i-manager's Journal on Mathematics (JMAT)


Volume 4 Issue 4 October - December 2015

Research Paper

A Digital Computational Design Psychometric for theCalculation of Electronic Tri-Squared Test OutcomesVia the Trichotomous Invariant InstrumentInequality [Tri–Triple I] Formula

James Edward Osler II*
Associate Professor, Department of Curriculum and Instruction, North Carolina Central University, USA.
Osler, J. E., II. (2015). A Digital Computational Design Psychometric for the Calculation of Electronic Tri-Squared Test Outcomes Via the Trichotomous Invariant Instrument Inequality [Tri–Triple I] Formula. i-manager’s Journal on Mathematics, 4(4), 1-8. https://doi.org/10.26634/jmat.4.4.3695

Abstract

This monograph provides an in-depth discourse on a model for the design and construction of digital instruments in the field of Educational Science first detailed in i-managers Journal on Mathematics earlier article. A research engineered computational instrument design model involves the methodology and the metrics used to conduct in-depth research investigations via the innovative Total Transformative Trichotomy-Squared (Tri-Squared) Test. The completion of digital instrumentation of the Tri–Squared will provide researchers with a means of creating qualitative metrics that can be qualitatively analyzed. The creation of a model of digital instruments based on Tri-Squared calculation presents a novel method for in-depth mixed methods research design based upon “Trichotomous Psychometric”. Trichotomous Psychometrics involves the development, deployment, and analysis of Trifold assessments for the holistic transformation of qualitative outcomes into quantitative data. This paper is a continuation of the published article entitled, “The Psychometrics of Educational Science: Designing Trichotomous Inventive Investigative Instruments for Qualitative and Quantitative for Inquiry” published in the i-managers Journal on Education Psychology.

Research Paper

On Some Properties of Linear Mappingin Fuzzy Anti n-Normed Spaces

Muhammed Recai Turkmen * , Hakan EFE**
* Faculty of Science and Arts, Mus Alparslan University, Guzeltepe, Turkey.
** Faculty of Science, Gazi University, Teknikokullar, Ankara, Turkey.
Turkmen, M.R., and Hakan, EFE. (2015). On Some Properties of Linear Mapping in Fuzzy Anti n-Normed Spaces. i-manager’s Journal on Mathematics, 4(4), 9-21. https://doi.org/10.26634/jmat.4.4.3696

Abstract

In this paper, the authors have studied some properties of continuity and boundedness of linear mapping in fuzzy anti nnormed spaces. Firstly, the authors have given some definitions and theorem, such as fuzzy anti n-normed , fuzzy anti nnormed space and α - n - norms on fuzzy anti n-normed space, convergent sequence and Cauchy sequence on fuzzy anti n-normed space and fuzzy anti-n-Banach space, open ball and closed ball. The authors have presented some examples by using these definitions. Secondly, the authors have studied linear mapping on fuzzy anti n-normed spaces and the authors redefine fuzzy anti n-continuity and fuzzy anti n-bounded by using previous definitions of contiunity and boundedness. Additionally, the authors have given some definitions, weakly fuzzy anti n-continuous, strongly fuzzy anti ncontinuous, sequentially fuzzy anti n-continuous, using these definitions. Moreover, the authors have given the relationship between fuzzy anti n-continuity and fuzzy anti n-boundedness. Finally, the authors have showed that, T is strongly fuzzy anti n-continuous if and only if T is strongly fuzzy anti n-bounded and, T is weakly fuzzy anti n-continuous if and only if T is weakly fuzzy anti n-bounded.

Research Paper

Similarity Having Perturbation in Newtonian Fluid

Samra* **, Syed Mohammed Rizwan***
* Department of Mathematics, National College of Business Administration and Economics, Gujrat, Pakistan.
**-*** Professor, Department of Mathematics & Statistics, Caledonian College of Engineering, Oman.
Samra, Mohyuddin, M.R., and Rizwan, S.M. (2015). Similarity Having Perturbation in Newtonian Fluid. i-manager’s Journal on Mathematics, 4(4), 22-27. https://doi.org/10.26634/jmat.4.4.3697

Abstract

This is the study of the grade-III fluid having the unidirectional and unsteady flow. Differential equation is solved using perturbation method to get linear forms of the velocities. The velocity u(y,t) is perturbed in ε to get the two-linear Partial Differential Equations (PDE's) in terms of u0(y,t) and u1(y,t). The solution of 1st linear is given in the exponent form f(y) eiat , that gives an ordinary differential equation that is easily solved to get the solution. This solution u0(y,t) is then utilized in Partial Differential Equation of 1st term velocity u1(y,t) and that gives linear Partial Differential Equation in the velocity u1(y,t). The solution of u1(y,t) is given in the exponent form F(y) e3iat , that gives an ordinary differential equation in F(y), that is solved to get the solution of F(y). This gives the perturbed solution for u1(y,t) in the form of F(y). First and zeroth solutions for the velocities give the solution for PDE.

Research Paper

Certain Subclasses of Bi-Univalent FunctionsInvolving Double Zeta Function

Dr. T. Ram Reddy* , R. Bharavi Sharma**, K. Rajya Lakshmi***
* Department of Mathematics, Kakatiya University, Telangana, India.
** Professor, Kakatiya University, Telangana, India.
*** Research Scholar, Kakatiya University, Telangana, India.
Reddy, T.R., Sharma, R.B., and Rajyalaxmi, K. (2015). Certain Subclasses o Bi-Univalent Functions Involving Double Zeta Function. i-manager’s Journal on Mathematics, 4(4), 28-33. https://doi.org/10.26634/jmat.4.4.3698

Abstract

In this paper, the authors have introduced and investigated two subclasses,of Analytic and Biunivalent functions in the open unit disc Δ. For functions belonging to these classes, the authors have obtained estimates on the first two Taylor-Maclaurin coefficients and . The results of this paper will generalize some of the earlier known results.

Research Paper

Coefficient Inequalities for TransformsOf Analytic Functions

R. Bharavi Sharma* , M. Haripriya**
* Assistant Professor, Department of Mathematics, Kakatiya University, Warangal, Telangana, India.
** Project Fellow, U.G.C Major Research Project, New Delhi, India.
Sharma, R.B., and Haripriya, M. (2015). Coefficient Inequalities for Transforms of Analytic Functions. i-manager’s Journal on Mathematics, 4(4), 34-40. https://doi.org/10.26634/jmat.4.4.3699

Abstract

In this paper, the authors have introduced a new subclass of analytic functions. The main objective of this work is to study the kth root transformations for the functions in some subclasses of analytic functions. The authors have obtained the sharp upper bounds for the coefficient functional corresponding to the Kth root transformation for the function f in this class. Similar results are obtained for the inverse function and for . The results will generalize the results obtained by earlier researchers in this direction. This paper will be interesting for the researcher’s working in the area of complex variables.