Least Action Principle Of Crystal Formation Of Dense Packing Type And Kepler S Conjecture

Author : Wu Yi Hsiang
Publisher : World Scientific
Page : 425 pages
File Size : 54,8 Mb
Release : 2001
Category : Mathematics
ISBN : 9789810246709

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Least Action Principle of Crystal Formation of Dense Packing Type and Kepler's Conjecture by Wu Yi Hsiang Pdf

The dense packing of microscopic spheres (i.e. atoms) is the basic geometric arrangement in crystals of mono-atomic elements with weak covalent bonds, which achieves the optimal ?known density? of B/û18. In 1611, Johannes Kepler had already ?conjectured? that B/û18 should be the optimal ?density? of sphere packings. Thus, the central problems in the study of sphere packings are the proof of Kepler's conjecture that B/û18 is the optimal density, and the establishing of the least action principle that the hexagonal dense packings in crystals are the geometric consequence of optimization of density. This important book provides a self-contained proof of both, using vector algebra and spherical geometry as the main techniques and in the tradition of classical geometry.

Author : Wu Yi Hsiang
Publisher : World Scientific
Page : 444 pages
File Size : 46,6 Mb
Release : 2001
Category : Mathematics
ISBN : 981238491X

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Least Action Principle of Crystal Formation of Dense Packing Type and Kepler's Conjecture by Wu Yi Hsiang Pdf

The dense packing of microscopic spheres (i.e. atoms) is the basic geometric arrangement in crystals of mono-atomic elements with weak covalent bonds, which achieves the optimal known density of p/OeU18. In 1611, Johannes Kepler had already conjectured that p/OeU18 should be the optimal density of sphere packings. Thus, the central problems in the study of sphere packings are the proof of Kepler''s conjecture that p/OeU18 is the optimal density, and the establishing of the least action principle that the hexagonal dense packings in crystals are the geometric consequence of optimization of density. This important book provides a self-contained proof of both, using vector algebra and spherical geometry as the main techniques and in the tradition of classical geometry."

Author : Jeffrey C. Lagarias
Publisher : Springer Science & Business Media
Page : 456 pages
File Size : 51,6 Mb
Release : 2011-11-09
Category : Mathematics
ISBN : 9781461411291

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The Kepler Conjecture by Jeffrey C. Lagarias Pdf

The Kepler conjecture, one of geometry's oldest unsolved problems, was formulated in 1611 by Johannes Kepler and mentioned by Hilbert in his famous 1900 problem list. The Kepler conjecture states that the densest packing of three-dimensional Euclidean space by equal spheres is attained by the “cannonball" packing. In a landmark result, this was proved by Thomas C. Hales and Samuel P. Ferguson, using an analytic argument completed with extensive use of computers. This book centers around six papers, presenting the detailed proof of the Kepler conjecture given by Hales and Ferguson, published in 2006 in a special issue of Discrete & Computational Geometry. Further supporting material is also presented: a follow-up paper of Hales et al (2010) revising the proof, and describing progress towards a formal proof of the Kepler conjecture. For historical reasons, this book also includes two early papers of Hales that indicate his original approach to the conjecture. The editor's two introductory chapters situate the conjecture in a broader historical and mathematical context. These chapters provide a valuable perspective and are a key feature of this work.

Author : Károly Bezdek
Publisher : Springer Science & Business Media
Page : 186 pages
File Size : 52,9 Mb
Release : 2013-08-04
Category : Mathematics
ISBN : 9781461481188

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Lectures on Sphere Arrangements – the Discrete Geometric Side by Károly Bezdek Pdf

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.

