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 focused on biotreatment of soil which polluted by petroleum compounds (Diesel) which caused serious environmental problems. One of the most effective and promising ways to treat diesel-contaminated soil is bioremediation. It is a choice that offers the potential to destroy harmful pollutants using biological activity. The capability of mixed bacterial culture was examined to remediate the diesel-contaminated soil in bio piling system. For fast ex-situ treatment of diesel-contaminated soils, the bio pile system was selected. Two pilot scale bio piles (25 kg soil each) were constructed containing soils contaminated with approximately 2140 mg/kg total petroleum hydrocarbons (TPHs). The amended soil: (contaminated soil with the a

This study was focused on biotreatment of soil which polluted by petroleum compounds (Diesel) which caused serious environmental problems. One of the most effective and promising ways to treat diesel-contaminated soil is bioremediation. It is a choice that offers the potential to destroy harmful pollutants using biological activity. The capability of mixed bacterial culture was examined to remediate the diesel-contaminated soil in bio piling system. For fast ex-situ treatment of diesel-contaminated soils, the bio pile system was selected. Two pilot scale bio piles (25 kg soil each) were constructed containing soils contaminated with approximately 2140 mg/kg total petroleum hydrocarbons (TPHs). The amended soil:

Among the different passive techniques heat pipe heat exchanger (HPHE) seems to be the most effective one for energy saving in heating ventilation and air conditioning system (HVAC). The applications for nanofluids with high conductivity are favorable to increase the thermal performance in HPHE. Even though the nanofluid has the higher heat conduction coefficient that dispels more heat theoretically but the higher concentration will make clustering .Clustering is a problem that must be solved before nanofluids can be considered for long-term practical uses. Results showed that the maximum value of relative power is 0.13 mW at nanofluid compared with other concentrations due to the low density of nanofluid at this concentration. For highe

Face Identification system is an active research area in these years. However, the accuracy and its dependency in real life systems are still questionable. Earlier research in face identification systems demonstrated that LBP based face recognition systems are preferred than others and give adequate accuracy. It is robust against illumination changes and considered as a high-speed algorithm. Performance metrics for such systems are calculated from time delay and accuracy. This paper introduces an improved face recognition system that is build using C++ programming language with the help of OpenCV library. Accuracy can be increased if a filter or combinations of filters are applied to the images. The accuracy increases from 95.5% (without ap

The work demonstrates the effect of cold atmospheric plasma (CAP) on adult female rats suffering from osteoporosis, the used plasma was generated by a floating electrode-dielectric barrier discharge system with an electrode diameter of 3 cm. The output power was from (12-20) watts. The effect of non-thermal plasma was observed on rats with various exposure times of 20, 30, and 40 sec. It was noted that the blood calcium percentage of animals exposed to cold plasma increased, as well as an increase in the level of vitamin D3 at the same time, it is noted that there is no effect on parathyroid hormone level. For the thyroid gland, it is noticed an increase in the level of T3, and T4 hormones in the blood during the period of induction for

In this study, the response and behavior of machine foundations resting on dry and saturated sand was investigated experimentally. In order to investigate the response of soil and footing to steady state dynamic loading, a physical model was manufactured to simulate steady state harmonic load at different operating frequencies. Total of 84 physical models were performed. The footing parameters are related to the size of the rectangular footing and depth of embedment. Two sizes of rectangular steel model footing were tested at the surface and at 50 mm depth below model surface. Meanwhile the investigated parameters of the soil condition include dry and saturated sand for two relative densities 30% and 80%. The response of the footing was ela