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Research & Reviews:

Discrete Mathematical Structures Jan - April 2014

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I take the privilege to present the print version for the [Volume 1 Issue (1)] of Research & Reviews: Discrete Mathematical Structures. The intension of RRDMS is to create an atmosphere that stimulates creativeness, research and growth in the area of Discrete Mathematical Structures. The development and growth of the mankind is the consequence of brilliant Research done by eminent Scientists and Engineers in every field. RRDMS provides an outlet for Research findings and reviews in areas of Discrete Mathematical Structures found to be relevant for National and International recent developments & research initiative. The aim and scope of the Journal is to provide an academic medium and an important reference for the advancement and dissemination of Research results that support high level learning, teaching and research in the domain of Discrete Mathematical Structures. Finally, I express my sincere gratitude and thanks to our Editorial/ Reviewer board and Authors for their continued support and invaluable contributions and suggestions in the form of authoring write ups/ reviewing and providing constructive comments for the advancement of the journals. With regards to their due continuous support and co-operation, we have been able to publish quality Research/Reviews findings for our customers base. I hope you will enjoy reading this issue and we welcome your feedback on any aspect of the Journal.

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Research & Reviews: Discrete Mathematical Structures

Contents

1. A New Approach to Find Non-simple Zero's of Functions Mohsen Jamali, Mehdi Delkhosh

2. Mass Transfer Process between the Fluid Flow and an Active Cylinder in Cross Flow J.M.P.Q. Delgado, M. Vázquez da Silva

3. On the Formula for Distribution of Prime Numbers Lukasz Andrzej Glinka

4. A Mathematical Approach to Represent Uncertain Data using Evidence and Possibility Theory Madhavi Kolukuluri, P. E. S. N. Krishna Prasad, B. D. C. N. Prasad

5. On The Pell Polynomýals Pn(x,s,q) and Tridiogonal Matrix Inci Gültekin, Yasemin Tasyurdu

Research & Reviews: Discrete Mathematical Structures Volume 1, Issue 1 www.stmjournals.com

A New Approach to Find Non-simple Zeroâ&#x20AC;&#x2122;s of Functions Mohsen Jamali1, Mehdi Delkhosh2* Islamic Azad University, Bardaskan Branch, Department of Mathematics, Bardaskan, Iran

Abstract Finding acceptable approximation of zeros of even multiplicity of functions by the prevalent method of numerical analysis is impossible or difficult. In this paper we introduce the Intersecting Lines Method and its modified version applying to approximate zeros of even multiplicity of functions. We apply this method to approximate relative extremum points of differentiable functions.

Keywords: Convex function, zero of even multiplicity of function, Newton-Raphson method, relative extrema of function.

Research & Reviews: Discrete Mathematical Structures Volume 1, Issue 1 www.stmjournals.com

Mass Transfer Process between the Fluid Flow and an Active Cylinder in Cross Flow J.M.P.Q. Delgado1*, M. Vázquez da Silva2,3 LFC – Laboratory of Building Physics, Civil Engineering Department, Faculdade de Engenharia da Universidade do Porto, Rua Dr. Roberto Frias, s/n, 4200-465 Porto, Portugal 2 Instituto Universitário da Maia - ISMAI, Av. Carlos Oliveira Campos, Castelo da Maia, Portugal 3 CEFT – Centro de Estudos de Fenómenos de Transporte, Faculdade de Engenharia, Universidade do Porto, Rua Dr. Roberto Frias, s/n, 4200-465 Porto, Portugal 1

Abstract This paper presents a theoretical and numerical analysis applies to a cylinder in cross flow that is large in comparison with the inert particles, so that the bed may be treated as a continuum. Fluid flow in the packed bed around the cylinder in cross flow was assumed to follow Darcy’s law and the partial differential equation (PDE), resulting from a differential material balance on the solute, was analysed numerically over a large range of the relevant hydrodynamic and geometrical parameters, in order to obtain the concentration field near the soluble surface. A mathematical expression is proposed to describing the dependence between the value of the Sherwood number and the relevant variables analysed, numerically. This expression obtained is very useful for different physical situations of practical interest, such as to estimate the concentration contour plots or the contaminant distance given by the “continuous point source” solution for two-dimensional solute transport.

Keywords: Mass transfer, diffusion, packed bed, numerical analyses, cylinder in cross flow *Author for Correspondence E-mail

jdelgado@fe.up.pt; mvazquez@fe.up.pt

Research & Reviews: Discrete Mathematical Structures Volume 1, Issue 1 www.stmjournals.com

On the Formula for Distribution of Prime Numbers Lukasz Andrzej Glinka* Science Editor, BSc. Physics, Member at American Research, Institute for Policy Development, Poland

Abstract The detailed derivation of the distribution of prime numbers, the research result originally presented in the 2013’ monograph Study of Analytic Number Theory: Riemann’s Hypothesis and Prime Number Theorem with Addendum on Integer Partitions published with Cam- bridge International Science Publishing, is once again presented in this paper with the purpose to give an insight to unfamiliar authors.

Keywords: analytic number theory, prime numbers, prime-counting function, Riemann e q u a t i o n , distribution of prime numbers, Mellin transforms

Research & Reviews: Discrete Mathematical Structures Volume 1, Issue 1 www.stmjournals.com

A Mathematical Approach to Represent Uncertain Data using Evidence and Possibility Theory Madhavi Kolukuluri1*, P. E. S. N. Krishna Prasad2, B. D. C. N. Prasad3 1 JNTUK University College of Engineering Vizianagaram, India 1,3 Prasad V. Potluri Siddhartha Institute of Technology, Vijayawada, India

Abstract The uncertainty involved in any problem solving situation is a result of some information deficiency. Information may be incomplete, in precise, not fully reliable, and contradictory. In general, the lack of information may result in different types of uncertainty. In this paper we discuss the statistical approach for representing uncertain data using evidence theory and possibility theory and applications to the evidence and possibility approximation problems are briefly presented.

Keywords: Uncertainty, fuzzy measures, evidence theory, belief measure, plausibility measure, possibility measure, necessity measure, dumpsterâ&#x20AC;&#x2122;s combination.

Research & Reviews: Discrete Mathematical Structures Volume 1 Issue 1 www.stmjournals.com

On The Pell Polynomıals Pn(x,s,q) and Tridiogonal Matrix İnci Gültekin*, Yasemin Taşyurdu Department of Mathematics, Faculty of Sciences, the University of Atatürk, Erzurum 25240, Turkey

Abstract In this study, the Polynomial Pn ( x, s, q) in the real variables x and s , called q Pell polynomials and its some properties are investigated. The some formulas for these polynomials are derivated by matrices. Tridiagonal determinant of the matrix is given by the relationship between the Polynomial Pn ( x, s, q) .

Mathematics Subjet Classification: 11B37, 11B39 Keywords: Binet formulas, pell polynomials