On generalized Hadamard matrices GH(q,q)'s and GH(q,q^2)'s

A matrix $H=[d_{ij}]$ is a generalized Hadamard matrix of order $u\lambda$ with entries from $U$ which is a finite group of order $u$ (for short $\mathrm{GH}(u,\,\lambda)$) such that whenever $i\neq \ell$ the set $\{d_{ij}d_{\ell j}^{-1}\,|\, 1\leq j\leq u\lambda \}$ contains each element of $U$ exactly $\lambda$ times. In this paper, we construct $\mathrm{GH}(q,\,q)$'s and $\mathrm{GH}(q,\,q^{2})$'s over additive groups of finite fields $\mathrm{GF}(q)$'s by using some sorts of functions

On a class of qq-Bernoulli, qq-Euler and qq-Genocchi polynomials

The main purpose of this paper is to introduce and investigate a class of $q$-Bernoulli, $q$-Euler and $q$-Genocchi polynomials. The $q$-analogues of well-known formulas are derived. The $q$-analogue of the Srivastava--Pint\'er addition theorem is obtained. Some new identities involving $q$-polynomials are proved

On Q-derived polynomials

It is known that Q-derived univariate polynomials (polynomials defined over Q, with the property that they and all their derivatives have all their roots in Q) can be completely classified subject to two conjectures: that no quartic with four distinct roots is Q-derived, and that no quintic with a triple root and two other distinct roots is Q-derived. We prove the second of these conjectures