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Kernel Ideals in Semigroups
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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
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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.
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.
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.
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.
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.
