the average distance of a vertex $v$ of a connected graph $g$is the arithmetic mean of the distances from $v$ to allother vertices of $g$. the proximity $pi(g)$ and the remoteness $rho(g)$of $g$ are defined as the minimum and maximum averagedistance of the vertices of $g$. in this paper we investigate the difference between proximity or remoteness and the classical distanceparameters diameter a...

We introduce a new problem in the study of doubling spaces: Given a point set S and a target dimension d∗, remove from S the fewest number of points so that the remaining set has doubling dimension at most d∗. We present a bicriteria approximation for this problem, and extend this algorithm to solve a group of proximity problems.

o bjective: to determine the etiology, signs and symptoms, angiography indications and angiography findings in patients with limb penetrating injuries suspected to have arterial injury. m e thods: this was a cross-sectional study being performed in imam reza hospital affiliated with mashhad university of medical sciences, iran between september 2011 and march 2013. we included those patients wi...

The best approximation problem in a hyperconvex metric space consists of finding conditions for given set-valued mappings F andG and a setX such that there is a point x0 ∈ X satisfying d G x0 , F x0 ≤ d x, F x0 for x ∈ X. When G I, the identity mapping, and when the set X is compact, best approximation theorems for mappings in hyperconvex metric spaces are given for the single-valued case in 1–...

Many algorithms have to deal with multiple representations of the same object. The process of aligning these representations is called registration. In this paper we present a new approach for the registration of free-form surfaces which is not based on finding closest points. Instead, our algorithm takes advantage of the graphics hardware and uses the depth buffer for determining the distance ...

The proximity relations inherent in triangulations of geometric data can be exploited in the implementation of nearest-neighbour search procedures. This is relevant to applications such as terrain analysis, cartography and robotics, in which triangulations may be used to model the spatial data. Here we describe neighbourhood search procedures within constrained Delaunay triangulations of the ve...

in this paper, using the best proximity theorems for an extensionof brosowski's theorem. we obtain other results on farthest points. finally, wede ne the concept of e- farthest points. we shall prove interesting relationshipbetween the -best approximation and the e-farthest points in normed linearspaces (x; ||.||). if z in w is a e-farthest point from an x in x, then z is also a-best ...

The main purpose of this paper is to study the approximate best proximity pair of cyclic maps and their diameter in fuzzy normed spaces defined by Bag and Samanta. First, approximate best point proximity points on fuzzy normed linear spaces are defined and four general lemmas are given regarding approximate fixed point and approximate best proximity pair of cyclic maps on fuzzy normed spaces. U...