There are no denting points in the unit ball of 𝒫(2H)

Covering Random Points in a Unit Ball

Choose random pointsX1, X2, X3, . . . independently from a uniform distribution in a unit ball in <. Call Xn a dominator iff distance(Xn, Xi) ≤ 1 for all i < n, i.e. the first n points are all contained in the unit ball that is centered at the n’th point Xn. We prove that, with probability one, only finitely many of the points are dominators. For the special casem = 2, we consider the unit disk...

There Are No Stable Points for Continuum-Wise Expansive Homeomorphisms

There are no Aspects

In this paper, we claim that a specialized aspect module is not required. Instead, we propose an expressive aspect-oriented composition mechanism which can be applied upon existing modules. At the design level, the CoCompose modeling framework is introduced which is based on Model Driven Development. CoCompose allows step-wise refinement from a high-level design to the lowest level design or co...

There Are Integral Heptagons, no Three Points on a Line, no Four on a Circle

We give two configurations of seven points in the plane, no three points in a line, no four points on a circle with pairwise integral distances. This answers a famous question of Paul Erd˝ os.

Denting Points in Tensor Products of Banach Spaces

Let dent A denote the set of denting points of a subset A of some Banach space. We prove dent cl co( K ® L) = dent K ® dent L for closed, bounded, absolutely convex subsets K and L of Banach spaces X and Y. Here the closure refers to the completion of X ® Y w.r.t. some reasonable crossnorm.