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There are different approaches to qualitative probability, which includes subjective probability. We developed a representation of qualitative probability based on relational systems, which allows modeling uncertainty by probability…
We simplify the proof of some widely used theoretical theorems, extending their applicability, while correcting some erroneous results. We also generalize key results and present new results that contribute to the development of the theory.…
We prove a generalization of classical Montel's theorem for the mixed differences case, for polynomials and exponential polynomial functions, in commutative setting.
Functional equations satisfied by additive functions have a special interest not only in the theory of functional equations, but also in the theory of (commutative) algebra because the fundamental notions such as derivations and…
We describe a method to evaluate multivariate polynomials over a finite field and discuss its multiplicative complexity.
The bifurcation sets of polynomial functions have been studied by many mathematicians from various points of view. In particular, N\'emethi and Zaharia described them in terms of Newton polytopes. In this paper, we will show analogous…
We characterize left and right amenable semigroups of polynomials of one complex variable with respect to the composition operation. We also prove a number of results about amenable semigroups of arbitrary rational functions. In particular,…
We show that two natural definitions of the relative pressure function for a locally constant potential function and a factor map from a shift of finite type coincide almost everywhere with respect to every invariant measure. With a…
We present various properties of algebraic potentials, and then prove that some Morales-Ramis theorems readily apply for such potentials even if they are not in general meromorphic potentials. This allows in particular to precise some…
In the probability theory \emph{selfdecomposable, or class $L_0$ distributions} play an important role as they are limiting distributions of normalized partial sums of sequences of independent, not necessarily identically distributed,…
We study a generalization of the discriminant of a polynomial, which we call the tolerant. The tolerant differs by multiplication by a square from the duplicant, which was discovered in recent work on $\mathbb{P}^1$-loop spaces in motivic…
Expanding upon recent work, a new class of $A$-functions is introduced that can be viewed as an appropriate generalization of the class of regular $A$-functions, the class of structured $A$-functions, and the class of perfect $A$-functions.…
We give the cumulative distribution functions, the expected values, and the moments of weighted lattice polynomials when regarded as real functions of independent random variables. Since weighted lattice polynomial functions include…
We show that given a suitable but essentially arbitrary function Q(x,t,h) there are "generalized" quantum theories having Q as a quantum potential.
In this survey, different aspects of the theory of orthogonal polynomials of one (real or complex) variable are reviewed. Orthogonal polynomials on the unit circle are not discussed.
The necessity of computing integrals with complex weights over manifolds with a large number of dimensions, e.g., in some field theoretical settings, poses a problem for the use of Monte Carlo techniques. Here it is shown that very general…
Probabilistic algorithms are applied to prove theorems about the finite general linear and unitary groups which are typically proved by techniques such as character theory and Moebius inversion. Among the theorems studied are Steinberg's…
In this article, we study several probabilistic properties of polynomials defined over the ring of $p$-adic integers under the Haar measure. First, we calculate the probability that a monic polynomial is separable, generalizing a result of…
Generalizations of some known results on the best, best linear and best one-sided approxima- tions by trigonometric polynomials of the classes of 2\pi - periodic functions presented in the form of convolutions to the case of set-valued…
The theory of Touchard polynomials is generalized using a method based on the definition of exponential operators, which extend the notion of the shift operator. The proposed technique, along with the use of the relevant operational…