Journal of the Nigerian Mathematical Society 2023-07-28T22:57:55+01:00 Professor J. A. Oguntuase Open Journal Systems <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> A STUDY OF GENERALIZED EILENBERG-MACLANE SPECTRUM THROUGH NEW $\Omega$-SPECTRUM 2023-01-13T09:56:27+01:00 PRAVANJAN KUMAR RANA RANA <p>In this paper first we construct the Eilenberg-MacLane spectrum then we study this spectrum to generalized the Eilenberg-MacLane spectrum through new $\Omega$ spectrum.</p> 2023-07-28T00:00:00+01:00 Copyright (c) 2023 TWO-STEP SECOND-DERIVATIVE BLOCK HYBRID METHODS FOR THE INTEGRATION OF INITIAL VALUE PROBLEMSs 2022-07-12T23:25:42+01:00 Gulibur Dauda Yakubu Momoh, L. Adelegan Geoffrey M. Kumleng Ali Shokri <p>One-step collocation and multistep collocation have recently emerged as powerful tools for the derivation of numerical methods for ordinary differential equations. The simplicity and the continuous nature of the collocation process have been the main attraction towards this development. In this paper we exploited some of these qualities of collocation to derive continuous block hybrid collocation methods based on collocation at some polynomial nodes inside the symmetric interval of integration and the two end points of the interval for dense output and for application which favor continuous approximations, like stiff and highly oscillatory initial value problem in ordinary differential equations. The analysis of the block hybrid collocation methods show that they are convergent and provide dense output at all interior selected points of integration within the interval of choice. Preliminary numerical computation carried out is an evidence of better performance of the methods compared with some strong property of algebraic stability required for stiff system integrators existing in the literature. Many examples are used to illustrate these properties.</p> <p>&nbsp;&nbsp;</p> 2023-07-28T00:00:00+01:00 Copyright (c) 2023 ALGEBRAIC POINTS OF DEGREE AT MOST 14 ON THE FERMAT SEPTIC 2022-09-17T20:20:03+01:00 Moussa FALL Moustapha CAMARA Oumar SALL <p>In this paper, we study the algebraic points of degree at most 14 over Q on the Fermat septic<br>curve F7 of projective equation X<sup>7</sup> + Y <sup>7</sup> + Z<sup>7</sup> = 0. Klassen and Tzermias gave in 1997 in ([5]) a geometric<br>description of algebraic points of degree at most 5 over Q on F<sub>7</sub> and O. Sall improved the results of Klassen<br>and Tzermias by determining in 2001 in ([9]), the algebraic points of degree at most 10 over Q. Using their<br>results and Abel Jacobi's theorem, we extend their work by giving a geometric description of algebraic points<br>of degree at most 14 over Q on F<sub>7</sub>.</p> 2023-07-28T00:00:00+01:00 Copyright (c) 2023 BIPOLAR PICTURE FUZZY SUBGROUP OF A GROUP 2023-05-18T21:38:01+01:00 Taiwo Olubunmi Sangodapo Babatunde Oluwaseun Onasanya <p>In this paper, the bipolar picture fuzzy set is extended to groups by introducing the concept of bipolar picture fuzzy subgroup of a group. This is a generalisation of both bipolar fuzzy subgroup and bipolar intuitionistic fuzzy subgroup. Several properties of bipolar picture fuzzy subgroup were established. Finally, the notions of bipolar picture fuzzy cosets and bipolar pseudo picture fuzzy cosets were introduced.</p> 2023-07-28T00:00:00+01:00 Copyright (c) 2023 On the subsemigroup generated by idempotents of the semigroup of order preserving and decreasing contraction mappings of a finite chain 2022-12-12T12:50:26+01:00 Muhammad Mansur Zubairu <p>Denote $[n]$ to be a finite chain $\{1,2,\ldots,n\}$ and let $\mathcal{ODP}_{n}$ be the semigroup of order preserving and order decreasing partial transformations on $[n]$. Let $\mathcal{CP}_{n}=\{\alpha\in \mathcal{P}_{n}: (\textnormal{for all}~x,y\in \dom~\alpha)~|x\alpha-y\alpha|\leq|x-y|\}$ be the subsemigroup of partial contraction mappings on $[n]$. Now let $\mathcal{ODCP}_{n}=\mathcal{ODP}_{n}\cap \mathcal{CP}_{n}$. Then $\mathcal{ODCP}_{n}$ is a subsemigroup of $\mathcal{ODP}_{n}$ In this paper, we identify the subsemigroup generated by the idempotents in the semigroup of order-preserving and order-decreasing partial contractions $\mathcal{ODCP}_n$. In particular, we characterize the idempotents in the semigroup and study factorization in the subsemigroup generated by the idempotents in $\mathcal{ODCP}_n$. We give a necessary and sufficient condition for product of two idempotents to be an idempotent and otherwise.</p> 2023-07-28T00:00:00+01:00 Copyright (c) 2023 ON THE CONVERGENCE BEHAVIOUR OF SOLUTIONS OF CERTAIN SYSTEM OF SECOND ORDER NONLINEAR DELAY DIFFERENTIAL EQUATIONS 2023-06-18T20:26:51+01:00 Akinwale Olutimo <p>Convergence criteria for the solutions of certain<br />system of two nonlinear delay differential equations with con-<br />tinuous deviating argument ϱ(t) using a suitable Lyapunov-<br />Krasovskii’s functional are established in this study. The new<br />result attained extends and updates some results mentioned in<br />the literature. A numerical illustration is given to show the va-<br />lidity of the result as well geometric analysis to describe the<br />behavior of solutions of the system.</p> 2023-07-28T00:00:00+01:00 Copyright (c) 2023