Related papers: Polynomials that preserve nonnegative matrices of …

We produce a new family of polynomials f(x) over fields K of characteristic 2 which are exceptional, in the sense that f(x)-f(y) has no absolutely irreducible factors in K[x,y] besides the scalar multiples of x-y; when K is finite, this…

Given a closed, convex cone $K\subseteq \mathbb{R}^n$, a multivariate polynomial $f\in\mathbb{C}[\mathbf{z}]$ is called $K$-stable if the imaginary parts of its roots are not contained in the relative interior of $K$. If $K$ is the…

Let L be a restricted Lie superalgebra with its enveloping algebra u(L) over a field F of characteristic p>2. A polynomial identity is called non-matrix if it is not satisfied by the algebra of 2\times 2 matrices over F. We characterize L…

There have been some effective tools for solving (constant/parametric) semi-algebraic systems in Maple's library RegularChains since Maple 13. By using the functions of the library, e.g., RealRootClassfication, one can prove and discover…

The ring of dual numbers over a ring $R$ is $R[\alpha] = R[x]/(x^2)$, where $\alpha$ denotes $x+(x^2)$. For any finite commutative ring $R$, we characterize null polynomials and permutation polynomials on $R[\alpha]$ in terms of the…

This brief note concerns the invertibility of certain alternant matrices. In particular those that consisting of polynomials and products of polynomials and logarithms are shown to be invertible under appropriate conditions on the degrees…

We prove that arbitrary (nonpolynomial) scalar evolution equations of order $m\ge 7$, that are integrable in the sense of admitting the canonical conserved densities $\ro^{(1)}$, $\ro^{(2)}$, and $\ro^{(3)}$ introduced in [MSS,1991], are…

We adapt (over $\mathbb{F}_2$) the general notions of multiplicative function, Dirichlet convolution and Inverse. We get some interesting results, namely necessary conditions for an odd binary polynomial to be perfect. Note that we are…

In recent years, the notion of characteristic polynomial of representations of Lie algebras has been widely studied. This paper provides more properties of these characteristic polynomials. For simple Lie algebras, we characterize the…

We prove that the only entrywise transforms of rectangular matrices which preserve total positivity or total non-negativity are either constant or linear. This follows from an extended classification of preservers of these two properties…

The concepts of differentiation and integration for matrices are known. As far as each matrix is differentiable, it is not clear a priori whether a given matrix is integrable or not. Recently some progress was obtained for diagonalizable…

In this article, we propose a few sufficient conditions on polynomials having integer coefficients all of whose zeros lie outside a closed disc centered at the origin in the complex plane and deduce the irreducibility over the ring of…

We consider bivariate polynomials orthogonal on the bicircle with respect to a positive linear functional. The lexicographical and reverse lexicographical orderings are used to order the monomials. Recurrence formulas are derived between…

We extend to several variables an earlier result of ours, according to which an entire function of one variable of sufficiently small exponential type, having all derivatives of even order taking integer values at two points, is a…

Power nonnegative matrices are defined as complex matrices having at least one nonnegative integer power. We exploit the possibility of deriving a Perron Frobenius-like theory for these matrices, obtaining three main results and drawing…

In a companion paper [On semiclassical orthogonal polynomials via polynomial mappings, J. Math. Anal. Appl. (2017)] we proved that the semiclassical class of orthogonal polynomials is stable under polynomial transformations. In this work we…

For matrices with all nonnegative entries, the Perron-Frobenius theorem guarantees the existence of an eigenvector with all nonnegative components. We show that the existence of such an eigenvector is also guaranteed for a very different…

We introduce an expressive subclass of non-negative almost submodular set functions, called strongly 2-coverage functions which include coverage and (sums of) matroid rank functions, and prove that the homogenization of the generating…

The matching polynomial of a graph is the generating function of the numbers of its matchings with respect to their cardinality. A graph polynomial is polynomial reconstructible, if its value for a graph can be determined from its values…

Let $p$ be a multilinear polynomial in several non-commuting variables with coefficients in a quadratically closed field $K$ of any characteristic. It has been conjectured that for any $n$, the image of $p$ evaluated on the set $M_n(K)$ of…