Fullerene graphs are mathematical models of fullerene molecules. The Wiener (r,s)-complexity a graph G with vertex set V(G) is the number pairwise distinct values (r,s)-transmiss...

Let S be any family of n c-oriented polygons of the two-dimensional Euclidean plane E, i.e., bounded intersection of halfplanes whose normal directions of edges belong to a .xed collection of c distinct directions. Let (S) denote the packing number of S, that is the maximum number of pairwise disjoint objects of S. Let (S) be the transversal number of S, that is the minimum number of points req...

W. P. Thurston introduced closed σd-invariant laminations (where σd = z : S → S, d ≥ 2) as a tool in complex dynamics. He defined wandering triangles as triples T ⊂ S such that σ d (T ) consists of three distinct points for all n ≥ 0 and the convex hulls of all the sets σ d (T ) in the plane are pairwise disjoint, and proved that σ2 admits no wandering triangles. We show that for every d ≥ 3 th...

Given an undirected n-node unweighted graph G = (V,E), a spanner with stretch function f(·) is a subgraph H ⊆ G such that, if two nodes are at distance d in G, then they are at distance at most f(d) in H. Spanners are very well studied in the literature. The typical goal is to construct the sparsest possible spanner for a given stretch function. In this paper we study pairwise spanners, where w...

We determine the velocity correlation function, pairwise peculiar velocity di erence, and root-mean-square pairwise peculiar velocity dispersion of rich clusters of galaxies, as a function of pair separation, for three cosmological models: = 1 and = 0:3 CDM, and = 0:3 PBI models (all at and COBEnormalized). We nd that close cluster pairs, with separation r 10h 1Mpc, exhibit strong attractive pe...

In the present paper we introduce and study the notion of pairwise weakly Lindelof bitopological spaces and obtain some results. Further, we also study the pairwise weakly Lindelof subspaces and subsets, and investigate some of their properties. It was proved that a pairwise weakly Lindelof property is not a hereditary property.

Our system treats coreference resolution as an integer linear programming (ILP) problem. Extending Denis and Baldridge (2007) and Finkel andManning (2008)’s work, we exploit loose transitivity constraints on coreference pairs. Instead of enforcing transitivity closure constraints, which brings O(n3) complexity, we employ a strategy to reduce the number of constraints without large performance d...

Abstract: In this paper, we analyze the pairwise error probability (PEP) of distributed space-time codes, in which the source and the relay generate Alamouti space-time code in a distributed fashion. We restrict our attention to the space-time code construction for Protocol III in Nabar et al. (IEEE Journal on Selected Areas Communications 22(6): 1099-1109, 2004). In particular, we derive two c...

Let G be a group. A subset X of G is a set of pairwise noncommuting elements if xy ̸= yx for any two distinct elements x and y in X. If |X| ≥ |Y | for any other set of pairwise non-commuting elements Y in G, then X is said to be a maximal subset of pairwise non-commuting elements. In this paper we determine the cardinality of a maximal subset of pairwise non-commuting elements in any non-abelian...