COVID-19, a brief overview of virus reproductive emergent behavior
EASL-Vol. 3 (2020), Issue 3, pp. 15 – 19 Open Access Full-Text PDF
Charles Roberto Telles
Abstract: Researches were investigated from January to March, \(2020\), searching for empirical evidences and theoretical approaches at that time to determine a mathematical modeling for COVID-\(19\) transmission for individual/community infection. It was found that despite traditional forms of transmission of the virus SARS-COV-\(2\) through SIR model equations early detected on \(2020\), empirical evidences suggested the use of more dynamic mathematical modeling aspects for this equation in order to estimate the disease spreading patterns. The SIR equation modeling limitations were found as far as common epidemic preventive methods did not explain effectively the spreading patterns of disease transmission due to the virus association with the human emergent behavior in a complex network model.
A linear algorithm for minimum dominator colorings of orientations of paths
EASL-Vol. 3 (2020), Issue 3, pp. 10 – 14 Open Access Full-Text PDF
Michael Cary
Abstract: In this paper we present an algorithm for finding a minimum dominator coloring of orientations of paths. To date this is the first algorithm for dominator colorings of digraphs in any capacity. We prove that the algorithm always provides a minimum dominator coloring of an oriented path and show that it runs in \(\mathcal{O}(n)\) time. The algorithm is available at https://github.com/cat-astrophic/MDC-orientations_of_paths/.
Magneto-squeezing flow and heat transfer analyses of third grade fluid between two disks embedded in a porous medium using Chebyshev spectral collocation method
OMS-Vol. 4 (2020), Issue 1, pp. 305 – 322 Open Access Full-Text PDF
M. G. Sobamowo, O. M. Kamiyo, A. A. Yinusa, T. A. Akinshilo
Abstract: The present study is based on the nonlinear analysis of unsteady magnetohydrodynamics squeezing flow and heat transfer of a third grade fluid between two parallel disks embedded in a porous medium under the influences of thermal radiation and temperature jump boundary conditions are studied using Chebyshev spectral collocation method. The results of the non-convectional numerical solutions verified with the results of numerical solutions using fifth-order Runge-Kutta Fehlberg-shooting method and also the results of homotopy analysis method as presented in literature. The parametric studies from the series solutions show that for a suction parameter greater than zero, the radial velocity of the lower disc increases while that of the upper disc decreases as a result of a corresponding increase in the viscosity of the fluid from the lower squeezing disc to the upper disc. An increasing magnetic field parameter, the radial velocity of the lower disc decreases while that of the upper disc increases. As the third-grade fluid parameter increases, there is a reduction in the fluid viscosity thereby increasing resistance between the fluid molecules. There is a recorded decrease in the fluid temperature profile as the Prandtl number increases due to decrease in the thermal diffusivity of the third-grade fluid. The results in this work can be used to advance the analysis and study of the behaviour of third grade fluid flow and heat transfer processes such as found in coal slurries, polymer solutions, textiles, ceramics, catalytic reactors, oil recovery applications etc.
Concerning the Navier-Stokes problem
OMA-Vol. 4 (2020), Issue 2, pp. 89 – 92 Open Access Full-Text PDF
Alexander G. Ramm
Abstract: The problem discussed is the Navier-Stokes problem (NSP) in \(\mathbb{R}^3\). Uniqueness of its solution is proved in a suitable space \(X\). No smallness assumptions are used in the proof. Existence of the solution in \(X\) is proved for \(t\in [0,T]\), where \(T>0\) is sufficiently small. Existence of the solution in \(X\) is proved for \(t\in [0,\infty)\) if some a priori estimate of the solution holds.
On centre properties of irreducible subalgebras of compact elementary operators
OMA-Vol. 4 (2020), Issue 2, pp. 80 – 88 Open Access Full-Text PDF
W. Kangogo, N. B. Okelo, O. Ongati
Abstract: In this paper, we characterize the centre of dense irreducible subalgebras of compact elementary operators that are spectrally bounded. We show that the centre is a unital, irreducible and commutative \(C^{*}\)-subalgebra. Furthermore, the supports from the centre are orthogonal and the intersection of a nonzero ideal with the centre is non-zero.
