GENERAL MATHEMATICS NOTES

Vol. 2, No. 2, February 2011

 Contents

Title: A Three-parameter Third-order Family of Methods for Solving Nonlinear Equations

Authors: Behzad Ghanbari, Bijan Rahimi and Mehdi Gholami Porshokouhi

Abstract: In this paper a new family of methods free from second derivative is presented. This new family of methods is constructed such that convergence is of order three and requires two require two evaluations of the function and first derivative per iteration. To illustrate the efficiency and performance of the new family of methods, several numerical examples are presented. Further numerical comparisons are made with several other existing third-order methods to show the abilities of the presented family of methods.

PP. 1-6

Title: On Some Absolute Summability Factors of Infinite  Series

Author: W. T. Sulaiman

Abstract: In this paper, a general theorem concerning  $\phi-|\bar{N}, p_n|_k$ factors of infinite series has been proved. The presented result giving improvement as well as generalization of some known results.

PP. 7-13

Title: Orders of Generalized Hypersubstitutions of Type τ =(3)

Authors: Sivaree Sudsanit, Sorasak Leeratanavalee

Abstract: The concept of generalized hypersubstitutions was introduced by S. Leeratanavalee and K. Denecke in 2000. We used it as the tool to study strong hyperidentities and strongly solid varieties. In this paper we characterize all idempotent generalized hypersubstitutions of type τ =(3) and determine the order of each generalized hypersubstitution of this type. It turns out that the order is 1, 2, 3 or infinite.

PP. 14-33

Title: Eccentric Connectivity Index, Hyper and Reverse-Wiener indices of the Subdivision Graph

Authors: Ranjini P. S  and V. Lokesha

Abstract: If G is a connected graph with vertex set V, then the eccentric connectivity index of G, $\xi^{(c)}(G)$ is defined as $\sum deg(v). ec(v)$ where deg(v) is the degree of a vertex v and ec(v) is its eccentricity. The Wiener index W(G)= $\frac{1}{2}[\sum d(u,v)]$, the hyper-Wiener index WW(G) = $\frac{1}{2}[\sum d(u,v) +  \sum d^{2}(u,v)]$ and the reverse-Wiener index $\wedge (G) = \frac{n(n-1)D}{2} -W(G)$, where d(u,v) is the distance of two vertices u, v in G, $d^{2}(u,v) = d(u,v)^{2} $, $n =|V(G)|$ and D is the diameter of G. In this paper, we determine the eccentric connectivity index of the subdivision graph of the complete graphs, tadpole graphs and the wheel graphs. Also, derive an expressions for the hyper  and reverse-Wiener indices of the same class of graphs.

PP. 34-46

Title: Three-Step Fixed Point Iteration Formultivalued Mapping with Errors in Banach Spaces

Authors: Zhanfei Zuo and Feixiang Chen

Abstract: In this paper, we consider the convergence of three-step fixed point iterative processes for multivalued nonexpansive mapping with errors, under some different conditions, the sequences of three-step fixed point iterates strongly or weakly converge to a fixed point of the multivalued nonexpansive mapping. Our results extend and improve some recent results.

PP. 47-57

Title: On  Some  Two–Generator  Finite  Solvable  Automorphism  Groups  of  Compact  Riemann  Surfaces

Authors: Gayatree Das and  Kuntala Patra

Abstract: A  finite  group  G  can  be  represented  as  a  group  of   automorphisms   of  a  compact  Riemann  surfaces.  In this  paper  we  prove  the  existence  of  some  infinite  families  of  two  generator  finite  solvable  groups  with  short  derived  series  acting  as  Riemann  surface  automorphism  groups.

PP. 58-63

Title: An improved Newton's method without direct function evaluations

Authors: Behzad Ghanbari and Mehdi Gholami Porshokouhi

Abstract: Due to the fact that systems of nonlinear equations arise frequently in science and engineering, they have recently attracted researchers’ interest. In this work, we present a new Newton-like approach which is independent of function evaluation and has been provided using an original idea that improves some definitions and notions of a recently proposed method [1] for solving systems of nonlinear. Also, the convergence of proposed method has been discussed. The computational advantages and convergence rate of the proposed method are also tested via some numerical experiments. From the obtained numerical results it seems that present approach affect considerably the overall performance in relation toNewton's method and its aforementioned variants.

PP. 64-72

Title: On the Cusp Catastrophe model and stability

Author: Muhammad Nokhas Murad

Abstract: In this paper, we present results on the projection of the folding part of the Cusp catastrophe model on the control space to find stability and catastrophic phenomenon of the periodic solutions of some nonlinear differential equations by using methods of catastrophe theory. We have shown here, that the occurrence of the folding of the Cusp surface is always accompanied with the saddle - node bifurcation, and that the saddle - node bifurcation can be classified as cusp type catastrophe.

PP. 73-82

Title: A Summation Formula of Half Argument Associated to Bailey Theorem

Author: Salahuddin

Abstract: The main objective of the present paper is to derive a summation formula of half argument associated to Bailey theorem .The result presented here is presumably new.

PP. 83-101

Title: Truncated Hypergeometric Series Motivated by the Works of Slater and Verma

Authors: M. I. Qureshi and Kaleem A. Quraishi

Abstract: Motivated by the works of L. J. Slater and A. Verma, we have derived some results on truncated unilateral generalized hypergeometric series of positive unit argument subject to certain conditions in numerator and denominator parameters. The results presented here are presumably new.

PP. 102-110

Title: New Types of Hardy-Hilbert’s Integral Inequality

Author: W. T. Sulaiman

Abstract: Two new form inequalities similar to Hardy-Hilbert’s integral inequality are given.

PP. 111-118

Title: Reliability Analysis and Mathematical Modeling of Washing System in Paper Industry

Author: Satyavati

Abstract: The objective of every industrial manager is that industry should be in an operative state for a long period of time. Keeping in mind the above objective the present work is done. In the present paper washing system which is an important system of paper industry have been discussed in detail. It involving many unit operations and processes Reliability, long run availability and M.T.T.F. have been studied. Reliability of the system can be analyzed by forming differential equations with the help of mnemonic rule and the transition diagram of the process. These differential equations can be solved using well known integrating factor technique. Recursive method has been used to calculate the long run availability of the process. The effects of failure and repair rates of different sub systems on long run availability have been studied through tables and graphs.

PP. 119-128

Title: Fractional Integrals involving General class of Polynomials, H–Function and Multivariable I–Function

Author: Shakeeluddin

Abstract: In this paper we obtain a Eulerian integral and a main theorem based on the functional operator associated with H–Function [2], general class of polynomial [8] and multivariable I–Function [14] having general arguments.  The special class of the main theorem has also been given.

PP. 129-138

 Suggested Citation

First Author, Second Author and Third Author, Title of the paper, Gen. Math. Notes, 2(2)(2011), pages xx-xx.

e.g., The first paper of this issue may be cited as follows:

B. Ghanbari, B. Rahimi and M. G. Porshokouhi, A three-parameter third-order family of methods for solving nonlinear equations, Gen. Math. Notes, 2(2) (2011), 1-6.