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 .

It is known that the oral administration of ibuprofen caused an irritation of stomach as a side effect due to its carboxylic moiety. Ibuprofen ester was synthesized by linking the carboxylic moiety of ibuprofen and the hydroxylic group of paracetamol to reduce its side effect. Study the kinetic hydrolysis of prepared ester was examined at different values of physiological pH (1.0, 5.8, 6.4 and 7.4) at 37 ± 0.1 of 1 hour period. Measurements of absorbance were carried out by UV-Visible spectrophotometer to follow the stability of ester, it showed Pseudo first order hydrolysis. The pH- apparent rate profiles of ester was exhibited a good stability at pH 1.0 and pH 5.8. Pharmacological activity in vivo of prepared ester was evaluated in re

This research examines the use of vibratory treatments to reduce residual stresses in small welded parts. In this experimental investigation, a post weld vibration treatment was applied to T- A106 steel pipe fitting specimens to study the effect of the treatment on the residual stress and the hardness of the material. The vibratory stress relief treatment was carried out at different vibration frequency. The results have demonstrated that post-weld vibratory stress relief of small size fittings is possible and residual stress may be relieved, and the treatment may be an alternative method for heat treatment especially when unchange in dimensions and material stability are required.

Leishmania parasites are the causative agent of leishmaniasis. Many studies are inspecting chemical drugs, including the use of miltefosine and amphotericin B, but curative values may be limited for these drugs with side effects due to the chemical origin, therefore, investigating less toxic therapies is essential. The aim of this study was to investigate the effectiveness of artemisinin on Iraqi strain of Leishmania tropica, by experimental macrophage ex vivo infection of amastigotes into mouse macrophage cell-line RAW264.7. Different concentrations (100, 200, 300, 400, 500)μM of artemisinin (ART) were screened to examine the susceptibility of L. tropica amastigotes to invade macrophage cell line along three times of follow up (24, 48 and

Lithium–Manganese ferrites having the chemical formula (Li0.5-0.5x Mnx Fe2.5-0.5x O4), (0 ≤ x ≤ 1) were prepared by double sintering powder processing. The density of the ferrite increased with Mn content while the porosity was noticed to decrease. The dielectric constant was found to increase at high frequencies more rapidly than the low ones. The dielectric constant found to decrease with Mn content. The decrease in loss factor with frequency agreed with Deby’s type relaxation process. A maximum of dielectric loss factor was observed when the hopping frequency is equal to the external electric field frequency. Manganese substitution reduced the dielectric loss in ferrite. The variation of tanδ with frequency shows a similar na