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 .

Recently, several concepts and expressions have emerged that have often preoccupied the world . around the concept of environment and sustainability. This is due to the negative and irresponsible impact of man and his innovations in various industrial and technological fieldsthat have damaged the natural environment. Architecture and cities at the broader level are some of the man made components that caused these negative impacts and in the same time affected by them. What distinguishes architectural and urban projects is the consumption of large . quantities of natural resources and production larger amounts of waste and pollution, along the life of these projects. At the end of the twentieth century and the beginning of the twenty-fir

The research work is "The passive voice as a grammatical phenomenon in four selected textbooks". The research deals with the grammatical phenomenon passive in German. The research consists of two parts, the theoretical and the empirical part. The present research work is divided into 3 sections:

The first section includes the definition of passive, passive types, process passive, state passive, passive with modal verbs, and other types of passive. The second section provides illustrations of the four selected textbooks. The third chapter presents the passive voice in textbooks, namely German language teaching for foreigners by Dora Schulz and Heinz Griesbach, Delfin von Aufderstrasse H. and others, Em von Balme, M. and others and

This research seeks to try to address one of the important issues in society that prevents the state from achieving its social, economic, political and financial goals, represented by the low tax proceeds, through which it can achieve those goals. What is reflected on the tax proceeds, knowing that the General Tax Authority does not take into account the issue of analyzing the opportunity cost of corporate capital as one of the profit indicators when setting the annual controls, which leads to a decrease in the tax proceeds, and therefore the research objective will be to shed light on the importance of adopting the concept of analysis The opportunity cost by the General Tax Authority to achieve a tax proceeds commensurate with t

Background: This study evaluate the immunohistochemical expression profile of transforming growth factor beta-1 in inflamed gingival tissue of patients with gingivitis and chronic periodontitis compared to healthy subjects and, determine the correlation between this cytokine and the clinical periodontal parameters, intensity of inflammation and chronic periodontitis severity. Materials and methods: Gingival tissue specimens were taken from 23 chronic periodontitis patients, 20 gingivitis patients and 20 periodontally healthy subjects. The periodontal status was evaluated by dichotomous measurements of the clinical periodontal parameters (PLI, GI, BOP, PPD, CAL). The gingival specimens were fixed immediately in 10% formalin and processed ro

Background Psoriasis is one of the most prevalent chronic inflammatory skin conditions; its prevalence ranges from 1 to 3%. Tumor necrosis factor-alpha (TNF-α), a cytokine that enhances inflammation, is overexpressed in synovium and skin plaques in psoriasis. TNF-α plays a critical role in the pathogenesis of psoriasis. IL-10 is the most crucial cytokine for reducing excessive immune responses and decreasing pro-inflammatory reactions in all autoimmune disorders.   Objective To evaluate the effect of Apremilast on ILـ10, TNFـα, and BMI in obese psoriatic patients.   Methods Thirty patients included in this investigative study to measure the concentrations of TNFـα, ILـ10 and BMI, before and after receiving Apremilast. TNFـα and

Objective : To study the effect of some risk factors like age, smoking and Diabetes mellitus (DM) among patients with
certain cardiovascular diseases (Angina pectoris and Myocardial infarction), in addition to the assessment of the Creactive
protein (CRP) in the sera of those patients.
Methodology: The study was carried out on (100) subjects who were hospitalized in the Iraqi Center of heart Diseases
in Baghdad city and were suffering from Myocardial InfarcƟon (MI) (16) and Angina Pectoris (AP) (79) or from both (5)
over a period from September 2009 to June 2010. The results of paƟents were compared with those of (30) healthy
and age-matched individuals as a control group. Data were obtained from patients who were alr

Abstract Objective: The underlying molecular basis of ischemic heart diseases (IHDs) has not yet been studied among Iraqi people. This study determined the frequency and types of some cardiovascular genetic risk factors among Iraqi patients with IHDs. Methods: This is a cross-sectional study recruiting 56 patients with acute IHD during a 2-month period excluding patients >50 years and patients with documented hyperlipidemia. Their ages ranged between 18 and 50 years; males were 54 and females were only 2. Peripheral blood samples were aspirated from all patients for troponin I and DNA testing. Molecular analysis to detect 12 common cardiovascular genetic risk factors using CVD StripAssay® (ViennaLab Diagnostics GmbH, Austria) was performed

Four major factories (Petroleum Refineries Company, Detergents Plant, Thermal Power Plant, and Gaseous Power Plant) are located to the north of Baiji City. They release pollutants in form of gases, liquids and solids; they find their way to the surrounding environment. To assess the environmental pollution of the area, 18 samples of surface soil distributed around the industrial establishments were collected and analyzed to determine the concentration of polycyclic aromatic hydrocarbons (PAH) components which are often targets in the environmental checking. Identification and quantification of the 16 PAHs components was accomplished using High Performance Liquid Chromatography (HPLC) had a model Shimadzu LC-10 AVP. The total concentratio

Total quality management  considers one of the modern scientific entrances  which practiced by productivity service organizations alike to provide appropriate quality required outputs according to the needs and desires of customers manage , enable the organization seeking to continue and grow in light of the increasing competition from the satisfy and provide the appropriate total quality management requirements whenever led to face risks that they may have  in a manner in which they can be addressed and find ways to avoid them in the future when repeated.                          &n