Semi-open sets and Pre open sets In Tri Topological space

Vol. 5  Issue 3
Year: 2016
Issue:Jul-Sep
Title:Semi-open sets and Pre open sets In Tri Topological space
Author Name:U.D. Tapi, Ranu Sharma and Bhagyashri A. Deole
Synopsis:
The main aim of this paper is to introduce two new types of open sets, namely tri semi open sets and tri pre open sets in tri topological spaces along with their several properties and characterization. As application to tri open sets, tri semi open sets and tri pre open set, the authors introduce tri continuous, tri semi continuous, and tri pre continuous functions to obtain some of their basic properties.

Common fixed points in intuitionistic fuzzy metric space

Vol. 5  Issue 3
Year: 2016
Issue:Jul-Sep
Title:Common fixed points in intuitionistic fuzzy metric space
Author Name:Pranjali Sharma and Shailesh Dhar Diwan
Synopsis:
In this paper, the authors have established some common fixed point theorems for Occasionally Weakly Compatible (OWC) mappings in intuitionistic fuzzy metric spaces. In this paper, using Occasionally Weakly Compatible (OWC) mappings, some common fixed point theorems for four mappings have been proved, that extend the scope of the study of common fixed point theorems from the class of weakly compatible mappings to a wider class of occasionally weakly compatible mappings. The obtained results significantly generalize and improve results of common fixed point theorems in intuitionistic fuzzy metric space. The obtained results generalize and improve several results of metric spaces and fuzzy metric spaces to intuitionistic fuzzy metric spaces using more general condition of OWC mappings. As an application to main results, they have presented some fixed point theorems for self mappings in fuzzy metric space by using an implicit relation. The paper has scope to extend the results for modified intuitionistic fuzzy metric spaces and intuitionistic m-fuzzy metric spaces.

Discrimination between two Inverted Distributions

Vol. 5  Issue 3
Year: 2016
Issue:Jul-Sep
Title:Discrimination between two Inverted Distributions
Author Name:R. Subba Rao, Pushpa Latha Mamidi and R.R.L. Kantam
Synopsis:
Two popular life testing models, namely Rayleigh distribution, Half Logistic distributions are considered. The inverted versions of these two distributions are worked out. The graphs of the frequency curves for these distributions on the same scale look identical, which drives to the motivation of testing whether one distribution can be used as an alternative to the other. Between these two distributions Inverse Rayleigh Distribution (IRD) appears in literature earlier than Inverse Half Logistic Distribution (IHLD). The authors have proposed to test IHLD as an alternative model to IRD. In statistical testing of hypothesis, they consider IRD as a null population and IHLD an alternative population and proposed a Likelihood Ratio test procedure to test this hypothesis. The critical values of the test statistic, the power of the test procedure are computed in order to assess the validity of the hypotheses.

The Mathematics of the Tri–Squared Triangulation Algorithmic Model

Vol. 5  Issue 3
Year: 2016
Issue:Jul-Sep
Title:The Mathematics of the Tri–Squared Triangulation Algorithmic Model
Author Name:James Edward Osler II
Synopsis:
This work provides a mathematical and an epistemological rational for the transformative process of qualitative data into quantitative outcomes through the Tri–Squared Test. The design of fixed-parameter algorithms for research engineering can prove to be beneficial to a variety of fields of learning. This novel methodology provides statistical power and mathematical elegance to research outcomes. It is a comprehensive approach that has a wide range of applicability as it practically addresses important and relevant problems with sample sizes that are small and research arenas that are rather complex. This research is the continuation of a dynamic mixed methods approach that is a transformative process which changes qualitative data into quantitative outcomes through the Tri–Squared statistical measure first introduced in i-manager's Journal of Mathematics.

Handling Fractions and Errors in Fractions

Vol. 5  Issue 3
Year: 2016
Issue:Jul-Sep
Title:Handling Fractions and Errors in Fractions
Author Name:R. Devika
Synopsis:
The concept of fractions seems to be very challenging, at the same time interesting to the students. It is introduced to the fourth graders in the school level. The concept of fragmentation from the 'whole' part becomes a real challenge for the teacher as well as for the students. There are enormous ways beginning from the concept of 'Numerator' and 'Denominator' by which students start generating errors while trying to conceptualise it. Teachers should understand and except a good number of errors while practicing the topic fractions. The anticipation of errors while learning like fractions, unlike fractions, mixed fractions, addition and subtraction of fractions, all needs to be attended properly as 'fractions' which is an important area in mathematics and the basics needs to be handled well. Thus when teaching fractions, teachers need to be on the lookout for errors as this may cause errors in the computation also. Some of the most common misconceptions that occur in the classrooms while teaching fractions and handling those errors are discussed in this paper.

