Extremal bases for finite cyclic groups

AbstractLet m and h be positive integers. A set A of integers is called a basis of orderh for Z(m) if every integer n is congruent to a sum of h elements in A modulo m. Let m(h, A) denote the greatest positive integer m such that A is a basis of order h for Z(m). For any k ≥ 1, define m(h, k) = max∥A∥ = k + 1 m(h, A). This generalizes a function of Graham and Sloane. In this paper, it is proved that, for fixed k ≥ 4 as h → ∞, m(h, k) ≥ αk (256125)⌞k4⌟ (hk)k + O(hk − 1), where αk = 1 if k ≡ 0 or 1 (mod 4), 43 if k ≡ 2 (mod 4), and 2716 if k ≡ 3 (mod 4). A lower bound for m(h, k) is also obtained for fixed h. Using these results, new lower bounds are proved for the order of subsets of asymptotic bases

Next-to-leading order QCD corrections to the single top quark production via model-independent t-q-g flavor-changing neutral-current couplings at hadron colliders

We present the calculations of the complete next-to-leading order (NLO) QCD effects on the single top productions induced by model-independent $tqg$ flavor-changing neutral-current couplings at hadron colliders. Our results show that, for the $tcg$ coupling the NLO QCD corrections can enhance the total cross sections by about 60% and 30%, and for the $tug$ coupling by about 50% and 20% at the Tevatron and LHC, respectively, which means that the NLO corrections can increase the experimental sensitivity to the FCNC couplings by about 10%$-$30%. Moreover, the NLO corrections reduce the dependence of the total cross sections on the renormalization or factorization scale significantly, which lead to increased confidence on the theoretical predictions. Besides, we also evaluate the NLO corrections to several important kinematic distributions, and find that for most of them the NLO corrections are almost the same and do not change the shape of the distributions.Comment: minor changes, version published in PR