We propose the idea of building a secure hash using quadratic or higher degree multivariate polynomials over a finite field as the compression function. We analyze some security properties and potential feasibility, where the compression functions are randomly chosen highdegree polynomials, and show that under some plausible assumptions, high-degree polynomials as compression functions has good...

‎let $g_{i} $ be a subgroup of $ s_{m_{i}}‎ ,‎ 1 leq i leq k$‎. ‎suppose $chi_{i}$ is an irreducible complex character of $g_{i}$‎. ‎we consider $ g_{1}times cdots times g_{k} $ as subgroup of $ s_{m} $‎, ‎where $ m=m_{1}+cdots‎ +‎m_{k} $‎. ‎in this paper‎, ‎we give a formula for the dimension of $h_{d}(g_{1}times cdots times g_{k}‎, ‎chi_{1}timescdots times chi_{k})$ and investigate the existe...

In this study, a relationship between scanner response (RGB) and CIE tristimulus values (XYZ) is established by regression technique with different polynomials for colored polyester fabrics. The results showed that the transformation process is material dependent and higher order polynomials will fit the experimental data better than lower polynomials. The results also showed that the way the c...

In this study, a relationship between scanner response (RGB) and CIE tristimulus values (XYZ) is established by regression technique with different polynomials for colored polyester fabrics. The results showed that the transformation process is material dependent and higher order polynomials will fit the experimental data better than lower polynomials. The results also showed that the way the c...

In this paper, we give some determinantal and permanental representations of generalized Lucas polynomials, which are a general form of generalized bivariate Lucas p-polynomials, ordinary Lucas and Perrin sequences etc., by using various Hessenberg matrices. In addition, we show that determinant and permanent of these Hessenberg matrices can be obtained by using combinations. Then we show, the ...

A general system of q-orthogonal polynomials is defined by means of its three-term recurrence relation. This system encompasses many of the known families of q-polynomials, among them the q-analogue of the classical orthogonal polynomials. The asymptotic density of zeros of the system is shown to be a simple and compact expression of the parameters which characterize the asymptotic behaviour of...

Abstract. It is well-known that orthogonal polynomials on the real line satisfy a three-term recurrence relation and conversely every system of polynomials satisfying a three-term recurrence relation is orthogonal with respect to some positive Borel measure on the real line. In this paper we extend this result and show that every system of polynomials satisfying some (2N + 1)-term recurrence re...

Graham Higman has defined coset diagrams for PSL(2,ℤ). These diagrams are composed of fragments, and the fragments are further composed of two or more circuits. Q. Mushtaq has proved in 1983 that existence of a certain fragment γ of a coset diagram in a coset diagram is a polynomial f in ℤ[z]. Higman has conjectured that, the polynomials related to the fragments are monic and for a fixed degree...

graham higman has defined coset diagrams for psl(2,ℤ). these diagrams are composed of fragments, and the fragments are further composed of two or more circuits. q. mushtaq has proved in 1983 that existence of a certain fragment γ of a coset diagram in a coset diagram is a polynomial f in ℤ[z]. higman has conjectured that, the polynomials related to the fragments are monic and for a fixed degree...

In the main this paper introduces the concept of chromatic harmonic polynomials denoted, $H^chi(G,x)$ and chromatic harmonic indices denoted, $H^chi(G)$ of a graph $G$. The new concept is then applied to finding explicit formula for the minimum (maximum) chromatic harmonic polynomials and the minimum (maximum) chromatic harmonic index of certain graphs. It is also applied to split graphs and ce...