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 .

Water quality planning relies on Biochemical Oxygen Demand BOD. BOD testing takes five days. The Particle Swarm Optimization (PSO) is increasingly used for water resource forecasting. This work designed a PSO technique for estimating everyday BOD at Al-Rustumiya wastewater treatment facility inlet. Al-Rustumiya wastewater treatment plant provided 702 plant-scale data sets during 2012-2022. The PSO model uses the daily data of the water quality parameters, including chemical oxygen demand (COD), chloride (Cl^-), suspended solid (SS), total dissolved solids (TDS), and pH, to determine how each variable affects the daily incoming BOD. PSO and multiple linear regression (MLR) findings are compared, and their perfor

This study aims to establish an empirical correlation between biochemical oxygen demand (BOD5) and chemical oxygen demand (COD) of the sewage flowing in Al-Diwaniyah wastewater treatment plant. The strength of the wastewater entering the plant varied from medium to high. High concentrations of BOD5 and COD in the effluent were obtained due to the poor performance of the plant. This was observed from the BOD5 /COD ratios that did not confirm with the typical ratios for the treated sewage. To improve the performance of this plant, regression equations for BOD5 and COD removal percentages were suggested which can be used to facilitate rapid effluent assessment or optimal process control. The equations relating the percentage removal of

Water quality planning relies on Biochemical Oxygen Demand BOD. BOD testing takes five days. The Particle Swarm Optimization (PSO) is increasingly used for water resource forecasting. This work designed a PSO technique for estimating everyday BOD at Al-Rustumiya wastewater treatment facility inlet. Al-Rustumiya wastewater treatment plant provided 702 plant-scale data sets during 2012-2022. The PSO model uses the daily data of the water quality parameters, including chemical oxygen demand (COD), chloride (Cl-), suspended solid (SS), total dissolved solids (TDS), and pH, to determine how each variable affects the daily incoming BOD. PSO and multiple linear regression (MLR) findings are compared, and their performance is evaluated usin

Oil industry played a major role in delineating the course and type o development in both imported and exported Arabic countries alike where its revenues has perform an essential role in forming programs and plans of development on both national and international level in addition to anticipation of future consuming.

Iraq, as an oil producer country with a revenues –based economy depends on oil in building its economy totally including its infrastructure having a the greatest conformed reservoir which make the government budget depends largely on oil revenues where its strategic importance lies in funding all aspects of expenders as it is considered the prime source of foreign currency.  The chall

The petrophysical analysis is very important to understand the factors controlling the reservoir quality and production wells. In the current study, the petrophysical evaluation was accomplished to hydrocarbon assessment based on well log data of four wells of Early Cretaceous carbonate reservoir Yamama Formation in Abu-Amood oil field in the southern part of Iraq. The available well logs such as sonic, density, neutron, gamma ray, SP, and resistivity logs for wells AAm-1, AAm-2, AAm-3, and AAm-5 were used to delineate the reservoir characteristics of the Yamama Formation. Lithologic and mineralogic studies were performed using porosity logs combination cross plots such as density vs. neutron cross plot and M-N mineralogy plot. Thes

well log analysis is used to determine the rock properties like porosity, water saturation, and shale volume. Archie parameters in Archie equation, which sometimes considered constants greatly affect the determination of water saturation, also these parameters may be used to indicate whether the rocks are fractured or not so they should be determined. This research involves well logging analysis for Zubair formation in Luhais field which involves the determination of Archie parameters instead of using them as constant.

The log interpretation proved that the formation is hydrocarbon reservoir, as it could be concluded from Rwa (high values) and water saturation values (low values), the lithology of Zubair from cro

The subject of demand on oil derivative has occupied an important position at present time in the daily life context. The fuel of benzene and gas oil and kerosene is one of basic elements of that concern, and on local , regional and international levels. The oil derivatives have played a leading role in determining the course and nature of development since early 1970 to the present time whether in the productive Arab countries or the importing. The researcher set out from the hypothesis that the increase of the local consumer demand on some of the oil derivatives is because of the internal and external factors accompanied by the inability of the productive capability and local production to confront this increase, and the resort

To test the effect of 4 levels of nitrogen (i.e. 0, 45, 90 and 135 Kg N ha^-1) as urea (46% N) and 3 levels of phosphorus (i.e. 0, 17.5 and 35 Kg P ha^-1) as triple superphosphate (21.8% P) on yield and concentration of dill (Anethum graveolens L. local cultivar) seed oil this experiment was carried out during winter season of 1999 - 2000 at the experimental field of Agriculture College, Abu-Ghraib.

 Both fertilizers were applied in two equal splits, first at seeds sowing and the second was added one month after emergence. Dried and ground seed samples were subjected to water distillation for extraction of volatile oils

 Result indicated that fertilization of dill plants with 90 Kg N