Gangyong Lee, S. Tariq Rizvi, and Cosmin S. Roman studied Dual Rickart modules. The main purpose of this paper is to define strong dual Rickart module. Let M and N be R- modules , M is called N- strong dual Rickart module (or relatively sd-Rickart to N)which is  denoted by M it is N-sd- Rickart if for every submodule A of M and every homomorphism fHom (M , N) , f (A) is a direct summand of N. We prove that for an R- module M , if R is M-sd- Rickart , then every cyclic submodule of M is a direct summand . In particular, if M<

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.

Let R be an associative ring with identity and let M be a unitary left R–module. As a generalization of small submodule , we introduce Jacobson–small submodule (briefly J–small submodule ) . We state the main properties of J–small submodules and supplying examples and remarks for this concept . Several properties of these submodules are given . Also we introduce Jacobson–hollow modules ( briefly J–hollow ) . We give a characterization of J–hollow modules and gives conditions under which the direct sum of J–hollow modules is J–hollow . We define J–supplemented modules and some types of modules that are related to J–supplemented modules and int

In this paper, certain types of regularity of topological spaces have been highlighted, which fall within the study of generalizations of separation axioms. One of the important axioms of separation is what is called regularity, and the spaces that have this property are not few, and the most important of these spaces are Euclidean spaces. Therefore, limiting this important concept to topology is within a narrow framework, which necessitates the use of generalized open sets to obtain more good characteristics and preserve the properties achieved in general topology. Perhaps the reader will realize through the research that our generalization preserved most of the characteristics, the most important of which is the hereditary property. Two t

phenomenon in the Arab women's contemporary literature, but it is rare in Iraqi women's
literature and falls short to the level of the phenomenon until now. Perhaps this is one of the
main reasons that caused the reluctance of researchers to study it, and this is probably the first
academic research in this field.
This research followed the discourse of Autobiography of women in Iraq, depending on the
two factors of charter and reference of the elements of Philippe Lejeune’s definition of the
genre of Autobiography, without focusing on narrative method, so it handled notes,
memories, diaries and biography of the other and counted all under the genre of the
Biography.
It came in three sections, the first follo

يسعى البحث إلى الاهتمام بإحدى الوظائف المهمة في إدارة الموارد البشرية وهي تقويم الأداء التي تواجه مجموعة من الانتقادات والآراء السلبية، اذ ظهر في الأّونة الأخيرة أنموذج جديد يمكن إن يتجاوز تلك السلبيات وهو أنموذج التغذية العكسية المتعدد المصادر درجة .وقد حاول الباحثان توظيف هذا المفهوم في اثنتين من المنظمات العامة العراقية هما (دائرة كهرباء الوسط) التابعة لوزارة الكهرباء
و (دائرة الماء والمجاري) ال

Background: Diabetes mellitus is a metabolic disorder affecting people worldwide, which require constant monitoring of their glucose levels. Commonly employed procedures include collection of blood or urine samples causing discomfort to the patients. Necessity arises to find alternative non invasive technique is required to monitor glucose levels. Saliva is one of most abundant secretions in the human body and its collection is easy, noninvasive and painless technique. Objective: The aim of this study was to determine the efficacy of saliva as a diagnostic tool by study the correlation between blood and salivary glucose levels and glycosylated hemoglobin (HbA1c%) in diabetes and non diabetes, and the comparison of salivary glucose level

Background: Osteoid osteoma(OO) is a relatively common benign skeletal neoplasm of unknown etiology that is composed of osteoid and woven bone, usually seen in adolescent and young males Although, the clinical, radiological and scintigraphic features of OO have been well described, these features may be misleading or altered in the cases of lesser trochanter of the femur which is relatively uncommon location for OO with a few number of cases reported up to date. Case Presentation: We report a case of a 20-year-old man who presented with painful limpThe pain had begun six months earlier and was made worse by walking and by exercise., with normal initial X-rays .The diagnosis was made after six months when typical Computed tomography, magneti

CNC machines are widely used in production fields since they produce similar parts in a minimum time, at higher speed and with possibly minimum error. A control system is designed, implemented and tested to control the operation of a laboratory CNC milling machine having three axes that are moved by using a stepper motor attached to each axis. The control system includes two parts, hardware part and software part, the hardware part used a PC (works as controller) connected to the CNC machine through its parallel port by using designed interface circuit. The software part includes the algorithms needed to control the CNC. The sample needs to be machined is drawn by using one of the drawing software like AUTOCAD or 3D MAX and is saved in a we