International Journal of Mathematical Sciences and Optimization: Theory and Applications

On Collapse Of Order-Preserving and Idempotent of Order-Preserving Full Contraction Transformation Semigroup

A. Ibrahim, E. A. Nwaibeh, M. O. Francis, C. J. Okigbo — Sun, 14 Apr 2024 21:00:46 +0000

Let Tn be the set of full transformation semigroup on Xn = {1, 2, 3, · · · , n}, C +(α) =|OCTn |= q be it’s subsemigroup on collapse of order-preserving full contraction transformation, C +(αE) =| E(OCTn) |= qE be the collapse on idempotent of order-preserving full contraction transformation and C +(α) =| C +(α) |= ∪t∈Imα | {tα−1 ≥ 2} | be the formula for total number of collapsible element.In this paper, we investigate the collapse element on order-preserving and idempotent of order- reserving full contraction transformation semigroup.

Isotopism Classes of 2-dimensional Leibniz Algebras

M. A. Mohammed, H. M. Balami, A. G. Dzarma — Sun, 14 Apr 2024 00:00:00 +0000

This paper gives the classification of two-dimensional Leibniz algebras into isotopism classes. The matrix structure constants of the algebras were used to determine the isotopism between them. An algorithm was developed for n-dimensional Leibniz to achieve this objective. The algorithm was tested on the Leibniz algebras of dimension two over Z2. From the result obtained, it was observed that there is no isotopism between the algebras. Consequently, we conclude that isotopism and isomorphism are equivalent in this case.

Another New Two Parameter Estimator in Dealing with Multicollinearity in the Logistic Regression Model

O. J. Oladapo, O. O. Alabi, K. Ayinde — Tue, 16 Apr 2024 06:52:24 +0000

In logistic regression models, the maximum likelihood method is always one of the commonly used to estimate the model parameters. However, unstable parameter estimates are obtained due to the problem of multicollinearity. In this article, a new two parameter biased estimator is proposed to combat the issue of multicollinearity in the binary logistic regression models. The proposed estimator is a general estimator which includes other biased estimators, such as the Logistic Ridge, Logistic Liu and the estimators with two biasing parameters as special cases. The properties of the proposed estimator were derived, and six (6) forms of biasing parameter k (generalized, maximum, median, mid-range, arithmetic and harmonic means) were used in this study. Necessary and sufficient conditions for the superiority of the new two parameter biased estimator over the existing estimators are obtained. Also, Monte Carlo simulation studies are executed to compare the performance of the proposed biased estimator. Finally, a numerical example is given to illustrate some of the theoretical results. The proposed estimator outperforms all the other estimators in the various design of experiment used in this study.

A Mathematical Model for the Prevention of HIV/AIDS in the Presence of Undetectable Equals Untransmittable Viral Load

Tue, 16 Apr 2024 16:42:33 +0000

Recent advancement in medicine has brought about the use of Antiretroviral Therapy (ART) treatment regime to reduce the viral load of a Human Immunodeficiency Virus (HIV) or Acquired Immune Deficiency Syndrome (AIDS) patients to an Undetectable equals Untransmittable (U=U) level. While half of HIV-positive individuals in the United States have achieved an undetectable viral load, African countries face distinct challenges, including unawareness of the possibility of attaining the U=U viral load. This paper presents a novel mathematical model for HIV/AIDS transmission in Africa, using Cape Verde as a case study, by incorporating the ART treatment, resulting in U=U. The qualitative properties of the model, including the boundedness and positivity of its solution were obtained. Local and global stability analyses of the Disease-Free Equilibrium (DFE) point of the model were performed using the next generation matrix approach and the direct Lyapunov method respectively. The result indicated that the DFE of the model is stable and the disease cannot invade the studied population. The
model equations were solved through the implementation of MATLAB ODE45 algorithm and simulations were performed to visualize the effects of the ART on attaining a U=U viral load.

On quaternion valued rectangular S-metric space

Thu, 18 Apr 2024 06:54:31 +0000

A metric space can be seen as a distance space having a geometric structure, with only a few axioms. In this paper we introduce the concept of quaternion valued rectangular S metric spaces. The paper treats material concerning quaternion valued rectangular S metric spaces that is important for the study of fixed point theory in Clifford analysis. We introduce the basic ideas of quaternion valued rectangular S metric spaces and Cauchy sequences and discuss the completion of a quaternion valued rectangular S metric space. In this work, we will work on H, the skew field of quaternions. This means we can write each element q ∈ H in the form q = a + bi + cj + dk where a, b, c, d ∈ R and i, j, and k are the fundamental quaternion units. For these elements we have the multiplication rules I 2 = j 2 = k 2 = −1, ij = −ji = k, kj = −jk = −i and ki = −ik = j. The conjugate element is given by q = a−bi−cj −dk. The quaternion modulus has the form of |q|= √a 2 + b 2 + c 2 + d 2. Quaternions can be defined in several different equivalent ways. Quaternion is non commutative in multiplication. There is also more abstract possibilty of treating quaternions as simply quadruples of real numbers [a, b, c, d], with operation of addition and multiplication suitably defined. The components naturally group into the imaginary part (b, c, d), for which we take this part as a vector and the purely real part, a, which called a scalar. Sometimes, we write a quaternion as [a, V ] with V = (b, c, d). For more information about metric spaces, its generalization and quaternion analysis

