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 .

          This study was done to evaluate a new technique to determine the presence of methamphetamine in the hair using nano bentonite-based adsorbent as the filler of extraction column. The state of the art of this study was based on the presence of silica in the nano bentonite that was assumed can interact with methamphetamine. The hair used was treated using methanol to extract the presence of methamphetamine, then it was continued by sonicating the hair sample. Qualitative analysis using Marquish reagent was performed to confirm the presence of methamphetamine in the isolate.The hair sample that has been taken in a different period confirmed that this current developing method can be used to analyzed methamphetamine. This m

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 discusses the rehabilitation of heritage markets in the historical centers of Islamic Arab cities and their use in the field of cultural tourism as one of the most important tourist attractions and the subsequent revival of the national economy in addition to preserving the urban heritage as these markets part of the historical centers of cities. The research also discusses the preservation of the continuity of heritage markets as a product of cultural heritage value within an integrated framework to preserve the urban heritage in the historic centers of cities. The study then reviews a number of experiences of Arab and Islamic countries in the field of preserving and rehabilitating heritage markets, which qualify them to b

يهدف البحث إلى تقييم الكفاءة الوظيفية لمؤسسات التعليم الأهلي في أداء وظيفتها بمستوى عالٍ لتشبع حاجة سكان المدينة الذين فضّلوا التعليم الأهلي على التعليم داخل المؤسسات الحكومية مما أدى إلى انتشارها، وصولا إلى أهم الآثار المترتبة على ذلك الانتشار إذ نافست فيه مؤسسات التعليم الحكومي، بل وتنافست المؤسسات الأهلية فيما بينها لتقديم أفضل خدمة تعليمية للصراع من أجل البقاء، وتهدف أيضا إلى  إظهار الوجه السلبي ا

This research aims to discuss an important issue because of its role in increasing the efficiency of financial markets and boost investor confidence by a insider trading, which arises as a result of leaking secret information to some investors and reliable in the process of trading shares in the Iraq Stock Exchange And thus obtain abnormal profits at the expense of other investors. Research was based on the assumption that " Where shortcomings in local regulations relating to disclosure and insider trading in accounting information leads to the activate the phenomenon of insider trading in accounting information in the Iraq Stock Exchange and including a negative impact on investors' decisions ". and Because of the difficulty the discove

This study aims to analyze the spectral properties of plasma produced from rice husk(Rh) using the laser breakdown spectroscopy (LIBS) method. The plasma generation process used the fundamental harmonic (1064 nm) of a Q-switched Nd:YAG laser. Yttrium aluminum garnet (YAG) is a man-made crystalline material. The laser fired pulses with a duration of 10 ns and a repetition rate of 6 Hz. Thus, the energy outputs achieved were 50–200 mJ at the wavelength of 1064 (nm). The silica content in the rice hulls was verified using an XRF measurement, which revealed the presence of silica in the rice hulls in a high percentage. Precise beam focusing was achieved by focusing the laser on the target material. This target material is placed with