Sphere packings

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  • 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. Contents 1. Introduction 2. Lattices, Fourier transforms, and Poisson summation 3. Principal theorems 4. Homogeneous spaces 5. Conditions for a sharp bound 6. Stationary points 7. Numerical results 8. Uniqueness Appendix A. ...

    pdf27p tuanloccuoi 04-01-2013 29 4   Download

  • Sphere packings is one of the most fascinating and challenging subjects in mathematics. Almost four centuries ago, Kepler studied the densities of sphere packings and made his famous conjecture. Several decades later, Gregory and Newton discussed the kissing numbers of spheres and proposed the Gregory-Newton problem. Since then, these problems and related ones have attracted the attention of many prominent mathematicians such as Blichfeldt, Dirichlet, Gauss, Hermite, Korkin, Lagrange, Minkowski, Thue, Voronoi, Watson, and Zolotarev, as well as many active today....

    pdf256p maket1311 16-10-2012 22 1   Download

  • Tuyển tập các báo cáo nghiên cứu khoa học trên tạp chí toán học quốc tế đề tài:Dense Packings of Equal Spheres in a Cube...

    pdf17p thulanh5 12-09-2011 30 1   Download


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