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 .

KE Sharquie, AA Noaimi, ER Shwail, J Clin Exp Dermatol Res, 2012 - Cited by 41

Thermal and catalytic pyrolysis of waste plastics in an inert atmosphere has been regarded as a creative method, since pyrolysis can convert plastics waste into hydrocarbons that can be used either as fuels or as a source of chemicals.

Natural Iraqi kaolin clay was used to synthesis the NaX nano- zeolite by hydrothermal conditions with average particle size equal to 77.63nm.Thermal decomposition kinetics of high-density polyethylene (HDPE) in the absence and presence of catalysts nano NaX Zeolite was investigated. Thermal and catalytic degradation of HDPE was performed using a thermogravimetric analyzer in nitrogen atmosphere under non-isothermal conditions 4, 7 and 10 °C/min heating rates were employed in thermogravimetric anal

Esterification considers the most important reaction in biodiesel production. In this study, oleic acid was used as a suggested feedstock in order to study and simulate production of biodiesel. The batch esterification reaction of oleic acid was carried out at various operating conditions; temperature from 40 to 70 °C, ethanol to oleic acid molar ratio from 3/1 and 6/1 and a reaction time up to 180 min.
The catalyst used was prepared NaY zeolite, which is added to the reaction mixture as 2, 5 and 10 wt.% of oleic acid.
The results show that the optimum conditions, gives 0.81 conversion of oleic acid, were 6/1 molar ratio of ethanol/oleic acid, 5 wt.% NaY relative to initial oleic acid, 70°C and 60 minutes. The activation energy o

0

     Estimating multivariate location and scatter with both affine equivariance and positive break down has always been difficult. Awell-known estimator which satisfies both properties is the Minimum volume Ellipsoid Estimator (MVE) Computing the exact (MVE) is often not feasible, so one usually resorts to an approximate Algorithm. In the regression setup, algorithm for positive-break down estimators like Least Median of squares typically recomputed the intercept at each step, to improve the result. This approach is called intercept adjustment. In this paper we show that a similar technique, called location adjustment, Can be applied to the (MVE). For this purpose we use the Minimum Volume Ball (MVB). In order

The research aims to diagnose the level of reflection of uncertainty management strategies (Ignoring uncertainty, knowledge generation , interaction , coping) managing of Organizational change strategies (power coercive, rational empirical, Normative reductive) to the importance of the two subjects and the importance of the expected results has been selected sample size (65) managers from Zain , Asia Cell Telecommunication (32 Zain and 33 company Asia),which alignment for the such a study being heavily dependent on the certainty or uncertainty subject . The researchers are attain there is the effect of uncertainty management strategies in Organizational change management strategies on the overall level in the two companies but have tended t

The aim of the research is to know the level of time management application and its impact on the performance of the job, a survey search in the general company for communication and information technology and provide recommendations that help employees to optimize the use of time and improve performance, which is an important element in controlling the various functions of the company. In order to achieve the objectives of the research, the questionnaire was based on two main variables and distributed to a random sample of (44) employees in the company out of (308) employees, thus the proportion of the sample (14%). After collecting the samples from the sample, there are (6) incomplete forms that have been retri