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Displaying 21 – 40 of 329

On a generalization of the Selection Theorem of Mahler

Gilbert Muraz, Jean-Louis Verger-Gaugry (2005)

Journal de Théorie des Nombres de Bordeaux

The set $𝒰 𝒟_{r}$ of point sets of $ℝ^{n}, n \geq 1$ , having the property that their minimal interpoint distance is greater than a given strictly positive constant $r > 0$ 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 $𝒰 𝒟_{r, f} \subset 𝒰 𝒟_{r}$ of the finite point sets is compatible with the restriction of this topology to $𝒰 𝒟_{r, f}$ . We show that its subsets of Delone sets of given constants in $ℝ^{n}, n \geq 1$ , are compact. Three (classes of) metrics, whose one of crystallographic nature,...

On a geometric inequality by J. Sándor.

Wu, Yu-Dong, Zhang, Zhi-Hua, Chu, Xiao-Guang (2009)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

On a geometrical interpretation of a sampling.

Szalay, László, Temesvári, Ágota H. (1994)

Beiträge zur Algebra und Geometrie

On a globalization property

Stefan Rolewicz (1993)

Applicationes Mathematicae

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 $x_{0}$ if there is a neighbourhood U of $x_{0}$ such that f(x) - f( $x_{0}$ ) ≥ ϕ(x) - ϕ( $x_{0}$ ) for all x ∈ U. A function ϕ ∈ Φ is called a global Φ-subgradient of f at $x_{0}$ 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...