whenever a belongs to the closed convex hull of the set of weak limit points of {an}∞n=1. In case X has the Banach-Saks property and {an}∞n=1 is bounded the converse assertion holds too. A characterization of reflexive spaces in terms of limit points and cores of bounded sequences is also given. The motivation for the problems investigated goes back to Lévy laplacian from potential theory in Hi...

The kernel of a polygon has long been an object of study in computational geometry, especially in the context of art gallery theorems. In this paper, we present two new algorithms for computing the kernel of a plane curve. We show that the computation of the kernel of a plane curve can be reduced to the computation of the convex hull of a plane curve, revealing the computational and structural ...

A novel algorithm is presented to compute the convex hull of a point set in R3 using the graphics processing unit (GPU). By exploiting the relationship between the Voronoi diagram and the convex hull, the algorithm derives the approximation of the convex hull from the former. The other extreme vertices of the convex hull are then found by using a two-round checking in the digital and the contin...

Convex hulls are fundamental geometric tools used in a number of algorithms. This paper presents a fast, simple to implement and robust Smart Convex Hull (S-CH) algorithm for computing the convex hull of a set of points in . This algorithm is based on “spherical” space subdivision. The main idea of the S-CH algorithm is to eliminate as many input points as possible before the convex hull constr...

Recently the invariant (copoint) pre-hull number ph(G) of a graph G that measures the nonconvexity of a convex space was introduced by Polat and Sabidussi in [18]. We introduce a similar invariant called convex pre-hull number which is a natural upper bound for the copoint pre-hull number and consider in this work both on the lexicographic product of graphs. We present exact values with respect...

In this paper we show that a variation of a technique of Mǐskin and Tall yields a cocompact completely regular Moore space that is Scott-domain-representable and has a closed Gδ-subspace that is not Scott-domain-representable. This clarifies the general topology of Scott-domain-representable spaces and raises additional questions about Scott-domain representability in Moore spaces. 2000 AMS Cla...

The domain-theoretic model of computational geometry provides us with continuous and computable predicates and binary operations. It can also be used to generalise the theory of computability for real numbers and real functions into geometric objects and geometric operations. A geometric object is computable if it is the effective limit of a sequence of finitary partial objects of the same type...

Let A be a self-adjoint operator on a Hilbert space H. Assume that the spectrum of A consists of two disjoint components σ0 and σ1 such that the convex hull of the set σ0 does not intersect the set σ1 . Let V be a bounded self-adjoint operator on H offdiagonal with respect to the orthogonal decomposition H = H0 ⊕H1 where H0 and H1 are the spectral subspaces of A associated with the spectral set...

A model of a space X is simply a continuous dcpo D and a homeomorphism : X ! max D, where max D is given its inherited Scott topology. We show that a space has a coherent model ii it has a Scott domain model and investigate the topological structure of spaces which have G models.