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

The aim of this paper is to present a method for solving high order ordinary differential equations with two point's boundary condition, we propose semi-analytic technique using two-point oscillatory interpolation to construct polynomial solution. The original problem is concerned using two-point oscillatory interpolation with the fit equal numbers of derivatives at the end points of an interval [0 , 1] . Also, many examples are presented to demonstrate the applicability, accuracy and efficiency of the method by comparing with conventional methods.

As the process of  estimate for model and variable selection significant is a crucial process in the semi-parametric modeling At the beginning of the modeling process often At there are many explanatory variables to Avoid the loss of any explanatory elements may be important as a result , the selection of significant variables become necessary , so the process of variable selection is not intended to simplifying  model complexity explanation , and also predicting. In this research was to use some of the semi-parametric methods (LASSO-MAVE , MAVE and The proposal method (Adaptive LASSO-MAVE) for variable selection and estimate semi-parametric single index model (SSIM) at the same time .

In this research, some robust non-parametric methods were used to estimate the semi-parametric regression model, and then  these methods were compared using the MSE comparison criterion, different sample sizes, levels of variance, pollution rates, and three different models were used. These methods are S-LLS S-Estimation -local smoothing, (M-LLS)M- Estimation -local smoothing, (S-NW) S-Estimation-NadaryaWatson Smoothing, and (M-NW) M-Estimation-Nadarya-Watson Smoothing.

The results in the first model proved that the (S-LLS) method was the best in the case of large sample sizes, and small sample sizes showed that the

Background. Najaf governorate was recorded as one of the most polluted Iraqi governorates with increased cancer, autoimmune, and abortion cases. Study Groups. A total of 88 adult volunteers from three test groups were divided based on their inhabitance in different geographical regions in Najaf governorate. Group 1 (G1; n, 29) inhabitants of Al‐Ansar, Al‐Abbaseyeh, and Al‐Manathera districts, Group 2 (G2; n, 27) inhabitants of 22 different scattered districts of the governorate, Group 3 (G3; n, 32) inhabitants of Kufa city and center districts in the old Najaf city. According to previous author

The study aims at  evaluating  the penalty of  semi- intentional killing felony in the Egyptian and Algerian criminal law following the Islamic Law (Shari'a). The  study used the descriptive, evalutive and analytical  methodology  to  reach the topic in question. To meet the theoretical significance of the study, much data has been collected to give a comprehensive picture about the topic under examination. As for the practical significance of the study, it helps the juridical power to reconsider and phrase the legal materials of the semi-intentional killing penalty based on the Islamic law. The study has come to the conclusions that the Islamic Law (Shari'a) imposes a compensation (blood-money) to be g