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.
