Reflection wave of a pulsed by a point source
OMS-Vol. 4 (2020), Issue 1, pp. 142 – 146 Open Access Full-Text PDF
Adel A. S. Abo Seliem
Abstract: We calculate the electromagnetic field contained by a pulsed above a planar interface by using the modified Cagniard technique. The power density of spectrum of the wave that is observed at the distance from its emptily science usually differs from that of the source excitation, the power spectrum depends strangles on the speed of the wave in two media and the position of the observation point with respect to the interface and the source, form results of the rendition form a past source a discretely layer medium.
Random attractors for semilinear reaction-diffusion equation with distribution derivatives and multiplicative noise on \(\mathbb{R}^{n}\)
OMS-Vol. 4 (2020), Issue 1, pp. 126 – 141 Open Access Full-Text PDF
Fadlallah Mustafa Mosa, Abdelmajid Ali Dafallah, Eshag Mohamed Ahmed, Mohamed Y. A. Bakhet, Qiaozhen Ma
Abstract: In this paper, we investigate the existence of random attractors for a semilinear reaction-diffusion equation with a nonlinearity having a polynomial growth of arbitrary order \(p-1(p\geq 2)\), and with distribution derivatives and multiplicative noise defined on unbounded domains. The random attractors are obtained in \(L^{2}(\mathbb{R}^{n})\) and \(L^{p}(\mathbb{R}^{n})\) respectively. The semilinear reaction-diffusion equation is recast as a continuous random dynamical system and asymptotic compactness for this demonstrated by using uniform a priori estimates for far-field values of solutions as well as the cut-off technique.
Pythagorean fuzzy multiset and its application to course placements
ODAM-Vol. 3 (2020), Issue 1, pp. 55 – 74 Open Access Full-Text PDF
Paul Augustine Ejegwa
Abstract: The concept of fuzzy set theory is of paramount relevance to tackling the issues of uncertainties in real-life problems. In a quest to having a reasonable means of curbing imprecision, the idea of fuzzy sets had been generalized to intuitionistic fuzzy sets, fuzzy multisets, Pythagorean fuzzy sets among others. The notion of intuitionistic fuzzy multisets (IFMS) came into the limelight naturally because there are instances when repetitions of both membership and non-membership degrees cannot be ignored like in the treatment of patients, where each consultations are key in diagnosis and therapy. In IFMS theory, the sum of the degrees of membership and non-membership is less than or equals one at each levels. Supposing the sum of the degrees of membership and non-membership is greater than or equal to one at any level, then the concept of Pythagorean fuzzy multisets (PFMS) is appropriate to handling such scenario. In this paper, the idea of PFMS is proposed as an extensional Pythagorean fuzzy sets proposed by R. R. Yager. In fact, PFMS is a Pythagorean fuzzy set in the framework of multiset. The main objectives of this paper are to expatiate the operations under PFMSs and discuss some of their algebraic properties with some related results. The concepts of level sets, cuts, accuracy and score functions, and modal operators are established in the setting of PFMSs with a number of results. Finally, to demonstrate the applicability of the proposed soft computing technique, a course placements scenario is discussed via PFMS framework using composite relation defined on PFMSs. This soft computing technique could find expression in other multi-criteria decision-making (MCDM) problems.
Capacitated vehicle routing problem with column generation and reinforcement learning techniques
ODAM-Vol. 3 (2020), Issue 1, pp. 41 – 54 Open Access Full-Text PDF
Abdullahi Ibrahim, Jeremiah Ishaya, Nassirou Lo, Rabiat Abdulaziz
Abstract: Capacitated vehicle routing problem is one of the variants of the vehicle routing problem which was studied in this research. In this research we applied a reinforcement learning algorithm to find set of routes from a depot to the set of customers while also considering the capacity of the vehicles, in order to reduce the cost of transportation of goods and services. Each vehicle originates from a depot, service the customers and return to the depot. We compare the reinforcement learning model with an exact method; column generation and Google’s OR-tool. Our objective is to solve a large-size of problem to near-optimality. We were able to use reinforcement learning to solve upto 101 nodes to near-optimality.
