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 .

One of the most distinguished instrumentsis being used by the state for implementing its strategy andachieving perfectly and effectively its goals and policies, and economizing the Public Finance and uplifting the services level for the sake of people, is truly thegovernmental accounting system.

 Thus, through this system the upper hand is located for supplying the accurate information, which does make the complete and just expressing concerning the budget implementing results. So,this research comes here because of the hugeness in this sector and the associations largeness and the dread of the governments failure in fulfilling its obligations and the provided services, and the required need for the effective and capable inf

This study investigated the prevalence of quinolones resistance proteins encoding genes (qnr genes) and co-resistance for fluoroquinolones and β-lactams among clinical isolates of Klebsiella pneumoniae.  Out of 150 clinical samples, 50 isolates of K. pneumoniae were identified according to morphological and biochemical properties. These isolates were collected from different clinical samples, including 15 (30%) urine, 12 (24%) blood, 9 (18%) sputum, 9 (18%) wound, and 5 (10%) burn. The minimum inhibitory concentrations (MICs) assay revealed that 15 (30%) of isolates were resistant to ciprofloxacin (≥4µg/ml), 11 (22%) of isolates were resistant to levofloxacin (≥8 µg/ml), 21 (42%) of isolates were re

Prodigiosin is a ‘natural red pigment produced by Serratia marcescens which exhibits immunosuppressive and anticancer properties in addition to antimicrobial activities. This work presents an attempt to maximize the production of prodigiosin by two different strategies: one factor at time (OFAT) and statistical optimization. The result of OFAT revealed that sucrose and peptone were the best carbon and nitrogen sources for pigment production with concentration of prodigiosin of about 135 mg/ L. This value was increased to 331.6mg/ L with an optimized ratio of C/N (60:40) and reached 356.8 with pH 6 and 2% inoculum size at end of classical optimization. Statistical experimental design based on Response surface methodology was co

New complexes of the [M(Ura)(Phen)(OH2)Cl2]Cl.2H2O type, where (Ura) uracil ; (Phen) 1,10-phenanthroline hydrate; M (Cr+3 , Fe+3 and La+3) were synthesized from mix ligand and characterized . These complexes have been characterized by the elemental micro analysis, spectral (FT-IR., UV-Vis, 1HNMR, 13CNMR and Mass) and magnetic susceptibility as well the molar conductive mensuration. Cr+3, Fe+3 and La+3- complexes of six–coordinated were proposed for the insulated for three metal(III) complexes for molecular formulas following into uracil property and 1,10-phenanthroline hydrate present . The proposed molecular structure for all metal (III) complexes is octahedral geometries .The biological activity was tested of metal(III) salts, ligands

Aim: The Aim of the study is to compare between Er,Cr:YSGG 2780 nm laser and carbide fissure bur in root-end resection regarding the morphological variations, temperature changes and the duration of resection process.

Settings and Design: 5 W, 25 Hz, 50% water, 80% air,25.47 J/cm2 .

Material and method: twenty-one extracted single rooted teeth endodontically were treated, twenty teeth were obturated and divided into two groups according to method of resection. Group 1 root-end resected using cross cut carbide bur while group 2 root-end resected using laser with MGG6 sapphire tip of 600 μm diameter. Temperature on external root surface and duration of resection were recor

This systematic review aimed to analyse available evidence to answer two focused questions about the efficacy of erythritol powder air‐polishing (EPAP) (i) as an adjunctive during active periodontal therapy (APT) and (ii) as an alternative to hand/ultrasonic instrumentation during supportive periodontal therapy (SPT). Additionally, microbiological outcomes and patient's comfort/perceptions were assessed as secondary outcomes.

A simple reverse-phase high performance liquid chromatographic method for the simultaneous analysis (separation and quantification) of furosemide (FURO), carbamazepine (CARB), diazepam (DIAZ) and carvedilol (CARV) has been developed and validated. The method was carried out on a NUCLEODUR® 100-5 C18ec column (250 x 4.6 mm, i. d.5μm), with a mobile phase comprising of acetonitrile: deionized water (50: 50 v/v, pH adjusted to 3.6 ±0.05 with acetic acid) at a flow rate 1.5 mL.min-1 and the quantification was achieved at 226 nm. The retention times of FURO, CARB, DIAZ and CARV were found to be 1.90 min, 2.79 min, 5.39 min and 9.56 min respectively. The method was validated in terms of linearity, accuracy, precision, limit of detection and li

Two field experiments were conducted at two different texture sites. The first site of the fields of AlMed-hateya Agriculture Division / Babil Governorate. The second site of the fields of Al-Nouriah Research Station / Ministry of Agriculture, the factors of the study in the two sites included several factors. The first factor includes two irrigation systems: sprinkler irrigation and surface irrigation. The second factor is the method of cultivation which includes the method of cultivation with basin and furrowing. The third factor is the type of the cultivated crop which includes a local variety (Fajr 3) and a hybrid variety (Drakma). The actual water consumption for the sprinkler irrigation system reached (587.13 and 637.62) mm season-1 f