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 .

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

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

To evaluate the toxicity of benzalkonium chloride in aquaculture, the hemato-serological indices of Nile tilapia Oreochromis niloticus are used as biomarkers. Following exposure to three concentrations of benzalkonium chloride BAC 0.1, 0.25, 0.50, and 1 mg/l (BAC1,2,3 and 4) in aquaria for two durations 21 and 42 days, the microbiological assay in fish aquaria, in addition to blood parameters were assessed. Except for the mean difference between BAC2 and BAC3 (P > 0.05) at 42 days, the mean values of the bacterial counts revealed a significant difference between all compared groups (0.05 ≥ P ≤ 0.01). Following exposure to the lower concentrations of BAC (1, 2 and 3), the main blood parameters of Oreochromis niloticus namely red bl

Rhythm is considered one of the creative concepts in the recent architectural thought; it has emerged clearly as a mean of creating the highest levels of creativity in architecture, especially in contemporary architectural movements. The importance of rhythm has  emerged, especially, when the architecture , its beginnings concentrated on the principle of the links with poetic structures. Many architectural studies deal with concept of rhythm in architecture with different ways various according to the trend of each study, this show the importance of studying the concept of rhythm in the architectural field in general. This study try to focus on the utilization of rhythm as creative system in architecture of heritage and contemporary

The advertising has emerged as an effective force and an effective instrument upon with all organizations and companies depend on achieving their goals. In additional to the need to use promote sales, The nature and objective of advertising go beyond the scope of specific personal communication to a broader and more effective range for consumers from multiple groups and combination play need to use as well as the need to use means of communication than com convey the message more professional, The coincides with the rapid and remarkable development of all different media technologies and as much as possible social networking sites including mobile phone companies. The advertising has emerged as an effective force and an effective instrum

   In this study the Individuals of Ostracoda crustacean Cyclocypria were used as bioclaner of two species of bacteria namely Escherichia coli & Staphylococcus aurous, these bacteria have been introduced to an artificial aquatic environment with known number from pure cultures. The aim was to check the predation efficiency and ecological role of Cyclocypria as biological cleaners.      The results showed that the predation rate was between 6 106 ×  and 7× 10 6 colony/ ml/ 3 days/ 10 crustacean in the first three days. This rate increased remarkably in the 9th, 12th & 15th day from the beginning of the experiment and it was 10 × 10 6 and 15 × 10 6 respectively.  &nb