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 .

Animal fats are a good, promising and ethical alternative source for biodiesel production, but they need more complex treatments than vegetable oils. Iraqi butchery plants waste fats (sheep fat) which are suggested as feedstock to produce biodiesel. This type of fat contains a large quantity of free fatty acids (FFAs) (acid number 49.13 mg KOH/g of fat). The direct transesterification of such fats produce high amount of soap instead of desired biodiesel, so a pre-treatment step (to reduce FFAs) is necessary before transesterification. This step was done by esterification of the free fatty acids in the fat by adding ethanol and using 1% acid catalyst (H2SO4) for 30 minutes. The results showed that the acid number of sheep fat after pre-tr

This research aims to clarify the importance of an accounting information system that uses artificial intelligence to detect earnings manipulation. The research problem stems from the widespread manipulation of earning in economic entities, especially at the local level, exacerbated by the high financial and administrative corruption rates in Iraq due to fraudulent accounting practices. Since earning manipulation involves intentional fraudulent acts, it is necessary to implement preventive measures to detect and deter such practices. The main hypothesis of the research assumes that an accounting information system based on artificial intelligence cannot effectively detect the manipulation of profits in Iraqi economic entities. The researche

This paper presents a numerical simulation for the combined effect of surface roughness and non-Newtonian behavior of the lubricant on the performance of misaligned journal bearing. The modified Reynolds equation to include the effect of non-Newtonian lubricant and bearing surface roughness has been formulated. The model accounts for the lubricant viscosity dependence on temperature and shear rate. In order to make a complete thermo-hydrodynamic analysis (THD) of rough surface misaligned journal bearing lubricated with non-Newtonian lubricant, the modified Reynolds equation coupled with the energy, heat conduction equations, the equation related the viscosity and temperature with appropriate boundary conditions have been solved simultane

Existence of these soils, sometimes with high gypsum content, caused difficult problems to the buildings and strategic projects due to dissolution and leaching of gypsum by the action of waterflow through soil mass. In this research, a new technique is adopted to investigate the performance of replacement and geosynthetic reinforcement materials to improve the gypseous soil behavior through experimential set up manufactured loaclally specially for this work. A series of tests were carried out using steel container (600*600*500) mm. A square footing (100*100) mm was placed at the center of the top surface of the bed soil. The results showed that the most effective thickness for the dune sand layer with geotextile at the interface, within

The numerical analysis was conducted to studying the influence of length to diameter ratio (L/D) on the behavior of the soil treated with sand columns treated with 8% sodium silicate for both floating and end bearing type by using finite element method (Plaxis 3D Foundation ) for isolated foundation of real dimensions. The analysis’s study indicate that in the floating type the best improvement ratio was achieved at (L/D=8) when using columns with a diameter of (0.5, 0.7), but when using columns with a diameter of 0.3 m, it was noticed that the bearing improvement ratio increases with increasing (L/d). While the results of the analysis for end bearing type show that the higher improvement ratio was achieved at (L/D=4) when using columns w

In the current analysis, the effects of circumferential scratches along the inner surface of a 170ᵒ -arc partial journal bearing has been numerically investigated. Their impact on the thermo-elasto-hydrodynamic performance characteristics, including maximum pressure, temperature, deformation, and stress, has been examined thoroughly. The ANSYS Fluent CFD commercial code was employed to tackle the iterative solution of flow and heat transfer patterns in the fluid film domain. They are then applied to the ANSYS Static Structure solver to compute the deformation and stress resulted in the solid bearing zone. A wide range of operating conditions has been considered, including the eccentricity ratio ( ) and scratch depth (

In the present study waste aluminium cans were recycled and converted to produce alumina catalyst. These cans contain more than 98% aluminum oxide in their structure and were successfully synthesized to produce nano sized gamma alumina under mild conditions. A comprehensive study was carried out in order to examine the effect of several important parameters on maximum yield of alumina that can be produced. These parameters were reactants mole ratios (1.5, 1.5, 2, 3, 4 and 5), sodium hydroxide concentrations (10, 20, 30, 40, 50 and 55%) and weights of aluminum cans (2, 4, 6, 8 and 10 g). The compositions of alumina solution were determined by Atomic absorption spectroscopy (AAS); and maximum yield of alumina solution was 96.3% obtain

Low-level microbial activity due to the production of organic acids is a recognized problem during the initial phase of food waste composting. Increasing such activity levels by adjusting the pH values during the initial composting phase is the primary objective to be investigated. In this study, sodium acetate (NaoAc) was introduced as an amendment to an in-vessel composting system. NaoAc was added when the pH of the compost mixture reached a low level (pH < 5), the addition increased pH to 5.8. This had a positive effect on the degradation of organic materials i.e. the formation of methane gas compared to the results without NaoAc addition.

The results also proved that anaerobic-aerobic in-vessel composting could reduce the

Municipal solid waste generation in Babylon Governorate is often affected by changes in lifestyles, population growth, social and cultural habits and improved economic conditions. This effect will make it difficult to plan and draw up future plans for solid waste management.In this study, municipal solid waste was divided into residential and commercial solid wastes. Residential solid wastes were represented by household wastes, while commercial solid wastes included commercial, institutional and municipal services wastes.For residential solid wastes, the relational stratified random sampling was implemented, that is the total population should be divided into clusters (socio-income level), a random sample was taken in e