arXiv subjects

Zarko Mijajlovic

Publications and source records attributed to Zarko Mijajlovic.

5 recordsLinked to original sources

arXiv2013

Computing finite models using free Boolean generators

A parallel method for computing Boolean expressions based on the properties of finite free Boolean algebras is presented. We also show how various finite combinatorial objects can be codded in the formalism of Boolean algebras and counted by this procedure. Particularly, using a translation of first order predicate formulas to propositional formulas, we give a method for constructing and counting finite models of the first order theories. An implementation of the method that can be run on multi-core CPUs as well as on highly parallel GPUs is outlined.

cs.LO↗

arXiv2008

Differentially Transcendental Functions

The aim of this paper is to exhibit a method for proving that certain analytic functions are not solutions of algebraic differential equations. The method is based on model-theoretic properties of differential fields and properties of certain known transcendental differential functions, as of $Γ(x)$. Furthermore, it also determines differential transcendency of solution of some functional equations.

math.GM↗

arXiv2008

Analytical and differential - algebraic properties of Gamma function

In this paper we consider some analytical relations between gamma function $Γ(z)$ and related functions such as the Kurepa's function $K(z)$ and alternating Kurepa's function $A(z)$. It is well-known in the physics that the Casimir energy is defined by the principal part of the Riemann function $ζ(z)$ (Blau, Visser, Wipf; Elizalde). Analogously, we consider the principal parts for functions $Γ(z)$, $K(z)$, $A(z)$ and we also define and consider the principal part for arbitrary meromorphic functions. Next, in this paper we consider some differential-algebraic $($d.a.$)$ properties of functions $Γ(z)$, $ζ(z)$, $K(z)$, $A(z)$. As it is well-known (H\" older; Ostrowski) $Γ(z)$ is not a solution of any d.a. equation. It appears that this property of $Γ(z)$ is universal. Namely, a large class of solutions of functional differential equations also has that property. Proof of these facts is reduced, by the use of the theory of differential algebraic fields (Ritt; Kaplansky; Kolchin), to the d.a. transcendency of $Γ(z)$.

math.GM↗

arXiv2006

Sums of Like Powers and Some Dense Sets

In this paper we introduce the notion of the $P$-sequences and apply their properties in studying representability of real numbers. Another application of $P$-sequences we find in generating the Prouhet-Tarry-Escott pairs.

math.NT↗

arXiv2005

Some Properties of Posynomial Rings

In this article we shall study some basic properties of posynomial rings with particular emphasis on rings ${\rm Pos}(K,\mathbb{Q})[\bar x]$, and ${\rm Pos}(K,\mathbb{Z})[\bar x]$. The latter ring is the well known ring of Laurent polynomials.

math.AC↗