i-manager's Journal on Mathematics (JMAT)


Volume 7 Issue 1 January - March 2018

Research Paper

The Tri–Sigma Test: The Triple–Sigma Trichotomous Summation Triostatistic for the Viability, Verifiability, and Validityof Multiple Tri–Squared Test Outcomes

James Edward Osler II*
Associate Professor, Department of Curriculum and Instruction, North Carolina Central University, USA.
Osler, J. E., II. (2018). The Tri-Sigma Test: The Triple-Sigma Trichotomous Summation Triostatistic for the Viability, Verifiability, and Validity of Multiple Tri-Squared Test Outcomes. i-manager’s Journal on Mathematics, 7(1), 1-12. https://doi.org/10.26634/jmat.7.1.14026

Abstract

This paper provides a novel statistical methodology called “Triple or Tri–Sigma” (“Tri-Σ”) that is designed to conceptually add to the research that has been conducted on and with the Tri–Squared Test (Osler, 2012a). The Tri–Sigma Test is an advanced statistical procedure that is used to analyze multiple Tri–Squared Tests that have been delivered at different times. Tripleseries summation provides an innovative way of investigating the data derived from a series of researchbased investigative instruments that are known as “Trichotomous Tri-Squared Test Triple-I's” (Osler and Mansaray, 2013b). The Triple–I is directly derived from specific research questions as an in-depth associated instrument [first introduced in the i-manager's Journal on Mathematics as a part of the “Tri-Squared Test” (Osler, 2012a)]. This new approach to research inquiry lends additional strength to trichotomous research designs. Trichotomous tests can now be offered at multiple stages, multiple times, and in multiple ways with multiple research questions.

Research Paper

A Homotopy Based Method for Nonlinear Fredholm Integral Equations

Javed Ali*
Senior Lecturer, Department of Mathematics and Statistics, Caledonian (University) College of Engineering, Oman.
Javed Ali. (2018). A Homotopy Based Method For Nonlinear Fredholm Integral Equations. i-manager’s Journal on Mathematics, 7(1), 13-17. https://doi.org/10.26634/jmat.7.1.14027

Abstract

In this work, the author extends the application of the optimal homotopy asymptotic method to the solution of nonlinear Fredholm integral equations of the second kind. Several examples are solved to demonstrate the efficiency of the proposed method. Numerical results are compared with the exact solution.

Research Paper

Finite Element Solution of Viscous Dissipative Effects on Unsteady MHD Flow Past A Parabolic Started Vertical Plate with Mass Diffussion and Variable Temperature

B .Shankar Goud* , Shekar, M.N.R.**
* Research Scholar, Department of Mathematics, JNTUH College of Engineering Kukatpally, Hyderabad, India.
** Professor, Department of Mathematics, JNTUH College of Engineering Nachupally, Hyderabad, India
Goud. B.S., and Shekar, M.N.R. (2018). Finite Element Solution of Viscous Dissipative Effects on Unsteady MHD Flow Past A Parabolic Started Vertical Plate with Mass Diffussion and Variable Temperature. i-manager’s Journal on Mathematics, 7(1), 20-27. https://doi.org/10.26634/jmat.7.1.14028

Abstract

In this paper, the authors have investigated an unsteady magneto hydrodynamic flow past a parabolic starting motion of the infinite vertical plate with variable temperature and variable mass diffusion. The plate temperature and the concentration level close to the plate are raised with time. The dimensionless governing equations are solved by using Galerkin Finite Element Technique. The effect of velocity, temperature and concentration distribution is studied for different physical parameters.

Research Paper

Common Fixed Point Theorems for Six occasionally weakly Compatible Mappings in Fuzzy Metric Spaces

T Rakesh Singh* , P. Srikanth Rao**
* Associate Professor, Department of Mathematics, Aurora's Technological Institute, Hyderabad, Telangana, India.
** Professor, Department of Mathematics, B.V. Raju Institute of Technology, Narsapur, Telangana, India.
Singh, T.R., and Rao, P.S. (2018). Common Fixed Point Theorems for Six Occasionally Weakly Compatible Mappings in Fuzzy Metric Spaces. i-manager’s Journal on Mathematics, 7(1), 28-33. https://doi.org/10.26634/jmat.7.1.14029

Abstract

The fixed point hypotheses in metric spaces are assuming a noteworthy part to develop techniques in arithmetic to take care of issues in connecting applied mathematics and sciences. So the fascination of metric spaces to substantial quantities of mathematicians is understandable. The aim of this paper is to prove common fixed point theorems for Occasionally Weakly Compatible six self mappings. The concept of Occasionally Weakly Compatible Mappings introduced by Al-Thagafi and Shahzad (2008) also generalized the concept of compatible maps and weakly compatible maps in fuzzy metric space. The authors aim to improve the results of Sanodia et al. (2017). Their result generalizes and improves other similar results in the literature.

Research Paper

A New Approach to Variant Assignment Problem

Uruturu balakrishna*
Professor of Mathematics, Department of Science & Humanities, Sreenivasa Institute of Technology and Management Studies, Chittoor, India.
Balakrishna, U. (2018). A New Approach to Variant Assignment Problem. i-manager’s Journal on Mathematics, 7(1), 34-42. https://doi.org/10.26634/jmat.7.1.14030

Abstract

It is a two dimensional problem where the time matrix T(i, j) is the time of the j job assigned to i person. The time matrix T(i.j) [i=1,2,3,…, m; j=1,2,3,…,n] is known. Each of the person is constrained to do the specified number of jobs. All the persons start working on the jobs simultaneously, but a person cannot work on more than one job at a time. The problem is to assign the n jobs to m persons, with minimum total time with the restriction that each person to do given specified number of jobs. A Lexi search approach is proposed using pattern recognition technique to find an optimal feasible assignment. For this problem a computer program is developed for the algorithm and is tested. It is observed that it takes less time for solving higher dimension problems also.

Research Paper

A Simple Method of Numerical Integration for a Class of Singularly Perturbed Two Point Boundary Value Problems

Rakesh Ranjan* , H. S. Prasad**, Md. Javed Alam***
*,*** Research Scholar, Department of Mathematics, National Institute of Technology, Jamshedpur, Jharkhand, India.
** Assistant Professor, Department of Mathematics, National Institute of Technology, Jamshedpur, Jharkhand, India.
Rakesh Ranjan., H. S. Prasad., Md. Javed Alam. (2018). A Simple Method of Numerical Integration for A Class of Singularly Perturbed Two Point Boundary Value Problems. i-manager’s Journal on Mathematics, 7(1), 43-52. https://doi.org/10.26634/jmat.7.1.14031

Abstract

This paper deals with a simple but efficient numerical integration method to solve a class of singularly perturbed twopoint boundary value problems. Using the methods of exact rule of integration with a finite difference approximation of first derivatives, a three-term recurrence relationship is obtained. The authors have employed Thomas algorithm to obtain the solution of the obtained system. Also, the stability and convergence of the proposed scheme are established. Several model example problems have been solved and the results are presented in terms of maximum absolute errors, which show the accuracy and efficiency of the method. The method produces highly accurate results for a fixed value of step size h when the perturbation parameter e tends to zero.