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 .

An optimization calculation is made to find the optimum properties of combined quadrupole lens which consists of electrostatic and magnetic lens. Both chromatic and spherical aberration coefficients are reduced to minimum values and the achromatic aberration is found for many cases. These calculations are achieved with the aid of transfer matrices method and using rectangular model of field distribution, where the path of charged-particles beam traversing the field has been determined by solving the trajectory equation of motion and then the optical properties for lens have been computed with the aid of the beam trajectory along the lens axis. The computations have been concentrated on determining the chromatic and spher

The use  analysis  value chain such  information in the provision as financial  so information quality meet and satisfy the needs of users such information , particularly investors and lenders   as the identification needs   financial information and the knowledge as their behavior influenced by that information can be based on the accounting profession to focus on improving their function in order to achieve its goal that satisfying their needs and rationalize their decisions . In accounting thought discovered fertile ground for users preferences as one of the entrances   theorising positive which is based on the need to include knowledge on accounting hypothesis that explain the

The purpose of the current research is to identify the reality and applicability of the entrepreneurial approach in its dimensions (creative, proactive, independent, risk tolerant, offensive) and its impact on the success factors of the project (organizational commitment, communication, project team, project monitoring) Access to information, treatment, storage), which is a significant and important link in the success and development of industrial projects with the possibility of studying and analyzing the provision of the appropriate environment for this.

 the research started from a problem expressed by a number of intellectual and practical questions aimed at answering them as well as To answer a

The rent is one of the sources of investment that generates returns for the owner of the housing unit, and it is also one of the importance expenditure for the tenant.

The importance of this research comes in addressing the deficiency in the field of analyzing the factors affecting the rental value of residential units, which affects many segments of the population of Baghdad.

The aim of this research is analyze and evaluate related variables on the rent value of residential units in neighbourhood 409 in city of BAGHDAD, which is a hypothesis that: There are a set of variables affecting the rental value, including those related to the internal environment of the dwelling, such as: income level, plot area, building area, n

The competition in the hotel sector, globalization and the development of new information have forced the sector to continuously seek new techniques and arrangements to remain competitive through hotel industry companies, including Benchmarking and the application of this method in the hotel sector. The selection of the Rashid International Hotel by the Ministry of Tourism as a leading hotel or benchmark for comparison of other hotels in Iraq, and the selection of two hotels in Baghdad for comparison, namely (Ishtar International Hotel, Baghdad International Hotel) and the choice also by the Ministry of Tourism, N is to correct the course of practice to manage the cost and diagnosis of the weakness of the strengths and weaknesses in the

In this work Different weight of pure Zinc powder suspended particles in 4ml base engine Oil were used.
Intensity of Kα Line was measured for the suspended particles ,also for mixture which consist from Zinc particle blended with Engine base Oil. Calibration Curve was drawn between Ikα line Intensity and Zinc concentration at different operation condition. The Lower Limit detection (LLD) and Sensitivity (m) of Spectrometer were determined for different Zinc Concentration (Wt%). The results of LLD and m for Samples were analyzed at Operation Condition of 30KV,17mA is best from Samples were analyzed at Operation Condition of 25KV,15mA

For a connected topological space M we define the homeomorphism and period noncoincidence indices of M, each of them is topological invariant reflecting the abundance of fixed point free self homeomorphisms and periodic point free self maps defined on M respectively. We give some results for computing each of these indices and we give some examples and some results relating these indices with Hoffman index.

This research aims to know the effect of the strategy of map bubbles on developing the skills of science operations among 5th grade literary students in the subject of rhetoric and application, and the design of the experimental and control groups with the pre and post-tests was used. The research sample consisted of (50) students divided into two groups, an experimental group of which reached the number of its members is (25) students and studied using the strategy of map bubbles, and a control group of its members reached (25) students and studied in the traditional (standard) method. The researchers prepared a multiple-choice achievement test with several (30) paragraphs, and its validity and consistency were extracted. Then the test was