On some new subclass of bi-univalent functions associated with the Opoola differential operator
OMA-Vol. 4 (2020), Issue 2, pp. 74 – 79 Open Access Full-Text PDF
Timilehin Gideon Shaba
Abstract: By applying Opoola differential operator, in this article, two new subclasses \(\mathcal{M}_{\mathcal{H},\sigma}^{\mu,\beta}(m,\psi,k,\tau)\) and \(\mathcal{M}_{\mathcal{H},\sigma}^{\mu,\beta}(m,\xi,k,\tau)\) of bi-univalent functions class \(\mathcal{H}\) defined in \(\bigtriangledown\) are introduced and investigated. The estimates on the coefficients \(|l_2|\) and \(|l_3|\) for functions of the classes are also obtained.
On a nonlinear differential equation with two-point nonlocal condition with parameters
OMA-Vol. 4 (2020), Issue 2, pp. 64 – 73 Open Access Full-Text PDF
A. M. A. El-Sayed, M. SH. Mohamed, E. M. Al-Barg
Abstract: Here we study the existence of solutions of a nonlocal two-point, with parameters, boundary value problem of a first order nonlinear differential equation. The maximal and minimal solutions will be proved. The continuous dependence of the unique solution on the parameters of the nonlocal condition will be proved. The anti-periodic boundary value problem will be considered as an application.
On the existence of solutions for fractional boundary valued problems with integral boundary conditions involving measure of non compactness
OMA-Vol. 4 (2020), Issue 2, pp. 56 – 63 Open Access Full-Text PDF
Ahmed Hamrouni, Said Beloul
Abstract: This paper presents an existence theorem of the solutions for a boundary value problem of fractional order differential equations with integral boundary conditions, by using measure of noncompactness combined with Mönch fixed point theorem. An example is furnished to illustrate the validity of our outcomes.
On conics and their tangents
OMS-Vol. 4 (2020), Issue 1, pp. 290 – 304 Open Access Full-Text PDF
François Dubeau
Abstract: We present, in a way quite accessible to undergraduate and graduate students, some basic and important facts about conics: parabola, ellipse and hyperbola. For each conic, we start by its definition, then consider tangent line and obtain an elementary proof of the reflexion property. We study intersection of tangents. We obtain the orthopic set for orthogonal tangents: the directrix for parabola and the Monge’s circle for ellipse and hyperbola. For ellipse and hyperbola we also consider intersection of tangents for parallel rays at points of intersection with the conic. Those analysis lead to geometric methods to draw conics. Finally we get the directrices for ellipse and hyperbola by considering intersections of tangents at endpoints of a secant passing through a focus.
Theoretical comparison of linear and nonlinear boundary sinks for species transport in isothermal multiple-compartment reactors
OMS-Vol. 4 (2020), Issue 1, pp. 280 – 289 Open Access Full-Text PDF
O. Adedire, J. N. Ndam
Abstract: In this paper, we examine linear and nonlinear boundary sinks in compartments whose adjacent sides are separated with sieve partitions allowing transport of chemical species. The sieve partitions serve as boundary sinks of the system separating each compartment from the subsequent one. With assumption of unidirectional transport of chemical species, constant physical properties and same equilibrium constant, system of partial differential equations are derived. The spatial variables of the derived PDEs are discretized using Method of Lines (MOL) technique. The semi-discrete system formed from this technique produced a system of 105 ODEs which are solved using MATLAB solver ode15s. The results show that for strongly nonlinear boundary sinks, concentration profile maintains low profile in interconnected adjacent compartments. This suggests that as nonlinearity increases at the boundary, the concentration profile becomes increasingly low in subsequent compartments.