On a Conjectured Characterization of the Sphere.
On a covering problem for equilateral triangles.
On a covering problem in the plane.
On a Differential Inequality and Its Applications to Geometry.
On a discrete Dido-type question.
On a dynamics in rational polygonal billiards
On a generalization of Craig lattices
In this paper we introduce generalized Craig lattices, which allows us to construct lattices in Euclidean spaces of many dimensions in the range which are denser than the densest known Mordell-Weil lattices. Moreover we prove that if there were some nice linear binary codes we could construct lattices even denser in the range . We also construct some dense lattices of dimensions in the range . Finally we also obtain some new lattices of moderate dimensions such as , which are denser than the...
On a generalization of the Selection Theorem of Mahler
The set of point sets of , having the property that their minimal interpoint distance is greater than a given strictly positive constant is shown to be equippable by a metric for which it is a compact topological space and such that the Hausdorff metric on the subset of the finite point sets is compatible with the restriction of this topology to . We show that its subsets of Delone sets of given constants in , are compact. Three (classes of) metrics, whose one of crystallographic nature,...
On a geometric inequality by J. Sándor.
On a geometrical interpretation of a sampling.
On a globalization property
Let (X,τ) be a topological space. Let Φ be a class of real-valued functions defined on X. A function ϕ ∈ Φ is called a local Φ-subgradient of a function f:X → ℝ at a point if there is a neighbourhood U of such that f(x) - f() ≥ ϕ(x) - ϕ() for all x ∈ U. A function ϕ ∈ Φ is called a global Φ-subgradient of f at if the inequality holds for all x ∈ X. The following properties of the class Φ are investigated: (a) when the existence of a local Φ-subgradient of a function f at each point implies...
On a Hadwiger-Wills inequality concerning lattice points.
On a measure of axiality for triangular domains.
On a New Method for Constructing Good Point Sets on Spheres.
On a probability inequality for multivariate normal distribution
On a Problem About Covering Lines by Squares.
On a problem about covering lines by squares.
On a problem by Shapiro.
On a problem of Ryškov concerning lattice coverings
On a property of pseudometrics and uniformities near to convexity