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.
