Related papers: Polynomial Divided Difference Operators Satisfying…
Banded bounded matrices, which represent non normal operators, of oscillatory type that admit a positive bidiagonal factorization are considered. To motivate the relevance of the oscillatory character the Favard theorem for Jacobi matrices…
General approach to the multiplication or adjoint operation of $2\times 2$ block operator matrices with unbounded entries are founded. Furthermore, criteria for self-adjointness of block operator matrices based on their entry operators are…
The aim of this paper is to bring into the picture a new phenomenon in the theory of orthogonal matrix polynomials satisfying second order differential equations. The last few years have witnessed some examples of a (fixed) family of…
We consider the following practical question: given a finite algebra A in a finite language, can we efficiently decide whether the variety generated by A has a difference term? We answer this question (positively) in the idempotent case and…
Mixed distributions are considered as a results of application of a linear operator, which maps mixing measures to mixed measures. The main result is a proof of continuity of this mixing operator. Corollaries for parametric families of…
In this paper, we introduce a new family of symmetric polynomials which depends on a parameter r. They are defined by specifying certain of their zeros. For the parameter values 1/2, 1, and 2 they have an interpretation in terms of Capelli…
In the first part of this note, we review and compare various instances of the notion of twisted coefficient system, a.k.a. polynomial functor, appearing in the literature. This notion hinges on how one defines the degree of a functor from…
We study multiple orthogonal polynomials exploiting their explicit determinantal representation in terms of moments. Our reasoning follows that applied to solve the Hermite-Pad\'{e} approximation and interpolation problems. We study also…
In this paper, six constructions of difference families are presented. These constructions make use of difference sets, almost difference sets and disjoint difference families, and give new point of views of relationships among these…
For permutations $v,w \in \mathfrak S_n$, Macdonald defines the skew divided difference operators $\partial_{w/v}$ as the unique linear operators satisfying $\partial_w(PQ) = \sum_v v(\partial_{w/v}P) \cdot \partial_vQ$ for all polynomials…
New concept of conditional differential invariant is discussed that would allow description of equations invariant with respect to an operator under a certain condition. Example of conditional invariants of the projective operator is…
We consider a class of optimization problems that involve determining the maximum value that a function in a particular class can attain subject to a collection of difference constraints. We show that a particular linear programming…
We have been working in many aspects of the problem of analyzing, understanding and solving ordinary differential equations (first and second order). As we have extensively mentioned, while working in the Darboux type methods, the most…
Permutation polynomials with explicit constructions over finite fields have long been a topic of great interest in number theory. In recent years, by applying linear translators of functions from $\mathbb{F}_{q^n}$ to $\mathbb{F}_q$, many…
We raise some questions about graph polynomials, highlighting concepts and phenomena that may merit consideration in the development of a general theory. Our questions are mainly of three types: When do graph polynomials have reduction…
We introduce new concepts in order to develop a general formalism for twisted differential operators in several variables. We investigate the notion of twisted coordinates on Huber rings that allows us to build various rings of twisted…
We study the theoretical and practical aspects of computing braids described by approximate descriptions of paths in the plane. Exact algorithms rely on the lexicographic ordering of the points in the plane, which is unstable under…
Necessary and sufficient conditions under which two real functions defined on the real interval can be separated by a polynomial are given. An immediate consequence of the main result is the existence of the polynomial separation of convex…
As a generalization of the classical knots, knotoids deal with the open ended knot diagrams in a surface. In recent years, many polynomial invariants for knotoids have appeared, such as the bracket polynomial, the index polynomial and the…
The properties of the Pastro polynomials on the real line are studied with the help of a triplet of $q$-difference operators. The $q$-difference equation and recurrence relation these polynomials obey are shown to arise as generalized…