Optimal polynomial decay for a coupled system of wave with past history
OMA-Vol. 4 (2020), Issue 1, pp. 49 – 59 Open Access Full-Text PDF
S. M. S. Cordeiro, R. F. C. Lobato, C. A. Raposo
Abstract: This work deals with a coupled system of wave with past history effective just in one of the equations. We show that the dissipation given by the memory effect is not strong enough to produce exponential decay. On the other hand, we show that the solution of this system decays polynomially with rate \(t^{-\frac{1}{2}}\). Moreover by recent result due to A. Borichev and Y. Tomilov, we show that the rate is optimal. To the best of our knowledge, there is no result for optimal rate of polynomial decay for coupled wave systems with memory in the previous literature.
Linear differential equations with fast growing coefficients in the unit disc
OMA-Vol. 4 (2020), Issue 1, pp. 38 – 48 Open Access Full-Text PDF
Benharrat Belaïdi, Mohamed Amine Zemirni
Abstract: In this article, we give new conditions on the fast growing analytic coefficients of linear complex differential equations to estimate the iterated \(p\)-order and iterated \(p\)-type of all solutions in the unit disc \(\mathbb{D}\), where \(p\in \mathbb{N}\backslash \{1\}\).
New fractional Hadamard and Fejér-Hadamard inequalities associated with exponentially \((h,m)\)-convex functions
EASL-Vol. 3 (2020), Issue 2, pp. 9 – 18 Open Access Full-Text PDF
Sajid Mehmood, Ghulam Farid,, Khuram Ali Khan, Muhammad Yussouf
Abstract: The aim of this paper is to establish some new fractional Hadamard and Fejér-Hadamard inequalities for exponentially \((h,m)\)-convex functions. These inequalities are produced by using the generalized fractional integral operators containing Mittag-Leffler function via a monotonically increasing function. The presented results hold for various kinds of convexities and well known fractional integral operators.
Leap Zagreb and leap hyper-Zagreb indices of Jahangir and Jahangir derived graphs
EASL-Vol. 3 (2020), Issue 2, pp. 1 – 8 Open Access Full-Text PDF
Fatima Asif, Zohaib Zahid, Sohail Zafar
Abstract: Topological indices are numerical parameters of a graph which characterize its topology. The second degree of a vertex in a graph is equal to the number of its second neighbors. In this paper, we will compute leap Zagreb indices and leap hyper-Zagreb indices of Jahangir graph and its line graph based on the 2-distance degree of the vertices. Moreover we will compute the same indices for the subdivision graph and the line graph of the subdivision of Jahangir graph.
A mathematical model of smoking behaviour in Indonesia with density-dependent death rate
OMS-Vol. 4 (2020), Issue 1, pp. 118 – 125 Open Access Full-Text PDF
Clara Mia Devira Simarmata, Nanang Susyanto, Iqbal J. Hammadi, Choirul Rahmaditya
Abstract: This work presents a mathematical model that investigates the impact of smokers on the transmission dynamics of smoking behavior in the Indonesian population. The population is classified into three classes: potential smokers, smokers, and ex-smokers. This model is described by non-linear differential equations using fractional quantities instead of actual populations by scaling the population of each class by the total population. There is also the density-dependent and density-independent death rate in the model to accommodate the difference between the death rate of potential smokers, smokers, and ex-smokers. In this model, two equilibrium points are found. One of them is the smoking-free equilibrium and the other relates to the presence of smoking. Then, the local stability of both equilibrium points is examined. Lastly, numerical simulations are carried out to illustrate the sensitivity of the smoker class to the parameters: the rate of non-smokers become smokers, the rate of smokers become smokers, also the rate of ex-smokers re-adapt smoking habit. The result of this paper can be considered to make a policy to reduce the number of smokers in Indonesia.
A few comments and some new results on JU-algebras
OMS-Vol. 4 (2020), Issue 1, pp. 110 – 117 Open Access Full-Text PDF
Daniel A. Romano
Abstract: In this article, we revisit the axioms of JU-algebras previously recognizable as ‘pseudo KU-algebras’, which we may call as ‘weak KU-algebras’ and discussed the definitions of some of their substructures. We also associate this class of algebras with the classes of BE-algebras and UP-algebras. In addition, we introduce and analyze some new classes of ideals in this class of algebras.