In this paper, we introduce and study the concepts of hollow – J–lifting modules and FI – hollow – J–lifting modules as a proper generalization of both hollow–lifting and J–lifting modules . We call an R–module M as hollow – J – lifting if for every submodule N of M with is hollow, there exists a submodule K of M such that M = K Ḱ and K N in M . Several characterizations and properties of hollow –J–lifting modules are obtained . Modules related to hollow – J–lifting modules are  given .

We dealt with the nature of the points under the influence of periodic function chaotic functions associated functions chaotic and sufficient conditions to be a very chaotic functions Palace

         This paper is mainly concerned with the study of the moral aspects that prompts William Shakespeare to attempt a romance in which he has embedded the epitome of his thought, experience, and philosophy concerning certain significant aspects of human life whose absence or negligence may threaten human existence, peace, and stability. From the beginning of history man realizes the importance of prosperity on the many and various levels that touch and address his needs and desires—natural, material,  and spiritual. The Tempest, due to the dramatist's awareness of the aforementioned values, reflects the dramatist's duty as to projecting and unfolding these important aspects, rec

      The definition of semi-preopen sets were first introduced by "Andrijevic" as were is defined by :Let (X ,  ) be a topological space, and let  A ⊆,    then A is called semi-preopen set if ⊆∘ .        In this paper, we study the properties of semi-preopen sets but by another  definition which is equivalent to the first definition and we also study the relationships among it and (open, α-open, preopen and semi-p-open )sets.

     This article is devoted to presenting results on invariant approximations over a non-star-shsped weakly compact subset of a complete modular space by introduced a new notion called S-star-shaped with center f:  if   be a mapping and , . Then the existence of common invariant best approximation is proved for Banach operator pair of mappings by combined the hypotheses with Opial’s condition or demi-closeness condition

In this paper we study the concepts of δ-small M-projective module and δ-small M-pseudo projective Modules as a generalization of M-projective module and M-Pseudo Projective respectively and give some results.

In this paper, we develop the work of Ghawi on close dual Rickart modules and discuss y-closed dual Rickart modules with some properties. Then, we prove that, if are y-closed simple -modues and if -y-closed is a dual Rickart module, then either Hom ( ) =0 or . Also, we study the direct sum of y-closed dual Rickart modules.

After studying the reality of application to occupational safety in new Iraqi building projects and sampling the situation wilt that in developed and neighboring countries, researcher found that there is a big gap in the level of safety application conditions, this indicates the need fora quick and clear reference for local engineers to use it on site for safety conditions in their projects . As a case study the monitors work the researcher studied a huge project in the United Arab Emirates.This project considered for safety requirements to highest grades. This case study may be far away from the projects in Iraq, but we hope to rise the Iraqi work level in the near future. After seeing the way of administration work and how they were ra

The structure of this paper includes an introduction to the definition of the nano topological space, which was defined by M. L. Thivagar, who defined the lower approximation of G and the upper approximation of G, as well as defined the boundary region of G and some other important definitions that were mentioned in this paper with giving some theories on this subject. Some examples of defining nano perfect mappings are presented along with some basic theories. Also, some basic definitions were presented that form the focus of this paper, including the definition of nano  pseudometrizable space, the definition of nano compactly generated space, and the definition of completely nano para-compact. In this paper, we presented images of nan