Discrete Geometric Analysis
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Discrete Geometric Analysis
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Author : Martin T.Barlow
language : en
Publisher:
Release Date : 2016-05
Discrete Geometric Analysis written by Martin T.Barlow and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05 with Mathematics categories.
This is a volume of lecture notes based on three series of lectures given by visiting professors of RIMS, Kyoto University during the year-long project 'Discrete Geometric Analysis', which took place in the Japanese academic year 2012-2013. The aim of the project was to make comprehensive research on topics related to discreteness in geometry, analysis and optimization.Discrete geometric analysis is a hybrid field of several traditional disciplines, including graph theory, geometry, discrete group theory, and probability. The name of the area was coined by Toshikazu Sunada, and since being introduced, it has been extending and making new interactions with many other fields.This volume consists of three chapters: (I) Loop Erased Walks and Uniform Spanning Trees, by Martin T Barlow; (II) Combinatorial Rigidity: Graphs and Matroids in the Theory of Rigid Frameworks, by Tibor Jordán; (III) Analysis and Geometry on Groups, by Andrzej Zuk.The lecture notes are useful surveys that provide an introduction to the history and recent progress in the areas covered. They will also help researchers who work in related interdisciplinary fields to gain an understanding of the material from the viewpoint of discrete geometric analysis.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets
Discrete Geometric Analysis
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Author : Motoko Kotani
language : en
Publisher: American Mathematical Soc.
Release Date : 2004
Discrete Geometric Analysis written by Motoko Kotani and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
Collects papers from the proceedings of the first symposium of the Japan Association for Mathematical Sciences. This book covers topics that center around problems of geometric analysis in relation to heat kernels, random walks, and Poisson boundaries on discrete groups, graphs, and other combinatorial objects.
Classical Topics In Discrete Geometry
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Author : Károly Bezdek
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-06-23
Classical Topics In Discrete Geometry written by Károly Bezdek 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 2010-06-23 with Mathematics categories.
Geometry is a classical core part of mathematics which, with its birth, marked the beginning of the mathematical sciences. Thus, not surprisingly, geometry has played a key role in many important developments of mathematics in the past, as well as in present times. While focusing on modern mathematics, one has to emphasize the increasing role of discrete mathematics, or equivalently, the broad movement to establish discrete analogues of major components of mathematics. In this way, the works of a number of outstanding mathema- cians including H. S. M. Coxeter (Canada), C. A. Rogers (United Kingdom), and L. Fejes-T oth (Hungary) led to the new and fast developing eld called discrete geometry. One can brie y describe this branch of geometry as the study of discrete arrangements of geometric objects in Euclidean, as well as in non-Euclidean spaces. This, as a classical core part, also includes the theory of polytopes and tilings in addition to the theory of packing and covering. D- crete geometry is driven by problems often featuring a very clear visual and applied character. The solutions use a variety of methods of modern mat- matics, including convex and combinatorial geometry, coding theory, calculus of variations, di erential geometry, group theory, and topology, as well as geometric analysis and number theory.
Topological Crystallography
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Author : Toshikazu Sunada
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-23
Topological Crystallography written by Toshikazu Sunada 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 2012-12-23 with Mathematics categories.
Geometry in ancient Greece is said to have originated in the curiosity of mathematicians about the shapes of crystals, with that curiosity culminating in the classification of regular convex polyhedra addressed in the final volume of Euclid’s Elements. Since then, geometry has taken its own path and the study of crystals has not been a central theme in mathematics, with the exception of Kepler’s work on snowflakes. Only in the nineteenth century did mathematics begin to play a role in crystallography as group theory came to be applied to the morphology of crystals. This monograph follows the Greek tradition in seeking beautiful shapes such as regular convex polyhedra. The primary aim is to convey to the reader how algebraic topology is effectively used to explore the rich world of crystal structures. Graph theory, homology theory, and the theory of covering maps are employed to introduce the notion of the topological crystal which retains, in the abstract, all the information on the connectivity of atoms in the crystal. For that reason the title Topological Crystallography has been chosen. Topological crystals can be described as “living in the logical world, not in space,” leading to the question of how to place or realize them “canonically” in space. Proposed here is the notion of standard realizations of topological crystals in space, including as typical examples the crystal structures of diamond and lonsdaleite. A mathematical view of the standard realizations is also provided by relating them to asymptotic behaviors of random walks and harmonic maps. Furthermore, it can be seen that a discrete analogue of algebraic geometry is linked to the standard realizations. Applications of the discussions in this volume include not only a systematic enumeration of crystal structures, an area of considerable scientific interest for many years, but also the architectural design of lightweight rigid structures. The reader therefore can see the agreement of theory and practice.
Geometry Analysis And Topology Of Discrete Groups
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Author : Lizhen Ji
language : en
Publisher:
Release Date : 2008
Geometry Analysis And Topology Of Discrete Groups written by Lizhen Ji and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
Presents 15 papers treating discrete groups as they occur in areas such as algebra, analysis, geometry, number theory and topology. This work helps graduate students and researchers to understand the structures and applications of discrete subgroups of Lie groups and locally symmetric spaces.
Lectures On Sphere Arrangements The Discrete Geometric Side
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Author : Károly Bezdek
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-08-04
Lectures On Sphere Arrangements The Discrete Geometric Side written by Károly Bezdek 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 2013-08-04 with Mathematics categories.
