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 .

The study of traffic on the roads the governorate of Karbala, Where is the study of traffic on the roads measure is necessary to determine the extent of the road and highlighting the importance of its role in the transfer of individuals from original to destination as well as the importance of the region that attracted its movement. This research aims to analyze the traffic in the governorate of Karbala through the study and analysis of surveys of traffic that were made in the governorate. Based on this analysis, it has been reached to identify volumes of the traffic and its density and how the roads are efficient and accommodating these volumes, the results of the traffic survey of the studied roads in the area of the study have shown t

When sites of new communication occurs which represents the merit of the development of communication technology which is characterized by the services of ( facebook-twiter-corapora-youtube-mass space-friendster-flicker-willnecked in addition to the direct services for viber-whatsup-telgram-and chat on) play important role in changing the infrastructure of Arabic societies which are consideredas closed and not changeable societies during near period and the significance of this study comes from the importounce of this subject which is considered as anew trend of the age on the field of media and public response and acceptance inspite of what is known about Arabic society-it doesn’t accept change-this occurance is associated with terms

The ceramic compound Mg1-xSixAl2O4 (x= 0, 0.1, 0.2, 0.3, 0.4) was prepared from nano powder of Al2O3 and MgO doped with Nano powder of SiO2 at different molar ratios. The specimens were prepared by standard chemical solid reaction technique and sintered at 1450 oC. Structure of the specimens was analyzed by using X-ray diffraction (XRD). The X-ray patterns of the specimens showed the formation of pure simple cubic spinel structure MgAl2O4 phase with space group of ̅ . The average grain size and surface topology were studied by atomic force microscopy. The results showed that the average grain size was about 73-90 nm. The DC electrical properties of the specimen were measured. The apparent density was found to increase and the porosity a

Dissolution of gypsum rock in water is significant, which may result in hydrocarbon reservoir formation and evaporate deposits. However, the complexity of the gypsum dissolution process is still of interest because of its uncleanness that requires more critical analysis. The objectives of this experimental study are emphasis on the dissolution characteristics of gypsum rock under room temperature and by various types of water; namely: deionized, tap, fresh, acidic, well, and normal rainwatre. In addition, the influences of dissolution on gypsum rock's mechanical and physical characteristics. Gypsum rock was obtained from Agjalar area, in the southwest of Sulaymaniyah city, Northern Iraq. Experimental results show that we

In the last decades, using mineral admixture in concrete became very necessary to improve concrete properties and reduce CO₂ emissions associated with the cement production process. Subsequently, more sustainable concrete can be obtained.  Ternary blended cement containing two different types of mineral admixture can achieve ambitious steps in this trend. In this research, the synergic effects of mineral admixtures in ternary blended cement and its effects on concrete fresh properties, strength, durability, and efficiency factors of mineral admixture in ternary blended cement, were reviewed. The main conclusion reached after reviewing many literature pieces is that the concrete with ternary blended cement

In this research an experimental study has done for testing the thermal performance of selective surfaces used in solar collectors for substrate of iron, galvanized iron and aluminum which are commercially available. The coating process for the samples has done in two ways, the electroplating and the chemical spray pyrolysis. The results of the thermal performance test of these samples are comparing with the thermal performance of a sample without paint and other paint with black paint without shines commercially available. For the electroplated samples, the performance study has done for different immersion time in plating bath, the
distance between electrical poles, the current density, and area ratio of the sample plated area to

The objective of the research is to measure the impact of social responsibility on the financial performance of the Bank of Baghdad for the period from 2014 to 2016 (3 years) through discussing and analyzing the level of practice of the Bank of Baghdad for social responsibility and the impact on their financial performance during the period. To measure the independent variable (CSR), the researcher used the CSR Disclosure Index and relied on the ROA as an indicator to measure the dependent variable (financial performance).The results of the research showed the main hypothesis of the research, which states that the social responsibility of the banks has no significant impact on the financial performance. In relation to the disclosure of s

The present study is considered the first on this sector of the Tigris River after 2003. It is designed for two aims, the first is to demonstrate the seasonal variations in physicochemical parameters of Tharthar-Tigris Canal and Tigris River; the second is to explain the possible effects of canal on some environmental properties in the Tigris River. Water samples were being collected monthly. Six sampling sites were selected, two on Tharthar Canal and four along the Tigris River, one before the confluence as a control site and the others downstream the confluence with the canal. For a period from January to December 2020, nineteen physicochemical parameters were investigated including air and water temperature, turbidity, electrical cond