Journal of Mathematics

In this study, a deterministic tuberculosis (TB)-hepatitis C (HCV) coinfection mathematical model with no intervention is analysed purposely to examine the dynamics of TB-HCV coinfection so as to find conditions for reducing the transmission of both TB and HCV. A unique solution to the model exists; it is positive and is bounded. The analytical and numerical analysis show that for basic reproduction number, , the TB and HCV disease-free equilibrium points are stable. Further analysis shows that when the TB-HCV coinfection basic reproduction number is greater than 1, the endemic equilibrium point is stable. Sensitivity analysis reveals that interventions to reduce TB or HCV infection need to aim and concentrate on minimizing the numbers of the effective contact rate with TB- or HCV-infected humans and the rate of progress from latent TB or acute HCV to infectious TB or chronic HCV stage. Numerical simulations reveal that over time, the number of TB latent humans, acute HCV humans, and the number of dually infected humans have a linear relationship with the effective contact and the progression rates for both TB- and HCV-infected humans. We recommend that health education campaigns to communities aimed at reducing the transmission rates of TB and HCV be conducted. These could include screening and isolation, wearing of face masks for TB cases and screening, sterilization of surgical instruments, and use of condoms for HCV-infected humans.

The variational inequality framework holds significant prominence across various domains including economic finance, network transportation, and game theory. In addition, a novel approach utilizing a neural network model is introduced in the current work to address a box constrained variational inequality problem. Initially, the original problem is reformulated into a nonsmooth equation, following which the neural network model is meticulously devised to tackle this reformulated equation. This study comprehensively investigated inherent characteristics and properties of this neural network model. In addition, employing the Lyapunov function method, stability analysis of the neural network model proposed is rigorously demonstrated in the Lyapunov sense. Furthermore, the efficacy of the proposed technique is substantiated through numerical simulations, providing empirical support for its applicability and effectiveness.

Let be an -dimensional lattice. For any -dimensional vector and positive real number , let and denote the continuous Gaussian distribution and the discrete Gaussian distribution over , respectively. In this paper, we establish the exact relationship between the second and fourth moments centered around of the discrete Gaussian distribution and those of the continuous Gaussian distribution , respectively. This provides a quantization form of the result obtained by Micciancio and Regev on the second and fourth moments of discrete Gaussian distribution. Using the relationship, we also derive an uncertainty principle for Gaussian functions, which extend the result of Zheng, Zhao, and Xu. Our proof is based on combination of the idea of Micciancio and Regev and the idea of Zheng, Zhao, and Xu, where the main tool is high-dimensional Fourier transform.

In this study, we present a novel framework for the sixtic B-spline collocation approach in n-dimensions. Building upon previous research that focused on developing B-spline functions in n-dimensions to solve mathematical models, this work represents an extension of those efforts. We provide formulations of the sixtic B-spline collocation algorithm in one-dimensional, two-dimensional, and three-dimensional settings. These structures play a crucial role in solving mathematical models across diverse fields of study. To showcase the efficacy and accuracy of the proposed method, we employ a range of test problems in two and three dimensions. These examples serve as demonstrations of the effectiveness and precision of the suggested approach.

The main purpose of this article is using the elementary methods and the properties of the Fubini polynomials to study the congruence properties of a signless Stirling number of the first kind and solve a conjecture proposed by J. H. Zhao and Z. Y. Chen. Without a doubt, the novel approach employed in this work provides a useful reference for researching the congruence properties of other nonlinear binary recursive sequences.

In this paper, we study the existence and uniqueness of solutions for impulsive Atangana-Baleanu-Caputo fractional integro-differential equations with boundary conditions. Schaefer’s fixed point theorem and Banach contraction principle are used to prove the existence and uniqueness results. An example is presented to illustrate the results.