This paper is attempt to study the nonlinear second order delay multi-value problems. We want to say that the properties of such kind of problems are the same as the properties of those with out delay just more technically involved. Our results discuss several known properties, introduce some notations and definitions. We also give an approximate solution to the coined problems using the Galerkin's method.

This work is concerned with studying the optimal classical continuous control quaternary vector problem. It is consisted of; the quaternary nonlinear hyperbolic boundary value problem and the cost functional. At first, the weak form of the quaternary nonlinear hyperbolic boundary value problem is obtained. Then under suitable hypotheses, the existence theorem of a unique state quaternary vector solution for the weak form where the classical continuous control quaternary vector is considered known is stated and demonstrated by employing the method of Galerkin and the compactness theorem. In addition, the continuity operator between the state quaternary vector solution of the weak form and the corresponding classical continuous control qua

     A partial temporary immunity SIR epidemic model involv nonlinear treatment rate is proposed and studied. The basic reproduction number  is determined. The local and global stability of all equilibria of the model are analyzed. The conditions for occurrence of local bifurcation in the proposed epidemic model are established. Finally, numerical simulation is used to confirm our obtained analytical results and specify the control set of parameters that affect the dynamics of the model.

Average per capita GDP income is an important economic indicator. Economists use this term to determine the amount of progress or decline in the country's economy. It is also used to determine the order of countries and compare them with each other. Average per capita GDP income was first studied using the Time Series (Box Jenkins method), and the second is linear and non-linear regression; these methods are the most important and most commonly used statistical methods for forecasting because they are flexible and accurate in practice. The comparison is made to determine the best method between the two methods mentioned above using specific statistical criteria. The research found that the best approach is to build a model for predi

In this article, a numerical method integrated with statistical data simulation technique is introduced to solve a nonlinear system of ordinary differential equations with multiple random variable coefficients. The utilization of Monte Carlo simulation with central divided difference formula of finite difference (FD) method is repeated n times to simulate values of the variable coefficients as random sampling instead being limited as real values with respect to time. The mean of the n final solutions via this integrated technique, named in short as mean Monte Carlo finite difference (MMCFD) method, represents the final solution of the system. This method is proposed for the first time to calculate the numerical solution obtained fo

 In this paper, we study the convergence theorems of the Modified Ishikawa iterative sequence with mixed errors for the uniformly continuous mappings and solving nonlinear uniformly continuous mappings equation in arbitrary real Banach space.

There is of great importance to know the values of the optical constants of materials due to their relationship with the optical properties and then with their practical applications. For this reason, it was proposed to study the optical constants of amorphous silicon nanostructures (quantum well, quantum wire, and quantum dot) because of their importance in the world of optical applications. In this study, it was adopted the Herve and Vandamme (HV) model of the refractive index because it was found that this model has very good optical properties for almost all semiconductors. Also, it was carried out by applying experimental results for the energy gaps of these three nanostructures, which makes the results of the theoretical calculations