A Note on the Mathematical Model of the Chemical Kinetics of a Laminar Premixed Flame

-- Rasaq Oyeyemi Olayiwola

The paper studies the conservation of mass, momentum, species and energy equations describing the chemical process of lean premixed methane air combustion. It proves the existence of unique solutions and examines the properties of solutions of the time-dependent problems under certain conditions. The time-dependent temperature and species mass fraction profiles are obtained using the finite difference method.

© 2011 IUP. All Rights Reserved.

Introduction to a New Abelian Group of n-Tuples

-- Sudha Singh and M K Singh

This paper introduces a new arithmetic group of n-tuples. Properties of circulant matrix and Galois field of prime order have been used in the construction. This group of n-tuples is highly useful in information security, cryptography, coding theory, communication and image processing.

© 2011 IUP. All Rights Reserved.

Reduction and Summation Formulae for Basic and Polybasic Hypergeometric Series of Two Variables

-- Ritu Khanna

In this paper, making use of a known identity and summation formulae for truncated q-series, an attempt has been made to establish certain reduction and summation formulae for basic and polybasic hypergeometric series of two variables.

© 2011 IUP. All Rights Reserved.

Edge Product Graph and Its Properties

-- J P Thavamani and D S T Ramesh

The notation of a sum graph was introduced by Harary in 1990. A graph is said to be a sum graph if there exists a bijective labeling f from V to a set of positive integers S such that xy E E if and only if f(x) + f(y)E S. This paper defines for any connected graph G the edge function, the edge product function, the edge product graph and the unit edge product graph. The properties of edge product graph are also discussed, and then the concepts are extended to prove the theorems.

© 2011 IUP. All Rights Reserved.

Solution of Multicollinearity by Generalized Inverse Regression

-- R Singh

This paper axiomatically characterizes Generalized Inverse Regression (GIR) only to combat multicollinearity. Generalized Inverse (GI) estimator is a better alternative to Ordinary Least Square (OLS) estimator in case of ill-conditioning. After discussing Moore-Penrose and Rao’s generalized inverses, the paper presents a discussion as to how these could lead to a unified theory of least square estimation when the design matrix is of less than full column rank. The GI estimator is biased and there exists a trade-off between bias and variance, like in the case of ridge estimator. The GI estimator and ridge estimator both coincide with the OLS estimator when biasing parameter is zero and the rank of design matrix is equal to the number of columns respectively.

© 2011 IUP. All Rights Reserved.

Some Experiments on Fitting of Gielis Curves by Simulated Annealing and Particle Swarm Methods of Global Optimization

-- S K Mishra

The Gielis superformula describes almost any closed curve in terms of deformed circle or ellipse. It has found many applications in design problems. By varying the parameters of the Gielis superformula or deforming a circle by different types of functions one can generate fascinating 2D or 3D figures. However, given a figure, it is not easy to obtain the parameters that generate the figure. Thus, reverse engineering to obtain the Gielis formula is indeterminate. The present study generates some interesting 2D shapes and makes an attempt to get back the parameters by two methods of global optimization—simulated annealing and particle swarm. It has been found that while the enterprise of fitting the curve to the given shapes (closed curves) is commendably successful, the parameters that generated those curves could not be reliably estimated. It shows that while the ‘formula to geometric shape’ has uniqueness, ‘the shape to the formula’ has nonunique solutions.

© 2011 IUP. All Rights Reserved.