Abstract We develop the Gompf fiber connected sum operation for symplectic orbifolds. use it to construct a 4-orbifold with b 1 = 0 {b_{1}=0} and containing surfaces of genus 1 2 that are disjoint span rational homology. This is used in turn K...

We derive constraints on the asymmetry a1 of the momentum fractions carried by quark and antiquark in K and K mesons in leading twist. These constraints follow from exact operator identities and relate a1 to SU(3) breaking quark-antiquark-gluon matrix elements which we determine from QCD sum rules. Comparing our results to determinations of a1 from QCD sum rules based on correlation functions o...

A matched sum graph G1MG2 of two graphs G1 and G2 of the same order n is obtained by adding to the union (or sum) of G1 and G2 a set M of n independent edges which join vertices in V (G1) to vertices in V (G2). When G1 and G2 are isomorphic, G1MG2 is just a permutation graph. In this work we derive bounds for the k-restricted edge connectivity λ(k) of matched sum graphs G1MG2 for 2 ≤ k ≤ 5, and...

We consider the set of squares n2, n < 2k, and split up the sum of binary digits s(n2) into two parts s[<k](n 2) + s[≥k](n 2), where s[<k](n 2) = s(n2 mod 2k) collects the first k digits and s[≥k](n 2) = s(bn2/2kc) collects the remaining digits. We present very precise results on the distribution on s[<k](n 2) and s[≥k](n 2). For example, we provide asymptotic formulas for the numbers #{n < 2k ...

In this paper, we define a distributionally robust k-sum optimization problem as the problem of finding a solution that minimizes the worst-case expected sum of up to the k largest costs of the elements in the solution. The costs are random with a joint probability distribution that is not completely specified but rather assumed to be known to lie in a set of probability distributions. For k = ...

Given a sequence of n real numbers A = a1, a2, . . . , an and a positive integer k, the Sum Selection Problem is to find the segment A(i, j) = ai, ai+1, . . . , aj such that the rank of the sum s(i, j) = j t=i at is k over all n(n−1) 2 segments. We present a deterministic algorithm for this problem that runs in O(n log n) time. The previously best known randomized algorithm for this problem run...

We consider the sum coloring (chromatic sum) and sum multi-coloring problems for restricted families of graphs. In particular, we consider the graph classes of proper intersection graphs of axis-parallel rectangles, proper interval graphs, and unit disk graphs. All the above mentioned graph classes belong to a more general graph class of (k+1)clawfree graphs (respectively, for k = 4, 2, 5). We ...

We present space efficient Monte Carlo algorithms that solve Subset Sum and Knapsack instances with n items using O(2) time and polynomial space, where the O∗(·) notation suppresses factors polynomial in the input size. Both algorithms assume random read-only access to random bits. Modulo this mild assumption, this resolves a long-standing open problem in exact algorithms for NP-hard problems. ...