Rotational Integral Geometry And Its Applications
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Rotational Integral Geometry And Its Applications
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Author : Eva B. Vedel Jensen
language : en
Publisher: Springer Nature
Release Date : 2025-07-14
Rotational Integral Geometry And Its Applications written by Eva B. Vedel Jensen and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-07-14 with Mathematics categories.
This self-contained book offers an extensive state-of-the-art exposition of rotational integral geometry, a field that has reached significant maturity over the past four decades. Through a unified description of key results previously scattered across various scientific journals, this book provides a cohesive and thorough account of the subject. Initially, rotational integral geometry was driven by applications in fields such as optical microscopy. Rotational integral geometry has now evolved into an independent mathematical discipline. It contains a wealth of theorems paralleling those in classical kinematic integral geometry for Euclidean spaces, such as the rotational Crofton formulae, rotational slice formulae, and principal rotational formulae. The present book presents these for very general tensor valuations in a convex geometric setting. It also discusses various applications in the biosciences, explained with a mathematical audience in mind. This book is intended for a diverse readership, including specialists in integral geometry, and researchers and graduate students working in integral, convex, and stochastic geometry, as well as geometric measure theory.
Tensor Valuations And Their Applications In Stochastic Geometry And Imaging
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Author : Eva B. Vedel Jensen
language : en
Publisher: Springer
Release Date : 2017-06-10
Tensor Valuations And Their Applications In Stochastic Geometry And Imaging written by Eva B. Vedel Jensen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-10 with Mathematics categories.
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.
Stochastic Geometry And Its Applications
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Author : Sung Nok Chiu
language : en
Publisher: John Wiley & Sons
Release Date : 2013-06-27
Stochastic Geometry And Its Applications written by Sung Nok Chiu and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-27 with Mathematics categories.
An extensive update to a classic text Stochastic geometry and spatial statistics play a fundamental role in many modern branches of physics, materials sciences, engineering, biology and environmental sciences. They offer successful models for the description of random two- and three-dimensional micro and macro structures and statistical methods for their analysis. The previous edition of this book has served as the key reference in its field for over 18 years and is regarded as the best treatment of the subject of stochastic geometry, both as a subject with vital applications to spatial statistics and as a very interesting field of mathematics in its own right. This edition: Presents a wealth of models for spatial patterns and related statistical methods. Provides a great survey of the modern theory of random tessellations, including many new models that became tractable only in the last few years. Includes new sections on random networks and random graphs to review the recent ever growing interest in these areas. Provides an excellent introduction to theory and modelling of point processes, which covers some very latest developments. Illustrate the forefront theory of random sets, with many applications. Adds new results to the discussion of fibre and surface processes. Offers an updated collection of useful stereological methods. Includes 700 new references. Is written in an accessible style enabling non-mathematicians to benefit from this book. Provides a companion website hosting information on recent developments in the field www.wiley.com/go/cskm Stochastic Geometry and its Applications is ideally suited for researchers in physics, materials science, biology and ecological sciences as well as mathematicians and statisticians. It should also serve as a valuable introduction to the subject for students of mathematics and statistics.
Stochastic Geometry Spatial Statistics And Random Fields
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Author : Volker Schmidt
language : en
Publisher: Springer
Release Date : 2014-10-24
Stochastic Geometry Spatial Statistics And Random Fields written by Volker Schmidt and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-24 with Mathematics categories.
This volume is an attempt to provide a graduate level introduction to various aspects of stochastic geometry, spatial statistics and random fields, with special emphasis placed on fundamental classes of models and algorithms as well as on their applications, e.g. in materials science, biology and genetics. This book has a strong focus on simulations and includes extensive codes in Matlab and R which are widely used in the mathematical community. It can be seen as a continuation of the recent volume 2068 of Lecture Notes in Mathematics, where other issues of stochastic geometry, spatial statistics and random fields were considered with a focus on asymptotic methods.
Random Fields And Geometry
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Author : R. J. Adler
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-01-29
Random Fields And Geometry written by R. J. Adler and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-01-29 with Mathematics categories.
This monograph is devoted to a completely new approach to geometric problems arising in the study of random fields. The groundbreaking material in Part III, for which the background is carefully prepared in Parts I and II, is of both theoretical and practical importance, and striking in the way in which problems arising in geometry and probability are beautifully intertwined. "Random Fields and Geometry" will be useful for probabilists and statisticians, and for theoretical and applied mathematicians who wish to learn about new relationships between geometry and probability. It will be helpful for graduate students in a classroom setting, or for self-study. Finally, this text will serve as a basic reference for all those interested in the companion volume of the applications of the theory.
