Sphere Packings Lattices And Groups

Author : J.H. Conway,N.J.A. Sloane
Publisher : Springer Science & Business Media
Page : 724 pages
File Size : 42,6 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475722499

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Sphere Packings, Lattices and Groups by J.H. Conway,N.J.A. Sloane Pdf

The second edition of this timely, definitive, and popular book continues to pursue the question: what is the most efficient way to pack a large number of equal spheres in n-dimensional Euclidean space? The authors also continue to examine related problems such as the kissing number problem, the covering problem, the quantizing problem, and the classification of lattices and quadratic forms. Like the first edition, the second edition describes the applications of these questions to other areas of mathematics and science such as number theory, coding theory, group theory, analog-to-digital conversion and data compression, n-dimensional crystallography, and dual theory and superstring theory in physics. Results as of 1992 have been added to the text, and the extensive bibliography - itself a contribution to the field - is supplemented with approximately 450 new entries.

Author : John Conway,Neil J. A. Sloane
Publisher : Springer Science & Business Media
Page : 778 pages
File Size : 45,5 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781475765687

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Sphere Packings, Lattices and Groups by John Conway,Neil J. A. Sloane Pdf

The third edition of this definitive and popular book continues to pursue the question: what is the most efficient way to pack a large number of equal spheres in n-dimensional Euclidean space? The authors also examine such related issues as the kissing number problem, the covering problem, the quantizing problem, and the classification of lattices and quadratic forms. There is also a description of the applications of these questions to other areas of mathematics and science such as number theory, coding theory, group theory, analogue-to-digital conversion and data compression, n-dimensional crystallography, dual theory and superstring theory in physics. New and of special interest is a report on some recent developments in the field, and an updated and enlarged supplementary bibliography with over 800 items.

Author : John Horton Conway,Neil James Alexander Sloane
Publisher : Unknown
Page : 703 pages
File Size : 54,5 Mb
Release : 1998
Category : Combinatorial packing and covering
ISBN : 7506292157

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Sphere Packings, Lattices and Groups by John Horton Conway,Neil James Alexander Sloane Pdf

Author : John H. Conway,Neil J.A. Sloane
Publisher : Springer
Page : 665 pages
File Size : 47,8 Mb
Release : 2013-02-14
Category : Mathematics
ISBN : 1475720173

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Sphere Packings, Lattices and Groups by John H. Conway,Neil J.A. Sloane Pdf

The main themes. This book is mainly concerned with the problem of packing spheres in Euclidean space of dimensions 1,2,3,4,5, . . . . Given a large number of equal spheres, what is the most efficient (or densest) way to pack them together? We also study several closely related problems: the kissing number problem, which asks how many spheres can be arranged so that they all touch one central sphere of the same size; the covering problem, which asks for the least dense way to cover n-dimensional space with equal overlapping spheres; and the quantizing problem, important for applications to analog-to-digital conversion (or data compression), which asks how to place points in space so that the average second moment of their Voronoi cells is as small as possible. Attacks on these problems usually arrange the spheres so their centers form a lattice. Lattices are described by quadratic forms, and we study the classification of quadratic forms. Most of the book is devoted to these five problems. The miraculous enters: the E 8 and Leech lattices. When we investigate those problems, some fantastic things happen! There are two sphere packings, one in eight dimensions, the E 8 lattice, and one in twenty-four dimensions, the Leech lattice A , which are unexpectedly good and very 24 symmetrical packings, and have a number of remarkable and mysterious properties, not all of which are completely understood even today.

