Journal of the Nigerian Mathematical Society

A REVIEW OF SOME RESEARCH PUBLICATIONS OF PROFESSOR ADEWALE ROLAND TUNDE SOLARIN

2025-03-18T16:27:35+01:00

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AN ACCURATE FIFTH-ORDER METHOD FOR SOLVING STIFF PHARMACOKINETICSS MODELS

2024-08-15T12:29:00+01:00

This paper presents a linear multistep interpolation and collocation block hybrid method that is zero stable and convergent. The method is formulated to approximate the solution of stiff pharmacokinetics models. By implementing the method, the maximum absolute error{s are} compared with a few existing methods and known stiff solvers. Results show that the new method performs better than the existing methods it was compared with.

NUMERICAL SOLUTION OF A COMBUSTION MODEL WITH THERMAL CONDUCTIVITY AND REACTANT DIFFUSIVITY IN ARBITRARY DOMAINS USING THE VARIATIONAL ITERATION METHOD

2024-08-12T13:51:02+01:00

 This paper presents the numerical solution of a combustion model with thermal conductivity and reactant diffusivity 
in arbitrary domains using the Variational Iteration Method (VIM). The paper begins with a brief introduction of the
 model and the basic idea of VIM. This is followed by the numerical solutions of the model and animated graphical
 representation of the solutions. The result obtained demonstrates that the model is highly sensitive to initial 
conditions, and its applicability is dependent on thermal conductivity and reactant diffusivity values. Computations
 are carried out using Maple 18 software.

AUTOTOPIC CHARACTERISATION OF RIGHT CHEBAN LOOP

2024-08-02T12:41:02+01:00

Some fundamental properties of right Cheban loop are established in the present study in relation to the autotopism of right Cheban loop. It is found that the autotopism is a right pseudo-automorphism with companion $c=u\dot vu^{-1}$. The autotopism and pseudo-automorphism are characterized in terms of the right and left translation. Thus, necessary and sufficient conditions are established for the Moufang part of right Cheban loops to be an autotopism and pseudo-automorphism with companion $c=(x^3)^{-1}\cdot x^{-1} x^3$. The study also describes the behaviour of the pseudo-automorphism of the right Cheban loops on the nuclei and Moufang part of the right Cheban loops.

A FURTHER INVESTIGATION ON THE CORE OF MIDDLE BOL LOOPS

2024-10-07T11:36:36+01:00

In this paper, further investigation of the core of middle Bol loop relative to the core of right Bol loop, is presented. The efforts revealed that, (i) if $T$ is any permutation of $Q$, then $xT\otimes yT=(x\oplus y)T$ if and only if $[(x\circ y\backslash\backslash x)T\circ f]I= (xT\circ f)I\circ(yT\circ f)I\backslash\backslash(xT\circ f)I, \forall\ x,y\in Q \textrm{~and some } f\in Q$, where $(Q,\oplus)$ and $(Q,\otimes)$ are respectively, the cores of the middle Bol loop $(Q,\circ)$ and its isotope $(Q,\ast)$. (ii) in particular it was also shown that a middle Bol loop satisfies the identity: $(x\circ f^{-1}\backslash\backslash x)\circ f=(x\circ f)\circ(x\circ f), \forall\ f,x\in Q$ if and only if for each isotope $(Q,\ast)$ of the middle Bol loop $(Q,\circ)$ given by $x\ast y=(xR^o_fT\circ yI)R^{o-1}_fI$, then $x\otimes y=x\oplus y, \forall\ x,y\in Q$, where $(Q,\otimes)$ and $(Q,\oplus)$ the cores of $(Q,\ast)$ and $(Q,\circ)$ respectively . (iii) it was shown also that, the core exhibits some left self symmetry, left self distributive and that, the middle Bol loop is right distributive over its core. It was also remarked that, the core of middle Bol loop exhibits a form of semi-automorphism. New results were obtained and old ones extended.

SOME BOHR-TYPE INEQUALITIES FOR CERTAIN CLASS OF HOLOMORPHIC FUNCTIONS

2024-11-09T08:39:07+01:00

In this paper, we generalize and extend the recent work of S. Alkaleefah in 2020 on Bohr inequality for certain family of holomorphic functions. Hence, some existed and new results are obtained.

OPTIMAL CONTROL STRATEGY OF HIV/AIDS MODEL WITH PRE-EXPOSED PROPHYLAXIS AND BEHAVIORAL CHANG.

2024-07-31T22:49:44+01:00

HIV/AIDS has had a devastating global impact, particularly in underdeveloped nations where it has led to decreased life expectancy, higher mortality rates, and widespread socio-economic challenges. In contrast, developed countries have made significant progress in containing the spread and improving quality of life for those infected through advanced medical care and public health initiatives. This disparity underscores the need for effective control strategies. This study presents a six-compartment optimal control HIV/AIDS model with a constant inflow of infected immigrants. The model incorporates optimal control strategies such as public sensitization $u_1$, the Pre-Exposure Prophylaxis strategy $u_2$, screening of new arrivals $u_3$, and sexual behavioral therapy $u_4$ to minimize the spread of the disease. Pontryagin's maximum principle was employed to characterize the optimal control problem and the numerical simulation was carried out using Maple 18 software. Optimal control analysis showed that a combination of the four controls $u_1$, $u_2$, $u_3$, and $u_4$ decreased infection in all classes. The inclusion of Pre-Exposure Prophylaxis reduced the spread of HIV infection. The proposed control strategies were effective in scaling down the number of new infections despite the inflow of infective immigrants.

POLYGROUPOID, POLYQUASIGROUP, POLYLOOP AND THEIR NUCLEI

2024-10-03T07:52:17+01:00

In this paper, new hyper-algebraic structures called polygroupoid, polyquasigroup and polyloop were introduced with concrete examples given. The first, second, third and fourth left (middle, right) nuclei of polygroupoid were introduced and studied. It was shown that first left (middle, right) nuclei of a polygroupoid is contained in second, third and fourth left (middle, right) nuclei of the polygroupoid. Hence, the second, third and fourth left (middle, right) nuclei of a polygroupoid generalize the first left (middle, right) nuclei of the polygroupoid. Examples of polyquasigroups and polyloops that satisfy the above results were provided.

THE CYCLICPOID LIFE STAGES OF A STAR-LIKE MATHEMATICIAN

2025-01-13T12:37:23+01:00

The star-like mathematician Adewale Roland Tunde Solarin $(ARTS)$ is a role model and mentor in pure mathematics who established the coexistence relations between particular algebraic operators and functional theory. The influence and contribution of $ARTS$ on the novel class of star-like semigroups $(students)$ and the characterization of cyclicpoid $C_{y}P\omega_n^*$ functions indicate a major relationship between group theory, semigroup theory, and tropical algebra. The present study uses a classical approach to build an equivalence relation between the ranks of the development phases of a star-like mathematician $ARTS$.

Editorial

2025-03-21T19:00:08+01:00