This research a study model of linear regression problem of autocorrelation of random error is spread when a normal distribution as used in linear regression analysis for relationship between variables and through this relationship can predict the value of a variable with the values of other variables, and was comparing methods (method of least squares, method of the average un-weighted, Thiel method and Laplace method) using the mean square error (MSE) boxes and simulation and the study included fore sizes of samples (15, 30, 60, 100). The results showed that the least-squares method is best, applying the fore methods of buckwheat production data and the cultivated area of the provinces of Iraq for years (2010), (2011), (2012),

Abstract Depending on their protective properties against different cases of Colorectal Cancer (CRC), vitamins C, D, and E are the main focus of this research. CRC is one of the global public health concerns. 30 healthy individuals provided serum samples, whereas the group of CRC patients was divided into three, totaling 90 individuals. Group I consisted of 30 newly diagnosed cases of CRC. Group II 30 consisted of consisted of 30 CRC patients who were administered three cycles of chemotherapy. Group III consisted of 30 diagnosed CRC patients who also have non-alcoholic fatty liver disease (NAFLD). The concentrations and groups of vitamins C, D, and E were evaluated using ELISA. The levels of Vitamin C were significantly lower (p &l

A two time step stochastic multi-variables multi-sites hydrological data forecasting model was developed and verified using a case study. The philosophy of this model is to use the cross-variables correlations, cross-sites correlations and the two steps time lag correlations simultaneously, for estimating the parameters of the model which then are modified using the mutation process of the genetic algorithm optimization model. The objective function that to be minimized is the Akiake test value. The case study is of four variables and three sites. The variables are the monthly air temperature, humidity, precipitation, and evaporation; the sites are Sulaimania, Chwarta, and Penjwin, which are located north Iraq. The model performance was

In this paper, Bayes estimators of the parameter of Maxwell distribution have been derived along with maximum likelihood estimator. The non-informative priors; Jeffreys and the extension of Jeffreys prior information has been considered under two different loss functions, the squared error loss function and the modified squared error loss function for comparison purpose. A simulation study has been developed in order to gain an insight into the performance on small, moderate and large samples. The performance of these estimators has been explored numerically under different conditions. The efficiency for the estimators was compared according to the mean square error MSE. The results of comparison by MSE show that the efficiency of Bayes est

In this paper, Bayes estimators of the parameter of Maxwell distribution have been derived along with maximum likelihood estimator. The non-informative priors; Jeffreys and the extension of Jeffreys prior information has been considered under two different loss functions, the squared error loss function and the modified squared error loss function for comparison purpose. A simulation study has been developed in order to gain an insight into the performance on small, moderate and large samples. The performance of these estimators has been explored numerically under different conditions. The efficiency for the estimators was compared according to the mean square error MSE. The results of comparison by MSE show that the efficiency of B

In this paper, the Monte-Carlo simulation method was used to compare the robust circular S estimator with the circular Least squares method in the case of no outlier data and in the case of the presence of an outlier in the data through two trends, the first is contaminant with high inflection points that represents contaminant in the circular independent variable, and the second the contaminant in the vertical variable that represents the circular dependent variable using three comparison criteria, the median standard error (Median SE), the median of the mean squares of error (Median MSE), and the median of the mean cosines of the circular residuals (Median A(k)). It was concluded that the method of least squares is better than the

In this paper the centralizing and commuting concerning skew left -derivations and skew left -derivations associated with antiautomorphism on prime and semiprime rings were studied and  the commutativity of Lie ideal under certain conditions were proved.

In this paper the variable structure control theory is utilized to derive a discontinuous controller to the magnetic levitation system. The magnetic levitation system model is considered uncertain, which subjected to the uncertainty in system parameters, also it is open-loop unstable and strongly nonlinear. The proposed variable structure control to magnetic levitation system is proved, and the area of attraction is determined. Additionally, the chattering, which induced due to the discontinuity in control law, is attenuated by using a non-smooth approximate. With this approximation the resulted controller is a continuous variable structure controller with a determined steady state error according to the selected control