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 Name of Allah Most Gracious Most Merciful

This is a study dedicated to explaining the conditions of the end of heaven, stage by stage; And to draw the final picture of it, through the facts of the Qur’an, and to make the contextual integration of the verses of the end of heaven, and their arrangement in an intentional arrangement, a path that guides us to knowing the integrated picture of it on the Day of Resurrection, according to scientific interpretation.

The importance and usefulness of the research lies in:

Extracting the order of the stages of the end of heaven, from its first state to its last, which came in separate verses of the Qur’an, each one of which was placed in a surah that was consistent w

In this study, the physical, and mechanical properties of low-cost and biocomposites were evaluated. The walnut shell and date palm frond fibers were thermally treated in an oven at a temperature of 70°C and then chemically treated with NaOH and distilled water solution, after these treatments, the biocomposite materials will be thermally treated again at 50°C. This procedure was performed for three types of biocomposite; Walnut shell Fiber Reinforced Polymer (WFRP), Date palm Fiber Reinforced Polymer (DFRP), and Hybrid Fiber Reinforced Polymer (HFRP), whereas the biocomposite sheets consisting of 30% biofibers and 70% unsaturated polyester, the mechanical test specimens were cut by a CNC machine according to ASTM standards. The e

The applications of herbal medicine have recently acquired growing interest in range of the prophylaxis and treatment of diseases. Olibanum has been used since ancient eras and several reports studied the pharmacological characteristics of boswellic acid, particularly their effect on the inflammatory response, analgesic properties, and anti-arthritic activity mostly in cell lines, but new approaches include animal models to assess these natural derivatives effects taking into consideration of being safer than synthetic preparations.  The impact of olibanum oil on several parameters was studied in rats during this study. These included white blood cell (WBC) count, lactate dehydrogenase (LDH), and C reactive protein (CRP), as well a

     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

In the current study, CuAl0.7In0.3Te2 thin films with 400 nm thickness were deposited on glass substrates using thermal evaporation technique. The films were annealed at various annealing temperatures of (473,573,673 and 773) K. Furthermore, the films were characterized by X-ray Diffraction spectroscopy (XRD), field emission scanning electron microscopy (FESEM), atomic force microscopy (AFM), and Ultra violet-visible (UV–vis). XRD patterns confirm that the films exhibit chalcopyrite structure and the predominant diffraction peak is oriented at (112). The grain size and surface roughness of the annealed films have been reported. Optical properties for the synthesized films including, absorbance, transmittance, dielectric constant, and refr

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.