Mathematical Modeling of Higher Overtone Vibrational Frequencies in Dichlorine Monoxide
Some Types of Generalized Closed and Generalized Star Closed Sets in Topological Ordered Spaces
Optimizing Capsule Endoscopy Detection: A Deep Learning Approach with L-Softmax and Laplacian-SGD
Kernel Ideals in Semigroups
Modeling the Dynamics of Covid-19 with the Inclusion of Treatment, Vaccination and Natural Cure
Calculation of Combined Vibrational Frequencies in Cl₂O using Lie Algebraic Method
An Introduction to Various Types of Mathematics Teaching Aids
A Simple Method of Numerical Integration for a Class of Singularly Perturbed Two Point Boundary Value Problems
A New Approach to Variant Assignment Problem
A Homotopy Based Method for Nonlinear Fredholm Integral Equations
Proof of Beal's Conjecture and Fermat Last Theorem using Contra Positive Method
Trichotomy–Squared – A Novel Mixed Methods Test and Research Procedure Designed to Analyze, Transform, and Compare Qualitative and Quantitative Data for Education Scientists who are Administrators, Practitioners, Teachers, and Technologists
Algorithmic Triangulation Metrics for Innovative Data Transformation: Defining the Application Process of the Tri–Squared Test
A New Hilbert-Type Inequality In Whole Plane With The Homogeneous Kernel Of Degree 0
Introducing Trinova: “Trichotomous Nomographical Variance” a Post Hoc Advanced Statistical Test of Between and Within Group Variances of Trichotomous Categorical and Outcome Variables of a Significant Tri–Squared Test
Surfaces in R3 with density
This discourse provides a novel statistic for the measurement of uniformity. This novel statistic has new notation, models, and operations that resolve the differences in the three primary statistical methodologies. It also extends the research that appeared in the July–September i-manager’s Journal of Educational Technology and the March–May i-manager’s Journal on Circuits and Systems. The “Coefficient of Consociation” is a unique statistic that is represented by the lower case Greek letter upsilon [ν]. The Coefficient of Consociation is a trichotomous research statistic that measures and analyzes research through the use of trichotomous models, methodology, and the Tri-Squared Meta-Analysis Test (Osler and Wright, 2015b) which is a part of its data measurement analytical methodology. Neuroscientific terminology is provided in the narrative review of literature to explain the foundations of trichotomous-based research and trichotomously-grounded research designs. Additional research into consociation as a measure of uniformity will further advance in-depth investigations into the tripartite aspects of nature and natural phenomena based on the mathematical law of trichotomy.
In this paper, the authors have synchronized the two identical systems of Circular Restricted Three Body Problem evolving from different initial conditions using a Robust Adaptive Sliding Mode Controller. The two chaotic identical systems have been synchronized under the effects of uncertainties and external disturbances with unknown parameters. A simple suitable sliding surface, which includes synchronization errors, is constructed and appropriate update laws are implemented to tackle the uncertainties, external disturbances, and unknown parameters. For the synchronization of the two identical systems under consideration, all simulations are being done using Mathematica. Furthermore, the secure communication scheme has also been demonstrated.
Because of central role played by Circular Uniform Distribution, the most important hypothesis about a distribution on the Circle is that of Uniformity. Though several tests were proposed, cut-off points for various sample sizes and level of significance were not made available in the literature. Hence, an attempt is made here to present tables of cut-off points and their utility in discussing goodness of fit of a model is presented.
The well known Burr type X distribution is considered as a null population. Log-logistic and Weibull-Exponential (Dubey - 1966) distributions are taken as alternative populations. Two test statistics based on population quantiles, Likelihood Ratio (LR) type criteria are suggested to discriminate between the considered null and alternative populations. The percentiles of the proposed test statistics are evaluated. The performance of the test procedures are compared through the respective values of computed power functions.
Glancing the literature, semicircular, arc and skewed angular data is observed in the applications such as Feldspar laths data (Fisher, 1993, p. 240), Face - cleat in a coal seam data (Fisher, 1993, p. 254), Fallen trees data (Toshihiro, et al., 2012), face recognition problem, etc., and not much was done to model such angular data. Moreover Chi – Square distribution can be used as a quick test of significance in most situations, especially using machine learning algorithms. This finer pointer has become a motivating factor to work on l - axial (arc) models, and they can be viewed as the most general angular models from which Circular, Semicircular and other kinds of models could be deduced as particular cases and also to derive new angular model from Chi-Square distribution. In this paper, the authors introduce a new semicircular model, induced by Modified Inverse Stereographic Projection on Chi-Square distribution for modeling semicircular data. The authors extend it to the l- axial Chi-Square distribution for modeling axial data and also they derive the first two trigonometric moments for the proposed distribution in closed forms.
