i-manager's Journal on Mathematics (JMAT)


Volume 5 Issue 1 January - March 2016 [Open Access]

Article

A Descriptive Note on Vedic Mathematics

P. Sumathi* , K. Mahadevamma**
* Assistant Professor, Department of Statistics & Mathematics, SV Agricultural College, Tirupati, India.
** Lecturer and HOD, Department of Social Work, SPW Degree & PG College, Tirupati, India.
Sumathi,P., and Mahadevamma,K. (2016). A Descriptive Note on Vedic Mathematics. i-manager’s Journal on Mathematics, 5(1), 1-5. https://doi.org/10.26634/jmat.5.1.4866

Abstract

The word “Veda” has the derivational meaning i.e, the fountain head and illimitable store-house of all knowledge. This means and implies that the Vedas contain within themselves all the knowledge required by mankind for the achievement of all round, complete and perfect success and able to throw the fullest necessary light on all matters which any aspiring seeker after knowledge can possibly seek to be enlightened on. Vedic Mathematics was not known to the world till it was rediscovered by Swami Bharathi Krishna Tirtha (1884-1960). The approach of Vedic Mathematics in learning Mathematics makes enjoyable and pleasant with the help of ultra easy 16 sutras and 13 sub - sutras contained in the parisista of Atharva Veda. The list of 16 sutras along with their meaning is tabulated in this paper. An attempt is made in this paper to describe about the significance and applications of Vedic Mathematics in the day-to-day life.

Research Paper

The Trichotomous–Cubed Test [Tri3]: An Advanced Statistical Data Analysis Methodology for Tri–Coordinate Meta–Analysis Using the Tri–Squared Test

James Edward Osler II*
Associate Professor, Department of Curriculum and Instruction, North Carolina Central University, USA.
Osler, J. E., II. (2016). The Trichotomous–Cubed Test [Tri3]: An Advanced Statistical Data Analysis Methodology for Tri–Coordinate Meta–Analysis Using the Tri–Squared Test. i-manager’s Journal on Mathematics, 5(1), 6-19. https://doi.org/10.26634/jmat.5.1.4867

Abstract

This monograph provides an epistemological rational for the design of an advanced and novel post hoc parametric statistic and meta-analysis metric. “Trichotomous-Cubed Tri-Coordinate Meta-Analysis (“Tri-Cubed Test” also “Tri-Cubed” or  Tri3 ”) is an advanced, highly precise research methodology for the accurate in-depth analysis of the existing reported data on a specifically identified criterion. The Tri-Cubed Test integrates and extends the Tri-Squared Test in a Tri- Coordinate [x, y, and z] Tri-Squared Meta-Analysis model and methodology. It is a statistic that involves a variety of robust and rigorous calculations, a precise isometric model, and a series of sequential and detailed computations to provide further insight on the inner workings of the reported statistically significant data. It actively makes use of Tri-Squared Meta- Analysis first presented in the i-managers Journal on Educational Technology and the Tri-Squared Test that was first introduced in the i-managers Journal on Mathematics.

Research Paper

Chaos control in HIV Infection of CD4+ T-cells System by Lie Algebraic Exact Linearization

Mohammad *
Assistant Professor, Department of General Requirements, College of Applied Sciences, Nizwa, Oman.
Shahzad,M. (2016). Chaos control in HIV Infection of CD4+ T-cells System by Lie Algebraic Exact Linearization. i-manager’s Journal on Mathematics, 5(1), 20-30. https://doi.org/10.26634/jmat.5.1.4868

Abstract

This Paper deals with the control of chaotic dynamics of healthy, infected CD+4 T-cells and free HIV (Human Immunodeficiency Virus) cells in a chaotic system of HIV infection of CD+4 T-cells by implementing a Lie algebraic exact  linearization technique. A nonlinear feedback control law is designed, which induces a co-ordinate transformation thereby changing the original chaotic HIV system into a controlled linear system. Numerical simulation has been carried by using Mathematica that witness the robustness of the technique implemented on the chosen chaotic system.

Research Paper

Adjacency and Degree of Graph of Mobius Function

K. K. Srimitra* , Shaik Sajana**, D. Bharathi***
*-** Research Scholar, Department of Mathematics, S.V. University, Tirupati, Andhra Pradesh, India.
*** Associate Professor, Department of Mathematics, S.V. University, Tirupati, Andhra Pradesh, India.
Srimitra,K.K., Sajana,S., and Bharathi,D. (2016). Adjacency and Degree of Graph of Mobius Function. i-manager’s Journal on Mathematics, 5(1), 31-38. https://doi.org/10.26634/jmat.5.1.4869

Abstract

In this paper, the authors have consider the graph of Mobius function for zero, G(µn(0)). For an integer n≥1, the graph of Mobius function for zero is a graph with vertex set {1, 2, 3, …, n} and an edge, between two vertices a,b if the Mobius function value, µ(ab)=0. The authors have studied the basic results of a graph as the degree of vertex, the adjacency of two vertices and the planarity. First, the authors have calculated the minimum degree and the maximum degree of graph of Mobius function for '0'. The sufficient conditions for two vertices to be adjacent in the graph of Mobius function for '0' based on the divisibility of numbers are discussed and also, proved the necessary and sufficient condition for adjacency of two consecutive vertices in the graph of Mobius function for '0'. At the end, the authors have discussed the planarity of the graph according to the number of vertices of the graph.

Research Paper

The Semicircular Reflected Gamma Distribution

Phani Yedlapalli* , S. V. S. Girija**, A. V. Dattatreya Rao***
* Associate Professor, Department of Mathematics, Shri Vishnu Engineering College for Women, Bhimavaram, India.
** Associate Professor, Department of Mathematics, Hindu College, Guntur, India
*** Professor, Department of Statistics, Acharya Nagarjuna University, Guntur, India.
Yedlapalli,P., Girija,S.V.S., and Rao,A.V.D. (2016). The Semicircular Reflected Gamma Distribution. i-manager’s Journal on Mathematics, 5(1), 39-46. https://doi.org/10.26634/JMAT.5.1.4870

Abstract

Modeling of circular data with limited number of available circular models such as, von Mises, Wrapped Cauchy, Cardioid, etc., was done in various domains like Neuro Science, Geography, Archaeology, Remote Sensing, Spatial Analysis, Plant Phenology and Political Science. Dattatreya Rao (2007; 2011a;2011b;2011c; 2013a; 2013b; 2016) and Girija (2010; 2013a; 2013b; 2014a; 2014b), Phani (2012a; 2012b; 2013a; 2013; 2014; 2015a; 2015b; 2015c; 2015d), Radhika (2013a; 2013b; 2014;2015) and Devaraaj (2012; 2014) have introduced several new models and a few new methodologies of constructing the new circular models. These circular models are constructed by applying wrapping method, inverse stereographic projection, offsetting and the rising sun function. It is observed that, the simple projection method is not a much paid attention in constructing circular models. Glancing the literature, semicircular, arc and skewed angular data were observed in the applications and sufficient number of models for such data is not available. Motivated by these points, the authors have introduced semicircular reflected gamma distribution for modelling semicircular data by a simple projection method on reflected gamma distribution. The authors have extend it to the laxial reflected gamma distribution by a simple projection for modeling any arc of arbitrary length, and also the first four trigonometric moments has been derived for the proposed model.