Related papers: Complement to algebraic differential equations ...
Polynomials commute under composition are referred to as commuting polynomials. In this paper, we study division properties for commuting polynomials with rational (and integer) coefficients. As a consequence, we show an algebraic…
We give necessary and sufficient existence criteria, and methods for finding, continuous solutions of linear equations whose coefficients are polynomials.
We consider a space of complex polynomials of degree $n\ge 3$ with $n-1$ distinguished periodic orbits. We prove that the multipliers of these periodic orbits considered as algebraic functions on that space, are algebraically independent…
The aim of this paper is to continue the study of asymptotic expansions and summability in a monomial in any number of variables. In particular we characterize these expansions in terms of bounded derivatives and we develop tauberian…
We present an algorithm to solve a system of diagonal polynomial equations over finite fields when the number of variables is greater than some fixed polynomial of the number of equations whose degree depends only on the degree of the…
We explain that in the study of the asymptotic expansion at the origin of a period integral like $\gamma$z $\omega$/df or of a hermitian period like f =s $\rho$.$\omega$/df $\land$ $\omega$ /df the computation of the Bernstein polynomial of…
In this paper, as an analogue of the integer case, we study detailedly the period and the rank of the generalized Fibonacci sequence of polynomials over a finite field modulo an arbitrary polynomial. We establish some formulas to compute…
We give an improved polynomial bound on the complexity of the equation solvability problem, or more generally, of finding the value sets of polynomials over finite nilpotent rings. Our proof depends on a result in additive combinatorics,…
In this paper we study the monomial dynamical systems of dimension one over finite fields from the viewpoints of arithmetic and graph theory. We give formulas for the number of periodic points with period r and cycles with length r. Then we…
We use ideas from our previous work to obtain some theorems that will allow us to obtain the integer solution of a quadratic polynomial in two variables that represents a natural number
The paper represents the method for construction of the families of particular solutions to some new classes of $(n+1)$ dimensional nonlinear Partial Differential Equations (PDE). Method is based on the specific link between algebraic…
Given two quasi-definite moment functionals, the corresponding orthogonal polynomial systems satisfy an algebraic differential relation(called an extended coherent pair). We study generalizing extended coherent pairs that unify extended…
By polynomial (or extended binomial) coefficients, we mean the coefficients in the expansion of integral powers, positive and negative, of the polynomial $1+t +\cdots +t^{m}$; $m\geq 1$ being a fixed integer. We will establish several…
Let $d>m>1$ be integers, let $c_1,\dots, c_{m+1}$ be distinct complex numbers, and let $\mathbf{f}(z):=z^d+t_1z^{m-1}+t_2z^{m-2}+\cdots + t_{m-1}z+t_m$ be an $m$-parameter family of polynomials. We prove that the set of $m$-tuples of…
The linear complete differential resultant of a finite set of linear ordinary differential polynomials is defined. We study the computation by linear complete differential resultants of the implicit equation of a system of $n$ linear…
A general description of the Vi\`ete coefficients of the gaussian period polynomials is given, in terms of certain symmetric representations of the subgroups and the corresponding quotient groups of the multiplicative group…
A general procedure which defines a partial ordering of cyclic permutations induced by continuous maps is known for constructing immediate successors to a cycle. We expound on this procedure in terms of labelled digraphs and characteristic…
In this paper, we consider several special polynomials related to associated sequences of polynomials. Finally, we give some new and interesting identities of those polynomials arising from transfer formula for the associated sequences.
In dimension two, we study complete monomial ideals combinatorially, their Rees algebras and develop effective means to find their defining equations.
In this article, we show that the algebraic degree in semidefinite programming can be expressed in terms of the coefficient of a certain monomial in a doubly symmetric polynomial. This characterization of the algebraic degree allows us to…