Author : Csaba D. Toth,Joseph O'Rourke,Jacob E. Goodman
Publisher : CRC Press
Page : 1928 pages
File Size : 50,6 Mb
Release : 2017-11-22
Category : Computers
ISBN : 9781498711425

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Handbook of Discrete and Computational Geometry by Csaba D. Toth,Joseph O'Rourke,Jacob E. Goodman Pdf

The Handbook of Discrete and Computational Geometry is intended as a reference book fully accessible to nonspecialists as well as specialists, covering all major aspects of both fields. The book offers the most important results and methods in discrete and computational geometry to those who use them in their work, both in the academic world—as researchers in mathematics and computer science—and in the professional world—as practitioners in fields as diverse as operations research, molecular biology, and robotics. Discrete geometry has contributed significantly to the growth of discrete mathematics in recent years. This has been fueled partly by the advent of powerful computers and by the recent explosion of activity in the relatively young field of computational geometry. This synthesis between discrete and computational geometry lies at the heart of this Handbook. A growing list of application fields includes combinatorial optimization, computer-aided design, computer graphics, crystallography, data analysis, error-correcting codes, geographic information systems, motion planning, operations research, pattern recognition, robotics, solid modeling, and tomography.

Author : Csaba D. Toth,Joseph O'Rourke,Jacob E. Goodman
Publisher : CRC Press
Page : 1557 pages
File Size : 43,8 Mb
Release : 2004-04-13
Category : Mathematics
ISBN : 9781420035315

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Handbook of Discrete and Computational Geometry, Second Edition by Csaba D. Toth,Joseph O'Rourke,Jacob E. Goodman Pdf

While high-quality books and journals in this field continue to proliferate, none has yet come close to matching the Handbook of Discrete and Computational Geometry, which in its first edition, quickly became the definitive reference work in its field. But with the rapid growth of the discipline and the many advances made over the past seven years, it's time to bring this standard-setting reference up to date. Editors Jacob E. Goodman and Joseph O'Rourke reassembled their stellar panel of contributors, added manymore, and together thoroughly revised their work to make the most important results and methods, both classic and cutting-edge, accessible in one convenient volume. Now over more then 1500 pages, the Handbook of Discrete and Computational Geometry, Second Edition once again provides unparalleled, authoritative coverage of theory, methods, and applications. Highlights of the Second Edition: Thirteen new chapters: Five on applications and others on collision detection, nearest neighbors in high-dimensional spaces, curve and surface reconstruction, embeddings of finite metric spaces, polygonal linkages, the discrepancy method, and geometric graph theory Thorough revisions of all remaining chapters Extended coverage of computational geometry software, now comprising two chapters: one on the LEDA and CGAL libraries, the other on additional software Two indices: An Index of Defined Terms and an Index of Cited Authors Greatly expanded bibliographies

Author : Steven G. Krantz
Publisher : CRC Press
Page : 323 pages
File Size : 46,5 Mb
Release : 2017-10-06
Category : Mathematics
ISBN : 9781351642941

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Essentials of Mathematical Thinking by Steven G. Krantz Pdf

Essentials of Mathematical Thinking addresses the growing need to better comprehend mathematics today. Increasingly, our world is driven by mathematics in all aspects of life. The book is an excellent introduction to the world of mathematics for students not majoring in mathematical studies. The author has written this book in an enticing, rich manner that will engage students and introduce new paradigms of thought. Careful readers will develop critical thinking skills which will help them compete in today’s world. The book explains: What goes behind a Google search algorithm How to calculate the odds in a lottery The value of Big Data How the nefarious Ponzi scheme operates Instructors will treasure the book for its ability to make the field of mathematics more accessible and alluring with relevant topics and helpful graphics. The author also encourages readers to see the beauty of mathematics and how it relates to their lives in meaningful ways.

Author : Steven G. Krantz
Publisher : Springer Science & Business Media
Page : 264 pages
File Size : 47,7 Mb
Release : 2011-05-13
Category : Mathematics
ISBN : 9780387487441

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The Proof is in the Pudding by Steven G. Krantz Pdf

This text explores the many transformations that the mathematical proof has undergone from its inception to its versatile, present-day use, considering the advent of high-speed computing machines. Though there are many truths to be discovered in this book, by the end it is clear that there is no formalized approach or standard method of discovery to date. Most of the proofs are discussed in detail with figures and equations accompanying them, allowing both the professional mathematician and those less familiar with mathematics to derive the same joy from reading this book.

