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

     In the present work, a kinetic study was performed to the extraction of phosphate from Iraqi Akashat phosphate ore using organic acid. Leaching was studied using lactic acid for the separation of calcareous materials (mainly calcite). Reaction conditions were 2% by weight acid concentration and 5ml/gm of acid volume to ore weight ratio. Reaction time was taken in the range 2 to 30 minutes (step 2 minutes) to determine the reaction rate constant k based on the change in calcite concentration. To determine value of activation energy when reaction temperature is varied from 25 to 65 , another investigation was accomplished. Through the kinetic data, it was found that selective leaching was controlled by surface chemical reactio

Nanocomposite was prepared using unsaturated polyester (UP) resin as a matrix and graphene nanoparticles as a reinforcement material in six percentage weights (0, 0.1, 0.2, 0.3, 1 and 1.5%). Mechanical, calorimetric and thermal studies were performed on the (UP) resin/graphene nanocomposite. All tests showed a clear improvement of all mechanical properties examined (hardness, flexural strength (F.S), impact strength (I.S) and tensile strength (T.S)) with increasing graphene percentage. In addition, the temperature of glass transition and thermal conductivity of this composite increased with increasing graphene content.

In this research, a sensor for chemical solutions was designed and formed using optical fiber-based on a surface Plasmon resonance technology. A single-mode optical fiber with three different diameters (25, 45 and 65) µm was used, respectively.  The second layer of the low refractive fiber was replaced by gold, which was electrically deposited at 40 µm thickness. For each of the three types of optical fiber, different saline concentrations (different index of refraction) were used to evaluate the performance of the refractive index sensor (chemical sensor) by measuring its sensitivity and resolutions. The highest values we could get for these two parameters were 240mm/RIU, and 6*10^-5 RIU respectively, when the diameter of a

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 purpose of this study is designate quenching and tempering heat treatment by using Taguchi technique to determine optimal factors of heat treatment (austenitizing temperature, percentage of nanoparticles, type of base media, nanoparticles type and soaking time) for increasing hardness, wear rate and impact energy properties of 420 martensitic stainless steel. An (L₁₈) orthogonal array was chosen for the design of experiment. The optimum process parameters were determined by using signal-to-noise ratio (larger is better) criterion for hardness and impact energy while (Smaller is better) criterion was for the wear rate. The importance levels of process parameters that effect on hardness, wear rate and impact energy propertie