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.
