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 .

The current study deals with host-guest complex formation between cucurbit [7] urils as host and lansoprazole as guesti using PM3 (semi empirical molecules orbital calculations) also DFT calculations. In this complex, the formation of hydrogen bonding may be occurred through portal oxygen atoms(O2) of cucurbit [7] urils and amine groups (NH 2 )of the drug. The energies of HOMO and LUMO orbital’s have been computed for the host guest complex and its components. The result of the stabilization energy explained a complex formation.

Numerous drilling additives and materials are used continuously because they are necessary to support and give the required properties of the drilling fluid so that to ensure the stability of the borehole. This paper aspires to evaluate the rheological properties of bentonite (montmorillonite) Trefawey as an alternative to using commercial bentonite. Monitoring and evaluating of the rheological and filtration properties were prepared. This exertion aims to focus on the effect of hematite, and barite on the rheological properties of the three aforementioned bentonite types. An improvement in the rheological properties of bentonite (montmorillonite). Trefawey was observed after adding the previous heavy materials. Hematite has by some

Background: Background : Patients with non-rheumatic atrial fibrillation have high risk of thromboembolism especially ischemic stroke usually arising from left atrial appendage .Transoesophageal echocardiography provides useful information for risk stratification in these patients as it detects thrombus in the left atrial or left atrial appendage. Objective : This study was conducted at Al-Kadhimiya Teaching Hospital to assess the prevalence of left atrial chamber thrombi in patients with chronic non-rheumatic atrial fibrillation using transoesophageal echocardiography and its clinical significance as well as to verify the superiority of transoesophageal over transthoracic echocardiography in the detection of these abnormalities. Type of

Is to obtain competitive advantage legitimate objective pursued by all organizations to achieve, because they live today in environments of rapid change and dynamic in order to meet the demands of the customer changing as well as intense competition between the organizations, which requires them to get the location of competitive markets in order to do this will remain to do the building and strengthening competitive advantage to be able to achieve, but that this feature is not easy and is not only through the identification and use of a successful strategy for a competitive standard and then manage it successfully. Hence the research problem of determining the sources of differentiation strategy and its impact on the dimensions of compe

In this research, the theme for employing a simple and sensitive method is to employ a new Schiff base ligand (N’-(4- (dimethyl amino) benzylidene)-3, 5-dinitrobenzohydrazide) to estimate Ni (II) to form orange complex (N-(4-(dimethyl amino) benzylidene)-3, 5-dinitrobenzohydrazide nickel (II) chloride) in acid medium (hydrochloric acid), it gives an absorption peak at the wavelength 485 nm. The preferred conditions were studied to form the complex and obtain the highest absorbance including concentration of Schiff base ligand, the best medium for complex formation, effects of addition sequence on complex formation, the effect of temperature on the absorbance of the complex formed, and the setting time of the formed complex. The obtained r

Background: Radiologic evaluation of breast lesions is being achieved through several imaging modalities. Mammography has an established role in breast cancer screening and diagnosis. Still however, it shows some limitations particulary in dense breast.

Methods : Magnetic resonance imaging is an attractive tool for the diagnosis of breast tumors¹ and the use of magnetic resonance imaging of the breast is rapidly increasing as this technique becomes more widely available.¹ As an adjunct to mammography and ultrasound, MRI can be a valuable addition to the work-up of a breast abnormality. MRI has the advantages of providing a three-dimensional view of the breast, performing wit

Fourier Transform-Infrared (FT-IR) spectroscopy was used to analyze gasoline engine oil (SAE 5W20) samples that were exposed to seven different oxidation times (0 h, 24 h, 48 h, 72 h, 96 h, 120 h, and 144 h) to determine the best wavenumbers and wavenumber ranges for the discrimination of the oxidation times. The thermal oxidation process generated oil samples with varying total base number (TBN) levels. Each wavenumber (400–3900 cm−1) and wavenumber ranges identified from the literature and this study were statistically analyzed to determine which wavenumbers and wavenumber ranges could discriminate among all oxidation times. Linear regression was used with the best wavenumbers and wavenumber ranges to predict oxidation time.