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.
Foreign vector measures
OMS-Vol. 4 (2020), Issue 1, pp. 248 – 252 Open Access Full-Text PDF
Abalo Douhadji, Yaovi Awussi
Abstract: We study the foreign measures in general by proving all operations possibilities with their characteristic relation \( \perp \) and deduce that the set of foreign vector measures is a subset of bounded vector measures; stable par linear combination.
Dominator colorings of digraphs
ODMA-Vol. 3 (2020), Issue 2, pp. 50 – 67 Open Access Full-Text PDF
Michael Cary
Abstract: This paper serves as the first extension of the topic of dominator colorings of graphs to the setting of digraphs. We establish the dominator chromatic number over all possible orientations of paths and cycles. In this endeavor we discover that there are infinitely many counterexamples of a graph and subgraph pair for which the subgraph has a larger dominator chromatic number than the larger graph into which it embeds. Most importantly, we use these results to characterize all digraph families for which the dominator chromatic number is two. Finally, a new graph invariant measuring the difference between the dominator chromatic number of a graph and the chromatic number of that graph is established and studied. The paper concludes with some of the possible avenues for extending this line of research.
Asymptotic estimates for Klein-Gordon equation on \(\alpha\)-modulation space
OMA-Vol. 4 (2020), Issue 2, pp. 42 – 55 Open Access Full-Text PDF
Justin G. Trulen
Abstract: Recently, asymptotic estimates for the unimodular Fourier multipliers \(e^{i\mu(D)}\) have been studied for the function \(\alpha\)-modulation space. In this paper, using the almost orthogonality of projections and some techniques on oscillating integrals, we obtain asymptotic estimates for the unimodular Fourier multiplier \(e^{it(I-\Delta)^{\frac{\beta}{2}}}\) on the \(\alpha\)-modulation space. For an application, we give the asymptotic estimate of the solution for the Klein-Gordon equation with initial data in a \(\alpha\)-modulation space. We also obtain a quantitative form about the solution to the nonlinear Klein-Gordon equation.
Blow-up result for a plate equation with fractional damping and nonlinear source terms
OMA-Vol. 4 (2020), Issue 2, pp. 32 – 41 Open Access Full-Text PDF
Soh Edwin Mukiawa
Abstract: In this work, we consider a plate equation with nonlinear source and partially hinged boundary conditions. Our goal is to show analytically that the solution blows up in finite time. The background of the problem comes from the modeling of the downward displacement of suspension bridge using a thin rectangular plate. The result in the article shows that in the present of fractional damping and a nonlinear source such as the earthquake shocks, the suspension bridge is bound to collapse in finite time.
Existence and uniqueness for delay fractional differential equations with mixed fractional derivatives
OMA-Vol. 4 (2020), Issue 2, pp. 26 – 31 Open Access Full-Text PDF
Ahmed Hallaci, Hamid Boulares, Abdelouaheb Ardjouni
Abstract: Using the Krasnoselskii’s fixed point theorem and the contraction mapping principle we give sufficient conditions for the existence and uniqueness of solutions for initial value problems for delay fractional differential equations with the mixed Riemann-Liouville and Caputo fractional derivatives. At the end, an example is given to illustrate our main results.
Numerical analysis of a quasistatic contact problem for piezoelectric materials
OMA-Vol. 4 (2020), Issue 2, pp. 15 – 25 Open Access Full-Text PDF
Youssef Ouafik
Abstract: A frictional contact problem between a piezoelectric body and a deformable conductive foundation is numerically studied in this paper. The process is quasistatic and the material’s behavior is modelled with an electro-viscoelastic constitutive law. Contact is described with the normal compliance condition, a version of Coulomb’s law of dry friction, and a regularized electrical conductivity condition. A fully discrete scheme is introduced to solve the problem. Under certain solution regularity assumptions, we derive an optimal order error estimate. Some numerical simulations are included to show the performance of the method.
Certain results on starlike and convex functions
OMA-Vol. 4 (2020), Issue 2, pp. 1 – 14 Open Access Full-Text PDF
Pardeep Kaur, Sukhwinder Singh Billing
Abstract: Using the technique of differential subordination, we here, obtain certain sufficient conditions for starlike and convex functions. In most of the results obtained here, the region of variability of the differential operators implying starlikeness and convexity of analytic functions has been extended. The extended regions of the operators have been shown pictorially.