منابع مشابه
Codes in spherical caps
We consider bounds on codes in spherical caps and related problems in geometry and coding theory. An extension of the Delsarte method is presented that relates upper bounds on the size of spherical codes to upper bounds on codes in caps. Several new upper bounds on codes in caps are derived. Applications of these bounds to estimates of the kissing numbers and one-sided kissing numbers are consi...
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It is proved that given H ≥ 0 and an embedded compact orientable constant mean curvature H surface M included in the half space z ≥ 0, not everywhere tangent to z = 0 along its boundary ∂M = γ ⊂ {z = 0}, the inequality H ≤ (min κ) ( min √ 1 − (κg/κ) ) is satisfied, where κ and κg are the geodesic curvatures of γ on z = 0 and on the surface M , respectively, if and only if M is a spherical cap o...
متن کاملAlmost Optimal Pseudorandom Generators for Spherical Caps
Halfspaces or linear threshold functions are widely studied in complexity theory, learning theory and algorithm design. In this work we study the natural problem of constructing pseudorandom generators (PRGs) for halfspaces over the sphere, aka spherical caps, which besides being interesting and basic geometric objects, also arise frequently in the analysis of various randomized algorithms (e.g...
متن کاملPacking twelve spherical caps to maximize tangencies
The maximum number of non-overlapping unit spheres in R that can simultaneously touch another unit sphere is given by the kissing number, k(3) = 12. Here, we present a proof that the maximum number of tangencies in any kissing configuration is 24 and that, up to isomorphism, there are only two configurations for which this maximum is achieved. The result is motivated by a three-dimensional crys...
متن کاملAn Upper Bound for Spherical Caps
We prove an useful upper bound for the measure of spherical caps. Consider the uniformly distributed measure σn−1 on the Euclidean unit sphere Sn−1 ⊂ R. On the sphere, as among only a handful other spaces, the isoperimetric problem is completely solved. This goes back to Lévy [Lé] and Schmidt [Sch] and states that caps have the minimal measure of a boundary among all sets with a fixed mass. For...
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ژورنال
عنوان ژورنال: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
سال: 2018
ISSN: 1364-5021,1471-2946
DOI: 10.1098/rspa.2017.0910