Related papers: A classification of barycentrically associative po…
We characterise piecewise Boolean domains, that is, those domains that arise as Boolean subalgebras of a piecewise Boolean algebra. This leads to equivalent descriptions of the category of piecewise Boolean algebras: either as piecewise…
Extension problems for polynomial valuations on different cones of convex functions are investigated. It is shown that for the classes of functions under consideration, the extension problem reduces to a simple geometric obstruction on the…
The paper studies constructions of irreducible polynomials over finite fields using polynomial composition method.
In this work we develop a novel recursive method for parametrizing the cone of copositive univariate polynomials of any arbitrary degree $d$. This parametrization is surjective, almost injective, and has the easily described domain of…
A new class of alternating convolutions concerning binomial coefficients and Catalan numbers are evaluated in closed forms.
The present note considers a certain family of sums indexed by the set of fixed length compositions of a given number. The sums in question cannot be realized as weighted compositions. However they can be be related to the hypergeometric…
We define an enumerative function F(n,k,P,m) which is a generalization of binomial coefficients. Special cases of this function are also power function, factorials, rising factorials and falling factorials. The first section of the paper is…
Hypercomplex numbers are unital algebras over the real numbers. We offer a short demonstration of the practical value of hypercomplex analytic functions in the field of partial differential equations.
In this paper we present algorithmic considerations and theoretical results about the relation between the orders of certain groups associated to the components of a polynomial and the order of the group that corresponds to the polynomial,…
We show that single-variable polynomial functors over the category $\mathcal{S}$ of infinity groupoids, as defined by Gepner-Haugseng-Kock, are exactly colimits of representable copresheaves indexed by infinity groupoid. This allows us to…
Motivated by existing results, we present some completely monotonic functions involving the polygamma functions.
We study the class of those linear relations that can be factorized as products of idempotent relations. We provide several characterizations of this class, extending known factorization results for operators to the more general setting of…
In this paper, we study the approximation of negative plurifinely plurisubharmonic function defined on a plurifinely domain by an increasing sequence of plurisubharmonic functions defined in Euclidean domains.
In the present work we explore relationships between multiplicative functions defined in \cite{Garonzi_2018}, \cite{Lazorec}. To do so, we use other important quotients defined and studied in \cite{ndeg}, \cite{Marius}, thus establishing…
We define a convenient $\infty$-operad parametrizing modules over commutative algebras in $\infty$-categories.
In this paper, approximation by means of algebraic polynomials of classes of functions defined by a generalised modulus of smoothness of operators of differentiation of these functions is considered. We give structural characteristics of…
We formulate several polynomial identities. One side of these identities has a nice simple form. Whereas the other has a form of a polynomial whose coefficients contain binomial coefficients double factorials or (and) rising factorials. The…
A classification is provided of functors, in particular polynomial ones, from a category with a zero object in which every object is a finite sum of copies of a generating object, into an abelian category. This classification is extended to…
We prove that certain quotients of entire functions are characteristic functions. Under some conditions, the probability measure corresponding to a characteristic function of that type has a density which can be expressed as a generalized…
An analytical approach to convolution of functions, which appear in perturbative calculations, is discussed. An extended list of integrals is presented.