Some Common Fixed Point Theorems in Fuzzy Metric Spaces Using the CLRg Property

Vol. 5  Issue 2
Year: 2016
Issue:Apr-Jun
Title:Some Common Fixed Point Theorems in Fuzzy Metric Spaces Using the CLRg Property
Author Name:Pranjali Sharma,and Shailesh Dhar Diwan
Synopsis:
In this paper, the authors have established some common fixed point theorems in fuzzy metric spaces using the Common Limit in the Range (i.e, (CLRg )) property. Since, CLRg property does not require condition of closeness of range and so the results extend, generalize and improve several known results of metric spaces and fuzzy metric space in several ways. The obtained results show that the completeness of space and continuity of mappings are not required. In the case of CLRg property, Containment of ranges of involved mappings and the closeness of subspace are not required. As an application to the main result, the authors present some fixed point theorems for self mappings in fuzzy metric space by using the notion of (EA) property. The (EA) property replaces the completeness requirement of the space with a more natural condition of closeness of the range. The (EA) property also relaxes the continuity of one or more mappings and containment of the range of one mapping into the range of another, which can be used to construct the sequences of some iterates. Some examples are furnished in the paper to support the validity of the results.

Finite difference solution for an MHD Free Convective Rotating Flow past an Accelerated Vertical Plate

Vol. 5  Issue 2
Year: 2016
Issue:Apr-Jun
Title:Finite difference solution for an MHD Free Convective Rotating Flow past an Accelerated Vertical Plate
Author Name:Y.Harnath , A.Sudhakaraiah, P.Venkatalakshmi,and M. Sivaiah
Synopsis:
Numerical solution of an MHD (Magneto Hydrodynamics) free convective flow with variable heat and mass transfer past an incompressible fluid past an infinite vertical plate, which is uniformly accelerated in the presence of rotation has been discussed in this paper. With linearly increasing time, the temperature as well as concentration levels near the plate are raised. Through graphs, the velocity profiles, temperature, concentration distributions, Shear stress at the wall, rates of heat and mass transfer are discussed in this paper. The observed conclusions are with the increase of magnetic field, thermal buoyancy, and Solutal Grashoff number, the transient velocity increases. The secondary velocity increases with the lessening of the magnetic field but decreases with the increase of thermal buoyancy, and Solutal Grashoff number. The velocity increases with decreasing values of the rotation parameter (Ω) and Dufour number (Du). This shows that the heat transfer is more in air than in water when in comparison. With the increase of the Dufour number, the temperature increases but gradually decreases in the boundary layer. With the increase of reaction of the chemicals, the distribution of concentration decreases and also in the boundary layer. The radiation decreases the velocity but for a lesser radiation atmosphere, temperature increases. With the increase of M, Pr, and K, the shear stress decreases. With the increase of M, , and Gr, there is no change in the rate of heat transfer. With increase of Du and Sc, its rate of heat transfer is increased. Similarly with the increase of M, and Gr there is no change in the rate of mass transfer.

Lexi-Search Algorithm for A Three Dimensional Group Assignment Problem

Vol. 5  Issue 2
Year: 2016
Issue:Apr-Jun
Title:Lexi-Search Algorithm for A Three Dimensional Group Assignment Problem
Author Name:A. Vidhyullatha 
Synopsis:
Application of Operations Research has traditionally arisen in response to solve the complex nature problems due to change in structure of human organizations, specialization in various fields and introduction of division of labour concept in each organization. In view of this, a variant Assignment Problem with the introduction of third dimension is studied in this paper. The problem is more versatile which influences the objective function. It is a mini-max combinatorial programming problem. A Lexi-Search exact algorithm based on the pattern recognition technique is developed to obtain an optimal solution and is illustrated with a numerical example. Lexi-Search method is an implicit enumeration method where it eliminates subsets of solutions called blocks which are not having an optimal feasible solution and converge fast to an optimum solution

