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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This paper details an algorithm for unfolding a class of convex polyhedra, where each polyhedron in the class consists of a convex cap over a rectangular base, with several restrictions: the cap’s faces are quadrilaterals, with vertices over an underlying integer lattice, and such that the cap convexity is “radially monotone,” a type of smoothness constraint. Extensions of Cauchy’s arm lemma ar...
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An unzipping of a polyhedron P is a cut-path through its vertices that unfolds P to a non-overlapping shape in the plane. It is an open problem to decide if every convex P has an unzipping. Here we show that there are nearly flat convex caps that have no unzipping. A convex cap is a “top” portion of a convex polyhedron; it has a boundary, i.e., it is not closed by a base.
متن کاملA characteristic property of spherical caps
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 کاملConvex Shapes and Planar Caps
Any planar shape P can be embedded isometrically as part of a convex surface S ⊂ R such that ∂P supports the positive curvature of S. Of particular interest is the case when P is a filled polynomial Julia set and the curvature is proportional to the measure of maximal entropy. The (flat) surface Q = S \P is the associated cap. In this article, we study the cap construction when the curvature is...
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ژورنال
عنوان ژورنال: Journal of the Chungcheong Mathematical Society
سال: 2013
ISSN: 1226-3524
DOI: 10.14403/jcms.2013.26.3.601