Print Email Facebook Twitter Upper bounds for packings of spheres of several radII Title Upper bounds for packings of spheres of several radII Author De Laat, D. De Oliveira Filho, F.M. Vallentin, F. Faculty Electrical Engineering, Mathematics and Computer Science Department Delft Institute of Applied Mathematics Date 2014-09-23 Abstract We give theorems that can be used to upper bound the densities of packings of different spherical caps in the unit sphere and of translates of different convex bodies in Euclidean space. These theorems extend the linear programming bounds for packings of spherical caps and of convex bodies through the use of semidefinite programming. We perform explicit computations, obtaining new bounds for packings of spherical caps of two different sizes and for binary sphere packings. We also slightly improve the bounds for the classical problem of packing identical spheres. To reference this document use: http://resolver.tudelft.nl/uuid:85d9c076-c273-4b11-a0fa-39204a93d3eb DOI https://doi.org/10.1017/fms.2014.24 Publisher Cambridge University Press Source Forum of Mathematics, Sigma, 2, (e23), 2014 Part of collection Institutional Repository Document type journal article Rights © The Author(s) 2014 This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/3.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited Files PDF S2050509414000243a.pdf 1.1 MB Close viewer /islandora/object/uuid:85d9c076-c273-4b11-a0fa-39204a93d3eb/datastream/OBJ/view