GPH - International Journal of Mathematics

ON THE NORM OF JORDAN ELEMENTARY OPERATOR IN TENSOR PRODUCT OF C*-ALGEBRAS

2024-03-07T15:33:12+00:00

The norm property of different types of Elementary operators has attracted a lot of researchers due to its wide range applications in functional analysis. From available literature the norm of Jordan elementary operator has been determined in C*-algebras, JB*-algebras,standard operator algebra and prime JB*-triple but not much has been done in tensor product of C*-algebras. This paper, dealt with the norm of Jordan elementary operator in a tensor product of C*-algebras. More precisely, the paper investigated the bounds of the norm of Jordan elementary operator in a tensor product of C*-algebras and obtained that The concept of finite rank operator and properties of tensor product of Hilbert spaces and operators and vectors in Hilbert spaces were used to achieve the paper’s objective.

EFFICIENT COMPUTATION OF THE M-CLOSURE FOR SOLVABLE PERMUTATION GROUPS

2024-03-17T15:50:03+00:00

This research presents a novel approach to efficiently compute the m-closure of solvable permutation groups of degree n. The m-closure is an essential concept in group theory, particularly in understanding the structure and properties of permutation groups. We propose an algorithm that constructs the m-closure with a time complexity of n^O^(m), significantly improving the computational efficiency compared to existing methods. Through rigorous mathematical analysis and computational experiments, we demonstrate the effectiveness and scalability of our approach.

ENHANCE CANONICAL IMAGE COMPUTATION FOR FINITE PERMUTATION GROUPS USING GRAPH BACKTRACKING

2024-03-17T16:02:47+00:00

In this paper, we present a novel algorithm for efficiently computing canonical images of objects under the action of finite permutation groups. Our approach builds upon previous work utilizing Graph Backtracking, an extension of Jeffrey Leon's Partition Backtrack framework. By generalizing both Nauty and Steve Linton's Minimal Image algorithm, our method achieves significant improvements in computational efficiency and accuracy. We introduce a systematic exploration of the permutation group structure to guide the canonical image computation process, resulting in enhanced performance compared to existing methods. Through rigorous theoretical analysis and empirical evaluation, we demonstrate the effectiveness and scalability of our algorithm across diverse application scenarios.

Effects of Algebra Tiles Teaching Approach on Students Achievement in Quadratic Equation in FCT Abuja, Nigeria

2024-03-21T21:08:35+00:00

This study investigated the effect of Algebra Tiles Teaching Approach on students’ achievement in quadratic equation in the Federal Capital Territory, Abuja. Two research questions and two null hypotheses guided the study. The study adopted a quasi-experimental research design (intact class, pre-test, post-test control group design). A sample size of 122 Senior Secondary School students made up of 64 SS 2A students drawn from Government Secondary School Gwagwalada; and 58 SS 2A students, drawn from Government Secondary School, Kwali. “Quadratic Equation Achievement Test (QEAT)” containing 20 Multiple Choice Test items was developed to elicit data for the study. Mean scores and standard deviation were used to answer the research questions; while t-test was used to test the null hypotheses. The findings of the study revealed that students taught quadratic equation using Algebra Tiles Teaching Approach had higher mean achievement scores than their counterparts taught using conventional teaching method. Also, the study found that there is a significant difference between the mean achievement scores of male and female students taught quadratic equation using Algebra Tiles Teaching Approach. The study concluded that Algebra Tiles Teaching Approach had significant effect on students’ achievement in quadratic equation in public senior secondary schools in FCT, Nigeria. It was recommended that mathematics teachers should create more time for extension classes in preparation for internal and external examinations. As this will enhance students’ academic achievements.

APPROXIMATE SOLUTION OF FRACTIONAL ORDER MATHEMATICAL MODEL ON THE CO-TRANSMISSION OF ZIKA AND CHIKUNGUNYA VIRUS USING LAPLACE ADOMIAN DECOMPOSITION METHOD

2024-04-19T05:13:27+00:00

Gaining insight into the transmission dynamics of the Zika and Chikungunya viruses, as well as their co-infection, is essential for implementing efficient public health interventions. This paper presents a comprehensive fractional order mathematical model consisting of thirteen non-linear compartments to accurately represent the intricate interactions between humans and infected mosquito populations, as well as the challenges associated with their identification. In order to solve this model, we utilize the Laplace Adomians Decomposition Method (LADM), which is a very effective analytical technique for solving nonlinear differential equations. By utilizing LADM, we obtained infinite series solutions for the previously given model that ultimately converged to its precise solutions. The numerical simulations of the model demonstrate the transmission patterns of Zika virus, Chikungunya virus, and their co-infections for different values of . We utilized the fmicon algorithm, a MATLAB optimization tool, to accurately fit into the model, real-life data from Espirito Santos State in Brazil, where two viruses are concurrently spreading. The simulation deduce that, reducing mosquito biting rates and promoting compliance with treated bed net usage can substantially mitigate Zika-Chikungunya co-infection dynamics.