A modified efficient difference-type estimator for population mean under two-phase sampling design

OMS-Vol. 4 (2020), Issue 1, pp. 195 – 199 Open Access Full-Text PDF
A. E. Anieting, J. K. Mosugu
Abstract: In this article, modified difference-type estimator for the population mean in two-phase sampling scheme using two auxiliary variables has been proposed. The mean squared error of the proposed estimator has also been derived using large sample approximation. The efficiency comparison conditions for the proposed estimator in comparison with other existing estimators in which the proposed estimator performed better than the other relevant existing estimators have been given.
Read more

Generalized the Liouville’s and Möbius functions of graph

OMS-Vol. 4 (2020), Issue 1, pp. 186 – 194 Open Access Full-Text PDF
Hariwan Fadhil M. Salih, Shadya Merkhan Mershkhan
Abstract: Let \(G = (V,E)\) be a simple connected undirected graph. In this paper, we define generalized the Liouville’s and Möbius functions of a graph \(G\) which are the sum of Liouville \(\lambda\) and Möbius \(\mu\) functions of the degree of the vertices of a graph denoted by \(\Lambda(G)=\sum\limits_{v\in V(G)}\lambda(deg(v))\) and \(M(G)=\sum\limits_{v\in V(G)}\mu(deg(v))\), respectively. We also determine the Liouville’s and Möbius functions of some standard graphs as well as determining the relationships between the two functions with their proofs. The sum of generalized the Liouville and Möbius functions extending over the divisor d of degree of vertices of graphs is also given.
Read more

Complete homogeneous symmetric functions of Gauss Fibonacci polynomials and bivariate Pell polynomials

OMS-Vol. 4 (2020), Issue 1, pp. 179 – 185 Open Access Full-Text PDF
Nabiha Saba, Ali Boussayoud
Abstract: In this paper, we introduce a symmetric function in order to derive a new generating functions of bivariate Pell Lucas polynomials. We define complete homogeneous symmetric functions and give generating functions for Gauss Fibonacci polynomials, Gauss Lucas polynomials, bivariate Fibonacci polynomials, bivariate Lucas polynomials, bivariate
Jacobsthal polynomials and bivariate Jacobsthal Lucas polynomials.
Read more

Second mixed problem for an Euler-Poisson-Darboux equation with dirac potential

OMS-Vol. 4 (2020), Issue 1, pp. 174 – 178 Open Access Full-Text PDF
Kaman Mondobozi Lélén, Togneme Alowou-Egnim, Gbenouga N’gniamessan, Tcharie Kokou
Abstract: We establish the strong generalized solution of the second mixed problem for an Euler-Poisson-Darboux equation in which the free term has the form: \(\gamma(t) u(x_0,t_0)\) where \(u(x,t)\) is the unknown function sought at the point \((x_0,t_0).\)
Read more

Covering radius of repetition codes over \(F_{2}+vF_{2}+v^2F_2\) with \(v^3=1\)

OMS-Vol. 4 (2020), Issue 1, pp. 168 – 173 Open Access Full-Text PDF
Sarra Manseri, Jinquan Luo
Abstract: In this paper, the exact value of covering radius of unit repetition codes and the bounds of covering radius of zero-divisor repetition codes have been determined by using Lee weight over the finite ring \(F_{2}+vF_{2}+v^2F_2\). Moreover the covering radius of different block repetition codes have been also studied.
Read more

Conorms over anti fuzzy vector spaces

OMS-Vol. 4 (2020), Issue 1, pp. 158 – 167 Open Access Full-Text PDF
Rasul Rasuli
Abstract: In this work, by using \(t\)-conorm \(C\), we introduce anti fuzzy vector spaces and define sum, union, direct sum and normality of anti fuzzy vector spaces. We prove that sum, union, direct sum and normality of anti fuzzy vector spaces is also anti fuzzy vector space under \(t\)-conorm \(C.\) Moreover, we investigate linear transformations over anti fuzzy vector spaces (normal anti fuzzy vector spaces) under \(t\)-conorms and prove that image and pre image of them is also anti fuzzy vector space (normal anti fuzzy vector space) under \(t\)-conorms.
Read more

An algorithm for choosing best shape parameter for numerical solution of partial differential equation via inverse multiquadric radial basis function

OMS-Vol. 4 (2020), Issue 1, pp. 147 – 157 Open Access Full-Text PDF
Kazeem Issa, Sulaiman M. Hambali, Jafar Biazar
Abstract: Radial Basis Function (RBF) is a real valued function whose value rests only on the distance from some other points called a center, so that a linear combination of radial basis functions are typically used to approximate given functions or differential equations. Radial Basis Function (RBF) approximation has the ability to give an accurate approximation for large data sites which gives smooth solution for a given number of knots points; particularly, when the RBFs are scaled to the nearly flat and the shape parameter is chosen wisely. In this research work, an algorithm for solving partial differential equations is written and implemented on some selected problems, inverse multiquadric (IMQ) function was considered among other RBFs. Preference is given to the choice of shape parameter, which need to be wisely chosen. The strategy is written as an algorithm to perform number of interpolation experiments by changing the interval of the shape parameters and consequently select the best shape parameter that give small root means square error (RMSE). All the computational work has been done using Matlab. The interpolant for the selected problems and its corresponding root means square errors (RMSEs) are tabulated and plotted.
Read more

Mathematical model for measles disease with control on the susceptible and exposed compartments

OMA-Vol. 4 (2020), Issue 1, pp. 60 – 75 Open Access Full-Text PDF
Samuel O. Sowole, Abdullahi Ibrahim, Daouda Sangare, Ahmed O. Lukman
Abstract: In this paper, we develop a mathematical deterministic modeling approach to model measles disease by using the data pertinent to Nigeria. Control measure was introduced into the susceptible and exposed classes to study the prevalence and control of the measles disease. We established the existence and uniqueness of the solution to the model. From the simulation results, it was realized that the control introduced on the susceptible class; and exposed individuals at latent period play a significant role in controlling the disease. Furthermore, it is recognized that if more people in the susceptible class get immunization and the exposed people at latent period goes for treatment and therapy during this state before they become infective, the disease will be eradicated more quickly with time.
Read more

Direct product of fuzzy multigroups under \(t\)-norms

ODAM-Vol. 3 (2020), Issue 1, pp. 75 – 85 Open Access Full-Text PDF
Rasul Rasuli
Abstract: This paper proposes the concept of direct product of fuzzy multigroups under \(t\)-norms and some of their basic properties are obtained. Next, we investigate and obtain some new results of strong upper alpha-cut, weak upper alpha-cut, strong lower alpha-cut and weak lower alpha-cut of them. Later, we prove conjugation and commutation between them. Finally, the notion of homomorphism in the context of fuzzy multigroups was defined and some homomorphic properties of fuzzy multigroups under \(t\)-norms in terms of homomorphic images and homomorphic preimages, respectively, were presented.
Read more

Reflection wave of a pulsed by a point source

OMS-Vol. 4 (2020), Issue 1, pp. 142 – 146 Open Access Full-Text PDF
Adel A. S. Abo Seliem
Abstract: We calculate the electromagnetic field contained by a pulsed above a planar interface by using the modified Cagniard technique. The power density of spectrum of the wave that is observed at the distance from its emptily science usually differs from that of the source excitation, the power spectrum depends strangles on the speed of the wave in two media and the position of the observation point with respect to the interface and the source, form results of the rendition form a past source a discretely layer medium.
Read more