Complex alloy structures regarded as sphere packings. I. Definitions and basic principles
نویسندگان
چکیده
منابع مشابه
Sphere Packings, I
We describe a program to prove the Kepler conjecture on sphere packings. We then carry out the first step of this program. Each packing determines a decomposition of space into Delaunay simplices, which are grouped together into finite configurations called Delaunay stars. A score, which is related to the density of packings, is assigned to each Delaunay star. We conjecture that the score of ev...
متن کاملNew Upper Bounds on Sphere Packings I
We develop an analogue for sphere packing of the linear programming bounds for error-correcting codes, and use it to prove upper bounds for the density of sphere packings, which are the best bounds known at least for dimensions 4 through 36. We conjecture that our approach can be used to solve the sphere packing problem in dimensions 8 and 24.
متن کاملNew Upper Bounds on Sphere Packings I
We develop an analogue for sphere packing of the linear programming bounds for error-correcting codes, and use it to prove upper bounds for the density of sphere packings, which are the best bounds known at least for dimensions 4 through 36. We conjecture that our approach can be used to solve the sphere packing problem in dimensions 8 and 24.
متن کاملNew Upper Bounds on Sphere Packings I
We develop an analogue for sphere packing of the linear programming bounds for error-correcting codes, and use it to prove upper bounds for the density of sphere packings, which are the best bounds known at least for dimensions 4 through 36. We conjecture that our approach can be used to solve the sphere packing problem in dimensions 8 and 24.
متن کاملSphere Packings
This paper is a continuation of the first two parts of this series ([I],[II]). It relies on the formulation of the Kepler conjecture in [F]. The terminology and notation of this paper are consistent with these earlier papers, and we refer to results from them by prefixing the relevant section numbers with I, II, or F. Around each vertex is a modification of the Voronoi cell, called the V -cell ...
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ژورنال
عنوان ژورنال: Acta Crystallographica
سال: 1958
ISSN: 0365-110X
DOI: 10.1107/s0365110x58000487