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 .

Nano-crystalline iron oxide nanoparticles (magnetite) was synthesized by open vessel ageing process. The iron chloride solution was prepared by mixing deionized water and iron chloride tetrahydrate. The product was characterized by X-Ray, Surface area and pore volume by Brunauer-Emmet-Teller, Atomic Force Microscope (AFM) and Fourier Transform Infrared Spectroscopy(FTIR)  .  The results showed that the XRD in compatibility of the prepared iron oxide (magnetite) with the general  structure of standard iron oxide, and in Fourier Transform Infrared Spectroscopy, it is strong crests in 586 bands, because of  the expansion vibration manner related to the metal oxygen absorption band (Fe–O bonds in the crystals of iron ox

         The objective of this research is to determine the relationship between the performance evaluation process and the training programs for the employees, to identify the extent of the organization's commitment to perform the performance evaluation process for its employees and to use the results of this process in determining the appropriate training programs. Performance evaluation, functional analysis, evaluation method used, dependent variable (training programs) and its dimensions, type of programs, program objectives, program curriculum, And the application of the field research methodology and the questionnaire, which included 146 individuals to know their views and analyz

Objectives To determine the prevalence of oral lesions by age and gender among the pediatric population in Iraq. Materials and methods A review of the archives of the oral pathology department of Baghdad University from, 1970 Materials and Methods: A review of the archives of the oral pathology department of Baghdad University from 1970 to 2013 for all biopsies from children aged 0–15 years old. Results A total of 1286 child specimens represented 11.98% of all biopsied lesions. The pyogenic granuloma was the most frequent lesion in children, and the periapical cyst was the most frequent lesion from an odontogenic origin. The incidence of malignant lesions was higher in the 0–3 age group than other groups. Conclusions The majority of les

In this research, the influence of the orientation and distance factors on the lowest usable frequency (LUF) parameter has been studied theoretically. The calculations of the (LUF) parameter have been made using the (VOACAP) international communication model for the connection links between the capital Baghdad and many other locations that distributed on different distances and directions over the Middle East region. The results shown in this study indicate there is a slight affection of the link direction (orientation) on the LUF parameter, while the influence of the distance factor is more significant on the values of the LUF parameter. The day/night effect appears for the long distance HF links (i.e. more than a 500 Km)

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While practicing of International business particularly that centered on foreign direct investment, let on one side, to achieving objectives of transnational corporations specially that represented in continuous pursue to improving its cash flows and maximization of stockholders wealth which is considered the most important objective to the transnational corporations, but in the same time its lead, on other side, to increasing the foreign exchange risk exposuring these corporations. So, the transnational corporations (TNCs) struggling to make strategies which are dealing in smart way, with this risk and its management in way that enable to avoiding risk comple

In this paper the behavior of the quality of the gradient that implemented on an image as a function of noise error is presented. The cross correlation coefficient (ccc) between the derivative of the original image before and after introducing noise error shows dramatic decline compared with the corresponding images before taking derivatives. Mathematical equations have been constructed to control the relation between (ccc) and the noise parameter.