In this paper we generalize Jacobsons results by proving that any integer  in   is a square-free integer), belong to . All units of  are generated by the fundamental unit  having the forms

Our generalization build on using the conditions

This leads us to classify the real quadratic fields  into the sets  Jacobsons results shows that  and Sliwa confirm that  and  are the only real quadratic fields in .

This Study presents and provides Variable thoughts and aspects for representing Scientific topics " Physics for instance " as Play Shows for high School Students, by Showing a suggested Method that will Contribute in illustrating the Steps of writing the educational Scientific topic, and this method will help teachers to deliver their message to the Students " receivers " easily.The researcher have used Puppets in this method as the assisting tool for teachers, to help them deliver message Clearlym easily and Joyful.The researcher in his experiment used " Archimedes Principle " as a typical example, by Converting it into a theatrical Script, with respect to the Concept of Science, and in accordance to the Scientific educational Curriculu

The present work deals with an experimental investigation of charging and discharging processes in thermal storage system using a phase change material PCM. Paraffin wax was used as the PCM which is formed in spherical capsules and packed in a cylindrical packed column which acted as an energy storage system. Air was used as the heat transfer fluid HTF in thermal storage unit. The effect of flow rate and inlet temperature of HTF on the time of charging and discharging process were studied. The results showed that the faster storage of thermal energy can be made by high flow rate of heat transfer fluid HTF and high inlet temperature of heat transfer fluid. It was found that at 65°C HTF inlet temperature, the melting and solidification pr

The objective of this study is to explain the role of credit policies in agricultural development of Iraq during the period 1979-1989 which were represented by the policy of co-operative agricultural bank the organization that responsible to finance agricultural sector for various reasons. It has been shown that there was no clear credit policy existed during the period concerned due to the differences between loans from year. The loan growth rate was low in general comparing with objectives of the agricultural development plans, a low production rates comparing with loans paid, the growth rate of average number of trees in each donum and the growth rate of livestock number was also low.In conclusion there should be a clear plan for cred

Research Objectives: The research aims to highlight the approach of Imam Al-Qaradawi in contemporary jurisprudence in the recent issues of the jurisprudence of minorities, and mentioning the foundations of jurisprudence of minorities, along with some of the practical applications of Imam Al-Qaradawi.

Study Methodology: The researcher applied the inductive, analytical and comparative approach by tracking the scientific material related to the subject of the study from the books of Al-Qaradawi in the first place, then by comparing the legal provisions with what had been stated in the four schools of jurisprudence.

Findings: The interest and need of Muslim minorities in non-

Background: Trauma is one of the most common
clinical problems that confront the maxillofacial
surgeon and radiologist alike. Middle third facial
fractures are diagnosed primarily on the bases of
clinical examination and plain radiographs than can
result in much preoperative speculation.
Objective: To assess the advantages of spiral
computerized tomography over conventional
radiography in the pre-surgical evaluation of middle
third facial fractures.
Methods: Thirty patients with thirty-eight facial
fractures were studied, all patients were examined
clinically, by plain radiography and then by spiral CT.
Results: Of the 38 middle-third fractures, 16
(42.1%) were zygomatic fractures, 8 (21.1%) were

Background: University dental students perceived a higher level of stress prior to the final exam associated with raised salivary cortisol levels which could be considered as a useful noninvasive biomarker for measuring acute stress. Using a Helkimo anamnestic and clinical dysfunction scoring for temporomandibular disorders can give a better insight about the association of this marker and temporomandibular joint disorders. The aim of this study was to evaluation level of salivary cortisol in stressor students with temporomandibular disorder and the relation between this marker in relation to temporomandibular disorder severity. This might give a better understanding to the role of psychological stress as an etiological factor for developin

A pure posteriorly posterior communicating artery (PCoA) aneurysm represents a surgical challenge. This is mainly when there is a need for good exposure of the aneurysmal neck, sac, PCoA, and anterior choroidal arteries. Ruptured pure posteriorly directed PCoA aneurysm imposes significantly extra challenge as the surgeon undergoes dissection through a tight brain. Even with measures commonly used to attain brain relaxation like the lumbar drain and cisternal fenestration. Here, we describe a technique for posterior temporal pole mobilization (TPM) as an integrated part of microsurgical clipping of ruptured pure posteriorly directed PCoA aneurysms. This technique is implicated in twenty-three successive cases of ruptured PCoA aneurys

Evaluation of the Antibacterial Efficacy of Electrolyzed Oxidizing Water as an Irrigant against Enterococcus faecalis (An In vitro Study), Noor A Khait*, Muna Saleem Kalaf