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 light of the developments and intense competition that the world has witnessed, the need to search for a sustainable and continuous competitive advantage for economic units has emerged, as the economic units must not lose sight of their interest in the activities they perform to achieve that advantage, and it can be said that the goal of the research is to identify the theoretical dimensions of the green value chain represented by: (Green research and development, green design, green manufacturing, green marketing, green services) and the dimensions of the sustainable competitive advantage represented by (quality, creativity, innovation, cost, response to the customer), as well as identifyi

This research involved synthesis of new β-Lactam derivative from Azo compound[4-amino-N-(pyrimidine-2-yl)-3-(pyrimidine-2-yldiazenyl) benzene sulfonamide] (S1) record previously by many steps. Starting conversion the free amino group in an azo comp. to chloro acetamide derivative(S2), then reacted it with urea to give the oxazole ring  derivative (S3) that which containing free amino group. The condensation reaction between the amino group and P-bromobenzaldehyde to produce Shiff base (B14). Finally staudinger's cyclo addition reaction go run between the Shiff base derivative (B14) and chloro acetyl chloride in the presence of tri ethyl amine (Et₃N) as Base catalyst and dioxane a

The objective of present study was to investigate the effect of using mixture volaticle oil of rosmarinus and nigella sativa to improve some of the meat quality characteristics, physical and limited storage time of minced cold poultry meat. Duplex volaticle oil was added at 0.025, 0.050 and 0.075 g/kg to minced poultry meat, these treatments were stored individually for 0 , 4 and 7 days at 4-7C⁰. After making several chemical, physical and oxidation indicators, the following results were obtained:

            The process of adding volaticle oil to minced poultry meat led to significant increase (P<0.01)in moisture, prot

This research introduces a developed analytical method to determine the nominal and maximum tensile stress and investigate the stress concentration factor. The required tooth fillets parametric equations and gears dimensions have been reformulated to take into account the asymmetric fillets radiuses, asymmetric pressure angle, and profile shifting non-standard modifications. An analytical technique has been developed for the determination of tooth weakest section location for standard, asymmetric fillet radiuses, asymmetric pressure angle and profile shifted involute helical and spur gears. Moreover, an analytical equation to evaluate gear tooth-loading angle at any radial distance on the involute profile of spur and hel

Polycyclicacetal was prepared from the reaction of PEG with aldehyde derived from Erythro-ascorbic acid (pentulosono-ɣ-lactone-2,3-enedianisoate).All these compounds were characterized by Thin Layer Chromatography (TLC) and FTIR spectra and aldehyde was also characterized by (U.V-Vis), 1HNMR, 13CNMR, and mass spectra.The inhibitory effect of prepared polymer on the activity of human serum AcetylCholinesterase has been studied in vitro. The polymer showed a remarkable activity at low concentration (4.7x10-3 – 4.7x10-8M).

Background: Mouthwashes used widely as ancillary to mechanical oral hygiene methods. Little information provided about the effect of mouthwashes on ions released from orthodontic brackets. Therefore, the present study has been established to evaluate the effect of different mouthwashes on the corrosion resistance and the biocompatibility of two brands of brackets. Materials and Methods: Eighty premolar stainless steel brackets were used (40 brackets from each brand). They were subdivided into four subgroups (n=10) according to immersion media (deionized distilled water, Corsodyl, Listerine and Silca herb mouthwashes). Each bracket was stored in a closely packed glass tube filled with 15ml of the immersion media and incubated for 45 days at

Background: The figure for the clinical application of computed tomography have been increased significantly in oral and maxillofacial field that supply the dentists with sufficient data enables them to play a main role in screening osteoporosis, therefore Hounsfield units of mandibular computed tomography view used as a main indicator to predict general skeleton osteoporosis and fracture risk factor. Material and Methods: Thirty subjects (7 males &23 females) with a mean age of (60.1) years underwent computed tomographic scanning for different diagnostic assessment in head and neck region. The mandibular bone quality of them were determined through Hounsfield units of CT scan images and were correlated with the bone mineral density v

characteristic tissues and cells, exerting their pharmacological aspects and alleviating a lot of diseased processes. Accordingly, this research is about introducing some isatins to be nucleophilically attacked at C3 forming products of azomethine ylide functionality. These iminium compounds were made by allowing certain isatins to be reacted with the secondary amino acid, proline, at acetic acid and methanol medium and then collected after purification to be identified with total Leukocyte count (TLC) and melting point. The structural characterization was performed by fourier-transform infrared spectroscopy (FTIR), proton nuclear magnetic resonance (1H-NMR), and community health nursing (CHN) analysis. The microbiological evaluatio