In this paper, we introduce a symmetric function in order to derive a new generating functions of bivariate Pell Lucas polynomials. We define complete homogeneous symmetric functions and give generating functions for Gauss Fibonacci polynomials, Gauss Lucas polynomials, bivariate Fibonacci polynomials, bivariate Lucas polynomials, bivariate
Jacobsthal polynomials and bivariate Jacobsthal Lucas polynomials.
We establish the strong generalized solution of the second mixed problem for an Euler-Poisson-Darboux equation in which the free term has the form: \(\gamma(t) u(x_0,t_0)\) where \(u(x,t)\) is the unknown function sought at the point \((x_0,t_0).\)
In this paper, the exact value of covering radius of unit repetition codes and the bounds of covering radius of zero-divisor repetition codes have been determined by using Lee weight over the finite ring \(F_{2}+vF_{2}+v^2F_2\). Moreover the covering radius of different block repetition codes have been also studied.
In this work, by using \(t\)-conorm \(C\), we introduce anti fuzzy vector spaces and define sum, union, direct sum and normality of anti fuzzy vector spaces. We prove that sum, union, direct sum and normality of anti fuzzy vector spaces is also anti fuzzy vector space under \(t\)-conorm \(C.\) Moreover, we investigate linear transformations over anti fuzzy vector spaces (normal anti fuzzy vector spaces) under \(t\)-conorms and prove that image and pre image of them is also anti fuzzy vector space (normal anti fuzzy vector space) under \(t\)-conorms.
Radial Basis Function (RBF) is a real valued function whose value rests only on the distance from some other points called a center, so that a linear combination of radial basis functions are typically used to approximate given functions or differential equations. Radial Basis Function (RBF) approximation has the ability to give an accurate approximation for large data sites which gives smooth solution for a given number of knots points; particularly, when the RBFs are scaled to the nearly flat and the shape parameter is chosen wisely. In this research work, an algorithm for solving partial differential equations is written and implemented on some selected problems, inverse multiquadric (IMQ) function was considered among other RBFs. Preference is given to the choice of shape parameter, which need to be wisely chosen. The strategy is written as an algorithm to perform number of interpolation experiments by changing the interval of the shape parameters and consequently select the best shape parameter that give small root means square error (RMSE). All the computational work has been done using Matlab. The interpolant for the selected problems and its corresponding root means square errors (RMSEs) are tabulated and plotted.
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 \(k\in\mathbb{N}.\)
