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.
Numerical analysis of least squares and perceptron learning for classification problems
ODAM-Vol. 3 (2020), Issue 2, pp. 30 – 49 Open Access Full-Text PDF
Larisa Beilina
Abstract: This work presents study on regularized and non-regularized versions of perceptron learning and least squares algorithms for classification problems. The Fréchet derivatives for least squares and perceptron algorithms are derived. Different Tikhonov’s regularization techniques for choosing the regularization parameter are discussed. Numerical experiments demonstrate performance of perceptron and least squares algorithms to classify simulated and experimental data sets.
On the solution of fractional Riccati differential equations with variation of parameters method
EASL-Vol. 3 (2020), Issue 3, pp. 1 – 9 Open Access Full-Text PDF
Ehtasham Ul Haq, Mazhar Ali, Abdullah Saeed Khan
Abstract: In this paper, Variation of Parameters Method (VPM) is used to find the analytical solutions of non-linear fractional order quadratic Riccati differential equation. The given method is applied to initial value problems of the fractional order Riccati differential equations. The proposed technique has no discretization, linearization, perturbation, transformation, preventive suspicions and it is also free from Adomian,s polynomials. The obtained results are compare with analytical solutions by graphical and tabular form.
Einstein equations for a Finsler-Larange space with canonical N-linear connections
OMS-Vol. 4 (2020), Issue 1, pp. 240 – 247 Open Access Full-Text PDF
Roopa M. K, Narasimhamurthy S. K
Abstract: This paper is devoted to study the geometry of Einstein equations of Finsler-Lagrange with \((\alpha, \beta)\)-metrics. We characterized the Einstein equations of Finsler Lagrange space with Randers metric, by using canonical N-metrical connection.
Valuations and their generalizations for UP-algebras
OMS-Vol. 4 (2020), Issue 1, pp. 220 – 239 Open Access Full-Text PDF
Siriwan Pawai, Tararat Khamsang, Aiyared Iampan
Abstract: In this paper, we introduce the notions of a weak pseudo-valuation, a \(0\)-weak pseudo-valuation, a weak valuation, a near pseudo-valuation, a near valuation, a pseudo-valuation, and a valuation and induce a pseudo-metric without triangle inequality, a quasi pseudo-metric, a pseudo-metric, and a metric by some these mappings on a UP-algebra. We also prove that the binary operation defined on a UP-algebra is uniformly continuous under the induced metric by a valuation in some conditions.