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 .

Research includes evaluation of projects implemented and which entered into trial operation period in accordance with the evaluation criteria and of (cost, quality and time) to determine the size deviations gap for the sample of projects during the years of assessment (2011-2012-2013-2014) of each of the three evaluation criteria, and then followed by a calculation the size of the overall gap to the problem based on the research problem to determine deviations from the specific implementation of each project by answering several questions to answer turns out the reasons for these deviations occur.

The importance of research Focus on the evaluation of received projects from contractors executing the projec

Some auditors may think that the audit process ends with discovering misstatements and informing management about them, while the discovery of misstatements may be classified by some as the first step in the phase of separating these distortions, as the auditor should collect these misstatements, evaluate them and detail them into misstatements involving errors or misstatements involving fraud Then evaluating it to material or immaterial according to what was stated in the international auditing standards and directing management to amend the essential ones.  The importance of this research lies in identifying the concept of distortions and their types, identifying the method of evaluating distortions into substantial and non-essent

<em>The aim of the research is to set a set of BioKinematic variables for the step of crossing barriers (3–6–9) in a 110-meter barrier for young runners. The researchers concluded the study by interpreting and discussing the results that the most important variables must be relied upon when training and selecting runners that got the best saturation on their factors: 1-The first factor which refers to the total distance of the plan to pass the third barrier + the total distance of the plan to pass the ninth barrier + the total distance Plan to cross the sixth barrier. 2-The second factor which refers to the total vertical speed before passing the third barrier + the total vertical speed before the sixth barrier + the total vertica

Thermal properties of soils are important in buried structures contact problems. Although laboratory is distinctly advantageous in measuring the thermal conductivity of soil under ideal condition, given the ability to simulate relatively large-scale in place of soil bed, the field thermal conductivity of soil is not yet commonly used in many types of research. The use of only a laboratory experiment to estimate thermal conductivity may be the key reason for overestimation or underestimation it. In this paper, an intensive site investigation including field thermal conductivity tests for six different subsoil strata were performed using a thermal probe method (TLS-100) to systematically understanding the effects of field dry density, water c