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.
