In this paper, we derive new recurrence relations and generating matrices for the sums of usual Tribonacci numbers and 4n subscripted Tribonacci sequences, fT4ng ; and their sums. We obtain explicit formulas and combinatorial representations for the sums of terms of these sequences. Finally we represent relationships between these sequences and permanents of certain matrices. 1. Introduction Th...

We consider linear rank-metric codes in Fqm . We show that the properties of being MRD (maximum rank distance) and non-Gabidulin are generic over the algebraic closure of the underlying field, which implies that over a large extension field a randomly chosen generator matrix generates an MRD and a non-Gabidulin code with high probability. Moreover, we give upper bounds on the respective probabi...

We construct linear codes over finite fields with prescribed minimum distance by selectiong columns of the generator matrix. This selection problem can be formulated as an integer programming problem. In order to reduce the search space we prescribe a group of automorphisms. Then, in many cases the resulting integer programming problem can be solved by lattice point enumeration. With this appro...

GRAPE-Dilepton is a Monte Carlo event generator for dilepton production in ep collisions. The cross-section calculation is based on the exact matrix elements in the electroweak theory at tree level. The dilepton productions via γγ, γZ, ZZ collisions and via photon internal conversion are taken into account. In addition, the effects of the Z on/offshell production are also included. The relevant...

We present a fully automated framework as part of the Sherpa event generator for the computation of tree-level cross sections in Beyond Standard Model scenarios, making use of model information given in the Universal FeynRules Output format. Elementary vertices are implemented into C++ code automatically and provided to the matrix-element generator Comix at runtime. Widths and branching ratios ...

A family of subadditive functions which contains the optimal solution of subadditive duals for integer programs has been presented by Klabjan (2007). In this paper we present a subadditive dual ascent procedure to find an optimal subadditive dual function based on Klabjan’s generator subadditive function. Then we use the proposed method to solve the so called uncapacitated facility location pro...

This paper is concerned with properties of the algebraic degree of the Laplace–Stieltjes transform of phase-type (PH) distributions. The main problem of interest is: given a PH generator, how do we find the maximum and the minimum algebraic degrees of all irreducible PH representations with that PH generator? Based on the matrix exponential (ME) order of ME distributions and the spectral polyno...

This paper presents a new photonic integrated circuit, namely optical pulse-train generator, which is developed based on the transfer matrix analysis of microrings and utilizes a time-interleaved architecture. This circuit can generate multiple optical pulses sequentially from a single trigger pulse, with the timing and amplitude of each pulse determined by circuit design. Hence it can be appli...

We describe amodification to a previously published pseudorandom number generator improving security while maintaining high performance. The proposed generator is based on the powers of a word-packed block upper triangular matrix and it is designed to be fast and easy to implement in software since it mainly involves bitwise operations between machine registers and, in our tests, it presents ex...

In this short note we state how we construct new good linear codes C over the finite field with q elements. We start with already good (= high minimum distance d for given length n and dimension k) codes which we got for example by our method [2,3,4,5]. The advantage of this method is that we explictly get the words of minimum weight d. We try to extend the generator matrix of C by adding colum...