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Branko Malesevic

Publications and source records attributed to Branko Malesevic.

At least 37 records · Page 2Linked to original sources
arXiv2017

The natural algorithmic approach of mixed trigonometric-polynomial problems

The aim of this paper is to present a new algorithm for proving mixed trigonometric-polynomial inequalities by reducing to polynomial inequalities. Finally, we show the great applicability of this algorithm and as examples, we use it to analyze some new rational (Pade) approximations of the function $\cos^2(x)$, and to improve a class of inequalities by Z.-H. Yang. The results of our analysis could be implemented by means of an automated proof assistant, so our work is a contribution to the library of automatic support tools for proving various analytic inequalities.

math.CA↗
arXiv2016

A proof of an open problem of Yusuke Nishizawa for a power-exponential function

This paper presents a proof of the following conjecture, stated by Nishizawa in [Appl. Math. Comput. 269, (2015), 146--154.]: for $\displaystyle 0 \! \left(\frac{2}π + \frac{π\!-\!2}{π^{3}}(π^{2}\!-\!4x^{2})\right)^{θ(x)}\! $ holds, where $\displaystyle θ(x) \! = \! -\frac{(48\!-\!24π\!+\!π^{3})x^{3} }{3(π\!-\!2)π^{3}}+\frac{π^{3}}{24(π\!-\!2)}.$

math.CA↗
arXiv2015

Accurate approximations of some expressions involving trigonometric functions

The aim of this paper is to apply an original computation method due to Malesevic and Makragic [5] to the problem of approximating some trigonometric functions. Inequalities of Wilker-Cusa-Huygens are discussed, but the method can be successfully applied to a wide class of problems. In particular, we improve the estimates recently obtained by Mortici [1] and moreover we show that they hold true also on some extended intervals.

math.CA↗
arXiv2015

Visualization in teaching and learning mathematics in elementary, secondary and higher education

In this paper we present our experience in using visualization in mathematics education. The experience with our university courses: "Computer tools in matematics" and "Symbolic algebra" provides the basis for mathematics teacher education program http://vizuelizacija.etf.rs/. The program is intended for elementary and high school teachers. The education program deals with modern techniques of visualization by using technologies such as GeoGegebra, JAVA and HTML.

cs.CY↗
arXiv2015

A Method of Proving a Class of Inequalities of Mixed Trigonometric Polynomial Functions

In this article we consider a method of proving a class of inequalities of the form (1). The method is based on the precise approximations of the sine and cosine functions by Maclaurin polynomials of given order. By using this method we present new proofs of some inequalities from the articles C.-P. Chen, W.-S. Cheung [J. Inequal. Appl. 2012:72 (2012)] and Z.-J. Sun, L. Zhu [ISRN Math. Anal. (2011)].

math.CA↗
arXiv2015

Block representations of generalized inverses of matrices

In this paper will be considered standard forms of generalized inverses for matrices in the shape of block representations {1, 2, 3, 4, 5, 5^k}-inverse. Especially will be considered Moore-Penrose inverse and the group inverse. Results from Rhode's technique are used and methods for calculating some inverse are shown on examples.

math.RA↗
arXiv2015

A Note on the Reduction Formulas for Some Systems of Linear Operator Equations

We consider partial and total reduction of a nonhomogeneous linear system of the operator equations with the system matrix in the same particular form as in paper [N. Shayanfar, M. Hadizadeh 2013]. Here we present two different concepts. One is concerned with partially reduced systems obtained by using the Jordan and the rational form of the system matrix. The other one is dealing with totally reduced systems obtained by finding the adjugate matrix of the characteristic matrix of the system matrix.

math.SP↗
arXiv2014

On the Extension of the Erdos-Mordell Type Inequalities

We discuss the extension of inequality R_A >= c/a * r_b + b/a * r_c to the plane of triangle ABC. Based on the obtained extension, in regard to all three vertices of the triangle, we get the extension of Erdos-Mordell inequality, and some inequalities of Erdos-Mordell type.

math.MG↗
arXiv2014

Geometry of some taxicab curves

In this paper we present geometry of some curves in Taxicab metric. All curves of second order and trifocal ellipse in this metric are presented. Area and perimeter of some curves are also defined.

math.HO↗
arXiv2014

The Geometry of Trifocal Curves with Applications in Architecture, Urban and Spatial Planning

In this paper we consider historical genesis of trifocal curve as an optimal curve for solving the Fermat's problem (minimizing the sum of distance of one point to three given points in the plane). Trifocal curves are basic plane geometric forms which appear in location problems. We also analyze algebraic equation of these curves and some of their applications in architecture, urbanism and spatial planning. The area and perimeter of trifocal curves are calculated using a Java application. The Java applet is developed for determining numerical value for the Fermat-Torricelli-Weber point and optimal curve with three foci, when starting points are given on an urban map. We also present an application of trifocal curves through the analysis of one specific solution in South Stream gas pipeline project.

math.HO↗
arXiv2013

A note on solutions of linear systems

In this paper we will consider Rohde's general form of {1}-inverse of a matrix A. The necessary and sufficient condition for consistency of a linear system Ax=c will be represented. We will also be concerned with the minimal number of free parameters in Penrose's formula x = A^(1) c + (I - A^(1)A)y for obtaining the general solution of the linear system. This results will be applied for finding the general solution of various homogenous and non-homogenous linear systems as well as for different types of matrix equations.

math.RA↗
arXiv2012

Some considerations in relation to the matrix equation AXB=C

In this paper we represent a new form of condition for the consistency of the matrix equation AXB=C. If the matrix equation AXB=C is consistent, we determine a form of general solution which contains both reproductive and non-reproductive solutions. Also, we consider applications of the concept of reproductivity for obtaining general solutions of some matrix systems which are in relation to the matrix equation AXB=C.

math.RA↗