Throughout this paper R represents commutative ring with identity, and M is a unitary left R-module. The purpose of this paper is to study a new concept, (up to our knowledge), named a semi-extending modules, as generalization of extending modules, where an Rmodule M is called semi-extending if every sub module of M is a semi-essential in a direct summand of M. Various properties of semi-extending module are considered. Moreover, we investigate the relationships between semi-extending modules and other related concepts, such as CLS-modules and FI- extending modules.

Let  be a commutative ring with 1 and  be left unitary  . In this paper we introduced and studied concept of semi-small compressible module (a     is said to be semi-small compressible module if  can be embedded in every nonzero semi-small submodule of . Equivalently,  is  semi-small compressible module if there exists a monomorphism  , ,     is said to be semi-small retractable module if  , for every non-zero  semi-small sub module in . Equivalently,  is semi-small retractable if there exists a homomorphism  whenever  .     In this paper we introduce and study the concept of semi-small compressible and semi-small retractable s as a generalization of compressible  and retractable  respectively and give some of their adv

The aim of this research is to estimate the parameters of the linear regression model with errors following ARFIMA model by using wavelet method depending on maximum likelihood and approaching general least square as well as ordinary least square. We use the estimators in practical application on real data, which were the monthly data of Inflation and Dollar exchange rate obtained from the (CSO) Central Statistical organization for the period from 1/2005 to 12/2015. The results proved that (WML) was the most reliable and efficient from the other estimators, also the results provide that the changing of fractional difference parameter (d) doesn’t effect on the results.

Net pay is one of the most important parameters used in determining initial oil in place of a reservoir. It can be delineated through the using of limiting values of the petrophysical properties of the reservoir. Those limiting values are named as the cutoff. This paper provides an insight into the application of regression line method in estimating porosity, clay volume and water saturation cutoff values in Mishrif reservoir/ Missan oil fields. The study included 29 wells distributed in seven oilfields of Halfaya, Buzurgan, Dujaila, Noor, Fauqi, Amara and Kumait.

This study is carried out by applying two types of linear regressions: Least square and Reduce Major Axis Regression.

The Mishrif formation was

   In this work, a novel technique to obtain an accurate solutions to nonlinear form by multi-step combination with Laplace-variational approach (MSLVIM) is introduced. Compared with the  traditional approach for variational it overcome all difficulties and enable to provide us more an accurate solutions with extended of the convergence region as well as covering to larger intervals which providing us a continuous representation of approximate analytic solution and it give more better information of the solution over the whole time interval. This technique is more easier for obtaining the general Lagrange multiplier with reduces the time and calculations. It converges rapidly to exact formula with simply computable terms wit