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 .

Achieving high achievement in the sport of fencing requires thinking, awareness and visual tracking, as visual tracking is one of the important visual abilities that a fencing player needs and is considered one of the special visual abilities as it contributes and helps in the correct motor, mental and mental performance and gives the fencing the ability to perfect and accomplished performance in training and competition. Where the research problem lies in the weak skill performance of the fencing players as a result of the weakness in possessing visual and mental abilities. The two researchers used the experimental method in a controlled manner (experimental and control groups) with a pre and post-test. The research community was identifie

To evaluate impact the difference in stages ofage and related incidence of hemodialysis patients.Two hundred and fifty patients undergoing hemodialysis were collected from general hospital in Baghdad city /Iraq. The samples with renal failure before hemodialysis were divided into (138) male,( 112)female. The sera were separated from samples to physiological investigation. We found that renal failure was more predominant among the patients ages group ranging from (51-70) years old. The results shows A significant increase in the levels of urea, creatinine, in younger patients (≤ 30 years) when compared with older patients (>70 years). Furthermore a significant decrease in serum levels of total protein in patients in older patients (>7

Rosemary (Rosmarinus officinalis L.) is one of the most economically important species of the family Lamiaceae. Rosemary extract was examined by applying 2.2-diphenyl-1- picrylhydrazyl (DPPH) radical-scavenging assays. The result proved that rosemary extract had a higher antioxidant activity by absorption at a wavelength of 517a nm by using three different concentrations (0.5, 1.0 and 3) mg/ml which performed the absorbance at (2. 314, 0. 211 and 0.296) nm in comparison with control (21.8, 92.2 and 90) nm respectively. Results obtained using chemical detection of the phytochemicals indicated the presence of flavonoids, phenols, saponins, Steroids and cardiac in rosemary water extract. Water extracts of R. officinalis leaves were inves

The study was conducted at the fields of the Department of Horticulture and Landscape Gardening, College of Agriculture, University of Baghdad " Abu Ghraib" during the growing seasons 2013-2014 to Evaluate the Vegetative growth , yield traits and genetic parameter of some tomato mutants. Results showed significantly increased of plant height in M6-2 mutant 245cm in Comparison with M6- 3 130 cm . M6-4 mutant significantly increasing of floral clusters 13 . Mutant M6-3 showed significantly increasing the average of, fruit weight 125.9g and plant yield 7.17 kg.plant-1 as comparison with M6-2 which showed decreasing of average of fruit weight and plant yield 79.40g and 4.38 kg.plant-1 respectively. Also results showed the highest Genetic variat

The members of the family of Eentrobacteriaceae harbour a gene cluster called polyketide synthase (pks) island. This cluster is responsible for the synthesis of the genotoxin colibactin that might have an important role in the induction of double-strand DNA breaks, leading to promote human colorectal cancer (CRC). Eleven out of the eighty eight isolates (12.5%) were pks+, distributed as 7 (8%) isolates of E. coli, 2 (2.25%) of K. pneumoniae and 2 (2.25%) of E. aerogenes. The cytotoxic effects of selected pks+ isolates (E. coli and E. aerogenes) on HeLa cells were represented by decreasing cell numbers and enlarged cell nuclei in comparison to the untreated cells. Cytological changes were observed when the infected HeLa cells culture

A new method for construction ion-selective electrode (ISE) by heating reaction of methyl orange with ammonium reineckate using PVC as plasticizer for determination methyl orange and determination Amitriptyline Hydrochloried drug by formation ion-pair on electrode surface . The characteristics of the electrode and it response as following : internal solution 10-4M , pH (2.5-5) ,temperature (20-30) and response time 2 sec. Calibration response for methyl orange over the concentrationrange 10-3 -10-9 M with R=0.9989 , RSD%=0.1052, D.O.L=0.315X10-9 MEre%=(-0.877- -2.76) , Rec%.=(97.230 -101.711) .