TRIMOD [Trichotomous–Cubic Parametric Model]:A Systemic Advanced Tri–Coordinate Post Hoc Data Morphological Analytic and Trend Analysis Procedure Designed to Comprehensively Analyze Tri–Squared Test Results

Vol. 5  Issue 2
Year: 2016
Issue:Apr-Jun
Title:TRIMOD [Trichotomous–Cubic Parametric Model]:A Systemic Advanced Tri–Coordinate Post Hoc Data Morphological Analytic and Trend Analysis Procedure Designed to Comprehensively Analyze Tri–Squared Test Results
Author Name:James Edward Osler 
Synopsis:
This monograph provides an epistemological rationale for the design of an advanced, novel, and sequential tri–coordinate post hoc parametric metric. The Trichotomous–Cubic Parametric Model (collectively abbreviated as “TRIMOD”) is a rigorous post hoc mathematical data analysis methodology designed to more accurately detail the outcomes of a statistically significant Tri–Squared Test. This particular statistical test is part two of the research published in the i-manager’s Journal on Mathematics entitled, “The Trichotomous–Cubed Test [Tri3]: An Advanced Statistical Data Analysis Methodology for Tri–Coordinate Meta–Analysis Using the Tri–Squared Test”. TRIMOD infuses the Tri–Cubed Test model with the Tri–Squared Test in a detailed sequential Tri–Coordinate series of x, y, and z planar vectors native to the Visualus Isometric Cuboid (Osler, 2010). A series of methodical mathematical calculation procedures are then conducted to yield the Tri–Cubic Parametric Model outcomes. This statistic further expands the field of post hoc trichotomous tests in terms of morphological and trend analysis analytics that are designed to provide in–depth insight into the Tri–Squared Test first introduced in the i-manager’s Journal on Mathematics.

g*b-Homeomorphisms

Vol. 5  Issue 2
Year: 2016
Issue:Apr-Jun
Title:g*b-Homeomorphisms
Author Name:S.Bharathi
Synopsis:
The aim of this paper is to define and develop a new type of homeomorphism called g*b-homeomorphism. Some of their properties and several characterizations of these types of functions with others are discussed in this paper. Some of the implications, relationships and independence relationships with few of the existing closed sets are studied and also, the author investigates the relationship between these classes of functions.

The Semicircular Reflected Gamma Distribution

Vol. 5  Issue 1
Year: 2016
Issue:Jan-Mar
Title:The Semicircular Reflected Gamma Distribution
Author Name:Phani Yedlapalli, S.V.S.Girija and A.V. Dattatreya Rao
Synopsis:
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.

Adjacency and Degree of Graph of Mobius Function

Vol. 5  Issue 1
Year: 2016
Issue:Jan-Mar
Title:Adjacency and Degree of Graph of Mobius Function
Author Name:K. K. Srimitra, Shaik Sajana, and D. Bharathi
Synopsis:
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.

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

Vol. 5  Issue 1
Year: 2016
Issue:Jan-Mar
Title:Chaos control in HIV Infection of CD4+ T-cells System by Lie Algebraic Exact Linearization
Author Name:Mohammad Shahzad
Synopsis:
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.

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

Vol. 5  Issue 1
Year: 2016
Issue:Jan-Mar
Title:The Trichotomous–Cubed Test [Tri3]: An Advanced Statistical Data Analysis Methodology for Tri–Coordinate Meta–Analysis Using the Tri–Squared Test
Author Name:James Edward Osler II
Synopsis:
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.

A Descriptive Note on Vedic Mathematics

Vol. 5  Issue 1
Year: 2016
Issue:Jan-Mar
Title:A Descriptive Note on Vedic Mathematics
Author Name:P. Sumathi and K. Mahadevamma
Synopsis:
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.

Coefficient Inequalities for Transforms Of Analytic Functions

Vol. 4  Issue 4
Year: 2015
Issue:Oct-Dec 
Title:Coefficient Inequalities for Transforms Of Analytic Functions
Author Name:R. Bharavi Sharma and M. Haripriya
Synopsis:
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.

