Release : 1999-12-01
Category : Mathematics
ISBN : 9056996819
A useful guide for researchers and professionals, graduate and senior undergraduate students, this book provides an in-depth look at applied and geometrical probability with an emphasis on statistical distributions. A meticulous treatment of geometrical probability, kept at a level to appeal to a wider audience including applied researchers who will find the book to be both functional and practical with the large number of problems chosen from different disciplines A few topics such as packing and covering problems that have a vast literature are introduced here at a peripheral level for the purpose of familiarizing readers who are new to the area of research.
Author : R.V. Ambartzumian
Publisher : Springer Science & Business Media
Page : 135 pages
File Size : 50,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789400939219
Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 47,8 Mb
Release : 2024-06-30
Category : Electronic
ISBN : 9789814479271
Author : Eric Grinberg
Publisher : World Scientific
Page : 240 pages
File Size : 40,7 Mb
Release : 2006
Category : Science
ISBN : 9789812565136
Integral geometry, known as geometric probability in the past, originated from Buffon's needle experiment. Remarkable advances have been made in several areas that involve the theory of convex bodies. This volume brings together contributions by leading international researchers in integral geometry, convex geometry, complex geometry, probability, statistics, and other convexity related branches. The articles cover both recent results and exciting directions for future research.
Author : Massimo Picardello
Publisher : CRC Press
Page : 194 pages
File Size : 46,9 Mb
Release : 2019-04-15
Category : Mathematics
ISBN : 9780429530319
Comprising a selection of expository and research papers, Harmonic Analysis and Integral Geometry grew from presentations offered at the July 1998 Summer University of Safi, Morocco-an annual, advanced research school and congress. This lively and very successful event drew the attendance of many top researchers, who offered both individual lecture
Author : Sigurdur Helgason
Publisher : Springer Science & Business Media
Page : 309 pages
File Size : 53,9 Mb
Release : 2010-11-17
Category : Mathematics
ISBN : 9781441960542
In this text, integral geometry deals with Radon’s problem of representing a function on a manifold in terms of its integrals over certain submanifolds—hence the term the Radon transform. Examples and far-reaching generalizations lead to fundamental problems such as: (i) injectivity, (ii) inversion formulas, (iii) support questions, (iv) applications (e.g., to tomography, partial di erential equations and group representations). For the case of the plane, the inversion theorem and the support theorem have had major applications in medicine through tomography and CAT scanning. While containing some recent research, the book is aimed at beginning graduate students for classroom use or self-study. A number of exercises point to further results with documentation. From the reviews: “Integral Geometry is a fascinating area, where numerous branches of mathematics meet together. the contents of the book is concentrated around the duality and double vibration, which is realized through the masterful treatment of a variety of examples. the book is written by an expert, who has made fundamental contributions to the area.” —Boris Rubin, Louisiana State University
