Local polynomials are polynomials

Some Families of Graphs whose Domination Polynomials are Unimodal

Let $G$ be a simple graph of order $n$. The domination polynomial of $G$ is the polynomial $D(G, x)=sum_{i=gamma(G)}^{n} d(G,i) x^{i}$, where $d(G,i)$ is the number of dominating sets of $G$ of size $i$ and $gamma(G)$ is the domination number of $G$. In this paper we present some families of graphs whose domination polynomials are unimodal.

Cariñena Orthogonal Polynomials Are Jacobi Polynomials

The relativistic Hermite polynomials (RHP) were introduced in 1991 by Aldaya et al. [3] in a generalization of the theory of the quantum harmonic oscillator to the relativistic context. These polynomials were later related to the more classical Gegenbauer (or more generally Jacobi) polynomials in a study by Nagel [4]. For this reason, they do not deserve any special study since their properties...

Local behaviour of polynomials

In this paper we study the local behaviour of a trigonometric polynomial t(θ) := ∑n ν=−n aν e iνθ around any of its zeros in terms of its estimated values at an adequate number of freely chosen points in [0 , 2π). The freedom in the choice of sample points makes our results particularly convenient for numerical calculations. Analogous results for polynomials of the form ∑n ν=0 aν x ν are also p...

Local Derivatives and Bernstein Polynomials

We introduce the local derivatives of a Weyl algebra and prove a theorem of I. N. Bernstein concerning the existence of certain polynomials relating to the action of local derivatives.

Factoring Polynomials over Local Fields