Discrete Mathematical Research & Reviews:

Structures

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STM JOURNALS

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

2. Mass Transfer Process between the Fluid Flow and an Active Cylinder in Cross Flow J.M.P.Q. Delgado, M. Vázquez da Silva 6

3. On the Formula for Distribution of Prime NumbersLukasz Andrzej Glinka 16

4. A Mathematical Approach to Represent Uncertain Data using Evidence and Possibility TheoryMadhavi Kolukuluri, P. E. S. N. Krishna Prasad, B. D. C. N. Prasad 20

5. On The Pell Polynomýals Pn(x,s,q) and Tridiogonal Matrix Inci Gültekin, Yasemin Tasyurdu 24

ContentsResearch & Reviews: Discrete Mathematical Structures

RRDMS (2014)© STM Journals 2014. All Rights Reserved

Research & Reviews: Discrete Mathematical Structures

Volume 1, Issue 1

www.stmjournals.com

A New Approach to Find Non-simple Zero’s of Functions

Mohsen Jamali1, Mehdi Delkhosh

2*

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.

RRDMS (2014) © STM Journals 2014. All Rights Reserved

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 Silva

2,3

1LFC – Laboratory of Building Physics, Civil Engineering Department, Faculdade de Engenharia da

Universidade do Porto, Rua Dr. Roberto Frias, s/n, 4200-465 Porto, Portugal 2Instituto Universitário da Maia - ISMAI, Av. Carlos Oliveira Campos,

Castelo da Maia, Portugal 3CEFT – Centro de Estudos de Fenómenos de Transporte, Faculdade de Engenharia, Universidade do

Porto, Rua Dr. Roberto Frias, s/n, 4200-465 Porto, Portugal

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

RRDMS (2014) © STM Journals 2014. All Rights Reserved

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

RRDMS (2014) © STM Journals 2014. All Rights Reserved

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 Prasad

2, B. D. C. N. Prasad

3

1JNTUK University College of Engineering Vizianagaram, India

1,3Prasad 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, dumpster’s combination.

RRDMS (2014)© STM Journals 2014. All Rights Reserved

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 ( , , )nP 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 ( , , )nP x s q .

Mathematics Subjet Classification: 11B37, 11B39

Keywords: Binet formulas, pell polynomials