Journal of the Nigerian Mathematical Society

A STUDY OF GENERALIZED EILENBERG-MACLANE SPECTRUM THROUGH NEW $\Omega$-SPECTRUM

PRAVANJAN KUMAR RANA RANA — Fri, 28 Jul 2023 00:00:00 +0100

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.

TWO-STEP SECOND-DERIVATIVE BLOCK HYBRID METHODS FOR THE INTEGRATION OF INITIAL VALUE PROBLEMSs

Gulibur Dauda Yakubu, Lukman, Kumleng, Shokri — Fri, 28 Jul 2023 00:00:00 +0100

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.

ALGEBRAIC POINTS OF DEGREE AT MOST 14 ON THE FERMAT SEPTIC

Moussa FALL, Moustapha CAMARA, Oumar SALL — Fri, 28 Jul 2023 00:00:00 +0100

In this paper, we study the algebraic points of degree at most 14 over Q on the Fermat septic
curve F7 of projective equation X⁷ + Y ⁷ + Z⁷ = 0. Klassen and Tzermias gave in 1997 in ([5]) a geometric
description of algebraic points of degree at most 5 over Q on F₇ and O. Sall improved the results of Klassen
and Tzermias by determining in 2001 in ([9]), the algebraic points of degree at most 10 over Q. Using their
results and Abel Jacobi's theorem, we extend their work by giving a geometric description of algebraic points
of degree at most 14 over Q on F₇.

BIPOLAR PICTURE FUZZY SUBGROUP OF A GROUP

Sangodapo T. O., Babatunde Oluwaseun Onasanya — Fri, 28 Jul 2023 00:00:00 +0100

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.

On the subsemigroup generated by idempotents of the semigroup of order preserving and decreasing contraction mappings of a finite chain

Muhammad Mansur Zubairu — Fri, 28 Jul 2023 00:00:00 +0100

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.

ON THE CONVERGENCE BEHAVIOUR OF SOLUTIONS OF CERTAIN SYSTEM OF SECOND ORDER NONLINEAR DELAY DIFFERENTIAL EQUATIONS

Akinwale Olutimo — Fri, 28 Jul 2023 00:00:00 +0100

Convergence criteria for the solutions of certain
system of two nonlinear delay differential equations with con-
tinuous deviating argument ϱ(t) using a suitable Lyapunov-
Krasovskii’s functional are established in this study. The new
result attained extends and updates some results mentioned in
the literature. A numerical illustration is given to show the va-
lidity of the result as well geometric analysis to describe the
behavior of solutions of the system.