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 .

Industrial and urban development has resulted in the spread of plastic waste and the increase in the emissions of carbon dioxide resulting from the cement manufacturing process. The current research aims to produce green (environmentally friendly) concrete by using plastic waste as coarse aggregates in different proportions (10% and 20%) and nano silica sand powder as an alternative to cement in different proportions (5% and 10% by weight). The results showed that compressive strength decreased by 12.10% and 19.23% for 10% and 20% plastic waste replacement and increased by 12.89% and 20.39% for 5% and 10% silica sand replacement respectively at 28 days. Flexural strength decreased by 12.95% and 19.64% for 10% and 20% plastic waste r

     The research aims to prepare a preliminary feasibility study that shows the importance of preliminary feasibility study in investment decision making, carrying out of the local demand of service provided in accordance with international standards and statement of investment opportunities available to the private sector in several investment methods. In order to reach the objectives of the study was adopted as a method of partial analysis at the level of economic unity through the study demand, supply, costs, economic and social profitability.

      The health sector in Iraq is one of the service sectors facing today a continuous deficiency

      The gravity anomalies of the Jurassic and deep structures were obtained by stripping the gravity effect of Cretaceous and Tertiary formations from the available Bouguer gravity map in central and south Iraq. The gravity effect of the stripped layers was determined depending on the density log or the density density obtained from the sonic log. The density relation with the seismic velocity of Gardner et al (1974) was used to obtain density from sonic logs in case of a lack of density log. The average density of the Cretaceous and Tertiary formation were determined then the density contrast of these formations was obtained. The density contrast and thickness of all stratigraphic formations in the area between the sea level to t

The purpose of this study was to evaluate the epidemiological characteristics of the mandibular fractures relating to gender, age, the etiology of injury, and the rendered treatment modalities and complications. The data of the patients who sustained mandibular fractures were retrieved and were analyzed retrospectively, and based on these data a descriptive analysis was conducted. A total of 112 patients were included in this study; the most common cause was road traffic accidents (RTAs) followed by assaults and missile injuries. The most frequently involved age group was 11 to 20 years, treatment modalities included conservative, closed reduction and indirect fixation, and open reduction and internal fixation (ORIF) in 11.6, 79.5, and 8.9%

The Dammam Formation in S and SW of Iraq is an Eocene carbonate succession consisting of limestone and dolostone. Two boreholes are selected in Al-Najaf and Al-Samawa area to investigate the biostratigraphy. The biostratigraphy of Dammam Formation consist of 22 species which belong to 13 genera of fossils foraminifera.
Two biozones were distinguished in Dammam Formation depending on benthonic foraminifera Nummulites. These biozones are; Nummulites gizehensis range zone and Alveolina sp. – Coskinolina sp. assemblage zone. According to thESE biozones the age of Dammam Formation represent Middle Eocene , whereas absent of these biozone represent Early and Late Eocene.

The study area intendes for agricultural investment and establishment stations of water pumping for human use to the nearby areas, southwest of Samawah city. Twelve Two-Dimension (2-D) survey points were performed by using Wenner-Schlumberger array configuration to take the measurements. The inverse models of two survey point appear the effect of the saline groundwater that raises from Rus Formation, which caused a significant reduction in resistivity of the groundwater-bearing zone within middle Dammam Formation along the fault plane.  

Primary productivity and chlorophyll-a were used in this study to monitor the restoration process of southern Iraqi marshes (Al-Hewaizeh, central marshes, and Al-Hammar). The phytoplankton primary productivity was based on oxygen light/dark bottle method. Two different depths samples were taken monthly from six studied marshes stations (two stations for each marsh) during November 2005 to October 2006, while chlorophyll-a samples taken from surface water. The phytoplankton primary productivity values ranged 9.38 – 249.79 mg C/m3.hr for all marshes, its values for surface water sample ranged 11.71 – 256.24 mg C/m3.hr, while for 1m depth ranged 9.38 – 142.5 mg C/m3.hr. Chlorophyll-a values ranged between (1.1 – 21.26) µg/l indicating

During the winter, in the industry region (Shaikh Omer) and by applying a passive radon detector (CR-39), lung cancer risk has been measured in twelve rooms of different workshops of two old factories in this site. The radon concentration is ranged from (123.345 Bq/m³) to (328.985 Bq/m³) with an average of (244.19±61.52 Bq/m³). Lung cancer risk ranged from 55.993 to 149.346 per million people and with an average of (110.855 per million people) which were lower than the recommended values (170-230 per million people), so there was no cancer risk on workers in these locations.