Sphere PackingsSpringer Science & Business Media, 20 de gen. 2008 - 242 pàgines 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. |
Continguts
| 1 | |
Positive Definite Quadratic Forms | 23 |
Lower Bounds for the Packing Densities of Spheres 47 | 46 |
Lower Bounds for the Blocking Numbers | 65 |
of Superspheres | 74 |
Upper Bounds for the Packing Densities | 91 |
Upper Bounds for the Packing Densities | 103 |
Upper Bounds for the Packing Densities | 132 |
The Kissing Numbers of Spheres in Eight | 139 |
Multiple Sphere Packings 153 | 152 |
Holes in Sphere Packings | 165 |
Problems of Blocking Light Rays | 183 |
Finite Sphere Packings | 199 |
| 218 | |
| 237 | |
Altres edicions - Mostra-ho tot
Frases i termes més freqüents
Assertion assume bd(Sn binary Blichfeldt blocking number Böröczky bq(Sn C.L. Siegel card{X cell complex centrally symmetric convex Clearly codeword convenience convex body corresponding cyclic code deduce define definite quadratic form denote det(A dihedral angle Dirichlet-Voronoi cells dis(Q easy equality holds Euclidean distance facets Fejes Tóth Figure function geodesic h(Sn Hamming distance Hence integer isometry Jacobi polynomial k(Sn Kepler’s conjecture Kissing Numbers Korkin L-S-M reduced lattice packing lattice sphere packing Lemma light rays starting linear linear code lower bound mathematics Minkowski Minkowski-Hlawka theorem n-dimensional convex body Numbers of Spheres obtain parallelepiped polynomial polytope positive definite quadratic positive number Proof of Theorem r(Sn Reed-Muller code Remark result Rogers routine argument routine computation yields set of points side length Sloane spherical simplex symmetric convex body tiling unit spheres upper bound vectors vertex vertices write Zong