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Sphere Packings 1999 ed. [Kietas viršelis]

  • Formatas: Hardback, 242 pages, aukštis x plotis: 235x155 mm, weight: 1210 g, XIV, 242 p., 1 Hardback
  • Serija: Universitext
  • Išleidimo metai: 19-Aug-1999
  • Leidėjas: Springer-Verlag New York Inc.
  • ISBN-10: 0387987940
  • ISBN-13: 9780387987941
Kitos knygos pagal šią temą:
  • Formatas: Hardback, 242 pages, aukštis x plotis: 235x155 mm, weight: 1210 g, XIV, 242 p., 1 Hardback
  • Serija: Universitext
  • Išleidimo metai: 19-Aug-1999
  • Leidėjas: Springer-Verlag New York Inc.
  • ISBN-10: 0387987940
  • ISBN-13: 9780387987941
Kitos knygos pagal šią temą:
Sphere Packings is one of the most attractive and challenging subjects in mathematics. Almost 4 centuries ago, Kepler studied the densities of sphere packings and made his famous conjecture. In the course of centuries, many exciting results have been obtained, ingenious methods created, related challenging problems proposed, and many surprising connections with othe subjects found. Thus, though some of its original problems are still open, sphere packings has been developed into an important discipline. This book tries to give a full account of this fascinating subject, especially its local aspects, discrete aspects and its proof methods.

Recenzijos

From the reviews:



"Problems dealing with sphere packings have attracted the interest of mathematicians for more than three centuries. Important contributions are due to Kepler, Newton and Gregory, Lagrange, Seeber and Gauss, Dirichlet, Hermite, Korkine and Zolotarev, Minkowski, Thue, Vorono\u\i, Blichfeldt, Delone, Davenport, van der Waerden and many living mathematicians. One reason for this interest is the fact that there are many completely different aspects of sphere packings. These include the following: dense lattice and non-lattice packing of spheres in low and in general dimensions, multiple packings, geometric theory of positive definite quadratic forms and reduction theory, reduction theory of lattices and their computational aspects, special lattices such as the Leech lattice and relations to coding, information and group theory, finite packings of spheres, problems dealing with kissing and blocking numbers and other problems of discrete geometry. There is a series of books in which some of these aspects are dealt with thoroughly,...



The merit of Zong's book is that it covers all of the above aspects in a concise, elegant and readable form and thus gives the reader a good view of the whole area. Several of the most recent developments are also included."  (Peter M. Gruber, Mathematical Reviews) 

Preface vii
Basic Notation ix
The Gregory--Newton Problem and Kepler's Conjecture
1(22)
Introduction
1(6)
Packings of Circular Disks
7(3)
The Gregory-Newton Problem
10(3)
Kepler's Conjecture
13(5)
Some General Remarks
18(5)
Positive Definite Quadratic Forms and Lattice Sphere Packings
23(24)
Introduction
23(2)
The Lagrange-Seeber-Minkowski Reduction and a Theorem of Gauss
25(6)
Mordell's Inequality on Hermite's Constants and a Theorem of Korkin and Zolotarev
31(2)
Perfect Forms, Voronoi's Method, and a Theorem of Korkin and Zolotarev
33(3)
The Korkin-Zolotarev Reduction and Theorems of Blichfeldt, Barnes, and Vetcinkin
36(5)
Perfect Forms, the Lattice Kissing Numbers of Spheres, and Watson's Theorem
41(1)
Three Mathematical Geniuses: Zolotarev, Minkowski, and Voronoi
42(5)
Lower Bounds for the Packing Densities of Spheres
47(18)
The Minkowski-Hlawka Theorem
47(4)
Siegel's Mean Value Formula
51(4)
Sphere Coverings and the Coxeter-Few-Rogers Lower Bound for δ(Sn)
55(7)
Edmund Hlawka
62(3)
Lower Bounds for the Blocking Numbers and the Kissing Numbers of Spheres
65(14)
The Blocking Numbers of S3 and S4
65(6)
The Shannon-Wyner Lower Bound for Both b(Sn) and k(Sn)
71(1)
A Theorem of Swinnerton-Dyer
72(2)
A Lower Bound for the Translative Kissing Numbers of Superspheres
74(5)
Sphere Packings Constructed from Codes
79(12)
Codes
79(3)
Construction A
82(2)
Construction B
84(1)
Construction C
85(4)
Some General Remarks
89(2)
Upper Bounds for the Packing Densities and the Kissing Numbers of Spheres I
91(12)
Blichfeldt's Upper Bound for the Packing Densities of Spheres
91(4)
Rankin's Upper Bound for the Kissing Numbers of Spheres
95(4)
An Upper Bound for the Packing Densities of Superspheres
99(2)
Hans Frederik Blichfeldt
101(2)
Upper Bounds for the Packing Densities and the Kissing Numbers of Spheres II
103(22)
Rogers' Upper Bound for the Packing Densities of Spheres
103(4)
Schlafli's Function
107(4)
The Coxeter-Boroczky Upper Bound for the Kissing Numbers of Spheres
111(11)
Claude Ambrose Rogers
122(3)
Upper Bounds for the Packing Densities and the Kissing Numbers of Spheres III
125(14)
Jacobi Polynomials
125(2)
Delsarte's Lemma
127(5)
The Kabatjanski-Levenstein Upper Bounds for the Packing Densities and the Kissing Numbers of Spheres
132(7)
The Kissing Numbers of Spheres in Eight and Twenty-Four Dimensions
139(14)
Some Special Lattices
139(2)
Two Theorems of Levenstein, Odlyzko, and Sloane
141(1)
Two Principles of Linear Programming
142(1)
Two Theorems of Bannai and Sloane
143(10)
Multiple Sphere Packings
153(12)
Introduction
153(1)
A Basic Theorem of Asymptotic Type
154(3)
A Theorem of Few and Kanagasahapathy
157(5)
Remarks on Multiple Circle Packings
162(3)
Holes in Sphere Packings
165(18)
Spherical Holes in Sphere Packings
165(11)
Spherical Holes in Lattice Sphere Packings
176(2)
Cylindrical Holes in Lattice Sphere Packings
178(5)
Problems of Blocking Light Rays
183(16)
Introduction
183(2)
Hornich's Problem
185(4)
L. Fejes Toth's Problem
189(9)
Laszlo Fejes Toth
198(1)
Finite Sphere Packings
199(20)
Introduction
199(1)
The Spherical Conjecture
200(4)
The Sausage Conjecture
204(10)
The Sausage Catastrophe
214(5)
Bibliography 219(18)
Index 237