Author : J. H. Conway
Publisher : Unknown
Page : 732 pages
File Size : 51,7 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 1475722508

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Sphere Packings, Lattices and Groups by J. H. Conway Pdf

Author : John H. Conway,Neil J.A. Sloane
Publisher : Springer Science & Business Media
Page : 690 pages
File Size : 45,9 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781475720167

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Sphere Packings, Lattices and Groups by John H. Conway,Neil J.A. Sloane Pdf

The main themes. This book is mainly concerned with the problem of packing spheres in Euclidean space of dimensions 1,2,3,4,5, . . . . Given a large number of equal spheres, what is the most efficient (or densest) way to pack them together? We also study several closely related problems: the kissing number problem, which asks how many spheres can be arranged so that they all touch one central sphere of the same size; the covering problem, which asks for the least dense way to cover n-dimensional space with equal overlapping spheres; and the quantizing problem, important for applications to analog-to-digital conversion (or data compression), which asks how to place points in space so that the average second moment of their Voronoi cells is as small as possible. Attacks on these problems usually arrange the spheres so their centers form a lattice. Lattices are described by quadratic forms, and we study the classification of quadratic forms. Most of the book is devoted to these five problems. The miraculous enters: the E 8 and Leech lattices. When we investigate those problems, some fantastic things happen! There are two sphere packings, one in eight dimensions, the E 8 lattice, and one in twenty-four dimensions, the Leech lattice A , which are unexpectedly good and very 24 symmetrical packings, and have a number of remarkable and mysterious properties, not all of which are completely understood even today.

Author : Jacques Martinet
Publisher : Springer Science & Business Media
Page : 535 pages
File Size : 49,9 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783662051672

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Perfect Lattices in Euclidean Spaces by Jacques Martinet Pdf

Lattices are discrete subgroups of maximal rank in a Euclidean space. To each such geometrical object, we can attach a canonical sphere packing which, assuming some regularity, has a density. The question of estimating the highest possible density of a sphere packing in a given dimension is a fascinating and difficult problem: the answer is known only up to dimension 3. This book thus discusses a beautiful and central problem in mathematics, which involves geometry, number theory, coding theory and group theory, centering on the study of extreme lattices, i.e. those on which the density attains a local maximum, and on the so-called perfection property. Written by a leader in the field, it is closely related to, though disjoint in content from, the classic book by J.H. Conway and N.J.A. Sloane, Sphere Packings, Lattices and Groups, published in the same series as vol. 290. Every chapter except the first and the last contains numerous exercises. For simplicity those chapters involving heavy computational methods contain only few exercises. It includes appendices on Semi-Simple Algebras and Quaternions and Strongly Perfect Lattices.

Author : Chuanming Zong
Publisher : Springer Science & Business Media
Page : 242 pages
File Size : 49,8 Mb
Release : 2008-01-20
Category : Mathematics
ISBN : 9780387227801

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Sphere Packings by Chuanming Zong Pdf

Sphere packings is one of the most fascinating and challenging subjects in mathematics. In the course of centuries, many exciting results have been obtained, ingenious methods created, related challenging problems proposed, and many surprising connections with other subjects found. This book gives a full account of this fascinating subject, especially its local aspects, discrete aspects, and its proof methods. The book includes both classical and contemporary results and provides a full treatment of the subject.

Author : Thomas M. Thompson
Publisher : Unknown
Page : 252 pages
File Size : 44,7 Mb
Release : 1983
Category : Error-correcting codes (Information theory)
ISBN : 0883850001

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From Error-correcting Codes Through Sphere Packings to Simple Groups by Thomas M. Thompson Pdf

Author : Thomas Callister Hales
Publisher : Cambridge University Press
Page : 286 pages
File Size : 43,9 Mb
Release : 2012-09-06
Category : Mathematics
ISBN : 9780521617703

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Dense Sphere Packings by Thomas Callister Hales Pdf

The definitive account of the recent computer solution of the oldest problem in discrete geometry.

Author : M. A. Wahab
Publisher : Springer Nature
Page : 397 pages
File Size : 48,6 Mb
Release : 2021-01-22
Category : Science
ISBN : 9789811597541

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Numerical Problems in Crystallography by M. A. Wahab Pdf

This book aims at enhancing the understanding of topics in crystallography through solving numerical problems. Designed into nine chapters on major topics in crystallography, the book deals with more than 600 carefully selected solved examples, problems, and multiple-choice questions. Unit cell composition, construction and calculations, Miller indices, structure factor calculations, and X-ray diffraction methods are some of the many useful topics discussed in this book. Each chapter begins with a brief theoretical explanation of the topic followed by solved numerical examples for further clarity on the subject. The topic “crystallography” is interdisciplinary in nature. Its rudimentary knowledge, therefore, is essential to the beginners in physics, chemistry, mathematics, molecular biology, geology, metallurgy, and particularly materials science and mineralogy. This book also is of immense value to senior undergraduate and graduate students of physics, chemistry, and other basic sciences.

