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 applications of herbal medicine have recently acquired growing interest in range of the prophylaxis and treatment of diseases. Olibanum has been used since ancient eras and several reports studied the pharmacological characteristics of boswellic acid, particularly their effect on the inflammatory response, analgesic properties, and anti-arthritic activity mostly in cell lines, but new approaches include animal models to assess these natural derivatives effects taking into consideration of being safer than synthetic preparations.  The impact of olibanum oil on several parameters was studied in rats during this study. These included white blood cell (WBC) count, lactate dehydrogenase (LDH), and C reactive protein (CRP), as well a

The paper deals with the study of the sciences of the Qur’an according to the interpreter, Ayatollah Sayyid Mahmoud al-Talaqani, a religious jihadist figure from Iran. He is the author of the exegesis (Ishraq from Al-Quran), which consists of six parts, which he wrote inside the prisons of the Shah and in exile. Mr. Al-Talaqani agreed with some of the commentators in his positions on the sciences of the Qur’an, and some of them disagreed with others.

This study deals with knowing the public relations activities of the Integrity Commission for the year 2007, knowing the contents of these activities, knowing the contents of the advertisements that it published, whether the contents of the advertisements were convincing, and whether press photographs were used in these advertisements, as well as whether symbols and slogans were used. What language and words were used to address the recipient? 1- What feelings do the contents of advertisements arouse? 2- Research objectives: This research aims to answer the following questions: What are the public relations activities carried out by the Integrity Commission? B: Are the contents of the advertisements published by the Authority convincing to

Industrial characteristics calculations concentrated on the physical properties for break down voltage in sf6, cf4 gases and their mixture with different concentrations are presented in our work. Calculations are achieved by using an improved modern code simulated on windows technique. Our results give rise to a compatible agreement with the other experimental published data.

<p><span>This research deals with the feasibility of a mobile robot to navigate and discover its location at unknown environments, and then constructing maps of these navigated environments for future usage. In this work, we proposed a modified Extended Kalman Filter- Simultaneous Localization and Mapping (EKF-SLAM) technique which was implemented for different unknown environments containing a different number of landmarks. Then, the detectable landmarks will play an important role in controlling the overall navigation process and EKF-SLAM technique’s performance. MATLAB simulation results of the EKF-SLAM technique come with better performance as compared with an odometry approach performance in terms of measuring the

This research takes up address the practical side by taking case studies for construction projects that include the various Iraqi governorates, as it includes conducting a field survey to identify the impact of parametric costs on construction projects and compare them with what was reached during the analysis and the extent of their validity and accuracy, as well as adopting the approach of personal interviews to know the reality of the state of construction projects. The results showed, after comparing field data and its measurement in construction projects for the sectors (public and private), the correlation between the expected and actual cost change was (97.8%), and this means that the data can be adopted in the re

This study confirms the ubiquitin conjugating enzyme 2B (Rad6) plays a significant role in the DNA repair pathway also because the ubiquitin-conjugating pathway. The DNA repair pathway could be a variety of bypass repair mechanism where the broken base pair is bypassed by permitting the replication fork to labor under the site of injury. This is often done by a shift mechanism wherever deoxyribonucleic acid enzyme - δ is switched with DNA enzyme - η (DNAP - η). Site of DNAP - η is massive enough to permit the broken ester to labor under, and so bypass the broken nucleotide. However, this is often potential solely through the involvement of Proliferating cell nuclear antigen (PCNA) that could be a processivity issue and it acts as a plat