A Duality Between Spheres and Spheres with Arcs

Arcs on Spheres Intersecting at Most Twice

Let p be a puncture of a punctured sphere, and let Q be the set of all other punctures. We prove that the maximal cardinality of a set A of arcs pairwise intersecting at most once, which start at p and end in Q, is |χ|(|χ| + 1). We deduce that the maximal cardinality of a set of arcs with arbitrary endpoints pairwise intersecting at most twice is |χ|(|χ|+ 1)(|χ|+ 2).

Covering Spheres with Spheres

Given a sphere of radius r > 1 in the n-dimensional Euclidean space, we study the coverings of this sphere with unit spheres. Our goal is to design a covering of the lowest covering density, which defines the average number of unit spheres covering a point in a bigger sphere. For growing n, we obtain the covering density of (n lnn)/2. This new upper bound is half the order n lnn established in ...

Affine Spheres: Discretization via Duality Relations

Heat Transfer in a Column Packed With Spheres

The purpose of the study is to investigate average and local surface heat transfer coefficients in a cylinder packed with spheres. Here the term «local» applies to a single sphere within the bed. Averages are derived from the sixteen different spheres that were instrumented and distributed throughout the bed. The experimental technique consisted of introducing a step - wise change in the temper...

MEAN VALUE INTERPOLATION ON SPHERES

In this paper we consider   multivariate Lagrange mean-value interpolation problem, where interpolation parameters are integrals over spheres. We have   concentric spheres. Indeed, we consider the problem in three variables when it is not correct.