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 .

Abstract

The leases, are regarded as one of the most controversial accounting issues in recent years, since they  represents one of the important sources of funding, which may be exploited by the tenant as off- Balance sheet Financing , which negatively affects the quality of financial reporting. The Financial Accounting Standards Board (FASB) and the International Accounting Standards Board (IASB) have "significant" interest in accounting for leases . FASB issued Statement of Financial Accounting Standards 13 on lease contracts in 1976 and IASB issued IAS 17 in 1980, which was amended in 1997 and IFRS 16, issued in January 2016, which will be effective on January 1, 2019 , to solve

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 research investigates the subject of the impact of wars (as a manifestation of crisis) on architecture, and the extent of continuing wars physical and moral results of wars, even after the end of the cause of the crisis. The impact of different rebuilding which exposed to the effects of the war seems different in crisis regions.

The problem of research is about the uncertainty of the impact of the way chooses for reconstructing the buildings after wars in the continuity of the crisis of war. The goals of this research are to clarify the influence of methods of reconstruction of buildings in a city chosen which is Beirut, on the continuation of the war crisis with the argument of demolishing and rebuilding newly or keeping tr

Iraqi crude Atmospheric residual fraction supplied from al-Dura refinery was treated to remove metals contaminants by solvent extraction method, with various hydrocarbon solvents and concentrations. The extraction method using three different type solvent (n-hexane, n-heptane, and light naphtha) were found to be effective for removal of oil-soluble metals from heavy atmospheric residual fraction. Different solvents with using three different hydrocarbon solvents (n-hexane, n-heptane, and light naphtha) .different variables were studied solvent/oil ratios (4/1, 8/1, 10/1, 12/1, and 15/1), different intervals of perceptual (15, 30-60, 90 and 120 min) and different temperature (30, 45, 60 and 90 °C) were used. The metals removal percent we

This paper provides an attempt for modeling rate of penetration (ROP) for an Iraqi oil field with aid of mud logging data. Data of Umm Radhuma formation was selected for this modeling. These data include weight on bit, rotary speed, flow rate and mud density. A statistical approach was applied on these data for improving rate of penetration modeling. As result, an empirical linear ROP model has been developed with good fitness when compared with actual data. Also, a nonlinear regression analysis of different forms was attempted, and the results showed that the power model has good predicting capability with respect to other forms.

Iraqi crude Atmospheric residual fraction supplied from al-Dura refinery was treated to remove metals contaminants by solvent extraction method, with various hydrocarbon solvents and concentrations. The extraction method using three different type solvent (n-hexane, n-heptane, and light naphtha) were found to be effective for removal of oil-soluble metals from heavy atmospheric residual fraction. Different solvents with using three different hydrocarbon solvents (n-hexane, n-heptane, and light naphtha) .different variables were studied solvent/oil ratios (4/1, 8/1, 10/1, 12/1, and 15/1), different intervals of perceptual (15, 30-60, 90 and 120 min) and different temperature (30, 45, 60 and 90 °C) were used. The metals removal perce

The principle of citizenship has international dimensions that affect the application of the principle, such as the structure of the international system, and the control of the concepts of globalization, international organizations which played an important role in the consolidation of this principle.

The problem of the study revolves around the effects of international variables on the principle of citizenship in Kuwait during the period 1991-2018.

The study used several indicators, such as: the rule of law, achieving the principle of separation of powers, the right to form parties, the application of the law of nationality, and racial discrimination, women's rights, and freedom of expression.

       The present study was performed to spotlight the potential role of soil bacteria in the Al-Rumaila oil field as a bioindicator of heavy metals pollution. For this purpose, nine soil samples were collected from different sites, with 20cm depth, to assess the pollution status depending on the total and available concentrations of heavy metals.  The result indicates pollution of the studied soils with the following metals: Cd, Cu, Fe, Zn, and Pb. The mean of total concentration for all studied metals was higher than the allowed maximum limit based on the international limit:(3.394, 3.994, 39.993, 8844.979,150.372, and 103.347 µg/g), respectively. While measuring the total Metal concentration is important in determining the de