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 .

Religion in its general and simplified form is defined as a set of values or moral laws, which include provisions that people should follow to organize their affairs and ratify that they are provisions sent from the divine. 

      The concept of religion is not limited to the narrower sense represented by the performance of the virtual rituals of worship and religious fashions, etc., but also includes all the moral and spiritual values, conduct and good dealing that reflect the true essence of religion, which boils down to a set of values – such as sincerity, honesty and dedication to work, merciful dealing and compassion, etc. All religions agree on the moral content of religion. The Prophet of Is

Internet of Things (IoT) technology could be an effective solution to accomplish real-time retrieval of historical electronic health records (EHRs) to present better service of healthcare. In a pilgrimage environment such as the Hajj, IoT can be applied by identifying the non-local patients as electronic tags, and the tag data can be read by wireless sensors. The data that is collected using Radio-Frequency Identification (RFID) can be acquired from a Wireless Sensor Network (WSN) in order to accomplish many decisions, such as sending an ambulance to a patient’s location, sending an emergency alert to his immediate family circle, and retrieving his EHR from a database. The main contribution of this research is to propose a conceptual IoT

This paper presents the effect of Cr doping on the optical and structural properties of TiO2 films synthesized by sol-gel and deposited by the dip- coating technique. The characteristics of pure and Cr-doped TiO2 were studied by absorption and X-ray diffraction measurement. The spectrum of UV absorption of TiO2 chromium concentrations indicates a red shift; therefore, the energy gap decreases with increased doping. The minimum value of energy gap (2.5 eV) is found at concentration of 4 %. XRD measurements show that the anatase phase is shown for all thin films. Surface morphology measurement by atomic force microscope (AFM) showed that the roughness of thin films decrease with doping and has a minimum value with 4 wt % doping ratio.

Low grade crude palm oil (LGCPO) presents as an attractive option as feedstock for biodiesel production due to its low cost and non-competition with food resources. Typically, LGCPO contains high contents of free fatty acids (FFA), rendering it impossible in direct trans-esterification processes due to the saponification reaction. Esterification is the typical pre-treatment process to reduce the FFA content and to produce fatty acid methyl ester (FAME). The pre-treatment of LGCPO using two different acid catalysts, such as titanium oxysulphate sulphuric acid complex hydrate (TiOSH) and 5-sulfosalicylic acid dihydrate (5-SOCAH) was investigated for the first time in this study. The optimum conditions for the homogenous catalyst (5-SOCAH) wer

In the present work the performance of semifluidized bed adsorber was evaluated for removal of phenolic compound from wastewater using commercial activated carbon as adsorbent. P-chlorophenol (4-Chlorophenol) and o-cresol (2-methylphenol) was selected as a phenolic compound for that purpose. The phenols percent removal, in term of breakthrough curves were studied as affected by hydrodynamics limitations which include minimum and maximum semifluidization velocities and packed bed formation in the column by varying various parameters such as inlet liquid superficial velocity (from U_minsf to 8U_minsf m/s), and retaining grid (sometimes referred to as adsorbent loading) to initial static bed height ratio (from 3-4.5). In

At different stages of the evolution of the modern Iraqi state ears last century did not receive the industrial sectors importance in  great domestic production (GDP) and  that the limited  resources available in the initial stage and the dominance of public sector industry in the late stage , so the continued decline in the contribution  of the private industrial sector in  GDP , and this is why imbalance in the labor market and reduced  demand for manpower in this sector despite the high rates of labor supply and the various skills and levels of investments, their human  and the different geographical distribution , and direction of labor to other economic sectors most  requested of the l