Mathematical Methods in the Applied Sciences最新文献

This article investigates the existence of coexistence states for a strongly coupled cooperative elliptic system with cross-diffusion, modeling two mutualistic species. By employing the method of upper and lower solutions coupled with monotone iterative techniques, we establish sharp sufficient conditions for the existence of positive coexistence states, revealing that strong interspecific cooperation and sufficiently large intrinsic growth rates can overcome the competitive exclusion induced by cross-diffusion in hostile environments. A novel transformation is introduced to handle the strongly coupled structure, and numerical simulations are provided to validate the main theoretical findings.

Stabilization of the linearized time fractional reaction-diffusion system in one-dimensional modeling glycolysis (LFRDG) has been rigorously studied. First, the nonlinear fractional reaction-diffusion (NLFRDG) system is linearized around a steady-state. Then, using semigroup theory on Banach spaces, we demonstrated that the LFRDG system with homogeneous Neumann boundary conditions admits a unique global solution. Furthermore, we have proven that such a solution is Mittag-Leffler (ML) stable. In the second part of this work, using a backstepping approach, we proved that there exists Neumann feedback boundary controls such that the LFRDG system is ML stable. In fact, the results obtained here are new in the context of the stabilization for the LFRDG models by Neumann-type boundary controls through the backstepping method. Finally, some numerical examples are presented to illustrate the theoretical results.

This artcile presents a novel algorithm for solving the split minimization problem that incorporates conjugate gradient direction, self-adaptive step size, and an alternative inertial method. We propose a generalized step size formulation that eliminates the need for prior knowledge of operator norms and establishes strong convergence results for the algorithm under suitable parameter conditions. The effectiveness of the proposed method is validated through various applications and numerical experiments. Furthermore, we provide comprehensive comparisons with existing image restoration algorithms. The numerical results demonstrate the superior performance of our algorithm compared to other methods.

We consider immuno-epidemiological SIS models. The models are based on two factors: the dynamics of the immune status and interactions between susceptible and infected individuals. The starting point is an individual-based model describing interactions between individuals. Through an appropriate limit passage with the number of individuals to infinity, we obtain a model acting on measures describing the distribution of immune status in both epidemic groups. We show that the densities of these measures satisfy a system of partial differential equations with a jump operator. This system generates a continuous semigroup of nonlinear operators on the space of densities. The main results are the existence and uniqueness of an endemic state and a method for determining stationary distributions. We also present simulations of the distribution of the number of infected people over time and the stationary distributions.

This paper introduces a Stancu-type generalization of the Jakimovski-Leviatan Szász operators generated by Meixner polynomials and studies their approximation behavior. The proposed operators extend the classical framework by providing a flexible approximation scheme with desirable convergence and asymptotic properties. Quantitative estimates of the approximation error are obtained using standard tools of approximation theory, while asymptotic formulas and convergence rates are established under suitable smoothness assumptions. The theoretical results are complemented by numerical and graphical examples that confirm the approximation performance of the proposed operators.

This article systematically investigates a new family of $�\; ��\; �q��$-special functions: the $�\; ��\; �q��$-truncated-Fubini–Appell polynomials. We first define the fundamental $�\; ��\; �q��$-truncated-Fubini polynomials through their generating function and establish their basic properties. For the extended family, we then develop explicit series representations, $�\; ��\; �q��$-recurrence relations, $�\; ��\; �q��$-integral formulas, quasi-monomial properties, differential equations, and a determinant representation. Applying this general theory yields specific results for notable cases such as the $�\; ��\; �q��$-truncated-Fubini–Bernoulli and Euler polynomials. Finally, a computational study using Mathematica offers visual and numerical analysis of the polynomials' zero distributions, providing support for the theoretical results.

The primary aim of this article is to present a sequence of positive linear operators utilizing 3-variable degenerate Hermite-Appell polynomials. We explore the approximation properties for functions within diverse spaces and evaluate the order of approximation for these operators. Finally, we support the approximation outcomes through visual representations.