M-Sequences play a big important role, as the other binary orthogonalsequences, for collection information on input links and distributionthese output of communication channelsand building new systems with more complexity, larger period, andsecurity, through multiplication these sequences. In our article we try tostudy construction sequence {zn}and its linearequivalent, this is multiple two seq...

My Ph.D. thesis centered on a class of univariate polynomials over finite fields known as composed products or root-based compositions . Work related to the thesis appears in [5], [6], and [41], while additional results pertaining to multivariate analogues appear in [48] and [49]. My post-thesis research in finite fields includes not only work with polynomials (see [14] and [44]), but also work...

In this paper, we consider a bilevel polynomial optimization problem where the objective and the constraint functions of both the upper and the lower level problems are polynomials. We present methods for finding its global minimizers and global minimum using a sequence of semidefinite programming (SDP) relaxations and provide convergence results for the methods. Our scheme for problems with a ...

A Laguerre polynomial sequence of parameter ε/2 was previously characterized in a recent work [Ana F. Loureiro and P. Maroni (2008) [28]] as an orthogonal Fε-Appell sequence, where Fε represents a lowering (or annihilating) operator depending on the complex parameter ε ≠ −2n for any integer n ⩾ 0. Here, we proceed to the quadratic decomposition of anFε-Appell sequence, and we conclude that the ...

A hyperbolic polynomial (HP) is a real univariate with all roots real. By Descartes' rule of signs HP coefficients nonvanishing has exactly $c$ positive and $p$ negative counted multiplicity, where are the numbers sign changes preservations in sequence its coefficients. We consider HPs distinct moduli roots. ask question when order w.r.t. on half-line completely determines polynomial. When ther...

The large n behaviour of the hypergeometric polynomial 3F2 ( −n, 1 2 , 1 2 1 2 − n, 1 2 − n ; −1 ) is considered by using integral representations of this polynomial. This 3F2 polynomial is associated with the Catalan-Larcombe-French sequence. Several other representations are mentioned, with references to the literature, and another asymptotic method is described by using a generating function...

The independence polynomial of the graph called the centipede has only real zeros. It follows that this polynomial is log-concave, and hence unimodal. Levit and Mandrescu gave a conjecture about the mode of this polynomial. In this paper, the exact value of the mode is determined, and some central limit theorems for the sequence of the coefficients are established.