On Coverings of Ellipsoids in Euclidean Spaces

On the Thinnest Coverings of Spheres and Ellipsoids with Balls in Hamming and Euclidean Spaces

In this paper, we present some new results on the thinnest coverings that can be obtained in Hamming or Euclidean spaces if spheres and ellipsoids are covered with balls of some radius ε. In particular, we tighten the bounds currently known for the ε-entropy of Hamming spheres of an arbitrary radius r. New bounds for the ε-entropy of Hamming balls are also derived. If both parameters ε and r ar...

On Homogeneous Coverings of Euclidean Spaces

The notion of a homogeneous covering of a given set is introduced and examined. Some homogeneous coverings of a Euclidean space, consisting of pairwise congruent geometric figures (spheres, hyperplanes, etc.), are constructed using the method of transfinite induction. 2000 Mathematics Subject Classification: 03E75, 05B40, 52C17.

On the Thinnest Coverings of Spheres and Ellipsoids with Balls in on the Thinnest Coverings of Spheres and Ellipsoids

In this paper, we present some new results on the thinnest coverings that can be obtained in Hamming or Euclidean spaces if spheres and ellipsoids are covered with balls of some radius ε. In particular, we tighten the bounds currently known for the ε-entropy of Hamming spheres of an arbitrary radius r. New bounds for the ε-entropy of Hamming balls are also derived. If both parameters ε and r ar...

On quasiplanes in Euclidean spaces

A variational inequality for the images of k-dimensional hyper-planes under quasiconformal maps of the n-dimensional Euclidean space is proved when 1 ≤ k ≤ n − 2 .

On Set Coverings in Cartesian Product Spaces