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 Production and Operations Management the specialists  have  tried to develop a strategy to counter the risks arising from the activities of the organization and of waste of various types and therefore the risk management in the contemporary framework represents a phenomenon of new quality, and can not be this phenomenon to take practical dimensions, but the development of culture of the organization towards the risks and deal with all aspects and paint ways to address them within an integrated program, and requires new skills and systems provide accurate information capable of coordination between the various parties within the organization.

     The research aims to develop a blu

This research presents a study for precipitating phosphorus (as phosphate ion) from simulated wastewater (5ppm initial concentration of phosphorus) using calcium hydroxide Ca(OH)₂ solution. The removal of phosphorus by Ca (OH)₂ solution is expected to be very effective since the chemical reaction is of acid-base type but Ca(OH)₂ forms complex compound with phosphate ions called. Hydroxyapatite Ca₅ (PO₄)₃OH. hydroxyapatite is slightly soluble in water. This research was directed towards sustainable elements as phosphorus. Kinetics of the dissolution reaction of hydroxyapatite was investigated to find the best factors to recover phosphorus. The effect of con

This research is focusing on finding more effective polymers that leads to enhance the rheological properties of Water Base Muds. The experiments are done for different types of mud for all substances which are Polyacrylamide, Xanthan gum, CMC (Carboxyl Methyl Cellulose). This study shows the effect of add polymer to red bentonite mud, effect of add polymer to Iraqi bentonite mud, the effect of add bentonite to polymer mud. The mud properties of Iraqi bentonite blank are enhanced after adding the polymers to the blank mix, CMC gives the highest value of plastic viscosity and Gel strength than others; X-anthan gives the highest value of yield point and gel strength than others. For the red bentonite mud, Polyacrylamide has the highes

The effect of considering the third dimension in mass concrete members on its cracking behavior is investigated in this study. The investigation includes thermal and structural analyses of mass concrete structures. From thermal analysis, the actual temperature distribution throughout the mass concrete body was obtained due to the generation of heat as a result of cement hydration in addition to the ambient circumstances. This was performed via solving the differential equations of heat conduction and convection using the finite element method. The finite element method was also implemented in the structural analysis adopting the concept of initial strain problem. Drying shrinkage volume changes were calculated using the procedure suggested

Hydatid cyst disease is one of the most common diseases in many places in the world. The infection occurs when human and livestock drinking or eating contaminated water and food with eggs of Echinococcus granulosus worm. Surgery is the best solution to eradicate cysts and rapid healing, but it may be accompanied by some risks such as rupture of the cyst and leakage its contents of protoscolices, which leads to the return of infection and spread in the body. Several methods have been used to reduce the risks of surgery, including withdrawal of hydatid fluid and its contents and injection scolicidal substances like ethanol and others. Researchers have recently tested the efficiency of nanoparticles such as selenium, silver, and gold nanoparti

Background: Adjustment of any premature occlusal contact of any zirconia restoration requires its polishing or glazing in order to restore the smoothness of the restoration. The objective of this in vitro study was to evaluate the effects of different polishing systems and glazing on the surface roughness of full-contour zirconia. Material and methods: Forty disks (diameter: 8 mm, thickness: 6.4 mm) were prepared from pre-sintered full-contoured zirconia block; they were colored and sintered in a high-temperature furnace at 1500ËšC for 8 hours. The specimens were then leveled and finished using grinding and polishing machine and adjusted using diamond disk. The specimens were then randomly divided into four groups (n=10), group I involves

The BEK family of flows have many important practical applications such as centrifugal pumps, steam turbines, turbo-machinery and rotor-stator devices. The Bödewadt, Ekman and von Kármán flows are particular cases within this family. The convective instability of the BEK family of rotating boundary-layer flows has been considered for generalised Newtonian fluids, power-law and Carreau fluids. A linear stability analysis is conducted using a Chebyshev collocation method in order to investigate the effect of shear-thinning and shear-thickening fluids for generalised Newtonian fluids on the convective Type I (inviscid crossflow) and Type II (viscous streamline curvature) modes of instability. The results reveal that shear-thinning power-law