Application of Games Theory to Crime Investigation of suspects (A Case Study of Delta State Police Divisional Head-quarters, Abraka)

C. R. Chikwendu, E. L. Eduiyovwiri — Wed, 24 Apr 2024 12:21:44 +0000

This paper discussed Games Theory and its application to real life situation. Emphasis was on the application of Games Theory to check some unlawful practice and even suspects under investigation such as multiple (or false) confession from suspects, use of physical violence during investigation and wrong conviction of suspects. This research was aimed at using game theory in combating crime in the society. The importance of a crime free society cannot be overemphasised as a result of the high level of insecurity and hence it is imperative to apply a more tactical approach to foster solution to insecurity. This paper uses the prisoner’s dilemma method, a situation where two suspects apprehended for a crime are held in separate rooms and cannot communicate with each other. Also, quantitative method was employed to examine the research problem effectively. Data collection that aided this research were sourced through systematic sampling from previously existing works from authors. This research was developed to check some sharp unlawful Police practice and even from suspect under investigation as well as employing the technique of Game Theory as a way of obtaining true from suspects, administering justice speedily and a strong avenue for prison decongestion due to the alarming conditions in most Nigerian Prisons.

Diphtheria Disease Transmission Dynamics In Low Vaccine Coverage Setting

O. S. Johnson, H. O. Edogbanya, A. Wakili, A. T. John — Wed, 24 Apr 2024 12:32:54 +0000

Diphtheria is a severely infectious respiratory disease which transmits through droplets and preventable by periodic vaccine programs. In this paper, A six (6) Compartmental model (S, E, IA, IS, Q, R) is presented to undersee the behaviour of diphtheria disease transmission within a group of people with low or zero vaccine coverage and immunity gaps. This research explores epidemiology and mathematically well-posed model. The reproduction number was analysed using the Next Generation Matrix, we underscored that a single infected individual can trigger an outbreak, and further investigation indicates that the disease will subside if the reproduction number (R0) is less than 1, and vice versa if R0 exceeds 1. The model captures disease mitigating strategies like maternally derived immunity, vaccination, Quarantine, and asymptomatic carriers to assess how contagious the disease is and what interventions might be most effective. To validate theoretical model predictions, we conducted numerical simulations using MATLAB 2021a software. Relevant and informative model Simulations are displayed in the full text.

Block Method Coupled with the Compact Difference Schemes for the Numerical Solution of Nonlinear Burgers’ Partial Differential Equations

B. I. Akinnukawe, E. M. Atteh — Wed, 24 Apr 2024 12:49:48 +0000

In this paper, a novel block method is proposed to solve the nonlinear time dependent Burgers’ equation. The Burgers’ PDE is semi discretized in spatial direction by using the standard fourth-order compact difference schemes to yield system of nonlinear ordinary differential equations (ODE) in time.The resulting system of first-order ODE from the Burgers’ equation is approximated by a new derived Block method. The new two-step hybrid methods are developed through the Interpolation and Collocation techniques. The derived methods are applied as a block method for the numerical solution of the nonlinear Burgers’ Partial Differential Equations (PDE) which is of physical relevance. The proposed block scheme has been proven to be zero-stable, consistent and convergent, also saving computational time while maintaining good accuracy. The efficiency of the derived method is demonstrated using three test problems.

Retrospective Study of the Impact of Sensitization on COVID-19 Pandemic in Rivers State, Nigeria

A. Nwankwo, E. E. Ukwajunor, A. Egonmwan — Wed, 24 Apr 2024 17:07:57 +0000

This study examines the impact of sensitization on COVID-19 dynamics in Rivers State, Nigeria, utilizing a mathematical model and data from the Nigeria Centre for Disease Control (NCDC). Parameter estimation involves meticulous fitting, refining key parameters like βc, cm, α1, α2, α3, α4, and the reproduction number Rc. The study employs a genetic algorithm for precise parameter estimation, ensuring the model aligns closely with observed COVID-19 data. Estimated values for βc, cm, α1, α2, α3, α4, and Rc provide a robust foundation for accurate simulations, enhancing the reliability of the model and facilitating a deeper understanding of the population dynamics of COVID-19 in human population. Uncertainty and sensitivity analyses highlight crucial parameters, emphasizing the relative infectiousness of asymptomatic individuals (ηs), face mask efficacy (ϵm), and sensitization effectiveness (ϵs, cm). Numerical simulations reveal that a combined strategy of sensitization and face mask use can significantly curtail the disease progression. Targeting susceptible and exposed individuals in sensitization efforts proves most beneficial, aligning with sensitivity analysis results. Notably, the combination of sensitization and face mask use results in a remarkable 98% reduction in cumulative cases. Sensitization emphasizing various preventive measures, when doubled, shows a 99% reduction. These findings suggest that a comprehensive sensitization approach can profoundly impact COVID-19 control. Policymakers can leverage these insights to optimize sensitization
programs, emphasizing the role of preventive measures beyond face mask use, ultimately guiding effective public health strategies in Rivers State and beyond.