Author : Anonim
Publisher : Unknown
Page : 844 pages
File Size : 43,8 Mb
Release : 2004
Category : Mathematics
ISBN : UOM:39015059777659

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Mathematical Reviews by Anonim Pdf

Author : Achill Schurmann
Publisher : American Mathematical Soc.
Page : 183 pages
File Size : 45,9 Mb
Release : 2009
Category : Discrete geometry
ISBN : 9780821847350

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Computational Geometry of Positive Definite Quadratic Forms by Achill Schurmann Pdf

"Starting from classical arithmetical questions on quadratic forms, this book takes the reader step by step through the connections with lattice sphere packing and covering problems. As a model for polyhedral reduction theories of positive definite quadratic forms, Minkowski's classical theory is presented, including an application to multidimensional continued fraction expansions. The reduction theories of Voronoi are described in great detail, including full proofs, new views, and generalizations that cannot be found elsewhere. Based on Voronoi's second reduction theory, the local analysis of sphere coverings and several of its applications are presented. These include the classification of totally real thin number fields, connections to the Minkowski conjecture, and the discovery of new, sometimes surprising, properties of exceptional structures such as the Leech lattice or the root lattices." "Throughout this book, special attention is paid to algorithms and computability, allowing computer-assisted treatments. Although dealing with relatively classical topics that have been worked on extensively by numerous authors, this book is exemplary in showing how computers may help to gain new insights."--BOOK JACKET.

Author : Molin Ge,Jiaxing Hong,Tatsien Li,Weiping Zhang
Publisher : World Scientific
Page : 372 pages
File Size : 45,8 Mb
Release : 2014-03-18
Category : Science
ISBN : 9789814578103

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Frontiers in Differential Geometry, Partial Differential Equations and Mathematical Physics by Molin Ge,Jiaxing Hong,Tatsien Li,Weiping Zhang Pdf

This book is a collection of papers in memory of Gu Chaohao on the subjects of Differential Geometry, Partial Differential Equations and Mathematical Physics that Gu Chaohao made great contributions to with all his intelligence during his lifetime. All contributors to this book are close friends, colleagues and students of Gu Chaohao. They are all excellent experts among whom there are 9 members of the Chinese Academy of Sciences. Therefore this book will provide some important information on the frontiers of the related subjects. Contents:A Profile of the Late Professor Gu Chaohao (Tatsien Li)List of Publications of Gu ChaohaoIn Memory of Professor Gu Chaohao (Xiaqi Ding)In Memory of Professor Gu Chaohao (Gongqing Zhang (Kung-Ching Chang))Stability of E-H Mach Configuration in Pseudo-Steady Compressible Flow (Shuxing Chen)Incompressible Viscous Fluid Flows with Slip Boundary Conditions and Their Numerical Simulations (Ben-yu Guo)Global Existence and Uniqueness of the Solution for the Generalized Schrödinger-KdV System (Boling Guo, Bolin Ma & Jingjun Zhang)Anomaly Cancellation and Modularity (Fei Han, Kefeng Liu & Weiping Zhang)On Interior Estimates for Mean Curvature of Convex Surfaces in R3 and Its Applications (Jiaxing Hong)Geometric Invariant Theory of the Space — A Modern Approach to Solid Geometry (Wu-Yi Hsiang)Optimal Convergence Rate of the Binomial Tree Scheme for American Options and Their Free Boundaries (Lishang Jiang & Jin Liang)Rademacher Φ Function, Jacobi Symbols, Quantum and Classical Invariants of Lens Spaces (Bang-He Li & Tian-Jun Li)Historical Review on the Roles of Mathematics in the Study of Aerodynamics (Jiachun Li)Toward Chern–Simons Theory of Complexes on Calabi–Yau Threefolds (Jun Li)Exact Boundary Synchronization for a Coupled System of Wave Equations (Tatsien Li)Scaling Limit for Compressible Viscoelastic Fluids (Xianpeng Hu & Fang-Hua Lin)Uniqueness Modulo Reduction of Bergman Meromorphic Compactifications of Canonically Embeddable Bergman Manifolds (Ngaiming Mok)The Application of Conditional Nonlinear Optimal Perturbation to Targeted Observations for Tropical Cyclone Prediction (Mu Mu, Feifan Zhou, Xiaohao Qin & Boyu Chen)Isometric Immersions in Minkowski Spaces (Yi-Bing Shen)Remarks on Volume Growth for Minimal Graphs in Higher Codimension (Yuanlong Xin)Separation of Variables for the Lax Pair of the Bogomolny Equation in 2+1 Dimensional Anti-de Sitter Space-Time (Zi-Xiang Zhou) Readership: Mathematicians and advanced graduate students in mathematics. Key Features:In memory of the highly distinguished mathematician Gu ChaohaoThe contributors are excellent experts, including 9 members of the CASProvides some important information on Differential Geometry, Partial Differential Equations, Mathematical Physics, etcKeywords:Differential Geometry;Partial Differential Equations;Mathematical Physics

