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 .

In this paper a comparison of the experimental of evacuated tube solar water heater systems with and without mirror flat reflector. The aim of using the reflector to improve thermal efficiency, and the data gathered which are (temperature, solar irradiation and time) for three days were compared. the results from compared data the temperature lower increase in evacuated tube solar water heater system without reflector than the temperature increase in evacuated tube solar water heater system with reflector .The results show (53, 39, 35) % for three days respectively that the evacuated tube solar water heater system with reflector has higher thermal efficiencies than the results (47, 28, 30) % for three days respectively thermal efficiencies

The present work involves studying the effect of electrolyte composition [@1= 0.5 wt.%  NH₄F / 5% H₂O / 5% Glycerol (GLY)/ 90%  Ethylene Glycol (EG)] and [ @2= 0.5 wt. % NH₄F / 5% H₂O / 95%  Ethylene Glycol (EG)]  on the structural and photoelectrochemical properties of titania nanotubes arrays (TNTAs). TNTAs substrates were successfully carried out via anodization technique and were carried out in 40 V for one hour in different electrolytes (@1, and @2). The properties of physicochemical of TNTAs were distinguished via an X-ray Diffractometer (XRD), Field Emission Scanning Electron Microscope (FESEM), an Energy Dispersive X-ray (EDX), and UV–visible diffuse reflectance. T

The present work involves studying the effect of electrolyte composition [@1= 0.5 wt.%  NH4F / 5% H2O / 5% Glycerol (GLY)/ 90%  Ethylene Glycol (EG)] and [ @2= 0.5 wt. % NH4F / 5% H2O / 95%  Ethylene Glycol (EG)]  on the structural and photoelectrochemical properties of titania nanotubes arrays (TNTAs). TNTAs substrates were successfully carried out via anodization technique and were carried out in 40 V for one hour in different electrolytes (@1, and @2). The properties of physicochemical of TNTAs were distinguished via an X-ray Diffractometer (XRD), Field Emission Scanning Electron Microscope (FESEM), an Energy Dispersive X-ray (EDX), and UV–visible diffuse reflectance. The photoelectrochemical response of TNTAs was evaluated

Emotional competence, is relatively a new concept, stands for the ability of people to perceive their feelings and emotions, and sharing them with others. It also refers to capability in optimizing these feeling and emotions, and managing them over various situations. Thus, this study aims to examine the efficiency of counseling program in developing an emotional competence among intermediate school students in Baghdad city. The sample included group of female students at intermediate stage. The findings revealed none of experimental and control groups have statistically significant differences in pre-posttests of emotional competence efficiency.

This study aims to evaluate the performance of the sewage treatment plant in Al-Diwaniya, one of cities in the southern part in Iraq. This evaluation could be used to facilitate effluent quality assessment or optimal process control of the plant. The influent reaching the plant is considered a medium to strong in strength with BOD5/COD ratio in the range 0.23 and 0.69 which can be considered an easily degradable sewage by the biological processes performed by the activated sludge unit. The quality of the effluent was found to be higher than the Iraqi standards for disposal to water bodies. The BOD5/COD ratios of the treated sewage varied over a wide range as low of 0.13 to 1.48 indicating operational problems in the plant. Regression ana

This study aims to evaluate the performance of the sewage treatment plant in Al- Diwaniya, one of cities in the southern part in Iraq. This evaluation could be used to facilitate effluent quality assessment or optimal process control of the plant. The influent reaching the plant is considered a medium to strong in strength with BOD5/COD ratio in the range 0.23 and 0.69 which can be considered an easily degradable sewage by the biological processes performed by the activated sludge unit. The quality of the effluent was found to be higher than the Iraqi standards for disposal to water bodies. The BOD5/COD ratios of the treated sewage varied over a wide range as low of 0.13 to 1.48 indicating operational problems in the plant. Regressio

The involvement of maxillofacial tissues in SARS‐CoV‐2 infections ranges from mild dysgeusia to life‐threatening tissue necrosis, as seen in SARS‐CoV‐2‐associated mucormycosis. Angiotensin‐converting enzyme 2 (ACE2) which functions as a receptor for SARS‐CoV‐2 was reported in the epithelial surfaces of the oral and nasal cavities; however, a complete understanding of the expression patterns in deep oral and maxillofacial tissues is still lacking.