k-d tree (or Multidimensional binary search tree) is often used as a data structure for organizing and manipulating spatial data. We present several algorithms for the parallel construction of k-d trees on coarse-grained distributed memory parallel machines. We analyze them both theoretically and experimentally. Experimental results on the CM-5 are reported. 1 Multidimensional Binary Search Tre...

This paper deals with the critical point of three-dimensional bootstrap percolation-like cellular automata. Some general sufficient or necessary conditions for pc = 0 are obtained. In the case of pc > 0, some explicit upper and lower bounds are provided in terms of the critical value of oriented site percolation.

fibre is the re-dimensional complex projective space (complex projective co-tangent bundle). This bundle of complex dimension 2re + l is our M. Considering the fibre of T(V) as the (2w+2)-dimensional real vector space, we take as P the co-tangent sphere bundle over V (i.e., the fibre of P is a sphere in the fibre of T(V)). T(V) — V is the principal fibre bundle associated with a line bundle L o...

We show that convex hull of extreme points a closed subset compact flat Riemannian manifold is equal to the itself.

We discuss topological structure of b-metric-like spaces and demonstrate a fundamental lemma for the convergence of sequences. As an application we prove certain fixed point results in the setup of such spaces for different types of contractive mappings. Finally, some periodic point results in b-metric-like spaces are obtained. Two examples are presented in order to verify the effectiveness and...

In this short note we give a criterion when a planar tree-like curve, i.e. a generic curve in R 2 each double point of which cuts it into two disjoint parts, can be send by a diffeomorphism of R 2 onto a curve with no inflection points. We also present some upper and lower bounds for the minimal number of inflection points on such curves unremovable by diffeomorphisms of R 2. §1. Introduction T...

Received ; accepted – 2 – ABSTRACT Motivated by Papadakis (2005a, 2005b), we study a Chermnykh-like problem, in which an additional gravitational potential from the belt is included. In addition to the usual five equilibrium points (three collinear and two triangular points), there are some new equilibrium points for this system. We studied the conditions for the existence of these new equilibr...

By a metric-like space, as a generalization of a partial metric space, we mean a pair (X ,σ ), where X is a nonempty set and σ : X × X →R satisfies all of the conditions of a metric except that σ (x, x) may be positive for x ∈ X . In this paper, we initiate the fixed point theory in metric-like spaces. As an application, we derive some new fixed point results in partial metric spaces. Our resul...