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

    Utilizing first principles calculations within PW91 exchange-correlation method, we investigated a boron sheet that exhibits related electronic properties. The 2-dimensional boron sheet is flattened and has an atomic structure where the pair cores of every three ordered hexagons within the hexagonal network are loaded up by extra atoms, which saves the triangular lattice symmetry. The boron sheet takes possession of intrinsic metal properties and the electronic bands are comparable to the  bands of the graphene that are close to the Fermi level. The real and imaginary parts of the dielectric function show a metallic or semiconductor behaviour, depending on the electric field direction.

The aim of the paper is to compute projective maximum distance separable codes, -MDS of two and three dimensions with certain lengths and Hamming weight distribution from the arcs in the projective line and plane over the finite field of order twenty-five. Also, the linear codes generated by an incidence matrix of points and lines of  were studied over different finite fields.  

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

Sansevieriatrifasciata was studied as a potential biosorbent for chromium, copper and nickel removal in batch process from electroplating and tannery effluents. Different parameters influencing the biosorption process such as pH, contact time, and amount of biosorbent were optimized while using the 80 mm sized particles of the biosorbent. As high as 91.3 % Ni and 92.7 % Cu were removed at pH of 6 and 4.5 respectively, while optimum Cr removal of 91.34 % from electroplating and 94.6 % from tannery effluents was found at pH 6.0 and 4.0 respectively. Pseudo second order model was found to best fit the kinetic data for all the metals as evidenced by their greater R2 values. FTIR characterization of biosorbent revealed the presence of carboxyl a

Investigation of the adsorption of Chromium (VI) on Fe₃O₄ is carried out using batch scale experiments according to statistical design using a software program minitab17 (Box-Behnken design). Experiments were carried out as per Box-Behnken design with four input parameters such as pH (2-8), initial concentration (50–150mg/L), adsorbent dosage (0.05–0.3 g) and time of adsorption (10–60min). The better conditions were showed at pH: 2; contact time: 60 min; chromium concentration: 50 mg/L and magnetite dosage: 0.3 g for maximum Chromium (VI) removal of (98.95%) with an error of 1.08%. The three models (Freundlich, Langmuir, and Temkin) were fitted to experimental data, Langmuir isotherm has bette

The focus of this article, reviewed a generalized  of contraction mapping and nonexpansive maps and recall some theorems about the existence and uniqueness of common fixed point and coincidence fixed-point for such maps under some conditions. Moreover, some schemes of different types as one-step schemes ,two-step schemes and three step schemes (Mann scheme algorithm, Ishukawa scheme algorithm, noor scheme algorithm, .scheme algorithm,  scheme algorithm Modified  scheme algorithm arahan scheme algorithm and others. The convergence of these schemes has been studied .On the other hands, We also reviewed the convergence, valence and stability theories of different types of near-plots in convex metric space.

Transparent thin films of CdO:Ce has been deposited on to glass and silicon substrates by spray pyrolysis technique for various concentrations of cerium (2, 4, and 6 Vol.%). CdO:Ce films were characterized using different techniques such as X-ray diffraction (XRD), atomic force microscopy(AFM) and optical properties. XRD analysis show that CdO films exhibit cubic crystal structure with (1 1 1) preferred orientation and the intensity of the peak increases with increasing's of Ce contain when deposited films on glass substrate, while for silicon substrate, the intensity of peaks decreases, the results reveal that the grain size of the prepared thin film is approximately (73.75-109.88) nm various with increased of cerium content. With a sur

Background: The aim of the study was to investigate the effect of surface treatments of zirconia (grinding and sandblast with 50μm, 100 μm) on shear bond strength between zirconia core and veneering ceramic. Material and methods: Twenty-eight presintered Y-TZP ceramic specimens (IPS e.max ZirCAD, Ivoclar vivadent) were fabricated and sintered according to manufacturer’s instructions. The core specimens were divided randomly in to 4 groups, group 1: no surface treatment, group2: zirconia specimens were ground with silicon carbide paper up to1200 grit under water cooling, group3: zirconia specimens were ground and sandblast with 100 μm alumina, group 4: zirconia specimens were ground and sandblast with 50 μm alumina. Surfa