If G is a connected graph, then the distance between two edges is, by definition, the distance between the corresponding vertices of the line graph of G. The edge-Wiener index We of G is then equal to the sum of distances between all pairs of edges of G. We give bounds on We in terms of order and size. In particular we prove the asymptotically sharp upper bound We(G) ≤ 25 55 n5 + O(n9/2) for gr...

This paper provides a parsing algorithm for the Lambek calculus which is polynomial time for a more general fragment of the Lambek calculus than any previously known algorithm. The algorithm runs in worst-case time O(n5) when restricted to a certain fragment of the Lambek calculus which is motivated by empirical analysis. In addition, a set of parameterized inputs are given, showing why the alg...

This paper provides a parsing algorithm for the Lambek calculus which is polynomial time for a more general fragment of the Lambek calculus than any previously known algorithm. The algorithm runs in worst-case time O(n5) when restricted to a certain fragment of the Lambek calculus which is motivated by empirical analysis. In addition, a set of parameterized inputs are given, showing why the alg...

The photomagnetic properties of a new Fe(II) macrocyclic family [Fe(L(xyz)N5)(CN)2]·nH2O were investigated with respect to the T(LIESST) versus T(1/2) relationship. These compounds are diamagnetic below 400 K with T(LIESST) values above 100 K, which indicates that this family presents an unconventional LIESST effect that is much higher than the expected T0 = 180 K line for macrocyclic complexes.

I show that there are sets of n points in three dimensions, in general position, such that any triangulation of these points has only O(n5/3) simplices. This is the first nontrivial upper bound on the MinMax triangulation problem posed by Edelsbrunner, Preparata and West in 1990: What is the minimum over all general-position point sets of the maximum size of any triangulation of that set? Simil...