Given a set P of n points on the real line and a (potentially in nite) family of functions, we investigate the problem of nding a small (weighted) subset S ⊆ P , such that for any f ∈ F, we have that f(P ) is a (1 ± ε)-approximation to f(S). Here, f(Q) = ∑ q∈Q w(q)f(q) denotes the weighted discrete integral of f over the point set Q, where w(q) is the weight assigned to the point q. We study th...

In this paper we study the conjugacy problem in polycyclic groups. Our main result is that we create polycyclic groups Gn whose conjugacy problem is at least as hard as the subset sum problem with n indeterminates. As such, the conjugacy problem over the groups Gn is NP-complete where the parameters of the problem are taken in terms of n and the length of the elements given on input.

Given an integer r > 0, let G r = (V; E) denote a graph consisting of a simple nite undirected connected nontrivial graph G together with r isolated vertices K r. Let L : V ! Z + denote a labelling of the vertices of G r with distinct positive integers. Then G r is said to be a sum graph if there exists a labelling L such that for every distinct vertex pair u and v of V , (u; v) 2 E if and only...

Let n be a large number. A subset A of Zn is complete if SA = Zn, where SA is the collection of the subset sums of A. Olson proved that if n is prime and |A| > 2n1/2, then SA is complete. We show that a similar result for the case when n is a composite number, using a different approach.

Consider the following problem which we call Maximum k-Subset Intersection (MSI): Given a collection C = {S1, . . . , Sm} of m subsets over a finite set of elements E = {e1, . . . , en}, and a positive integer k, the objective is to select exactly k subsets Sj1 , . . . , Sjk whose intersection size |Sj1 ∩ . . . ∩ Sjk | is maximum. In [2], Clifford and Popa studied a related problem and left as ...

We present a QCD sum rule calculation of the strange-quark mass including four-loop QCD corrections to the correlator of scalar currents. We obtain ¯ m s (1 GeV) = 203.5 ± 20 MeV.

We calculate the radiative corrections to the current-current correlator of the hybrid current g ¯ q(x)γ ν iG a µν T a q(x). Based on this new result we use the QCD sum rule approach to estimate lower bounds on the masses of the J P C =1 −+ and 0 ++ light hybrids.

We present a QCD sum rule calculation of the strange-quark mass including four-loop QCD corrections to the correlator of scalar currents. We obtain ¯ m s (1 GeV) = 205.5 ± 19.1 MeV.