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 .

Records of two regionalized variables were processed for each of porosity and permeability of reservoir rocks in Zubair Formation (Zb-109) south Iraq as an indication of the most important reservoir property which is the homogeneity,considering their important results in criterion most needed for primary and enhanced oil reservoirs.The results of dispersion treatment,the statistical incorporeal indications,boxes plots,rhombus style and tangents angles of intersected circles indicated by confidence interval of porosity and permeability data, have shown that the reservoir rocks of Zubair units (LS),(1L) and (DJ) have reservoir properties of high quality,in contrast to that of Zubair units (MS) and (AB)which have reservoir properties of less q

The concept of deficit in public budget becomes a chronic economic phenomenon in most of the world, whether the advanced countries or developing countries. Despite  the difference in the visions of the economic schools to accept or reject the deficit in public budget but the opinion that prevailed is the necessity of the state to reduce the public spending which led to a continuous deficits in the public budget which consequently increased the government borrowing ,increase income taxes and wealth, consequently this weakened the in motivation in private investment which contributed to the increase of in factionary stagnation , so that governments have to cover the lack of local funding sources which become difficult to be eq

            A new, simple, rapid and sensitive spectrophotometric method for the determination of sulfamethoxazole in both pure form and pharmaceutical preparations has been reported.The adapted technique based on utilization 4-aminobenzene sulfonic acid as a new modern chromogenic through an oxidative coupling reaction with sulfamethoxazole and potassium iodate in basic media to form orange soluble dye product with absorption maxima at 490 nm. Subject to Beer's law in the range 2–32μg mL^-1. The values of molarabsorption coefficient (ε) and correlation coefficient were found to be 9.118 × 10³ and0.9999 respectively whereas the Sandels index was

Concentrated research topic in the study of key variables in the work of the inspectors general offices , which are in the application of quality management standards audit work and reduce the incidence of corruption. It highlights the importance of current research in being a serious attempt aimed at highlighting the role of the importance of standards of quality management audit work , because they represent a router and leader of the accountant or ( Sergeant ) in the performance of his work and the extent of compliance with these standards , as well as highlight the role of quality audit in reducing the incidence of corruption , of during the professional performance of Higher auditors and determine the responsibilities entrus

The subject of this research involves studying adsorption to removal herbicide Atlantis WG from aqueous solutions by bentonite clay. The equilibrium concentration have been determined spectra photometry by using UV-Vis spectrophotometer. The experimental equilibrium sorption data were analyzed by two widely, Langmuir and Freundlish isotherm models. The Langmuir model gave a better fit than Freundlich model The adsorption amount of (Atlantis WG) increased when the temperature and pH decreased. The thermodynamic parameters like ?G, ?H, and ?S have been calculated from the effect of temperature on adsorption process, is exothermic. The kinetic of adsorption process was studied depending on Lagergren ,Morris ? Weber and Rauschenberg equati

Background: CYP1A1 gene polymorphisms and tobacco smoking are among several risk factors for various types of cancers, but their influence on breast cancer remains controversial. We analyzed the possible association of CYP1A1 gene polymorphisms and tobacco smoking-related breast cancer in women from Iraq. Materials and methods: In this case-control study, gene polymorphism of CYP1A1 gene (CYP1A1m1, T6235C and CYP1A1m2, A4889G) of 199 histologically verified breast cancer patients' and 160 cancer-free control women's specimens were performed by using PCR-based restriction fragment length polymorphism. Results: Three genotype frequencies (TT, TC, and CC) of CYP1A1m1T/C appeared in 16.1, 29.6, and 54.3% of women with breast cancer, respectiv

Cyprinidae species are the most abundant and widely distributed fish species in the inland waters of Iraq. Cyprinids are complex species, and it is difficult to identify them on the basis of morphology. Thus, the morphological characteristics must be achieved and confirmed by molecular analysis. Twenty specimens of Cyprinion kais Heckel, 1843 (Piscies, Cypriniformes, Cyprinidae) were collected from two localities at Tigris River in the middle of Iraq: five specimens from Al-Tharthar Lake, Saladin Province, and 15 specimens from Al- Zubaydiyah sub-district, Wasit Province