Related papers: On Monomial Deformations of Generalized Delsarte P…
The polynomial algebra is a deformed SU(2) algebra. Here, we use polynomial algebra as a method to solve a series of deformed oscillators. Meanwhile, we find a series of physics systems corresponding with polynomial algebra with different…
In this paper, we consider the problem of representing any polynomial in terms of the degenerate Bernoulli polynomials and more generally of the higher-order degenerate Bernoulli polynomials. We derive explicit formulas with the help of…
Based on the theory of Dunkl operators, this paper presents a general concept of multivariable Hermite polynomials and Hermite functions which are associated with finite reflection groups on $\b R^N$. The definition and properties of these…
A brief survey of the theory of soliton perturbations is presented. The focus is on the usefulness of the so-called Generalised Fourier Transform (GFT). This is a method that involves expansions over the complete basis of `squared olutions`…
We study a class of bivariate deformed Hermite polynomials and some of their properties using classical analytic techniques and the Wigner map. We also prove the positivity of certain determinants formed by the deformed polynomials. Along…
Generic Newton polygons for L-functions of exponential sums associated to Laurent polynomials in one variable are determined. The corresponding Hasse polynomials are also determined.
We study the umbral "classical" orthogonal polynomials with respect to a generalized derivative operator $\cal D$ which acts on monomials as ${\cal D} x^n = \mu_n x^{n-1}$ with some coefficients $\mu_n$. Let $P_n(x)$ be a set of orthogonal…
In the present paper we derive complicated families of orthogonal polynomials in one variable from scratch using the known ones as building blocks. We recall the basics of operational formalism and introduce the notations we use throughout…
In this paper, we establish the decomposition of morphisms from lattice of subgroup sets to generalized solvable extension formations. To achieve this, we develop a unified framework involving maximal subgroup functors, generating formation…
In this paper, we show that for each $n\geq 1$, the generalised Hermite-Laguerre Polynomials $G_{\frac{1}{4}}$ and $G_{\frac{3}{4}}$ are either irreducible or linear polynomial times an irreducible polynomial of degree $n-1$.
We obtain deformations of a crossed product of a polynomial algebra with a group, under some conditions, from universal deformation formulas. We show that the resulting deformations are nontrivial by a comparison with Hochschild cohomology.…
We study the roots of the generalised Hermite polynomials $H_{m,n}$ when both $m$ and $n$ are large. We prove that the roots, when appropriately rescaled, densely fill a bounded quadrilateral region, called the elliptic region, and organise…
We define two new families of polynomials that generalize permanents and prove upper and lower bounds on their determinantal complexities comparable to the known bounds for permanents. One of these families is obtained by replacing…
Let $\mathcal F$ be either the set of all bounded holomorphic functions or the set of all $m$-homogeneous polynomials on the unit ball of $\ell\_r$. We give a systematic study of the sets of all $u\in\ell\_r$ for which the monomial…
We investigate which polynomials can possibly occur as factors in the denominators of rational solutions of a given partial linear difference equation (PLDE). Two kinds of polynomials are to be distinguished, we call them /periodic/ and…
Deformations of complex structures by finite Beltrami differentials are considered on general Riemann surfaces. Exact formulas to any fixed order are derived for the corresponding deformations of the period matrix, Green's functions, and…
We give a criterion which characterizes a real multi-variate Laurent polynomial with full-dimensional smooth Newton polytope to have the property that all sufficiently large powers of the polynomial have fully positive coefficients. Here a…
We compute the deformations in the sense of generalized complex structures of the standard classical complex structure on a primary Kodaira surface and we prove that the obtained family of deformations is a smooth locally complete family…
The Tutte polynomial and Derksen's $\mathcal{G}$-invariant are the universal deletion-contraction and valuative matroid and polymatroid invariants, respectively. There are only a handful of well known invariants (like the matroid…
The generalized Maxwell equations including an additional scalar field are considered in the first-order formalism. The gauge invariance of the Lagrangian and equations is broken resulting the appearance of a scalar field. We find the…