Journal of the Nigerian Mathematical Society <p>Journal of the Nigerian Mathematical Society (JNMS)</p> <p>JNMS provides a means of communication and exchange of ideas among workers in mathematical sciences (mathematics, mathematical physics, statistics, computer science), and offers an effective method of bringing new results quickly to the public. By doing so the journal establishes an informal vehicle enabling the field of mathematical sciences to be understood in a broad sense. It will include theoretical and experimental results, and fundamental and practical research.<br /><br /></p> en-US (Professor J. A. Oguntuase) (ICTS) Tue, 27 Dec 2022 12:19:23 +0100 OJS 60 Block Bi-Basis Collocation Method for Direct Approximation of Fourth-order IVP <p>This study presents the derivation of two-step fifth-order hybrid scheme based on the combination of Hermite and shifted Chebyshev polynomials as bases functions of the collocation techniques. The technique was used to generate a set of hybrid schemes at selected grid and non-grid points and implemented as a block method. The derived block method (Block Bi-basis Collocation Method) was applied as a simultaneous integrator to linear and non-linear fourth-order initial value problems of ordinary differential equations. The zero stability, order, error constants, consistency, convergence and numerical results of the proposed block method are analysed. The application of the block bi-basis collocation method to some fourth-order initial value problems demonstrated the effectiveness and accuracy of the method. The block bi-basis collocation method compared favorably with existing methods in literature.</p> Blessing Iziegbe Akinnukawe, Mathew Remilekun Odekunle Copyright (c) 2022 SOME GEOMETRIC PROPERTIES OF A FAMILY WALKER METRIC ON A EIGHT-DIMENSIONAL MANIFOLDS <p>A pseudo-Riemannian manifold which admits a field of parallel<br>null r-planes, with r ≤ n 2 is a Walker n-manifold. A.G. Walker in [12] investi-<br>gated the canonical forms of the metrics and came out with some interesting re-<br>sults. Of special interest are the even-dimensional Walker manifolds (n = 2m)<br>with fields of parallel null planes of half dimension (r = m). In this paper, we<br>consider a perticular eight-dimensional Walker manifold, derive and investigate<br>some geometric properties of the curvature tensors of the Manifold. We give<br>some theorems for the metric to be Einstein and Locally Conformally Flat.</p> Silas Longwap, ABDOUL SALAM DIALLO Copyright (c) 2022 Tue, 27 Dec 2022 00:00:00 +0100 LATTICE POINTS OF DILATIONS OF THE STANDARD 2-SIMPLEX AND THE GRASSMANNIAN Gr(2,n) <p>The connection between the combinatorics of the lattice points of the dilation r∆2 of the standard 2-simplex ∆2 and the cohomology ring of the Grasmmannian Gr(2, r+2) is explored. Specifically, two important refinements of the Ehrhart polynomial<br>are realized from this connection. One of the refinements interprets the Poincar´epolynomial P(Gr(2, r + 2), z) as the number of lattice points on each of the slicing lines of r∆2 with respect to a fixed weight.<br><br><br><br></p> Dr. Praise Adeyemo Copyright (c) 2022 Tue, 27 Dec 2022 00:00:00 +0100 ON THE CONSTRUCTION OF QUANDLES OF ORDER 3N <p>We present methods of constructing examples of quandles of order 3n; n &gt; or =  3. The<br>necessary and sucient conditions for the constructed examples to be (i) connected<br>(ii) group (conjugate) (iii) involutory and (iv) Alexander quandles are examined and<br>presented. Two particular examples from these methods are presented for&nbsp; illustra-<br>tion purpose and their properties are obtained, and these are used in classifying the<br>constructed examples up to isomorphism.</p> Abednego Orobosa Isere, Abraham Elakhe, Cletus Ugbolo Copyright (c) 2022 Tue, 27 Dec 2022 00:00:00 +0100 On the numerical solution of the Kuramoto-Sivashinsky equation using operator-splitting method <p>An operator-splitting scheme for the Kuramoto-Sivashinsky equation, $u_t+uu_x+u_{xx}+u_{xxxx}=0$, is proposed. The method is based on splitting the convective and the diffusive differential terms thereby permitting an efficient scheme choice for each of them, and when combined give a reliable solution for the entire equation. We demonstrate the accuracy and capability of the proposed split scheme via several numerical experiments. Computations of the bound, $\displaystyle{\limsup_{t\rightarrow \infty}\|u(x,t)\|_2}$ for the equation is also presented.</p> Adebayo Abiodun Aderogba, Michael Chapwanya, Jules Djoko Kamdem Copyright (c) 2022 Tue, 27 Dec 2022 00:00:00 +0100 Stability and Boundedness Analysis of a Prey-Predator System with Predator Cannibalism <p>The prey-predator system with predator cannibalism is considered in this<br>papper. We employ the Lyapunov’s direct method for the prey-predator system<br>and demonstrate its efficacy. This method is built upon theoretical Lyapunov’s<br>function that is constructed such that the scalar function and its derivative is<br>positive and negative definite respectively to determine the dynamic behaviour<br>of the system considered including stability and boundedness. The results show<br>that the density functions describing the prey-predator system is better rapidly<br>converging under certain sufficient conditions obtained by the Lyapunov functional.<br>We give numeric example to support our findings.</p> Dr. Akinwale Olutimo, Dr. Daniel Adams, Abdullai Abdurasid Copyright (c) 2022 Tue, 27 Dec 2022 00:00:00 +0100 Impact of entropy generation on hydromagnetic nanofluid flow dispersed over a radiative vertical porous plate with Newtonian heating <p>Recently and over the years, the industrial applications of second law analysis is becoming famous. Hence, this work intend to address the combined impacts of water-based nanofluids, convective boundary state, thermal radiation, magnetic field and second law of thermodynamics .The governing equations that unravel the flow within the boundary layer are provided. The transformed governing equations are obtained by guided similarity variables, the transformed equations are solved analytically by method of undetermined coefficient. Entropy generation rate and Bejan number in dimensionless form are obtained by deriving an expression through the analytical solutions of temperature and velocity. The emerging parameters of the flow are: Bejan number, Biot number, radiation parameter, entropy generation rate, skin friction, Hartman number, suction, Prandtl, Nusselt and Reynolds number. Also, the effects of these parameters are presented in graphs and tables. In addition, Entropy generation are enhanced by Eckert number, radiation parameter, permeability parameter, suction , prandtl number and Brinkman number for both copper and alumina water. Finally, the results of this work is compared with published work in the literature, this result is in consonant with this work.</p> John Omowaye, Olubode Koriko Copyright (c) 2022 Tue, 27 Dec 2022 00:00:00 +0100 ON INDEPENDENCE POLYNOMIALS OF QUOTIENT BASED GRAPHS FOR FINITE ABELIAN GROUPS <p>In this paper we investigated the independence polynomial of quotient based graph {\LARGE${\varphi}$}$_{\scriptscriptstyle H}({ G } )$ of an abelian group $G$ relative to all it's subgroups since a subgroup $H$ of an abelian group is normal . The graph {\LARGE${\varphi}$}$_{\scriptscriptstyle H}({ G } )$ is a graph with condition of adjacency where two distinct elements $x,y \in G$ are adjacent in the graph iff $xy \notin H$. A formula for computing the independence polynomial is obtained.</p> Aliyu Suleiman, A.I . Kiri Copyright (c) 2022 Tue, 27 Dec 2022 00:00:00 +0100