Journal of the Nigerian Mathematical Society

ON SUBGROUPS OF A CLASS OF FINITE MINIMAL NONABELIAN 3-GROUP

Olusola Ogunfolu — 2024-03-23

In this paper, we determined the number of subgroups of a finite nonabelian 3-group $G $ defined by a presentation
$\rho_{1} \in G = \left\lbrace a,b \mid a^{9} = b^{9} = e, \left[ a,b \right]
= a^{3} \right\rbrace $, where $a, b $ are generators of the same order. The form and the order of elements of the presentation group were obtained. We also drew the diagram of subgroups lattice and derived an explicit formula for counting the number of subgroups of the group.

COMPARISON OF BLOCK IMPLICIT ALGORITHM AND RUNGE KUTTA METHOD FOR THE SOLUTION OF NON LINEAR FIRST ORDER PROBLEMS WITH LEGENDRE POLYNOMIAL AS THE BASIC FUNCTIONS

ADEMOLA MUDASHIRU BADMUS — 2024-03-23

A family of uniform and non-uniform order Linear
Multistep Block Methods was developed using Legendre Polyno-
mial as the basic functions and reconstructed to its equivalent
Runge { Kutta type Methods. The implicit block method at
k = 3 give a uniform order 6 while implicit block method at
k = 4 gives non uniform order 6 x 9 . The continuous for-
mulation of the method was evaluated at some grid and o grid
points to obtain our implicit block methods. Also both methods
were demonstrated on non-linear rst order initial value prob-
lems (ivps) and the results obtained compared favorably with
the analytic solution

INERTIAL SELF ADAPTIVE ALGORITHM FOR SOLVING EQUILIBRIUM FIXED POINT AND PSEUDOMONOTONE VARIATIONAL INEQUALITY PROBLEMS IN HILBERT SPACES

Olufemi Ogunsola — 2024-03-23

In this paper, we study an iterative approximation of a common solution to equilibrium problem, fixed point problem and variational inequality problems. We introduced an inertial Tseng method with a viscosity approach for approximating a solution to the problem in a Hilbert space. The method is self adaptive so that it's execution does not rely on the Lipschitz condition of the cost operator. Under mild conditions, we show that the sequence generated by our algorithm converges strongly to a common solution of the fixed point and variational inequality problems associated with demicontractive and pseudomonotone operator which is also a solution to a generalized equilibrium problem. Our results extend and improve several existing results in the literature.

A NUMERICAL ANALYSIS OF THE FLOW AND HEAT TRANSFER CHARACTERISTICS OF EYRING \\POWELL FLUID WITH MIXED CONVECTION OVER A STRATIFIED SHEET

R. A. Mustapha — 2024-03-23

This article explores the importance of mixed convection in the analysis of heat transfer within fluid flow, which holds significant relevance in the fields of hydrodynamics and engineering. The focus of this study is to investigate the impact of mixed convection on heat transfer and to assess the significance of heat generation and absorption in the flow of an Eyring Powell fluid. The fluid being examined is assumed to possess properties such as viscosity, incompressibility, two-dimensionality, and laminar behavior. To facilitate the analysis, the governing system of partial differential equations (PDEs) that describes the flow is transformed into a system of nonlinear ordinary differential equations (ODEs) using an appropriate similarity transformation. These nonlinear equations are then numerically solved utilizing Maple software. The article discusses the effects of various relevant parameters on both the velocity and temperature profiles through graphical representations. Additionally, the skin friction coefficient and Nusselt number, which characterize the flow, are examined using graphs and tables. The results indicate that an increase in the mixed convection parameter leads to a reduction in skin friction, which in turn results in an increase in the velocity profile. Similarly, a similar trend is observed for the heat absorption and generation parameter.

ASYMPTOTIC STABILITY AND BOUNDEDNESS CRITERIA FOR CERTAIN SECOND ORDER NONLINEAR DIFFERENTIAL EQUATIONS

Daniel Adams — 2024-03-23

In this paper, we examined some criteria for the stability and boundedness of solutions to certain second order nonlinear differential equation
$$x^{\prime\prime} + b(t)f(x,x^\prime) + c(t)g(x)h(x^\prime) = p(t,x,x^\prime),$$
where $b,c,f,g,h$ and $p$ are real valued functions which depend on the argument displayed explicitly. By applying a suitable Lyapunov function to study the qualitative properties mentioned earlier, we are able to extablish the asymptotic stability and boundedness of solutions. An example on the stability of solutions is hereby included to corroborate our result.

SOME ALGEBRAIC PROPERTIES OF GENERALISED CENTRAL LOOPS

Olusola Adeniran — 2024-03-23

Generalised central loops ($GCL$) are loops satisfying the identity\\ $x(z\cdot z^{\sigma}y) = (xz\cdot z^{\sigma})y$. In this work, three generalised identities corresponding to three of the four left central identities are newly introduced and all of these three generalised identities together with identity $z(z^{\sigma}\cdot xy) = (z\cdot z^{\sigma}x)y$, which was introduced in \cite{ref12} are shown to be equivalent in any loop. It is shown that every $GCL$ $(G, \cdot, \sigma) = (G, \cdot)$ is a $\sigma-$central square loop. Furthermore, it is established that a loop $(G, \cdot, \sigma) = (G, \cdot)$ is a $GCL$ if and only if $L_{z^{\sigma}}L_z$ and $R_zR_{z^{\sigma}}$ are crypto-automorphisms of $(G, \cdot, \sigma) = (G, \cdot)$ with companions $c_1 = (zz^{\sigma})^{-1}$ and $c_2 = e$, and companions $d_1 = e$ and $d_2 = (zz^{\sigma})^{-1}$ respectively. The necessary and sufficient conditions for a $GCL$ to be isomorphic to its principal isotopes are also formulated. Every pseudo-automorphism of a $GCL$ $(G, \cdot, \sigma) = (G, \cdot)$ with companion $zz^{\sigma}$ is shown to be a semi-automorphism. Lastly, a $GCL$ was constructed using a group together with an arbitrary subgroup of it.