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 solvent free oxidation of benzyl alcohol was conducted employing Au and Pd supported catalysts, while utilizing hydrogen peroxide 35% (H2O2) as the oxidant, H2O2 is  very cheap, mild, and an environment friendly reagent, which produced water as the only by-product. Various proportions of Au-Pd catalysts on carbon and titanium oxide activated as supports were synthesized through the use of sol immobilization catalyst synthesis technique. Characterization of the synthesized catalysts was performed using X-Ray Diffraction (XRD), Brunauer-Emmett-Teller (BET), Field Emission Scanning Electron Microscopy (FESEM), and Transmission Electron Microscopy (TEM). It was found that the synthesized Au-Pd/ activated carbon catalyst was  benef

This study examines patterns of exposure of Iraqi university students to selective daily Iraqi newspapers and the motives of this exposure, as well as its associated factors that affect the average exposure. It tries to answer several questions, including those related to the levels of exposure of Iraqi university students to daily Iraqi newspapers and classification of patterns of selective exposure to daily Iraqi newspapers and the most prominent Iraqi daily newspapers that are selectively exposed by Iraqi university students. It also examines the motives of this selective exposure and factors that increase the degree of exposure to the daily Iraqi newspapers, and the most prominent stages in which Iraqi university students find their

This study was done at Al-Balad City Hospital on 60 diabetic patients (25 male and 35 female). The study included Fasting Blood Sugar and fungal diagnosis (systemic and superficial fungus). The results showed that the high concentration of blood sugar belonged to the group > 70 years among the diabetic patients with high significant differences in comparison with other groups P<0.001 . The result showed that percentage of female systemic fungus infection was higher than male systemic fungus infection ( female 63% and male 24%) and vice versa about superficial fungus infection (female 37% and male 76%) . Data showed that the percentage of nail fungus infection among female diabetic patients was higher than the percentage of male diabetic p

Renal transplantation is a principal treatment option for end-stage kidney failure. Bone loss and fracture are serious complication of kidney transplantation, associated with morbidity and mortality. The pathogenesis of post transplantation bone loss is multifactorial and complex

Elevated Interleukin-13 (IL-13) may play an important role in the pathophysiology of COVID-19, yet, the attenuated response did not notice across all severe cases. Susceptibility to asthma in specific populations is associated with several SNPs of multifunctional cytokines, such as IL-13, IL-31 and IL-33. This prospective case-control study is designed to investigate the extent of genetic susceptibility in subsets of Iraqi patients with COVID-19 by targeting the variants of interleukin IL-13rs20541 polymorphism in relation to disease susceptibility and severity of clinical presentation. One hundred samples were obtained from the throat, nasopharyngeal and nasal swabs enrolled in this study. Eighty samples of the throat, nasopharyngeal and

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The researcher tackles the most outstanding conditions of experimentation, the importance of the study lies in being helpful to the workers in the field of theatre in general and directors in particular which the conditions of experimentation that should be taken.The study aims at knowing the experimental basis which the director (Sami Abdulhamid) followed in the realization of this.The researcher tackles in the First inquiry the concept of experimentation and the second tackles the conditions of experimentation.In the methodology of study the researcher analyzed the show of the "Othello in the Kitchen" and comes up to the following: 1. the dhows has cone with the nature of the previous shows experienced the methods that were not familia