Some relations of inclusion and their properties are investigated for functions of type " -valent that involves the generalized operator of Srivastava-Attiya by using the principle of strong differential subordination.

Let R be a semiprime ring with center Z(R) and U be a nonzero ideal of R. An additive mappings are called right centralizer if ( ) ( ) and ( ) ( ) holds for all . In the present paper, we introduce the concepts of generalized strong commutativity centralizers preserving and generalized strong cocommutativity preserving centralizers and we prove that R contains a nonzero central ideal if any one of the following conditions holds: (i) ( ) ( ), (ii) [ ( ) ( )] , (iii) [ ( ) ( )] [ ], (iv) ( ) ( ) , (v) ( ) ( ) , (vi) [ ( ) ( )] , (vii) ( ) ( ) ( ), (viii) ( ) ( ) for all .

     In this paper, we introduce the concept of generalized strong commutativity (Cocommutativity) preserving right centralizers on a subset of a Γ-ring. And we generalize some results of a classical ring to a gamma ring.

      In this study, we prove that let N be a fixed positive integer and R be a semiprime -ring with extended centroid . Suppose that additive maps  such that  is onto,  satisfy one of the following conditions  belong to Г-N- generalized strong commutativity preserving for short; (Γ-N-GSCP) on R   belong to Г-N-anti-generalized strong commutativity preserving for short; (Γ-N-AGSCP)  Then there exists an element  and  additive maps  such that  is of the form  and   when condition (i) is satisfied, and     when condition (ii) is satisfied   

In this research, Artificial Neural Networks (ANNs) technique was applied in an attempt to predict the water levels and some of the water quality parameters at Tigris River in Wasit Government for five different sites. These predictions are useful in the planning, management, evaluation of the water resources in the area. Spatial data along a river system or area at different locations in a catchment area usually have missing measurements, hence an accurate prediction. model to fill these missing values is essential.
The selected sites for water quality data prediction were Sewera, Numania , Kut u/s, Kut d/s, Garaf observation sites. In these five sites models were built for prediction of the water level and water quality parameters.

This paper discusses reliability of the stress-strength model. The reliability functions 𝑅1 and 𝑅2 were obtained for a component which has an independent strength and is exposed to two and three stresses, respectively. We used the generalized inverted Kumaraswamy distribution GIKD with unknown shape parameter as well as known shape and scale parameters. The parameters were estimated from the stress- strength models, while the reliabilities 𝑅1, 𝑅2 were estimated by three methods, namely the Maximum Likelihood,  Least Square, and Regression.

 A numerical simulation study a comparison between the three estimators by mean square error is performed. It is found that best estimator between

    This work aims to investigate the dependence of gravitational lensing properties on the lens redshift and source redshift.

The angular diameter distance hereafter referred to as ADD has been determined using two different numerical integral methods, Simpson's rule, and definite integral methods. Both of those two methods gave identical results. In addition, observational data of gravitational Lensing systems have been used to find the most probable value of lens redshift and source redshift. The result showed that the lens redshift and source redshift are more likely to occur in the ranges of z_L=0.2-0.6 and z_S=1-3, respectively.

Einstein radius and the critical surface mass density

High frequency (HF) radio wave propagation depends on the ionosphere status which is changed with the time of day, season, and solar activity conditions. In this research, ionosonde observations were used to calculate the values of maximum usable frequency (MUF) the ionospheric F2- layer during strong geomagnetic storms (Dst ≤ -100 nT) which were compared with the predicted MUF for the same layer by using IRI-16 model. Data from years 2015 and 2017, during which five strong geomagnetic storms occurred, were selected from two Japanese ionosonde stations (Kokubunji and Wakkanai) located at the mid-latitude region. The results of the present work do not show a good correlation between the observed and predicted MUF values for F2- laye

     In this paper, suggested formula as well a conventional method for estimating the twoparameters (shape and scale) of the Generalized Rayleigh Distribution was proposed. For different sample sizes (small, medium, and large) and assumed several contrasts for the two parameters a percentile estimator was been used. Mean Square Error was implemented as an indicator of performance and comparisons of the performance have been carried out through data analysis and computer simulation between the suggested formulas versus the studied formula according to the applied indicator. It was observed from the results that the suggested method which was performed for the first time (as far as we know), had highly advantage than t