Let R be a ring and let A be a unitary left R-module. A proper submodule H of an R-module A is called 2-absorbing , if rsa∈H, where r,s∈R,a∈A, implies that either ra∈H or sa∈H or rs∈[H:A], and a proper submodule H of an R-module A is called quasi-prime , if rsa∈H, where r,s∈R,a∈A, implies that either ra∈H or sa∈H. This led us to introduce the concept pseudo quasi-2-absorbing submodule, as a generalization of both concepts above, where a proper submodule H of an R-module A is called a pseudo quasi-2-absorbing submodule of A, if whenever rsta∈H,where r,s,t∈R,a∈A, implies that either rsa∈H+soc(A) or sta∈H+soc(A) or rta∈H+soc(A), where soc(A) is socal of an

In this research note approximately prime submodules is defined as a new generalization of prime submodules of unitary modules over a commutative ring with identity. A proper submodule  of an -module  is called an approximaitly prime submodule of  (for short app-prime submodule), if when ever , where , , implies that either  or . So, an ideal  of a ring  is called app-prime ideal of  if   is an app-prime submodule of -module . Several basic properties, characterizations and examples of approximaitly prime submodules were given. Furthermore, the definition of approximaitly prime radical of submodules of modules were introduced, and some of it is properties were established.

"In this article, "we introduce the concept of a WE-Prime submodule", as a stronger form of a weakly prime submodule". "And as a "generalization of WE-Prime submodule", we introduce the concept of WE-Semi-Prime submodule, which is also a stronger form of a weakly semi-prime submodule". "Various basic properties of these two concepts are discussed. Furthermore, the relationships between "WE-Prime submodules and weakly prime submodules" and studied". "On the other hand the relation between "WE-Prime submodules and WE-Semi-Prime submodules" are consider". "Also" the relation of "WE-Sime-Prime submodules and weakly semi-prime submodules" are explained. Behind that, some characterizations of these concepts are investigated".

In''this"article, we"study",the"concept""of WN"-"2"-''Absorbing'''submodules and WNS''-''2''-''Absorbing"submodules as generalization of "weakly 2-absorbing and weakly semi 2-absorbing submodules respectively. We investigate some of basic properties, examples and characterizations of them. Also, prove, the class of WN-2-Absorbing "submodules is contained in the class of WNS-2-Absorbing "submodules. Moreover, many interesting results about these concepts, were proven.

      Let R be a commutative ring with identity and M be an unitary R-module. Let (M) be the set of all submodules of M, and : (M)  (M)  {} be a function. We say that a proper submodule P of M is -prime if for each r  R and x  M, if rx  P, then either x  P + (P) or r M  P + (P) . Some of the properties of this concept will be investigated. Some characterizations of -prime submodules will be given, and we show that under some assumptions prime submodules and -prime submodules are coincide. 

      Let R be a commutative ring with identity and M  an unitary R-module. Let (M)  be the set of all submodules of M, and : (M)  (M)  {} be a function. We say that a proper submodule P of M is end--prime if for each   EndR(M) and x  M, if (x)  P, then either x  P + (P) or (M)  P + (P). Some of the properties of this concept will be investigated. Some characterizations of end--prime submodules will be given, and we show that under some assumtions prime submodules and end--prime submodules are coincide.

Shear and compressional wave velocities, coupled with other petrophysical data, are vital in determining the dynamic modules magnitude in geomechanical studies and hydrocarbon reservoir characterization. But, due to field practices and high running cost, shear wave velocity may not available in all wells. In this paper, a statistical multivariate regression method is presented to predict the shear wave velocity for Khasib formation - Amara oil fields located in South- East of Iraq using well log compressional wave velocity, neutron porosity and density. The accuracy of the proposed correlation have been compared to other correlations. The results show that, the presented model provides accurate

     Let R be a commutative ring with unity and an R-submodule N is called semimaximal if and only if

 the sufficient conditions of F-submodules to be semimaximal .Also the concepts of (simple , semisimple) F- submodules and quotient F- modules are  introduced and given some  properties .

The significance of the work is to introduce the new class of open sets, which is said Ǥ- -open set with some of properties. Then clarify how to calculate the boundary area for these sets using the upper and lower approximation and obtain the best accuracy.

  In this work we shall introduce the concept of weakly quasi-prime modules and give some properties of this type of modules.