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 this paper, the ability of using corn leaves as low-cost natural biowaste adsorbent material for the removal of Indigo Carmen (IC) dye was studied. Batch mode system was used to study several parameters such as, contact time (4 days), concentration of dye (10-50) ppm, adsorbent dosage (0.05-0.25) gram, pH (2-12) and temperature (30-60) ^oC. The corn leaf was characterized by Fourier-transform infrared spectroscopy device before and after the adsorption process of the IC dye and scanning electron microscope device was used to find the morphology of the adsorbent material. The experimental data was imputing with several isotherms where it fits with Freundlich (R² = 0.9

During the last few years, the greener additives prepared from bio-raw materials with low-cost and multifunctional applications have attracted considerable attention in the field of lubricant industry. In the present work, copolymers derived from sunflower and linseed oils with decyl methacrylate were synthesized by a thermal method using benzoyl peroxide (BPO) as a radical initiator. Direct polymerization of fatty acid double bonds in the presence of a free radical initiator results in the development of environmentally friendly copolymeric additives (Co-1 and Co-2). Fourier Transform Infrared (FTIR) and Proton Nuclear Magnetic Resonance (1H-NMR) were used to characterize the resulting copolymers. Thermal decomposition of copolymers was de

In this work, lead oxide nanoparticles were prepared by laser ablation of lead target immersed in deionized water by using pulsed Nd:YAG laser with laser energy 400 mJ/pulse and different laser pulses. The chemical bonding of lead oxide nps was investigated by Fourier Transform Infrared (FTIR); surface morphology and optical properties were investigated by Scanning Electron Microscope (SEM) and UV-Visible spectroscopy respectively, and the size effect of lead oxide nanoparticles was studied on its antibacterial action against two types of bacteria Gram-negitive (Escherichia coli) and Gram-positive (Staphylococcusaurus) by diffusion method. The antibacterial property results show that the antibacterial activity of the Lead oxide NPs was

This paper presents the ability to use cheap adsorbent (corn leaf) for the removal of Malachite Green (MG) dye from its aqueous solution. A batch mode was used to study several factors, dye concentration (50-150) ppm, adsorbent dosage (0.5-2.5) g/L, contact time (1-4) day, pH (2-10), and temperature (30-60)   The results indicated that the removal efficiency increases with the increase of adsorbent dosage and contact time, while inversely proportional to the increase in pH and temperature. An SEM device characterized the adsorbent corn leaves. The adsorption's resulting data were in agreement with Freundlich isotherm according to the regression analysis, and the kinetics data followed pseudo-first-order kinetic with a correlation

A study was conducted to evaluate the antibacterial effect of Phyllanthus emblica extract (ethanol:methanol, 1:1) against Pseudomonas aeruginosa, Staphylococcus aureus and Escherichia coli at different concentrations, i.e. 0.625, 1.25, 2.50, 5.0, 10.0 and 20.0 mg/ml. The antibacterial activity was determined by the agar well diffusion method to investigate the minimum inhibitory concentration (MIC) and minimum bactericidal concentration (MBC). The alcoholic extract of Phyllanthus emblica had the highest antibacterial activity at 20 mg/ml and 5 mg/ml except for Pseudomonas aeruginosa where the value of inhibition was between 20 and 10 mg/ml. The MIC concentrations were mostly very high and ranged from 5 to 1.25 mg/ml, while the MBC range fro

An International Publisher for Academic and Scientific Journals The mucilage of white and black chia seeds were extracted and determining their contents of bioactive compounds such as tannins, glycosides, flavonoids, phenols, and studying their activity as anti-filamentary and anticancer. Results showed that tannins exist in white chia seeds with 35%while it is 38% in black seeds, flavonoids represent 0.98mg/ml in white chia seeds and 1.5 mg/ml for black seeds. Both kinds of seeds showed anti-filamentaryactivity, the inhibition ratio was 86.5% for white seeds and 97.3% for black seeds. Chia black seeds showed anticancer activity and the inhibition of the tumor muscle cell line ratio (GI%) was 34.8% at 50mg/ml concentration and 88.4%

The present study aims at scrutinizing the impoliteness types, causes, and purposes utilized by Iraqi English language learners when refusing marriage proposals. Thus, it attempts to answer the questions: (1) what are the impoliteness formulas used by the Iraqi learners of English in refusing marriage proposals?, and (2) What are their impoliteness triggers/causes and the purposes? The study is significant in bridging the gap that few linguistic types of research concentrate on studying intentionality and emotions allied with impoliteness. Data were collected from 35 Iraqi learners of English responding to 6 situations of marriage. The data were analyzed using Culpeper’s (2011) formulas of impoliteness and Bousfield’s (2007) impolite

This paper presents the ability to use cheap adsorbent (corn leaf) for the removal of Malachite Green (MG) dye from its aqueous solution. A batch mode was used to study several factors, dye concentration (50-150) ppm, adsorbent dosage (0.5-2.5) g/L, contact time (1-4) day, pH (2-10), and temperature (30-60)   The results indicated that the removal efficiency increases with the increase of adsorbent dosage and contact time, while inversely proportional to the increase in pH and temperature. An SEM device characterized the adsorbent corn leaves. The adsorption's resulting data were in agreement with Freundlich isotherm according to the regression analysis, and the kinetics data followed pseudo-first-or

The present study aims at scrutinizing the impoliteness types, causes, and purposes utilized by Iraqi English language learners when refusing marriage proposals. Thus, it attempts to answer the questions: (1) what are the impoliteness formulas used by the Iraqi learners of English in refusing marriage proposals?, and (2) What are their impoliteness triggers/causes and the purposes? The study is significant in bridging the gap that few linguistic types of research concentrate on studying intentionality and emotions allied with impoliteness. Data were collected from 35 Iraqi learners of English responding to 6 situations of marriage. The data were analyzed using Culpeper’s (2011) formulas of impoliteness and Bousfield’s (2007) imp