Author : Denis Weaire,Tomaso Aste
Publisher : CRC Press
Page : 147 pages
File Size : 51,7 Mb
Release : 2000-01-01
Category : Mathematics
ISBN : 9781420033311

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The Pursuit of Perfect Packing by Denis Weaire,Tomaso Aste Pdf

In 1998 Thomas Hales dramatically announced the solution of a problem that has long teased eminent mathematicians: what is the densest possible arrangement of identical spheres? The Pursuit of Perfect Packing recounts the story of this problem and many others that have to do with packing things together. The examples are taken from mathematics, phy

Author : Jan de Gier,Cheryl E. Praeger,Terence Tao
Publisher : Springer Nature
Page : 803 pages
File Size : 49,7 Mb
Release : 2021-02-10
Category : Mathematics
ISBN : 9783030624972

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2019-20 MATRIX Annals by Jan de Gier,Cheryl E. Praeger,Terence Tao Pdf

MATRIX is Australia’s international and residential mathematical research institute. It facilitates new collaborations and mathematical advances through intensive residential research programs, each 1-4 weeks in duration. This book is a scientific record of the ten programs held at MATRIX in 2019 and the two programs held in January 2020: · Topology of Manifolds: Interactions Between High and Low Dimensions · Australian-German Workshop on Differential Geometry in the Large · Aperiodic Order meets Number Theory · Ergodic Theory, Diophantine Approximation and Related Topics · Influencing Public Health Policy with Data-informed Mathematical Models of Infectious Diseases · International Workshop on Spatial Statistics · Mathematics of Physiological Rhythms · Conservation Laws, Interfaces and Mixing · Structural Graph Theory Downunder · Tropical Geometry and Mirror Symmetry · Early Career Researchers Workshop on Geometric Analysis and PDEs · Harmonic Analysis and Dispersive PDEs: Problems and Progress The articles are grouped into peer-reviewed contributions and other contributions. The peer-reviewed articles present original results or reviews on a topic related to the MATRIX program; the remaining contributions are predominantly lecture notes or short articles based on talks or activities at MATRIX.

Author : Matthias Schütt,Tetsuji Shioda
Publisher : Springer Nature
Page : 431 pages
File Size : 43,6 Mb
Release : 2019-10-17
Category : Mathematics
ISBN : 9789813293014

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Mordell–Weil Lattices by Matthias Schütt,Tetsuji Shioda Pdf

This book lays out the theory of Mordell–Weil lattices, a very powerful and influential tool at the crossroads of algebraic geometry and number theory, which offers many fruitful connections to other areas of mathematics. The book presents all the ingredients entering into the theory of Mordell–Weil lattices in detail, notably, relevant portions of lattice theory, elliptic curves, and algebraic surfaces. After defining Mordell–Weil lattices, the authors provide several applications in depth. They start with the classification of rational elliptic surfaces. Then a useful connection with Galois representations is discussed. By developing the notion of excellent families, the authors are able to design many Galois representations with given Galois groups such as the Weyl groups of E6, E7 and E8. They also explain a connection to the classical topic of the 27 lines on a cubic surface. Two chapters deal with elliptic K3 surfaces, a pulsating area of recent research activity which highlights many central properties of Mordell–Weil lattices. Finally, the book turns to the rank problem—one of the key motivations for the introduction of Mordell–Weil lattices. The authors present the state of the art of the rank problem for elliptic curves both over Q and over C(t) and work out applications to the sphere packing problem. Throughout, the book includes many instructive examples illustrating the theory.

Author : Otton Martin Nikodym
Publisher : Springer Science & Business Media
Page : 962 pages
File Size : 49,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642460302

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The Mathematical Apparatus for Quantum-Theories by Otton Martin Nikodym Pdf