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.
Investigation on the temporal evolution of the covid’19 pandemic: prediction for Togo
OMS-Vol. 4 (2020), Issue 1, pp. 273 – 279 Open Access Full-Text PDF
Komi Agbokou, Kossi Gneyou, Kokou Tcharie
Abstract: A state of health emergency has been decreed by the Togolese government since April 01 for a period of 3 months, with the introduction of a curfew which ended on June 9, following the first case of contamination of the corona Sars- Cov-2 in Togo, case registered on March 06, 2020. This first wave of contamination started from March 19. The data observed in Togo are cases tested positive and which are cured using a protocol based on the combination of hydroxychloroquine and azithromycin. This manuscript offers a forecast on the number of daily infections and its peak (or maximum), then the cumulative numbers of those infected with the covid’19 pandemic. The forecasts are based on evolution models which are well known in the literature, which consist in evaluating the evolution of the cumulative numbers of infected and a Gaussian model representing an estimate of the number of daily infections for this first wave of contamination. over a period of 8 months from the sample of observed data.
Next-generation matrices and basic reproductive numbers for all phases of the Coronavirus disease
OMS-Vol. 4 (2020), Issue 1, pp. 261 – 272 Open Access Full-Text PDF
Gabriel Obed Fosu, Emmanuel Akweittey, Albert Adu-Sackey
Abstract: During the early phase of Covid-19, the transmissibility of the coronavirus disease was estimated using the classical SIR and SEIR models. However, with the advent of some controlling measures in its informative stages, these classical compartmental models have been ameliorated to provide accurate insight of the coronavirus disease. The paper seeks to derive the basic reproductive formulas for these improved models using the matrix approach. These transmissibility equations detail the dynamics of the coronavirus disease for all phases of the pandemic; either the infected population is on lockdown or not; either infectious persons are quarantined or not; either a vaccination program has been rolled out or yet to be rolled out. With the availability of data, any of these transmissibility equations could be adopted to report on the endemicity of the coronavirus disease.
Von Neumann-Jordan constants in quasi-Banach spaces
OMS-Vol. 4 (2020), Issue 1, pp. 253 – 260 Open Access Full-Text PDF
Qi Liu, Shaomo Zhuang, Yongjin Li
Abstract: We introduce the generalized von Neumann-Jordan constant of a quasi-Banach space \(X\). Also, the quasi-Hilbert characteristic is introduced. An attempt has been made to investigate the relationship between them. At the end, a characterization of uniformly non-square is given.
