In this paper we investigate the distribution of trimmed sums of dependent observations with heavy tails. We consider the case of autoregressive processes of order one with independent innovations in the domain of attraction of a stable law. We show if the d largest (in magnitude) terms are removed from the sample, then the sum of the remaining elements satisfies a functional central limit theo...

This paper considers the computational complexity of the discrete logarithm and related problems in the context of \generic algorithms"|that is, algorithms which do not exploit any special properties of the encodings of group elements, other than the property that each group element is encoded as a unique binary string. Lower bounds on the complexity of these problems are proved that match the ...

With respect to multiple attribute decision making (MADM) problems in which the attribute values take the form of hesitant fuzzy elements, the traditional grey relational projection (GRP) method is extended to solve multiple attribute decision making problems under hesitant fuzzy environment. Based on the hesitant fuzzy decision matrix provided by decision makers, all feasible alternatives are ...

Themaximum subarray problem is to find the contiguous array elements having the largest possible sum. We extend this problem to find K maximum subarrays. For general K maximum subarrays where overlapping is allowed, Bengtsson and Chen presented OðminfK + n logn‚ n ffiffiffiffi K p gÞ time algorithm for one-dimensional case, which finds unsorted subarrays. Our algorithm finds K maximum subarrays...

At future electron-positron colliders, one of the largest irreducible backgrounds to top searches in the channel ‘4 jets + lepton + missing energy’ comes from QCD events of order α2s. We compute here such processes exactly at the parton level by resorting to 2 → 6 matrix elements exploiting helicity amplitude techniques. We adopt a typical selection procedure based on the tagging of a high mome...

We describe two problems and their optimal solutions for partially ordered sets. We rst describe an optimal algorithm for computing the largest anti-chain of a partially ordered set given its decomposition into its chains. Our algorithm requires O(n 2 m) comparisons where n is the number of chains and m is the maximum number of elements in any chain. We also give an adversary argument to prove ...

Recently developed correlation consistent basis sets for the first row transition metal elements Sc-Zn have been utilized to determine complete basis set (CBS) scalar relativistic electron affinities, ionization potentials, and 4s(2)3d(n-2)-4s(1)d(n-1) electronic excitation energies with single reference coupled cluster methods [CCSD(T), CCSDT, and CCSDTQ] and multireference configuration inter...

Semi-leptonic and radiative semi-inclusive decays of heavy mesons are currently under intense investigation. Non perturbative physics seems to be more manageable in such decays, and there is hope for a reduction of theoretical assumptions and a more stringent comparison with experimental data. Several effective approaches to such decays are available. Most commonly, in order to calculate the de...

For a natural number n, let λ(n) denote the order of the largest cyclic subgroup of (Z/nZ). For a given integer a, let Na(x) denote the number of n ≤ x coprime to a for which a has order λ(n) in (Z/nZ). Let R(n) denote the number of elements of (Z/nZ) with order λ(n). It is natural to compare Na(x) with ∑ n≤x R(n)/n. In this paper we show that the average of Na(x) for 1≤ a ≤ y is indeed asympto...