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.

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 purpose of this paper is to study some results concerning reduced ring with another concepts as semiprime ring ,prime ring,essential ideal ,derivations and homomorphism ,we give some results a bout that.

The purpose of this paper is to introduce a new type of compact spaces, namely semi-p-compact spaces which are stronger than compact spaces; we give properties and characterizations of semi-p-compact spaces.

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

S Khalifa E, N Adil A, S Husam Ali, H Nibras A…, 2009

During the course of fixed orthodontic therapy, patients should be instructed to eat specific food stuffs and beverages in order to maintain good health for the dentition and supporting structures and prevent frequent attachment debonding that prolong the treatment duration. After searching and collecting articles from 1930 till July 2021, the current review was prepared to emphasize various types of foods that should be taken during the course of fixed orthodontic therapy and to explain the effect of various food stuffs and beverages on the growth and development of craniofacial structures, tooth surfaces, root resorption, tooth movement, retention and stability after orthodontic treatment and the effect on the components of fixed ortho

This research aims to deal with contemporary knowledge  methodology to correlate between operations strategy and technological change or modernization in productive paths for industrial organizations depend on practical indicators for competitive  priorities that is objectives of operations performance.

The research is based on main hypothesis, concentrates on determination of technological change which is decided by the level of technology deterioration in current operations path compared with the competitors leaders-technology leaders.

We apply these concepts on hypothetical case to two similar companies in their production nature and te

The Christian religion came in love and co-existence with all human beings, united in the minds of its people, including the great creation to form a strong unit of high ethics that contributes to the unity among the members of society and coexistence in security, peace and love of harmony.