Certain Subclasses of Bi-Univalent Functions Involving Double Zeta Function

Vol. 4  Issue 4
Year: 2015
Issue:Oct-Dec 
Title:Certain Subclasses of Bi-Univalent Functions Involving Double Zeta Function
Author Name:T. Ram Reddy, R. Bharavi Sharma and K. Rajyalaxmi 
Synopsis:
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.

Similarity Having Perturbation in Newtonian Fluid

Vol. 4  Issue 4
Year: 2015
Issue:Oct-Dec 
Title:Similarity Having Perturbation in Newtonian Fluid
Author Name:Samra, Muhammad Raheel Mohyuddin and Syed Mohammad Rizwan
Synopsis:
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.

On Some Properties of Linear Mapping in Fuzzy Anti n-Normed Spaces

Vol. 4  Issue 4
Year: 2015
Issue:Oct-Dec 
Title:On Some Properties of Linear Mapping in Fuzzy Anti n-Normed Spaces
Author Name:M. Recai Turkmen and Hakan EFE
Synopsis:
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.

A Digital Computational Design Psychometric for the Calculation of Electronic Tri-Squared Test Outcomes Via the Trichotomous Invariant Instrument Inequality [Tri–Triple I] Formula

Vol. 4  Issue 4
Year: 2015
Issue:Oct-Dec 
Title:A Digital Computational Design Psychometric for the Calculation of Electronic Tri-Squared Test Outcomes Via the Trichotomous Invariant Instrument Inequality [Tri–Triple I] Formula
Author Name:James Edward Osler II
Synopsis:
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.

New Exponential Smoothing for Intraday Data

Vol. 4  Issue 3
Year: 2015
Issue:Jul-Sep
Title:New Exponential Smoothing for Intraday Data
Author Name:S. Venkatramana Reddy, B. Hari Mallikarjuna Reddy , B. Sarojamma , R. Abbaiah
Synopsis:
Now-a-days intraday time series models are playing a wide role in various sectors like wind speed data, temperature data, sensex data etc. In this paper, the authors have introduced a new exponential smoothing model and Auto Regressive Moving Average (ARMA) models for intraday data. These two models are empirically tested using wind speed data of Gadanki, Chittoor District. Between these two models which model is better performed and the wind speed data is tested using Root Mean Square Error (RMSE). Kolmogorov Smirnov test is used for goodness of fit. Among the compared 25 ARMA models and new exponential smoothing model, RMSE of new exponential smoothing model is low. Therefore, the authors have concluded that, the new exponential smoothing model is the best model for wind speed data of Gadanki.

Unsteady Magnetohydrodynamic (MHD) Convective Heat Generating Flow Through A Porous Medium in A Vertical Plate In the Presence of Radiative Heat Transfer

Vol. 4  Issue 3
Year: 2015
Issue:Jul-Sep
Title:Unsteady Magnetohydrodynamic (MHD) Convective Heat Generating Flow Through A Porous Medium in A Vertical Plate In the Presence of Radiative Heat Transfer
Author Name:J. Girish Kumar
Synopsis:
Free convective oscillatory mass transfer flow past an infinite vertical porous plate with heat and mass fluxes in the presence of uniform magnetic field and heat generation through porous medium is analytically investigated. Effects of radiation and viscous dissipation on the unsteady two-dimensional flow of a viscous incompressible, electrically conducting with optical thin gray fluid are considered. Approximate solutions have been derived from the velocity, temperature and concertation fields, coefficient of skin-friction, Nusselt number and Sherwood number using multi-parameter perturbation technique. It is observed that the increase in radiation parameter decreases the both velocity and temperature.

A New Multiple Hilbert-Type Integral Inequality With A Non-Homogeneous Form

Vol. 4  Issue 3
Year: 2015
Issue:Jul-Sep
Title:A New Multiple Hilbert-Type Integral Inequality With A Non-Homogeneous Form
Author Name:Zheng Zeng and Zitian Xie 
Synopsis:
Hilbert-type inequalities are important in analysis and its applications. In recent years, some authors have studied and published a few Hilbert-type multiple integral inequalities, which are hard and interesting. In this paper, by estimating the weight function and technique of real analysis, the authors give a new multiple Hilbert-type integral inequality with a non-Homogeneous form as, F(x,y) f(x)g(y)dxdy < K f g (p >1). The best possible Rn+ x Rn+ p,w q,w constant factor is given, and the equivalent form is also considered. Many particular cases of Hilbert-type integral inequality with a non-homogeneous form are included. As its applications, the authors have considered some particular results.

