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 .

Urban planning task and the control of constructional planning and urban management for cities considers the main tasks that the government takes care off. The paper discusses the concept of power from historical view of ancient Islamic cities to discover the strategies of urban management that the Islamic city adopt and to employ it in contemporary cities ,the more problems that modern cities suffer from which appears through poorness of urban context ,belongs to the loss of balance exists between the different faces of power that takes the tasks of urban management .therefore enhancement of urban environment is being through re-back that balance in administrative structures that make the cities go ahead . So the attention has b

Background: The demand for esthetic orthodontic appliances is increasing; so the esthetic orthodontic archwires were introduced. Among them, Teflon and Epoxy coated stainless steel archwires. The amount of force available from the archwire depends on the structural properties and susceptibility to corrosion. All metallic alloys are changed during immersion in artificial saliva, chlorhexidine mouthwash andtoothpaste, but their behaviors differ from one type to another. They corrode at different rates, which lead to decrease the amount of force applied to the teeth. This in vitro study was designed to evaluate the corrosion pits in stainless steel archwires coated with Teflon and with Epoxy in dry and after immersion in artificial saliva, chl

In this research, an analysis for the standard Hueckel edge detection algorithm behaviour by using three dimensional representations for the edge goodness criterion is presents after applying it on a real high texture satellite image, where the edge goodness criterion is analysis statistically. The Hueckel edge detection algorithm showed a forward exponential relationship between the execution time with the used disk radius. Hueckel restrictions that mentioned in his papers are adopted in this research. A discussion for the resultant edge shape and malformation is presented, since this is the first practical study of applying Hueckel edge detection algorithm on a real high texture image containing ramp edges (satellite image).

Free Space Optics (FSO) plays a vital role in modern wireless communications due to its advantages over fiber optics and RF techniques where a transmission of huge bandwidth and access to remote places become possible. The specific aim of this research is to analyze the Bit-Error Rate (BER) for FSO communication system when the signal is sent the over medium of turbulence channel, where the fading channel is described by the Gamma-Gamma model. The signal quality is improved by using Optical Space-Time Block- Code (OSTBC) and then the BER will be reduced. Optical 2×2 Alamouti scheme required 14 dB bit energy to noise ratio (Eb/N0) at 10-5 bit error rate (BER) which gives 3.5 dB gain as compared to no diversity scheme. Th

Orthogonal polynomials and their moments have significant role in image processing and computer vision field. One of the polynomials is discrete Hahn polynomials (DHaPs), which are used for compression, and feature extraction. However, when the moment order becomes high, they suffer from numerical instability. This paper proposes a fast approach for computing the high orders DHaPs. This work takes advantage of the multithread for the calculation of Hahn polynomials coefficients. To take advantage of the available processing capabilities, independent calculations are divided among threads. The research provides a distribution method to achieve a more balanced processing burden among the threads. The proposed methods are tested for va

The enhancement of heat exchanger performance was investigated using dimpled tubes tested at different Reynolds numbers, in the present work four types of dimpled tubes with a specified configuration manufactured, tested and then compared performance with the smooth tube and other passive techniques performance. Two dimpled arrangements along the tube were investigated, these are inline and staggered at constant pitch ratio X/d=4, the test results showed that Nusselts number (heat transfer) of the staggered array is higher than the inline array by 13%.  The effect of different depths of the dimple (14.5 mm and 18.5 mm) has been also investigated; a tube with large dimple diameter enhanced the Nusselts number by about 25% for the ran

This study aims to identify the impact of using the infrastructure of the Information Technology (IT) on the performance of human resources in the public universities. This process is done by doing research in the size, quality, and efficiency of the performance, also speed of achievement and simplification of procedures. Diyala University was chosen for the diagnosis through the opinions and attitudes of its employees.  Consequently, suggestions that contribute to improve the performance of the employees and thus its overall performance are obtained. Another objective of this study is identifying the human resources which are currently used in academic institutions and educational services systems because the significant role of th

In this paper, we made comparison among different parametric ,nonparametric and semiparametric estimators for partial linear regression model users parametric represented by ols and nonparametric methods represented by cubic smoothing spline estimator and Nadaraya-Watson estimator, we study three nonparametric regression models and samples sizes  n=40,60,100,variances used σ²=0.5,1,1.5 the results  for the first model show that N.W estimator for partial linear regression model(PLM) is the best followed the cubic smoothing spline estimator for (PLM),and the results of the second and the third model show that the best estimator is C.S.S.followed by N.W estimator for (PLM) ,the