Degree tolerant number of power graph: finite Albenian group
ODAM-Vol. 3 (2020), Issue 3, pp. 1 – 3 Open Access Full-Text PDF
Johan Kok
Abstract: The degree tolerant number of the power graph of the finite Albenian group, \(\mathbb{Z}_n\) under addition modulo \(n\), \(n\in \mathbb{N}\) is investigated. A surprising simple result, \(\chi_{dt}(\mathcal{P}((\mathbb{Z}_{n},+_{n}))) = k\) for the product of primes, \(n=p_1p_2p_3\cdots p_k\) is presented.
Boundedness of Calderón-Zygmund operators and their commutator on Morrey-Herz Spaces with variable exponents
OMS-Vol. 4 (2020), Issue 1, pp. 323 – 336 Open Access Full-Text PDF
Omer Abdalrhman, Afif Abdalmonem, Shuangping Tao
Abstract: In this paper, the boundedness of Calderón-Zygmund operators is obtained on Morrey-Herz spaces with variable exponents \(MK_{q(\cdot),p(\cdot)}^{\alpha(\cdot),\lambda}(\mathbb{R}^{n})\) and several norm inequalities for the commutator generated by Calderón-Zygmund operators, BMO function and Lipschitz function are given.
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.