This monograph gives a short introduction to the relevant modern parts of discrete geometry, in addition to leading the reader to the frontiers of geometric research on sphere arrangements. The readership is aimed at advanced undergraduate and early graduate students, as well as interested researchers. It contains more than 40 open research problems ideal for graduate students and researchers in mathematics and computer science. Additionally, this book may be considered ideal for a one-semester advanced undergraduate or graduate level course. The core part of this book is based on three lectures given by the author at the Fields Institute during the thematic program on “Discrete Geometry and Applications” and contains four core topics. The first two topics surround active areas that have been outstanding from the birth of discrete geometry, namely dense sphere packings and tilings. Sphere packings and tilings have a very strong connection to number theory, coding, groups, and mathematical programming. Extending the tradition of studying packings of spheres, is the investigation of the monotonicity of volume under contractions of arbitrary arrangements of spheres. The third major topic of this book can be found under the sections on ball-polyhedra that study the possibility of extending the theory of convex polytopes to the family of intersections of congruent balls. This section of the text is connected in many ways to the above-mentioned major topics and it is also connected to some other important research areas as the one on coverings by planks (with close ties to geometric analysis). This fourth core topic is discussed under covering balls by cylinders.
Applications Of Discrete Geometry And Mathematical Morphology
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Author : Ullrich Köthe
language : en
Publisher: Springer
Release Date : 2012-07-30
Applications Of Discrete Geometry And Mathematical Morphology written by Ullrich Köthe and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-07-30 with Computers categories.
This book constitutes the refereed proceedings of the first Workshop on Applications of Discrete Geometry and Mathematical Morphology, WADGMM 2010, held at the International Conference on Pattern Recognition in Istanbul, Turkey, in August 2010. The 11 revised full papers presented were carefully reviewed and selected from 25 submissions. The book was specifically designed to promote interchange and collaboration between experts in discrete geometry/mathematical morphology and potential users of these methods from other fields of image analysis and pattern recognition.
Geometric Analysis And Nonlinear Partial Differential Equations
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Author : Stefan Hildebrandt
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Geometric Analysis And Nonlinear Partial Differential Equations written by Stefan Hildebrandt 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 2012-12-06 with Mathematics categories.
This book is not a textbook, but rather a coherent collection of papers from the field of partial differential equations. Nevertheless we believe that it may very well serve as a good introduction into some topics of this classical field of analysis which, despite of its long history, is highly modem and well prospering. Richard Courant wrote in 1950: "It has always been a temptationfor mathematicians to present the crystallized product of their thought as a deductive general theory and to relegate the individual mathematical phenomenon into the role of an example. The reader who submits to the dogmatic form will be easily indoctrinated. Enlightenment, however, must come from an understanding of motives; live mathematical development springs from specific natural problems which can be easily understood, but whose solutions are difficult and demand new methods or more general significance. " We think that many, if not all, papers of this book are written in this spirit and will give the reader access to an important branch of analysis by exhibiting interest ing problems worth to be studied. Most of the collected articles have an extensive introductory part describing the history of the presented problems as well as the state of the art and offer a well chosen guide to the literature. This way the papers became lengthier than customary these days, but the level of presentation is such that an advanced graduate student should find the various articles both readable and stimulating.
Discrete Geometry And Symmetry
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Author : Marston D. E. Conder
language : en
Publisher: Springer
Release Date : 2018-06-11
Discrete Geometry And Symmetry written by Marston D. E. Conder and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-11 with Mathematics categories.
This book consists of contributions from experts, presenting a fruitful interplay between different approaches to discrete geometry. Most of the chapters were collected at the conference “Geometry and Symmetry” in Veszprém, Hungary from 29 June to 3 July 2015. The conference was dedicated to Károly Bezdek and Egon Schulte on the occasion of their 60th birthdays, acknowledging their highly regarded contributions in these fields. While the classical problems of discrete geometry have a strong connection to geometric analysis, coding theory, symmetry groups, and number theory, their connection to combinatorics and optimization has become of particular importance. The last decades have seen a revival of interest in discrete geometric structures and their symmetry. The rapid development of abstract polytope theory has resulted in a rich theory featuring an attractive interplay of methods and tools from discrete geometry, group theory and geometry, combinatorial group theory, and hyperbolic geometry and topology. This book contains papers on new developments in these areas, including convex and abstract polytopes and their recent generalizations, tiling and packing, zonotopes, isoperimetric inequalities, and on the geometric and combinatorial aspects of linear optimization. The book is a valuable resource for researchers, both junior and senior, in the field of discrete geometry, combinatorics, or discrete optimization. Graduate students find state-of-the-art surveys and an open problem collection.
Modern Approaches To Discrete Curvature
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Author : Laurent Najman
language : en
Publisher: Springer
Release Date : 2017-10-04
Modern Approaches To Discrete Curvature written by Laurent Najman and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-04 with Mathematics categories.
This book provides a valuable glimpse into discrete curvature, a rich new field of research which blends discrete mathematics, differential geometry, probability and computer graphics. It includes a vast collection of ideas and tools which will offer something new to all interested readers. Discrete geometry has arisen as much as a theoretical development as in response to unforeseen challenges coming from applications. Discrete and continuous geometries have turned out to be intimately connected. Discrete curvature is the key concept connecting them through many bridges in numerous fields: metric spaces, Riemannian and Euclidean geometries, geometric measure theory, topology, partial differential equations, calculus of variations, gradient flows, asymptotic analysis, probability, harmonic analysis, graph theory, etc. In spite of its crucial importance both in theoretical mathematics and in applications, up to now, almost no books have provided a coherent outlook on this emerging field.