Physical Properties Mathematics And Its Application English Version
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Author : Chen Shuxuan
language : en
Publisher: Dorrance Publishing
Release Date : 2020-04-17
Physical Properties Mathematics And Its Application English Version written by Chen Shuxuan and has been published by Dorrance Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-17 with Education categories.
Physical Properties Mathematics and its Application(English Version) By: Chen Shuxuan Chen Shuxuan（陈叔瑄) was born on March 30, 1936 in Fuzhou, Fujian Province. He graduated from the Department of Physics at Xiamen University. He has been engaged in teaching and scientific research for many years in colleges and universities. He has taught courses such as electrician principle, electronic circuit, pulse circuit, digital logic, computer composition principle, computer application, assembly language programming, and so on. Based on many years of teaching experience, he compiled the IBM Microcomputer System and Assembly Language Programming guide which was published by Xiamen University Press in March 1990. In addition to teaching, he has made great efforts to develop the application of scientific theory and technology, participated in the development of many electronic circuits and computer applications projects, and published many research papers and works. Among them, "MM-1000 Friction Testing Machine Microcomputer System" software and hardware development, passed provincial technical appraisal in December 1987.The system plays an important role in the research of wet friction and wear testing technology and it has won the third prize of the Ministry of Electricity. Before retirement, he was an associate professor in the Department of Computer Science, Xiamen University.
Theory Of Spinors An Introduction
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Author : Moshe Carmeli
language : en
Publisher: World Scientific Publishing Company
Release Date : 2000-04-12
Theory Of Spinors An Introduction written by Moshe Carmeli and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-04-12 with Science categories.
Spinors are used extensively in physics. It is widely accepted that they are more fundamental than tensors, and the easy way to see this is through the results obtained in general relativity theory by using spinors — results that could not have been obtained by using tensor methods only.The foundation of the concept of spinors is groups; spinors appear as representations of groups. This textbook expounds the relationship between spinors and representations of groups. As is well known, spinors and representations are both widely used in the theory of elementary particles.The authors present the origin of spinors from representation theory, but nevertheless apply the theory of spinors to general relativity theory, and part of the book is devoted to curved space-time applications.Based on lectures given at Ben Gurion University, this textbook is intended for advanced undergraduate and graduate students in physics and mathematics, as well as being a reference for researchers.
Encyclopaedia Of Mathematics
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Author : Michiel Hazewinkel
language : en
Publisher: Springer Science & Business Media
Release Date : 1989-08-31
Encyclopaedia Of Mathematics written by Michiel Hazewinkel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-08-31 with Mathematics categories.
V.1. A-B v.2. C v.3. D-Feynman Measure. v.4. Fibonaccimethod H v.5. Lituus v.6. Lobachevskii Criterion (for Convergence)-Optical Sigman-Algebra. v.7. Orbi t-Rayleigh Equation. v.8. Reaction-Diffusion Equation-Stirling Interpolation Fo rmula. v.9. Stochastic Approximation-Zygmund Class of Functions. v.10. Subject Index-Author Index.
Canadian Journal Of Mathematics
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Author :
language : en
Publisher:
Release Date : 1970
Canadian Journal Of Mathematics written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with categories.
Convex Geometry
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Author : Shiri Artstein-Avidan
language : en
Publisher: Springer Nature
Release Date : 2023-12-13
Convex Geometry written by Shiri Artstein-Avidan and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-12-13 with Mathematics categories.
This book collects the lecture notes of the Summer School on Convex Geometry, held in Cetraro, Italy, from August 30th to September 3rd, 2021. Convex geometry is a very active area in mathematics with a solid tradition and a promising future. Its main objects of study are convex bodies, that is, compact and convex subsets of n-dimensional Euclidean space. The so-called Brunn--Minkowski theory currently represents the central part of convex geometry. The Summer School provided an introduction to various aspects of convex geometry: The theory of valuations, including its recent developments concerning valuations on function spaces; geometric and analytic inequalities, including those which come from the Lp Brunn--Minkowski theory; geometric and analytic notions of duality, along with their interplay with mass transportation and concentration phenomena; symmetrizations, which provide one of the main tools to many variational problems(not only in convex geometry). Each of these parts is represented by one of the courses given during the Summer School and corresponds to one of the chapters of the present volume. The initial chapter contains some basic notions in convex geometry, which form a common background for the subsequent chapters. The material of this book is essentially self-contained and, like the Summer School, is addressed to PhD and post-doctoral students and to all researchers approaching convex geometry for the first time.