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 .

The study aims to demonstrate the importance of instructional methods in teaching Arabic language as a second language or teaching the Arabic language to non-native speakers. The study is in line with the tremendous development in the field of knowledge, especially in the field of technology and communication, and the emergence of many electronic media in education in general and language teaching in particular. It employs an image in teaching vocabulary and presenting the experience of the Arabic Language Institute for Non-Speakers-King Abdul-Aziz University. The study follows the descriptive approach to solve the problem represented by the lack of interest in the educational methods when teaching Arabic as a second language. Accordingl

                The advertising mail is considered as one of potential tools that followed to transfer the printed messages to the consumers and public customers whom are located at homes or works. This type of advertising is preferable due to the zero expense to receive the announcements of products, which became recently one of the successful procedures to create new customers and keep them in touch with direct communication. It is also possible to send them to specific group of people who can be classified by the advertisers to select even by name their own clients to give the personality to the clients for a long term of communication.

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In this study, plastic wastes named (PET and PVC) were used to prepare polymer matrix composite (PMC) which can be used in different applications. Composite materials were prepared by mixing unsaturated polyester resin (UP) with plastic wastes, two types of plastic waste were used in this work included polyethylene-terephthalate (PET) and Polyvinyl chloride (PVC) with various weight fractions (0, 5,10,15, 20 and 25%) added as a filler in flakes form. In this work, some of the tests that were carried out included (tensile, bending, and compressive strength) as mechanical tests, in addition to (thermal conductivity and water absorption) as physical tests. The values of tensile, compressive strength and Young's modulus of UP increased after

In the period immediately following the end of World War II, American theatre was transformed by the work of playwright Arthur Miller. Miller tapped into a sense of dissatisfaction and unrest within the greater American psyche because he was profoundly influenced by the depression and the war that immediately followed it. His dramas proved to be both the conscience and redemption of the times; allowing people an honest view of the direction the country had taken.1 Miller has his own concept of tragedy as a modern playwright. He believes that tragedy may depict ordinary people in domestic surroundings instead of talking about a character from a high rank, a king or a queen. Miller’s main concern lies in dramatizing the whole man as he i

Background. The anterior communicating artery (ACoA) complex consists of the ACoA, the pre-and post-communicating segments of the anterior cerebral artery, and the recurrent artery of Heubner. It is the most common site for anatomical variations in the circle of Willis. Such variations can mimic intracranial aneurysms. Case description. A 30-year-old female presented with recurrent episodes of extreme headache and bilateral tinnitus. A brain computed tomography (CT) scan showed no significant lesions, while her CT-angiography (CTA) showed an enlarged vascular lesion at the ACoA, raising the suspicion for an ACoA aneurysm. A repeated CTA revealed a rare anatomical variation with a pattern of cross dominance in the ACoA complex;

Forty patients with acute lymphoblastic leukemia(ALL) were tested for the serum levels of total sialic acid(TSA) and the immunoglobulins before and after treatnemnt with six diffrent chemotherapy protocols while significantly

The aim of this research is to find out why some matrix verbs are no longer complemented by the two types of infinitive clauses as it is the case in Elizabethan English . At that time (when Shakespeare was writing ), the same matrix verb triggers the two types of infinitive clauses as its complex transitive complementation .Such free variation is not possible in Present –Day English . In this corpus – based study , it is shown that the choice of the form of the infinitive clause is not free; there are certain syntactic ,sem- antic constraints that dete, - infinitive.