The energy expectation values for Li and Li-like ions ( , and ) have been calculated and examined within the ground state and the excited state in position space. The partitioning technique of Hartree-Fock (H-F) has been used for existing wave functions.

Let  be a commutative ring with identity, and  be a unitary left -module. In this paper we introduce the concept pseudo weakly closed submodule as a generalization of -closed submodules, where a submodule  of an -module  is called a pseudo weakly closed submodule, if for all , there exists a -closed submodule  of  with  is a submodule of  such that . Several basic properties, examples and results of pseudo weakly closed submodules are given. Furthermore the behavior of pseudo weakly closed submodules in class of multiplication modules are studied. On the other hand modules with chain conditions on pseudo weakly closed submodules are established. Also, the relationships of  pseudo weakly closed

The aims of this thesis are to study the topological space; we introduce a new kind of perfect mappings, namely j-perfect mappings and j-ω-perfect mappings. Furthermore, we devoted to study the relationship between j-perfect mappings and j-ω-perfect mappings. Finally, certain theorems and characterization concerning these concepts are studied. On the other hand, we studied weakly/ strongly forms of ω-perfect mappings, namely -ω-perfect mappings, weakly -ω-perfect mappings and strongly-ω-perfect mappings; also, we investigate their fundamental properties. We devoted to study the relationship between weakly -ω-perfect mappings and strongly -ω-perfect mappings. As well as, some new generalizations of some definitions wh

  The aim of this paper is to introduce a new type of proper mappings called semi-p-proper mapping by using semi-p-open sets, which is weaker than the proper mapping. Some properties and characterizations of this type of mappings are given.

Generalized Additive Model has been considered as a multivariate smoother that appeared recently in Nonparametric Regression Analysis. Thus, this research is devoted to study the mixed situation, i.e. for the phenomena that changes its behaviour from linear (with known functional form) represented in parametric part, to nonlinear (with unknown functional form: here, smoothing spline) represented in nonparametric part of the model. Furthermore, we propose robust semiparametric GAM estimator, which compared with two other existed techniques.

           Let R be  commutative Ring , and let T be  unitary left .In this paper ,WAPP-quasi prime submodules are introduced as  new generalization of Weakly quasi prime submodules , where  proper submodule C of an R-module T is called WAPP –quasi prime submodule of T, if whenever 0≠rstϵC, for r, s ϵR , t ϵT, implies that either  r tϵ C +soc   or  s tϵC +soc  .Many examples of characterizations and basic properties are given . Furthermore several characterizations of WAPP-quasi prime submodules in the class of multiplication modules are established.

The metric dimension and dominating set are the concept of graph theory that can be developed in terms of the concept and its application in graph operations. One of some concepts in graph theory that combine these two concepts is resolving dominating number. In this paper, the definition of resolving dominating number is presented again as the term dominant metric dimension. The aims of this paper are to find the dominant metric dimension of some special graphs and corona product graphs of the connected graphs  and , for some special graphs  . The dominant metric dimension of  is denoted by  and the dominant metric dimension of corona product graph G and H is denoted by .