Open Journal of Mathematical Sciences (OMS)

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.

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.

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.

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.

We present a method to find the sum of a convergent series based on the computation of Hadamard finite part limits of partial sums. We give several illustrations, the main being the formulas for convergent series of the type \(\sum_{n=2}^{\infty}\frac{\left( -1\right) ^{n}\zeta\left( n,a\right) b^{n+k}}{n+k},\) where \(\zeta\left( s,a\right)\) is Hurwitz zeta function, \(\left\vert b\right\vert \leq\left\vert a\right\vert ,\) \(b\neq-a,\) and \(k\in\mathbb{N}.\)

We concentrate on investigating the existence of positive solutions for the system of second order singular semipositone m-point boundary value problems in this article. We emphasize that the nonlinear term may take a negative value and be singular. By the properties of Green’s function and applying fixed point theorem in cones, existence results for positive solutions are obtained. Also, we provide an example to make our results clear and easy for readers to understand the existence result.

>Fractional integral operators are very useful in mathematical analysis. This article investigates bounds of generalized fractional integral operators by exponentially \(m\)-convex functions. Furthermore, a Hadamard type inequality have been analyzed and, special cases of established results have been discussed.

In this paper we characterize a bounded vector measure on Lie compact group \(G = GL(2;\mathbb{R})\). It is a question of considering a bounded vector measure \(m\) defined from \(K(G;E)\) the space of \(E\) valued functions with compact support on \(G\) and giving its integral form.

In this research work, we applied some solving techniques on Travelling salesman problem (TSP) and Capaciated Vehicle routing problem (CVRP) which are some of the variants of vehicle routing problem. For each of the considered problem, Branch-and-cut was applied on TSP and Column generation technique was used on CVRP. We obtained optimal solution and tour. Hence, these methods can be used to solve similar problem for optimal solution.

In this paper, we investigate the equivalence between the Backlund transformation of Riccati equation method and the extended tanh-function method. It is proved that the two methods are equivalent when applying them to partial differential equations and differential-difference equations. Two examples are introduced to justify our results.