Journal of the Nigerian Mathematical Society

A quandle of order 2n and the concept of quandles isomorphism

A. O. Isere — 2020-08-31

Quandles (non-trivial) are non-associative algebraic structures that are idempotent
and distributive. The concept of quandles is still relatively new. Hence, this work is
aimed at developping methods of constructing new quandles of nite even orders. The concept of quandles isomorphism is discussed. The inner automorphism structure and the centralizer of certain element(s) of some of the quandles constructed were obtained, and these were used to classify the constructed examples up to isomorphism.

The fuzzy subgroups for the Abelian structure Z_8 X Z_(2^n ), n>2,n>2; n > 2

S. A. Adebisi — 2020-08-31

Any nite nilpotent group can be uniquely written as a direct product of p-groups. In this paper, we give explicit formulae for the number of distinct fuzzy subgroups of the cartesian product of two abelian groups of orders 2^n and 8 respectively for every integer n > 2.

Linear sum of analytic functions defined by a convolution operator

A. O. Ajiboye — 2020-08-31

ABSTRACT. In this paper, a new family R σ n(β,λ) of analytic functions deﬁned by a con- volution operator and a linear combination of some geometric expressions is presented. We established some early coeﬃcient bounds, the Fekete-Szeg¨o estimate and the Toeplitz determinant of family R σ n(β,λ).

Bayesian estimation of time-varying parameters in dynamic state space models in the presence of discounted evolution variance

O. O. Awe — 2020-08-31

Considerable attention has been devoted in literature to the estimation of linear models with constant location parameters. However, many phenomena in real life situations exhibit a non-linear time-varying pattern, indicating a need to adopt Bayesian dynamic models and deal with the complexity involved in estimating the resulting time-varying parameters. In this paper, we present a novel application involving the estimation of time-varying parameters in dynamic state space regression models in the presence of discounted evolution variance. A conceptual review of the derivation of the posterior distribution of the time-varying parameters was done with the application of the proposed technique examined with simulated and real data. The results showed substantial time-variation in the slope parameters associated with the studied location parameters, thereby highlighting the empirical relevance and advantage of the discounting method as well as its computationally less intensive nature.

Adomain Decomposition Method for Direct Integration of Bernoulli Differential Equations

Z. A. Adegboye — 2020-08-31

We introduce the basic and less known methodology of Adomian Decomposition Method (ADM) for differential equations. We then formulate the method to obtain analytic solutions in a rapidly convergent series to some class of higher order differential equations.The concept of ADM is further applied to various Bernoulli Differential Equations (BDEs) and the results show excellent potentials of applying this method.

A modified spectral conjugate gradient method for solving unconstrained minimization problems

A. A. Danhausa — 2020-08-31

The development a modified spectral conjugate gradient method for solving unconstrained minimization problem is considered in this paper. A new Conjugate (update) parameter is obtained by the idea of Dai-Kou's technique for generating conjugate parameters. A new spectral parameter is also presented based on quasi-Newton direction and quasi-Newton condition. Under the strong Wolfe line search, the proposed method is proved to be globally convergent. Numerical results showed that the algorithm takes lesser number of iteration to obtain the minimum of a given function compared to the method Loannis and Panagiotis’s spectral CGM [36] (LP for short), Birgin and Martinez’s spectral CGM [2] (BM for short), and Jinbao, Qian, Xianzhen, Youfang and Jianghua’s spectral CGM [31] ( JQXYJ for short). We hereby recommend this method for the solution of both linear and Non-linear Unconstrained optimization problem.

Keywords: Unconstrained minimization problem, Spectral conjugate gradient method, Global convergence, numerical results.

Variant of finite symmetric inverse semigroup

M. Balarabe — 2020-08-31

In a semigroup $S$ fixed an element $a\in S$ and, for all $x,y\in S$, define a binary operation $*_{a}$ on $S$ by $x*_{a}y=xay$, (where the juxterposition on the left denote the original semigroup operation on $S$). The operation $*_{a}$ is clearly associative and so $S$ forms a new semigroup under this operation, which is denoted by $S^{a}$ and called {\emph{variant}} of $S$ by $a$. For a finite set $X_{n} = \{1, 2,\ldots, n\}$, let $\mathcal{I}_{n}$ be the symmetric inverse semigroup on $X_{n}$ and fix an idempotent $a\in \mathcal{I}_{n}$. In this paper, we study the variant $\mathcal{I}^a_{n}$ of $\mathcal{I}_{n}$ by $a$. In particular, we characterised Green's relations and starred Green's relations $\mathcal{L}^{*}$, $\mathcal{R}^{*}$ in $\mathcal{I}^a_{n}$ and also showed that the variant semigroup $\mathcal{I}^a_{n}$ is abundant.

On Lie SL(n;R)-Foliation

A. Ndiaye — 2020-08-31

In this paper, we show that any compact manifold that carries a SL(n;R)-foliation is fibered on the circle S1. Every manifold in this paper is compact and our Lie group G is connected and simply connected.

On numerical computational solution of seventh order boundary values problems

K. I. Falade — 2020-08-31

In this paper, we present and applied Exponentially Fitted Collocation Approximate Method for the numerical solution of seventh order boundary value problems. The
approximate solution of the problem is computed using Maple
18 software after the problem was slightly perturbed and collocated. Three examples have been considered to illustrate the efficiency and implementation of the method and the results are compared with the exact solution and some existing proposed work.

Rhotrix-Modules and the Multi-Cipher Hill ciphers

S. M. Tudunkaya — 2020-08-31

Now a days, Hill cipher is almost relegated. It is mostly referred to as a reference or rather history material. This is due to its weaknesses in terms of security, difficulty in both the multiplication and inverse computation of matrices. This
paper presented a variant of the Hill Cipher that can be used to encrypt several ciphertexts together via the concept of rhotrices. In the proposed scheme, computation of products and inverses is easier and faster since computing products and inverses of rhotrices using heart based multiplication method is known to be easier than that of matrices. Also each plaintext rhotrix is indirectly encrypted by using its own key since it is presented in a row or column major similar to a plaintext block. Therefore, the presented scheme

Solving systems of nonlinear equations using improved double direction method

A. S. Halilu — 2020-08-31

The fundamental reason behind double direction approach is that, there are two corrections in the scheme. If one correction fails during iterative process then the other one will correct the system. Therefore, this research aims to present a
derivative-free method for solving large-scale system of nonlinear equations via double direction approach. The acceleration parameter used in this approach approximated the Jacobian matrix in order to form a derivative-free method by reducing two direction presented in double direction scheme into a single one.
under mild conditions, the proposed method is proved to be globally convergent using derivative-free line search. Numerical results recorded in this paper using a set of large-scale test problems show that the proposed approach is successful for solving large-scale problems.