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Author: Luis A. Santaló
Publisher: Cambridge University Press
Published: 2004-10-28
Total Pages: 426
ISBN-13: 0521523443
DOWNLOAD EBOOKClassic text on integral geometry now available in paperback in the Cambridge Mathematical Library.
Author: Daniel A. Klain
Publisher: Cambridge University Press
Published: 1997-12-11
Total Pages: 196
ISBN-13: 9780521596541
DOWNLOAD EBOOKThe 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: Rolf Schneider
Publisher: Springer Science & Business Media
Published: 2008-09-08
Total Pages: 692
ISBN-13: 354078859X
DOWNLOAD EBOOKStochastic 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: R.V. Ambartzumian
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 135
ISBN-13: 9400939213
DOWNLOAD EBOOKAuthor: Luis Antonio Santaló Sors
Publisher:
Published: 1976
Total Pages: 404
ISBN-13:
DOWNLOAD EBOOKAuthor: Sigurdur Helgason
Publisher: Springer Science & Business Media
Published: 2010-11-17
Total Pages: 309
ISBN-13: 1441960546
DOWNLOAD EBOOKIn 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
Author: Hassler Whitney
Publisher: Princeton University Press
Published: 2015-12-08
Total Pages: 404
ISBN-13: 1400877571
DOWNLOAD EBOOKA complete theory of integration as it appears in geometric and physical problems must include integration over oriented r-dimensional domains in n-space; both the integrand and the domain may be variable. This is the primary subject matter of the present book, designed to bring out the underlying geometric and analytic ideas and to give clear and complete proofs of the basic theorems. Originally published in 1957. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Author: Marek Capinski
Publisher: Springer Science & Business Media
Published: 2013-06-29
Total Pages: 229
ISBN-13: 1447136314
DOWNLOAD EBOOKThis very well written and accessible book emphasizes the reasons for studying measure theory, which is the foundation of much of probability. By focusing on measure, many illustrative examples and applications, including a thorough discussion of standard probability distributions and densities, are opened. The book also includes many problems and their fully worked solutions.
Author: Georges Matheron
Publisher: John Wiley & Sons
Published: 1974
Total Pages: 294
ISBN-13:
DOWNLOAD EBOOKAuthor: Sigurdur Helgason
Publisher: Springer Science & Business Media
Published: 1999-08-01
Total Pages: 214
ISBN-13: 9780817641092
DOWNLOAD EBOOKThe 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.
