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 .

         It is clear that correct application of antibiotic prophylaxis can reduce the incidence of infection  resulting from the bacterial  inoculation in a variety of clinical situations; it cannot   prevent  all  infections  any  more  than it  can   eliminate  all  established infections. Optimum  antibiotic   prophylaxis  depends on:  rational  selection  of the drug(s),  adequate  concentrations  of the  drug  in  the  tissues that  are at risk, and attention to  timing  of  administration.  Moreover,  the  risk  of

         It is clear that correct application of antibiotic prophylaxis can reduce the incidence of infection  resulting from the bacterial  inoculation in a variety of clinical situations; it cannot   prevent  all  infections  any  more  than it  can   eliminate  all  established infections. Optimum  antibiotic   prophylaxis  depends on:  rational  selection  of the drug(s),  adequate  concentrations  of the  drug  in  the  tissues that  are at risk, and attention to  timing  of  administration.  Moreover,  the  risk  of  infection  in  some situations  does not outweigh  the risks which  attend the administration of even the safest antibiotic drug. The aim of this study was to comp

COVID-19 is a unique viral infectious illness that causes a variety of symptoms and health hazards, particularly to the respiratory system and has been declared a worldwide pandemic. The disease is characterized by a cytokine release in severe conditions. Interleukin-6 (IL-6), a proinflammatory cytokine, mediates an important immunomodulatory process. Also, vitamin D was identified to have a role in the innate immunity of individuals. Our study was designed to find the role of IL-6 and vitamin D in COVID-19 patients, as well as, to see whether there is a link between vitamin D deficiency and cytokine syndrome development. The study included 90 COVID-19 patients and 30 control people from Baghdad, Iraq. The age of the participants was non-s

Background: Although radiological diagnostic studies (RDS) are an important and acceptable part of medical practice, it is not without hazards. It is associated with increased risk of cancer. Unfortunately the typical and safe dose of each radiological examination is not known. Most of our knowledge of cancer risk comes from studies of survivors of those exposed to whole body radiation from atomic bomb in Hiroshima & Nagasaki, jobs associated with radiation exposure, Chernobyl survivors & patients treated with radiation therapy for cancer and other diseases.

 Objectives   To estimate radiation dose received by patients from diagnostic radiological examinations and lifetime

The target of this study was to synthesize several new Ciprofloxacin drug analogs by providing a nucleophilic substitution procedure that provides new functionality at the carboxylic group location. The analogs were synthesized, designed, and characterized by ¹HNMR, and FTIR. The synthetic path began from the reaction of ciprofloxacin drug with morpholine to give compound[B], ciprofloxacin derivative was linked with a variety of primary and secondary amines to give compounds[B1-B9]. The above-mentioned prepared compounds [B3 and B5] were applied to liver enzymes, and the increase in the activity of these enzymes was observed. In addition, a theoretical study was conducted to study the energies and properties of the prepared co

The need for an intellectual understanding of the context from many aspects' dictates understanding the ways through which the graphic designer walks in simulating the intent of the design process and elevating it to levels of communicative perception that leads to communicating the idea to the recipient, and it is thus a need closely related to the context, if it is historical. Culturally or socially, and between the mechanisms of selecting and operating the elements and units of the graphic and design achievement. On this basis, the role of context in graphic design can be studied.

The research included four chapters, the first chapter of the research problem and the need for it, and the aim of the research was (discovering the

African-American writers during the 19th century wrote in the shadow of the prominent romance, sentimental, and domestic fiction. Harriet Wilson’s Our Nig (1859) reflects an “alternative social character”, for the female protagonist suffers racism in the free North, because she is a mulatto child. Through depicting the life of free blacks, who supposedly lives a better life than Southern slaves, Wilson exposes how she has actually lived and sensed life in antebellum America. According to Raymond Williams (2011), there are two kinds of literary writings. The first represents the general tendency of the age, and he calls it “dominant social character”; representing the majority content of both the public writing and speaking. But, a

This work aimed to design, construct and operate a new laboratory scale water filtration system. This system was used to examine the efficiency of two ceramic filter discs as a medium for water filtration. These filters were made from two different ceramic mixtures of local red clay, sawdust, and water.  The filtration system was designed with two rotating interfered modules of these filters.  Rotating these modules generates shear force between water and the surfaces of filter discs of the filtration modules that works to reduce thickness of layer of rejected materials on the filters surfaces. Each module consists of seven filtration units and each unit consists of two ceramic filter discs.    The average measured hy

That the diplomatic work and its importance in foreign policy planning assumes the following points: 1. Choosing the tool in the sense of choosing the most correct tool that reflects the reality of the situation on the one hand and the disposal of strong energy to reach the implementation of the political decision. The declaration of war and entering into a resolution that uses force merely to face insulting ambassadors does not mean Power of the State concerned. But an imbalance in its foreign policy. 2. The coordination of the tools, that the foreign policy scheme must be such a role, and on the external style, diplomatic work, military action and propaganda must complement each other, to the extent that each of them is the first attac