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 .

     Kp index correlates with the many magnetosphere properties, which are used to measure the level of magnetic activity. In the solar system, the two different planets, Mercury with weak magnetic field and Jupiter with strong magnetic field, are selected for this study to calculate the planet's magnetosphere radius (R_MP) which represents the size of magnetosphere compared with solar activity through Kp index,  through two types of geomagnetic conditions; quiet and strong for the period (2016-2018). From the results, we found that there are reversible relations between them during strong geomagnetic storms, while there are direct relations during quiet geomagnetic conditions. Also it is found that the

A comparative study was carried out to evaluate alkaloid antibacterial activity which was extracted from the root bark Punica granatum L. by liquid membrane techniques (SA) and organic solvent traditional techniques (SB). The screening of the antimicrobial activity was conducted by agar well diffusion method against Staphylococcus aureus, Enterobacter cloacae, Escherichia coli, Klebsiella pneumoniae, and Proteus mirabilis at three concentration levels (5, 10 and 15 mg/ml). Alkaloid extracts were analyzed by a high performance liquid chromatography (HPLC) method. Among the tested extractions, SB showed the highest antibacterial activity against all five bacterial strains, especially at 15 mg/ml concentration. However, all the B type solution

Composting is one of the solid waste management (SWM) methods where the organic component decomposed biologically under controlled conditions. In this study, a 0.166 m³ bioreactor tank was designed to compose 59.2Kg of simulated common municipal solid food waste having a bulk density, organic matter, organic carbon, pH, nitrogen content, C/N and nitrification index (NH₄-N/ NO₃-N) of 536.62 kg/m³, 62.34%, 34.76%, 6.53, 1.86%, 23 and 0.34 respectively. The bioreactor operated aerobically for 30 days, and anaerobically for 70 days, until the end of the composting process. Results proved that the composting process could reduce the mass of the waste by 69%.  Nitrogen content,

Polymer films of PEG and PVA and their blend with different
concentrations of MnCl2 (0, 2, 4, 6 and 10 %.wt) were study using
casting technique. The X-ray spectra of pure PEG, PVA and
PVA:PEG films and with addition of 2% concentrations from
(MnCl2) show amorphous structures. The results for FTIR show the
interaction between the filler and polymer blend results in
decreasing crystallinity with rich amorphous phase. This
amorphous nature confirms the complexation between the filler and
the polymer blend. The optical properties of (PVA:PEG/MnCl2)
contain the recording of absorbance (A) and explain that the
absorption coefficient (α), refractive index (n), extinction coefficient
(ko) and the dielectric cons

Fao region is characterized by weak soft silty clay to clayey silt thick layer which extends to a depth of about 20 m. The construction of some structures on such soils may needs piles. During the installation of driven piles, the soil geotechnical properties are exposed to significant changes result due to shearing under large shear strains. These changes significantly decrease the shear strength of the virgin soil due to the destruction of soil structure caused by remolding. The degradation of shear strength is usually followed by strength regaining which is called “Thixotropy”. In this study, the thixotropic effect on Fao clay was investigated. Many disturbed and undisturbed soil samples were brought from Fao regi

The current research aims at knowing the impact of the mind-clearing method in teaching second year intermediate students “reading book”. To achieve the study objective, the researchers intentionally chose Arjwan middle school, located in Baghdad Directorate of Education Al-Rusafa/2, which includes five classes for the second intermediate class. Division (A) was chosen randomly to represent the experimental group, which is taught in the mind-clearing method, while Division (B) represented the control group, which is taught in the traditional way. The sample of the research included (79) female students divided into (39) students in the experimental group, and (40) female students in the control group.To achieve the objective of the res

Zinc Oxide is an indispensable substance in the field of dental treatment. It is used daily and intensively in all governmental and private dental clinics, leading to the disposal of very high concentrations of zinc with waste and eventually in landfill sites as a final destination for solid waste removal. This indicates the urgent need to investigate its behavior upon disposal due to the surrounding conditions. Approximately 4195 g of mixed dental waste samples were collected from (17) healthcare centers in Baghdad Al-Karkh. The leaching behavior of ZnO powder was investigated through batch reactors using makeup dental solid waste samples. The ZnO leaching was tested with 3 conditions; acidic, alkaline, and Ionic Streng

Films of pure Poly (methyl methacrylate) PMMA and Iron chromate doped PMMA have been prepared using casting method. Transmission and absorptance spectra have been recorded in the wavelength range (300-900) nm, in order to calculate, single oscillator energy, dispersion energy proposed by Wemple - DiDomenico model, average oscillator strength, average oscillator wavelength. The refractive index data at infinite wavelength which was found to obey single oscillator model which was found to increase from 2.27-2.56 as the doping percentage increase. The decreasing in the optical energy gap which was found according to Tauc model were (3.74-3.63) eV , is in good agreement with that obtained by wimple-DiDomenico model. The inverse behavior comp

 Indium antimony (InSb) alloy were prepared successfully. The InSb films were prepared by flash thermal evaporation technique on glass and Si p-type substrate at various substrate temperatures (Ts= 423,448,473, and 498 K).       The compounds concentrations for prepared alloy were examined by using Atomic Absorption Spectroscopy (AAS) and X-ray fluorescence (XRF). The structure of prepared InSb alloy and films deposited at various Ts were examined by X-ray diffraction (XRD).It was found that all prepared InSb alloy and films were polycrystalline with (111) preferential direction .       The electrical properties of the films are studied with the varying Ts. It is found that