Let R be a commutative ring with identity 1 and M be a unitary left R-module. A submodule N of an R-module M is said to be approximately pure submodule of an R-module, if for each ideal I of R. The main purpose of this paper is to study the properties of the following concepts: approximately pure essentialsubmodules, approximately pure closedsubmodules and relative approximately pure complement submodules. We prove that: when an R-module M is an approximately purely extending modules and N be Ap-puresubmodulein M, if M has the Ap-pure intersection property then N is Ap purely extending.

The security of message information has drawn more attention nowadays, so; cryptography has been used extensively. This research aims to generate secured cipher keys from retina information to increase the level of security. The proposed technique utilizes cryptography based on retina information. The main contribution is the original procedure used to generate three types of keys in one system from the retina vessel's end position and improve the technique of three systems, each with one key. The distances between the center of the diagonals of the retina image and the retina vessel's end (diagonal center-end (DCE)) represent the first key. The distances between the center of the radius of the retina and the retina vessel's end (ra

In the present paper, we have introduced some new definitions On D- compact topological group and D-L. compact topological group for the compactification in topological spaces and groups, we obtain some results related to D- compact topological group and D-L. compact topological group.

It is shown that if a subset of a topological space (χ, τ) is δ-semi.closed, then it is semi.closed. By use this fact, we introduce the concept regularity of a topological space (χ, τ) via δ-semi.open sets. Many properties and results were investigated and studied. In addition we study some maps that preserve the δ-semi.regularity of spaces.

The main aim of this paper is to introduce the concept of a Fuzzy Internal Direct Product of fuzzy subgroups of group . We study some properties and prove some theorems about this concept ,which is very important and interesting of fuzzy groups and very useful in applications of fuzzy mathematics in general and especially in fuzzy groups.

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

    In this paper, we calculate the electron energy distribution function (EEDF) and transport parameters including the electron mean energy, mobility, drift velocity and diffusion coefficient for the gas mixtures of the H₂ and N₂ using the EEDF program. It is concentrated on the effect of assorted concentrations of the mixtures on the EEDF and the electron transport coefficients. The work exhibits the variation amongst the different mixtures on the EEDF and the transport parameter. The results are graphically offered and discussed. In this concept, it is shown that for each mixture has a specific impact on EEDF and the transport parameter. The important of this study comes from the usage of these mix

he planning process is generally aimed at developing the city and making it meet the needs of different citizens. The green areas constitute one of the basic needs of the city and with the rapid and unusual growth in the size of cities, especially in the third world countries, which is often embodied in capitals. Which was achieved as a result of many reasons, including political, economic and social and even enshrined through some of the decisions that were issued and the city of Baghdad, but a clear example of these cities. The city and the environment are inseparable terms. The city is where people spend their lives and their daily experiences, and the environment is the center in w

The importance of the current study  lies in the  importance of the  Tax policy that  being considered one of the most important tools working on fulfilling  the  social,  financial  and economic  goals  and improving  the investment environment  in the country  to become  having the ability to  activate the  national economy. The current study  has  referred  that  (  Has  the  tax planning  practiced by  the Iraqi  contribution  companies  led to increase  the  far-term tax  outcome through  getting  benefit of   the monetary  funds  and expansion in&nbs