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 .

Abstract
        This research aims to identify the relationship and the impact of the behavior of organizational citizenship in the performance of employees, as practiced behaviors organizational citizenship substantial role in achieving the objectives of both the organization and its staff at the same time, so it affects a large extent on the characteristics and performance of individuals employees and thus influence the success of the organization as a whole, problem of the research has indicated that there is a clear failure in the study of the impact of the behavior of organizational citizenship in the performance of employees, was chosen

    In this paper, a theoretical study was introduced to discussion the  Influence of donor senstizer on efficiency of solar cell with clear  focusing on dye senstized solar cell DSSCs applications was presented. Use of donor  as -sensitizer dye in solar cells was a viable contender in photovoltaics due to their spectrum of excited state to transfer more elkectrons to conduction band of semiconductor  .In this study, two systems Alq3/ZnO and D149/ZnO devices taken with same two solvents .Transtion energy ,coupling strength and transtion parameters are used to calculate the  electron current density , it  uses to calculate the photovoltic characteristic I-V ,fill factor and the efficiency of th

The success of an organization is significantly influenced by strategic performance, a focal point in recent scholarly investigations and regulatory considerations. This study delves into the examination of the impact of strategy formulation, implementation, and evaluation on the strategic performance within the context of the oil industry in Iraq. Additionally, the research explores the moderating influence of leadership style on the relationship between strategy formulation, implementation, evaluation, and strategic performance in the Iraqi oil industry. Data collection involved the utilization of survey questionnaires distributed to selected employees of Iraqi oil companies. Statistical analysis, specifically SPSS-AMOS, was employed to s

Background: Red clover oil (Trifolium pratense) has isoflavones bunches which have estrogen-like exercises and may establish an option in contrast to hormone substitution treatment. The present study investigated the impact of Red clover oil on bone healing in rats by histomorphometric study. Materials and Methods: Intra bony defect was performed in right femur of thirty six healthy male albino rats. Then these rats were randomly divided into three groups (12 rats each): one control and 2 experimental groups. For control, the bony defect was left for normal healing; for the experimental (S) group, the defect was treated with hemostatic absorbable gelatin sponge; and for experimental (RS) group, the bony defect was treated with 0.2 ml red

A computational investigation is carried out to describe the behaviour of reflected electrons upon a charged insulator sample and producing mirror effect images. A theoretical expression for the scanning electron path equation is derived concerning Rutherford scattering and some electrostatic aspects. The importance of the derived formula come from its correlation among some of the most important parameters that controls the mirror effect phenomena. These parameters, in fact, are the trapped charges, incident angle and the scanning potential which investigated by considering its influences on the incident electrons. A pervious experimental operation requirements are adopted for operating the introduced expression. However, the obtained r

Methotrexate (MTX), a folate antagonist agent, is mainly used in treatment of malignant tumors and autoimmune diseases. The present study was undertaken to determine whether antioxidant vitamin (vitamin A) could ameliorate methotrexate induced oxidative stress in male rabbits. Twenty male rabbits were randomly assigned into four groups. Group 1: control group, Group 2: MTX-treated group (received 20 mg/kg MTX intraperitoneally), Group 3: Vit.A treated group received 5000 IU Vit.A orally) and Group 4: MTX+Vit.A treated group received MTX 20 mg/kg plus 5000 IU vit.A). After 4 weeks of treatment, blood samples were collected by cardiac puncture to determine the serum malondialdehyde (MDA), as a good indicator for lipid peroxidation and

       The effect of 0.66 µeV gamma radiation on the structural and optical properties of the CdTe thin films prepared by thermal evaporation at thickness 350nm, The samples were irradiated with time (50 h and 79h) at room temperature. The absorption spectra for all the samples were recorded using UV-VIS spectrometer in order to calculate the energy gap, refractive index and others parameter . The optical energy gap was found decrease from (1.9 to 1.67) eV.