Synchronization of Three Dimensional Cancer Model with Chen System using a Robust Adaptive Sliding Mode Controller with application to secure communications

Vol. 4  Issue 3
Year: 2015
Issue:Jul-Sep
Title:Synchronization of Three Dimensional Cancer Model with Chen System using a Robust Adaptive Sliding Mode Controller with application to secure communications
Author Name:Mohammad Shahzad and Mohammed Raziuddin
Synopsis:
In this computational research paper, the authors have synchronized the Three Dimensional Cancer Model (TDCM) with Chen System (CS) using a Robust Adaptive Sliding Mode Controller (RASMC) together with uncertainties, external disturbances and fully unknown parameters. A simple suitable sliding surface, which includes synchronization errors, is constructed and appropriate update laws are used to tackle the uncertainties, external disturbances and unknown parameters. All simulations to achieve the synchronization for the proposed technique for the two non-identical systems under consideration are being done using Mathematica. Furthermore, application to secure communication is also demonstrated on tumor cells.

Introducing TRICOVA:“ Trichotomous Covariance” A Post Hoc Advanced Statistical Test of Qualitative and Quantitative Group Variances to Determine the Strength of the Relationships Between Variables of the Tri–Squared Test

Vol. 4  Issue 3
Year: 2015
Issue:Jul-Sep
Title:Introducing TRICOVA:“ Trichotomous Covariance” A Post Hoc Advanced Statistical Test of Qualitative and Quantitative Group Variances to Determine the Strength of the Relationships Between Variables of the Tri–Squared Test
Author Name:James Edward Osler II
Synopsis:
This monograph provides an epistemological rational for novel “Trichotomous Covariance” statistic represented by the acronym [“TRICOVA”]. This new statistic is an innovative in depth way of investigating a Post Hoc Tri–Squared Test as an advanced data analytical methodology. TRICOVA is a detailed statistical procedure for the internal testing of the outcomes of a significant transformation of qualitative data into quantitative outcomes through the Tri–Squared Test (first introduced in the i-manager’s Journal on Mathematics, and detailed further in the Journal on Educational Technology, Journal on School Educational Technology, and in the Journal on Educational Psychology). TRICOVA as an advanced statistical procedure; is designed to measure the overall size of the movement (or change) between inputted and outputted Tri–Squared variables. It is also designed to identify the magnitude and type of covariant relationship in existence between Tri–Squared Test qualitative and quantitative variables. This new innovative approach to the advanced statistical post hoc metrics of the Tri–Squared Test adds an additional layer of richness and insight into the inner workings of the Tri–Squared Test. It also adds considerable value to the mixed methods approach of research design that involves the holistic combination and comparison of qualitative and quantitative data outcomes. Two TRICOVA equations are presented as well as the entire process of advanced statistical Tri–Covariance analytics that display how to conduct Trichotomous Covariance inquiry.

Chemical Reaction and Thermo Diffusion Effects on Hydro Magnetic Flow of Rivlin-Erickson Fluid in an Inclined Channel

Vol. 4  Issue 2
Year: 2015
Issue:Apr-Jun
Title:Chemical Reaction and Thermo Diffusion Effects on Hydro Magnetic Flow of Rivlin-Erickson Fluid in an Inclined Channel
Author Name:V. Prabhakara Reddy, R V M S S Kiran Kumar, G. Viswanatha Reddy, P. Durga Prasad and S.V.K. Varma 
Synopsis:
The objective of this paper is to analyse the flow of viscoelastic fluid of Rivilin-Ericksen type down, an inclined plate under the influence of uniform transverse magnetic field, in the presence of viscous dissipation, thermo diffusion and chemical reaction effects. It is assumed that the flow of fluid is between two inclined heated parallel plates. In the case of stationary convection, the Rivlin-Erickson fluid behaves like an ordinary Newtonian fluid. The dimensionless governing equations are solved analytically by using perturbation method. The effects of velocity, temperature, concentration, the skin-friction coefficient, the Nusselt number and the Sherwood number for different flow parameters are shown in the graphical and the tabular forms.