Basrah Journal of Science

In this study, a novel neural network for the multivariance Bernstein operators' rational powers was developed. A positive integer is required by these networks. In the space of all real-valued continuous functions, the pointwise and uniform approximation theorems are introduced and examined first. After that, the Lipschitz space is used to study two key theorems. Additionally, some numerical examples are provided to demonstrate how well these neural networks approximate two test functions. The numerical outcomes demonstrate that as input grows, the neural network provides a better approximation. Finally, the graphs used to represent these neural network approximations show the average error between the approximation and the test function.

The Vibrio cholera bacterium, which belongs to the Vibrionaceae family, is the source of the cholera virus. A bacterium known as Vibrio cholerae is the cause of the human disease cholera. This study developed a fractional epidemic model to describe the transmission of cholera. The model consists of four elements: susceptible people, infected people, recovered people, and a setting where the germs may flourish. The endemic and disease-free equilibrium points were calculated. The next-generation matrix was used in order to calculate the reproduction number. It has been proven that a disease-free equilibrium is capable of being locally asymptotically stable. To make sense of them and to compare them to the qualitative answers, numerical simulations of the fractional equations of the epidemic model were performed. According to the findings, the system's susceptible population decreases when more populations are restored. This study suggests that for outbreak and preventive initiatives, health professionals should make good use of the media.

Using the isotropic diffusion model as a foundation, a novel method for image inpainting was suggested. To restore various missing areas of diverse natural images, a modified version of the original isotropic model is used. When employing the original isotropic model, the results of the suggested technique are compared to those obtained results. Regarding building texture in the missing area and restoring significant missing sections, the results of the suggested model performed better than the results of the obtained isotropic model. The performance of the suggested model in comparison to the original isotropic model is examined using a number of picture quality measures, including MSE, PSNR, and SSIM. In comparation to the widely used isotropic model, the improved model performs better and provides better measures of quality assessment for a greater number of natural photos.

The Lyapunov-Schmidt reduction for nonhomogeneous problems is modified when the dimension of the null space is two. The novel method was utilized to approximate the solutions of the nonlinear wave equation. This equation's related key function has been identified.