6 Consider the continuum of points on the edges of a network, i.e., a connected, undirected graph 7 with positive edge weights. We measure the distance between these points in terms of the weighted 8 shortest path distance, called the network distance. Within this metric space, we study farthest points 9 and farthest distances. We introduce optimal data structures supporting queries for the far...

In this article we consider the distribution of N points on the unit sphere S in R interacting via logarithmic potential. A characterization theorem of the stationary configurations is derived when N = d + 2 and two new log-optimal configurations minimizing the logarithmic energy are obtained for six points on S and seven points on S. A conjecture on the log-optimal configurations of d + 2 poin...

Consider the continuum of points on the edges of a network, i.e., a connected, undirected graph with positive edge weights. We measure the distance between these points in terms of the weighted shortest path distance, called the network distance. Within this metric space, we study farthest points and farthest distances. We introduce optimal data structures supporting queries for the farthest di...

There is a longstanding conjecture of Nussbaum, which asserts that every finite set in R on which a cyclic group of sup-norm isometries acts transitively contains at most 2 points. The existing evidence supporting Nussbaum’s conjecture only uses abelian properties of the group. It has therefore been suggested that Nussbaum’s conjecture might hold more generally for abelian groups of sup-norm is...

The Turin Shroud (TS) is a linen cloth commonly associated with Jesus Christ, his crucifixion and burial. Several medical specialists have debated the injuries of the TS Man, nevertheless there are no detailed and quantitative data about the anatomy of the TS face. The purpose of this study was to analyse the cephalometric measurements of the face image of the TS. The TS face image was acquired...

contemporary enhancement of medical sciences along with the possibility of cure for barrenness via (art) made hope for many barren couples; so that, the technique was soon warmly received by infertile couples all over the world. the new situation has raised certain questions in respects of morality, legal, sanitation, social, psychology and religion status. consequently, comprehensive supportin...

according to the well-known view among the imami jurists, if a sick man marries a woman and die before coition ,his wife is deprived of dower and inheritance. the article 945 of civil law also mentions coition as a condition for the woman to have a share of the sick man's inheritance. so, in this paper it is tried to criticize the reasons by people who agree with depriving, in order to rev...

In this paper, using the best proximity theorems for an extensionof Brosowski's theorem. We obtain other results on farthest points. Finally, wedene 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 approximati...