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.

Abstract We consider two recent conjectures made by Harrington, Henninger-Voss, Karhadkar, Robinson and Wong concerning relationships between the sum index, difference index exclusive number of graphs. One conjecture posits an exact relationship first invariants; we show that in fact predicted value may be arbitrarily far from truth either direction. In process establish some new bounds on both...