The aim of this paper is to present the mathematical and numerical study of a nonlocal nonlinear model based on the variable exponent p(x)-Laplacian for removing Cauchy noise, which is a type of impulsive and non-Gaussian degradation. The proposed model benefits from the performance of the nonlocal approach to preserve small details and textures, and the efficiency of the variable exponent to reduce the execution time. To demonstrate the reliability of our proposed model, we provide some experimental denoising results and illustrate the comparison with some models from the literature.
In the history of option pricing, Black-Scholes model is one of the most significant models. In this paper, we present a new numerical strategy for valuing American option pricing problems governed by Black-Scholes model (BSM). Numerical computations are carried out to show the efficiency and robustness of the proposed method. We compare our numerical solution with the ones based on Finite Element Method (FEM) and the Enriched Finite Element Method (PUFEM). Our result shows the efficiency of the proposed strategy. In addition, that approach can be used to treat nonlinear evolutionary problems.
We propose a novel diffusion process having a mean function equal to the Pareto probability density function up to a constant of proportionality. We examine the probabilistic properties of the proposed model. Then, referring to the problem of statistical inference, we describe the approach employed to tackle the issue of obtaining parameter estimates by maximizing the likelihood function based on discrete sampling. This estimation reduces to solving a set of complex equations, that is accomplished using the simulated annealing algorithm. A simulation study is also given to validate the methodology presented. Finally, using a real-world example of the Moroccan child mortality rate, we obtain the fits and forecasts by employing the suggested stochastic process and nonlinear regression model.
We study the existence and uniqueness of a bounded weak solution for a triply nonlinear thermistor problem in Sobolev spaces. Furthermore, we prove the existence of an absorbing set and, consequently, the universal attractor.
In this paper, we prove the following generalization of the classical Darbo fixed point principle : Let X be a Banach space and µ be a montone measure of noncompactness on X which satisfies the generalized Cantor intersection property. Let C be a nonempty bounded closed convex subset of X and T : C → C be a continuous mapping such that for any countable set Ω ⊂ C, we have µ(T(Ω)) ≤ kµ(Ω), where k is a constant, 0 ≤ k < 1. Then T has at least one fixed point in C. The proof is based on a combined use of topological methods and partial ordering techniques and relies on the Schauder and the Knaster-Tarski fixed point principles.
