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Branko J. Malesevic

Publications and source records attributed to Branko J. Malesevic.

16 recordsLinked to original sources
arXiv2015

Some notes on a method for proving inequalities by computer

In this article we consider mathematical fundamentals of one method for proving inequalities by computer, based on the Remez algorithm. Using the well-known results of undecidability of the existence of zeros of real elementary functions, we demonstrate that the considered method generally in practice becomes one heuristic for the verification of inequalities. We give some improvements of the inequalities considered in the theorems for which the existing proofs have been based on the numerical verifications of Remez algorithm.

math.CA↗
arXiv2013

A Computer Verification of a Conjecture About Erdös-Mordell Curve

In this paper we consider Erdös-Mordell inequality and its extension in the plane of triangle to the Erdös-Mordell curve. Algebraic equation of this curve is derived, and using modern computer tools in mathematics, we verified one conjecture that relates to Erdös-Mordell curve.

math.MG↗
arXiv2013

A note on solutions of the matrix equation AXB=C

This paper deals with necessary and sufficient condition for consistency of the matrix equation $AXB = C$. We will be concerned with the minimal number of free parameters in Penrose's formula $X = A^(1)CB^(1) + Y - A^(1)AYBB^(1)$ for obtaining the general solution of the matrix equation and we will establish the relation between the minimal number of free parameters and the ranks of the matrices A and B. The solution is described in the terms of Rohde's general form of the {1}-inverse of the matrices A and B. We will also use Kronecker product to transform the matrix equation $AXB = C$ into the linear system $(B^T \otimes A)vecX = vec C$.

math.RA↗
arXiv2010

Groebner bases in Java with applications in computer graphics

In this paper we present a Java implementation of the algorithm that computes Buchbereger's and reduced Groebner's basis step by step. The Java application enables graphical representation of the intersection of two surfaces in 3-dimensional space and determines conditions of existence and planarity of the intersection.

cs.MS↗
arXiv2008

Some considerations in connection with alternating Kurepa's function

In this paper we consider the functional equation for alternating factorial sum and some of its particular solutions (alternating Kurepa's function $A(z)$ from [Petojevic_02] and function $A_{1}(z)$). We determine an extension of domain of functions $A(z)$ and $A_{1}(z)$ in the sense of the principal value at point [Slavic_73], [Mijajlovic & Malesevic_07]. Using the methods from [Slavic_73] and [Malesevic_03] we give a new representation of alternating Kurepa's function $A(z)$, which is an analog of Slavi\' c's representation of Kurepa's function $K(z)$ [Slavic_73], [Marichev_83]. Also, we consider some representations of functions $A(z)$ and $A_{1}(z)$ via incomplete gamma function and we consider differential transcendency of previous functions too.

math.NT↗
arXiv2007

A Note About the {Ki(z)} Functions

In the article [Petojevic 2006], A. Petojevi\' c verified useful properties of the $K_{i}(z)$ functions which generalize Kurepa's [Kurepa 1971] left factorial function. In this note, we present simplified proofs of two of these results and we answer the open question stated in [Petojevic 2006]. Finally, we discuss the differential transcendency of the $K_{i}(z)$ functions.

math.NT↗
arXiv2006

One method for proving inequalities by computer

In this article we consider a method for proving a class of analytical inequalities via minimax rational approximations. All numerical calculations in this paper are given by Maple computer program.

math.CA↗
arXiv2004

The Mobius-Pompeiu metric property

In the paper we consider an extension of Mobius-Pompeiu theorem of the elementary geometry over metric spaces. We specially take into consideration Ptolemaic metric spaces.

math.MG↗
arXiv2004

Some combinatorial aspects of composition of a set of functions

In this paper we determine a number of meaningful compositions of higher order of a set of functions, which is considered in Malesevic (1998), in implicit and explicit form. Results which are obtained are applied to the vector analysis in order to determine the number of meaningful differential operations of higher order.

math.CO↗
arXiv2004

Some considerations in connection with Kurepa's function

In this paper we consider the functional equation for factorial sum and its particular solutions (Kurepa's function $K(z)$ \cite{Kurepa_71} and function $K_{1}(z)$). We determine an extension of domain of functions $K(z)$ and $K_{1}(z)$ in the sense of Cauchy's principal value at point \cite{Slavic_70}. In this paper we give an addendum to the proof of Slavi\' c's representation of Kurepa's function $K(z)$ \cite{Slavic_73}. Also, we consider some representations of functions $K(z)$ and $K_{1}(z)$ via incomplete gamma function and we consider differential transcendency of previous functions too.

math.NT↗