The aim of this work is to evaluate the onc-electron expectation values < r > from the radial electronic density funetion D(r) for different wave ?'unctions for the 2s state of Li atom. The wave functions used were published in 1963,174? and 1993 , respectavily. Using " " ' wave function as a Slater determinant has used the positioning technique for the analysis open shell system of Li (Is2 2s) State.

In this article, performing and deriving the probability density function for Rayleigh distribution by using maximum likelihood estimator method and moment estimator method, then crating the crisp survival function and crisp hazard function to find the interval estimation for scale parameter by using a linear trapezoidal membership function. A new proposed procedure used to find the fuzzy numbers for the parameter by utilizing (     to find a fuzzy numbers for scale parameter of Rayleigh distribution. applying two algorithms by using ranking functions to make the fuzzy numbers as crisp numbers. Then computed the survival functions and hazard functions by utilizing the real data application.

In the present paper, we will study the generalized ( p, q) -type and
generalized lower ( p, q) -type of an entire function in several complex
variables with respect to the proximate order with index pair ( p, q) are
defined and their coefficient characterizations are obtained.

      A food chain model in which the top predator growing logistically has been proposed and studied. Two types of Holling’s functional responses type IV and type II have been used in the first trophic level and second trophic level respectively, in addition to Leslie-Gower in the third level. The properties of the solution are discussed. Since the boundary dynamics are affecting the dynamical behavior of the whole dynamical system, the linearization technique is used to study the stability of the subsystem of the proposed model. The persistence conditions of the obtained subsystem of the food chain are established. Finally, the model is simulated numerically to understand the global dynamics of the food chain un

     The operator ψ has been introduced as an associated set-valued set function. Although it has importance for the study of minimal open sets as well as minimal I-open sets. As a result of this study, we introduce minimal I^*-open sets . In this study, several characterizations of minimal I^*-open sets are also investigated. This study also discusses the role of minimal  I^*-open sets in the *-locally finite spaces. In an aspect of topological invariant, the homeomorphic images of minimal I^*-open set has been discussed here.

This study aimed to examine the effects of electronic training to improve the skills of designing electronic courses for teachers of Arabic language in the colleges of education in Iraq. The descriptive approach is applied and the sample included 145 teachers of Arabic who were selected randomly from the colleges of education in Iraq. Moreover, the results reflected that e-training is effective in improving the skills related to designing online educational courses for teachers of Arabic in the colleges of education in Iraq. Besides, there was no difference between the mean of the respondents' responses to the total score of the tool on the role of electronic training to develop the skills related to electronic courses designing for teacher

The experiences in the life are considered important for many fields, such as industry, medical and others. In literature, researchers are focused on flexible lifetime distribution.

In this paper, some Bayesian estimators for the unknown scale parameter  of Inverse Rayleigh Distribution have been obtained, of different two loss functions, represented by Suggested and Generalized loss function based on Non-Informative prior using Jeffery's and informative prior represented by Exponential distribution. The performance of   estimators is compared empirically with Maximum Likelihood estimator, Using Monte Carlo Simulation depending on the Mean Square Error (MSE). Generally, the preference of Bayesian method of Suggeste

Transforming the common normal distribution through the generated Kummer Beta model to the Kummer Beta Generalized Normal Distribution (KBGND) had been achieved. Then, estimating the distribution parameters and hazard function using the MLE method, and improving these estimations by employing the genetic algorithm. Simulation is used by assuming a number of models and different sample sizes. The main finding was that the common maximum likelihood (MLE) method is the best in estimating the parameters of the Kummer Beta Generalized Normal Distribution (KBGND) compared to the common maximum likelihood according to Mean Squares Error (MSE) and Mean squares Error Integral (IMSE) criteria in estimating the hazard function. While the pr