相关论文: On some sufficient conditions of strong uniqueness…
The theory of strong uniqueness polynomials, satisfying the separation condition (first introduced by Fujimoto \cite{Fuj1}), for complex meromorphic functions is quite complete. We construct examples of strong uniqueness polynomials which…
We consider the problem of finding a condition for a univariate polynomial having a given multiplicity structure when the number of distinct roots is given. It is well known that such conditions can be written as conjunctions of several…
Let F be a homogeneous real polynomial of even degree in any number of variables. We consider the problem of giving explicit conditions on the coefficients so that F is positive definite or positive semi-definite. In this note we produce a…
We give necessary conditions satisfied by the set of odd prime divisors of binary perfect polynomials. This allows us to get a new characterization of all the known perfect binary polynomials.
In this article, we prove some factorization results for several classes of polynomials having integer coefficients, which in particular yield several classes of irreducible polynomials. Such classes of polynomials are devised by imposing…
The problem "A general characterization of uniqueness polynomial for non-critically injective polynomials" has been remained open since the last two decades. In this paper, we explore this open problem. To this end, we initiate a new…
We give necessary and sufficient existence criteria, and methods for finding, continuous solutions of linear equations whose coefficients are polynomials.
We consider systems of ordinary differential equations with quadratic homogeneous right hand side. We give a new simple proof of a result already obtained in [8,10] which gives the necessary conditions for the existence of polynomial first…
Condition numbers of random polynomial systems have been widely studied in the literature under certain coefficient ensembles of invariant type. In this note we introduce a method that allows us to study these numbers for a broad family of…
Using polynomial evaluation, we give some useful criteria to answer questions about divisibility of polynomials. This allows us to develop interesting results concerning the prime elements in the domain of coefficients. In particular, it is…
A recently-established necessary condition for polynomials that preserve the class of entrywise nonnegative matrices of a fixed order is shown to be necessary and sufficient for the class of nonnegative monomial matrices. Along the way, we…
We evaluate the number of monic polynomials (of arbitrary degree $N$) the zeros of which equal their coefficients when these are allowed to take arbitrary complex values. In the following, we call polynomials with this property {\em…
We obtain explicit upper bounds for the number of irreducible factors for a class of compositions of polynomials in several variables over a given field. In particular, some irreducibility criteria are given for this class of compositions…
This paper gives a necessary and sufficient condition for robust D-stability of Polytopic Polynomial Matrices. Edge theorem is extended to multi-input-multi-output case.
Linear differential equations of arbitrary order with polynomial coefficients are considered. Specifically, necessary and sufficient conditions for the existence of polynomial solutions of a given degree are obtained for these equations. An…
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 identify new sufficiency conditions for coercivity of general multivariate polynomials $f\in\mathbb{R}[x]$ which are expressed in terms of their Newton polytopes at infinity and which consist of a system of affine-linear inequalities in…
We prove that the Eulerian polynomial satisfies certain polynomial congruences. Furthermore, these congruences characterize the Eulerian polynomial.
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…
We consider polynomials of bi-degree $(n,1)$ over the skew field of quaternions where the indeterminates commute with each other and with all coefficients. Polynomials of this type do not generally admit factorizations. We recall a…