In this paper, we first define the multiple Appell polynomials and find several equivalent conditions for this class of polynomials. Then we give a characterization theorem that if multiple Appell polynomials are also multiple orthogonal, then they are the multiple Hermite polynomials.

To guarantee the security of communication in the public channel, many key agreement protocols have been proposed. Recently, Gong et al. proposed a key agreement protocol based on chaotic maps with password sharing. In this paper, Gong et al.’s protocol is analyzed, and we find that this protocol exhibits key management issues and potential security problems. Furthermore, the paper presents a n...

Let $\iota:K\hookrightarrow L\cong K(x)$ be a simple transcendental extension of valued fields, where $K$ is equipped with valuation $\nu$ rank 1. That is, we assume given 1 and its $\nu'$ to $L$. $(R_\nu,M_\nu,k_\nu)$ denote the ring $\nu$. The purpose this paper present refined version MacLane's theory key polynomials, similar those considered by M. Vaqui\'e, reminiscent related objects studi...

formulae expressing explicitly the coefficients of an expansion of double jacobi polynomials which has been partially differentiated an arbitrary number of times with respect to its variables in terms of the coefficients of the original expansion are stated and proved. extension to expansion of triple jacobi polynomials is given. the results for the special cases of double and triple ultraspher...

Bivariate Gončarov polynomials are a basis of the solutions of the bivariate Gončarov Interpolation Problem in numerical analysis. A sequence of bivariate Gončarov polynomials is determined by a set of nodes Z = {(xi,j, yi,j) ∈ R2} and is an affine sequence if Z is an affine transformation of the lattice grid N2, i.e., (xi,j, yi,j) = A(i, j)T + (c1, c2) for some 2 × 2 matrix A and constants c1,...

This paper presents a new generalization of the Genocchi numbers and theorem. As consequences, we obtain some important families integer-valued polynomials those are closely related to Bernoulli polynomials. Denoting by ${(B_n)}_{n \in \mathbb{N}}$ sequence ${(B_n(X))}_{n polynomials, especially that for any natural number $n$, reciprocal polynomial $\big(B_n(X) - B_n\big)$ is integer-valued.

In this paper, for a valued field [Formula: see text] of arbitrary rank and an extension to relation between induced complete sequences abstract key polynomials MacLane-Vaquié chains is given.