In this paper, our purpose is to study the classical continuous optimal control (CCOC)  for quaternary nonlinear parabolic boundary value problems (QNLPBVPs). The existence and uniqueness theorem (EUTh) for the quaternary state vector solution (QSVS) of the weak form (WF) for the QNLPBVPs with a given quaternary classical continuous control vector (QCCCV) is stated and proved via the Galerkin Method (GM) and the first compactness theorem under suitable assumptions(ASSUMS). Furthermore, the continuity operator for the existence theorem of a QCCCV dominated by the QNLPBVPs is stated and proved under suitable conditions.

Iraq has the second largest proven oil reserves in the world. According to oil experts, it is expected that the Iraq's reserves to rise to 200+ billion barrels of high-grade crude.

Oil is a strategic commodity for producing and exporting countries in general, and Iraq in particular, as demonstrated by the international experience that oil is an important means to achieve economic growth, an important tool in the overall economic, social and political development. It is also an important source of hard currency for any national economy and a means to connect the local economy and the global economy. In this paper we focus our attention on selecting the best regression model that explain the effect of human capita

Abstract:

The models of time series often suffer from the problem of the existence of outliers ​​that accompany the data collection process for many reasons, their existence may have a significant impact on the estimation of the parameters of the studied model. Access to highly efficient estimators  is one of the most important stages of statistical analysis, And it is therefore important to choose the appropriate methods to obtain good  estimators. The aim of this research is to compare the ordinary estimators and the robust estimators of the estimation of the parameters of

In this paper, for the first time we introduce a new four-parameter model called the Gumbel- Pareto distribution by using the T-X method. We obtain some of its mathematical properties. Some structural properties of the new distribution are studied. The method of maximum likelihood is used for estimating the model parameters. Numerical illustration and an application to a real data set are given to show the flexibility and potentiality of the new model.

           In this paper, the homotopy perturbation method (HPM) is presented for treating a linear system of second-kind mixed Volterra-Fredholm integral equations. The method is based on constructing the series whose summation is the solution of the considered system. Convergence of constructed series is discussed and its proof is given; also, the error estimation is obtained. Algorithm is suggested and applied on several examples and the results are computed by using MATLAB (R2015a). To show the accuracy of the results and the effectiveness of the method, the approximate solutions of some examples are compared with the exact solution by computing the absolute errors.

By driven the moment estimator of ARMA (1, 1) and by using the simulation some important notice are founded, From the more notice conclusions that the relation between the sign   and moment estimator for ARMA (1, 1) model that is: when the sign is positive means the root      gives invertible model and when the sign is negative means the root      gives invertible model. An alternative method has been suggested for ARMA (0, 1) model can be suitable when

In this paper, author’s study sub diffusion bio heat transfer model and developed explicit finite difference scheme for time fractional sub diffusion bio heat transfer equation by using caputo fabrizio fractional derivative. Also discussed conditional stability and convergence of developed scheme. Furthermore numerical solution of time fractional sub diffusion bio heat transfer equation is obtained and it is represented graphically by Python.

In this paper, the proposed phase fitted and amplification fitted of the Runge-Kutta-Fehlberg method were derived on the basis of existing method of 4(5) order to solve ordinary differential equations with oscillatory solutions. The recent method has null phase-lag and zero dissipation properties. The phase-lag or dispersion error is the angle between the real solution and the approximate solution. While the dissipation is the distance of the numerical solution from the basic periodic solution. Many of problems are tested over a long interval, and the numerical results have shown that the present method is more precise than the 4(5) Runge-Kutta-Fehlberg method.

In some cases, researchers need to know the causal effect of the treatment in order to know the extent of the effect of the treatment on the sample in order to continue to give the treatment or stop the treatment because it is of no use. The local weighted least squares method was used to estimate the parameters of the fuzzy regression discontinuous model, and the local polynomial method was used to estimate the bandwidth. Data were generated with sample sizes (75,100,125,150 ) in repetition 1000. An experiment was conducted at the Innovation Institute for remedial lessons in 2021 for 72 students participating in the institute and data collection. Those who used the treatment had an increase in their score after

The research dealt with a comparative study between some semi-parametric estimation methods to the Partial linear Single Index Model using simulation. There are two approaches to model estimation two-stage procedure and MADE to estimate this model. Simulations were used to study the finite sample performance of estimating methods based on different Single Index models, error variances, and different sample sizes , and the mean average squared errors were used as a comparison criterion between the methods were used. The results showed a preference for the two-stage procedure depending on all the cases that were used