Author : Chi-Sing Man
Publisher : Springer Nature
Page : 438 pages
File Size : 41,5 Mb
Release : 2023-01-13
Category : Technology & Engineering
ISBN : 9789402421583

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Crystallographic Texture and Group Representations by Chi-Sing Man Pdf

This book starts with an introduction to quantitative texture analysis (QTA), which adopts conventions (active rotations, definition of Euler angles, Wigner D-functions) that conform to those of the present-day mathematics and physics literature. Basic concepts (e.g., orientation; orientation distribution function (ODF), orientation density function, and their relationship) are made precise through their mathematical definition. Parts II and III delve deeper into the mathematical foundations of QTA, where the important role played by group representations is emphasized. Part II includes one chapter on generalized QTA based on the orthogonal group, and Part III one on tensorial Fourier expansion of the ODF and tensorial texture coefficients. This work will appeal to students and practitioners who appreciate a precise presentation of QTA through a unifying mathematical language, and to researchers who are interested in applications of group representations to texture analysis. Previously published in the Journal of Elasticity, Volume 149, issues 1-2, April, 2022

Author : Eiichi Bannai,Etsuko Bannai,Tatsuro Ito,Rie Tanaka
Publisher : Walter de Gruyter GmbH & Co KG
Page : 303 pages
File Size : 48,6 Mb
Release : 2021-02-22
Category : Mathematics
ISBN : 9783110627732

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Algebraic Combinatorics by Eiichi Bannai,Etsuko Bannai,Tatsuro Ito,Rie Tanaka Pdf

This series is devoted to the publication of high-level monographs which cover the whole spectrum of current discrete mathematics and its applications in various fields. One of its main objectives is to make available to the professional community expositions of results and foundations of methods that play an important role in both the theory and applications of discrete mathematics. Contributions which are on the borderline of discrete mathematics and related fields and which stimulate further research at the crossroads of these areas are particularly welcome.

Author : Weilin Wang
Publisher : Unknown
Page : 276 pages
File Size : 43,8 Mb
Release : 2006
Category : Electronic
ISBN : UOM:39015069228123

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Optimization of Communication and Coverage in Classes of Distributed Systems by Weilin Wang Pdf

Author : Anonim
Publisher : Unknown
Page : 2252 pages
File Size : 54,9 Mb
Release : 2002
Category : Books
ISBN : STANFORD:36105111052903

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American Book Publishing Record by Anonim Pdf