Related papers: Potential theory and a characterization of polynom…
We give a criterion which characterizes a homogeneous real multi-variate polynomial to have the property that all sufficiently large powers of the polynomial (as well as their products with any given positive homogeneous polynomial) have…
We explain the exact meaning of a statement we made in a previous paper on invariants, namely that a complex-valued function of the data of the functional equation of an $L$-function is an invariant if and only if it is stable under the…
In this paper we suggest new classification of polynomials and evolution equations for the roots and the coefficients remaing the polynomials within proper class. In the basis of the developed evolution equations we built new dynamics…
We use double categories to obtain a single theorem characterizing certain exponentiable morphisms of small categories, topological spaces, locales, and posets.
Our aim is to explain instances in which the value of the logarithmic Mahler measure of a polynomial can be written in an unexpectedly neat manner. To this end we examine polynomials defining rational curves, which allows their zero-locus…
It is well known, from Newtonian physics, that apparent forces appear when the motion of masses is described by using a non-inertial frame of reference. The generalized potential of such forces is rigorously analyzed focusing on their…
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…
Brief Description: The book provides a unique highly self-contained text introducing the reader to the classical and modern theory of polyanalytic functions and their generalizations. This is a subbranch of complex analysis of several…
We reveal a natural algebraic problem whose complexity appears to interpolate between the well-known complexity classes BQP and NP: (*) Decide whether a univariate polynomial with exactly m monomial terms has a p-adic rational root. In…
The paper deals with different properties of polynomials in random elements: bounds for characteristics functionals of polynomials, stochastic generalization of the Vinogradov mean value theorem, characterization problem, bounds for…
We develop an extension of valuations theorem for suitable extensions of idempotent semirings. As an application, we give a new proof for the classical case of fields. Along the way, we develop characteristic one analogues of some central…
Polynomial interpretations are a useful technique for proving termination of term rewrite systems. They come in various flavors: polynomial interpretations with real, rational and integer coefficients. As to their relationship with respect…
We study monic univariate polynomials whose coefficients are analytic functions of a real variable and whose roots lie in a specified analytic curve. These include characteristic polynomials of unitary and hermitian matrices whose entries…
Polynomials are common algebraic structures, which are often used to approximate functions including probability distributions. This paper proposes to directly define polynomial distributions in order to describe stochastic properties of…
Supertropical matrix theory was investigated in [6], whose terminology we follow. In this work we investigate eigenvalues, characteristic polynomials and coefficients of characteristic polynomials of supertropical matrices and their powers,…
The Euclidean algorithm makes possible a simple but powerful generalization of Taylor's theorem. Instead of expanding a function in a series around a single point, one spreads out the spectrum to include any number of points with given…
We present the model theoretic concepts that allow mathematics to be developed with the notion of the potential infinite instead of the actual infinite. The potential infinite is understood as a dynamic notion, being an indefinitely…
Techniques for the evaluation of complex polynomials with one and two variables are introduced. Polynomials arise in may areas such as control systems, image and signal processing, coding theory, electrical networks, etc., and their…
We examine connections between rationality of certain indefinite integrals and equilibrium of Coulomb charges in the complex plane.
The problem of separation of variables in some coordinate systems obtained with the use of $L$-transformations is studied. Potentials are shown that allow separation of regular variables in a perturbed two-body problem. The potential…