In the classical paper [PS14] I. Schur and G. Polýa introduced and characterized two types of multiplier sequences, i.e. linear operators acting diagonally in the monomial basis of R[x] and sending real-rooted (resp. with all real roots of the same sign) polynomials to real-rooted polynomials. Motivated by a fundamental property of amoebae and discriminants discovered in [GKZ94] we introduce be...

the non-split extension group $overline{g} = 5^3{^.}l(3,5)$ is a subgroup of order 46500000 and of index 1113229656 in ly. the group $overline{g}$ in turn has l(3,5) and $5^2{:}2.a_5$ as inertia factors. the group $5^2{:}2.a_5$ is of order 3 000 and is of index 124 in l(3,5). the aim of this paper is to compute the fischer-clifford matrices of $overline{g}$, which together with associated parti...

Recently, the authors obtained Schur multiplier, non-abelian tensor square and exterior of $d$-generator generalized Heisenberg Lie algebras rank $ \frac{1}{2}d(d-1).$ Here, we intend to obtain same results for t$ when \frac{1}{2}d(d-1)-3 \leq t\leq \frac{1}{2}d(d-1)-1.$ Then, as a result, give similar consequences nilpotent algebra L class two \dim (L/Z(L))=d,$ L^2=t such that

This article is part of the program described in [3]. We study the Phan amalgams and their universal completions that occur for q = 3 in rank n = 3 for the diagram A3 = D3, corresponding to SU(4, 3) ∼= Spin−(6, 3). We show that the associated geometries admit universal 9-fold coverings, by showing that the universal completion of the Phan amalgam is the central extension of SU(4, 3) by its Schu...

Given a nilpotent Lie algebra L of dimension $$\le 6$$ on an arbitrary field characteristic $$\ne 2$$ , we show direct method to detect whether is capable or not via computations the size its nonabelian exterior square $$L \wedge L$$ . For dimensions higher than 6, result general nature, based evidences low dimensional case, but also large families algebras, namely generalized Heisenberg algebr...

We define a new class of functions, connected to the classical Laguerre-P\'{o}lya class, which we call shifted class. Recent work Griffin, Ono, Rolen, and Zagier shows that Riemann Xi function is in this prove being equivalent Taylor coefficients, once shifted, degree $d$ multiplier sequence for every $d$, coefficients satisfying all higher T\'{u}ran inequalities. This mirrors result P\'{o}lya ...