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 .

    Rainfall in the mid-latitudes is highly related to the synoptic pattern at the upper-levels, this study focuses on the relationship between 500 hPa geopotential height patterns and the cyclone at the surface. Synoptic studies that there is a correlation between cyclone at the surface and deepening of the trough at the upper in the mid-latitudes. The results show that when the upper trough is situated over the eastern Mediterranean, this will enhance the advection of warm and moist air from the tropical region, which will cause baroclinic instability over Iraq, leading to heavy precipitation and torrents in some situations.

A cut-off low is a closed low with a low value of geopotential height at the upper atmospheric levels that has been fully detached (cut-off) from the westerly flow and move independently. A cut-off low causes extreme rainfall events in the mid-latitudes regions. The main aim of this paper is to investigate the cut-off low at 500 hPa over Iraq from a synoptic point of view and the behavior of geopotential height at 500 hPa. To examine the association of the cut-off low at 500 hPa with rainfall events across Iraq, two case studies of heavy rainfall events from different times were conducted. The results showed that the cut-off low at 500 hPa with a low value of geopotential height will strengthen the low-pressure system at the surface, lea

The objective of the research was to evaluate consumer purchasing behavior through the Internet, such as consumer behavior, reasons for buying online, purchasing advantages over the Internet, personal variables (gender, age, marital status, education level, income, and income and job type). The questionnaire was adopted as a main tool in the survey of the views of a sample of consumers in Baghdad governorate (100) people and analyzed their answers using the statistical program SPSS in calculating the mean and standard deviation Centigrade, correlation coefficient (R) and test ( ). The main findings of the research were:

1. There is a positive and positive relationship between consumer purchasing behavior via the Internet and

In this research, the TEC parameter has been determined for the ionosphere layer over the Iraqi zone. The calculations of this parameter have been conducted using the IRI model that considered as one of the recommended international models which used to calculate the ionosphere parameter (TEC). The determinations have been made for several sites or sites that located within the Iraqi territory. The years (2011-2013) of the solar cycle 24 have been adopted to make the determinations for the TEC parameter.The capital Baghdad has been selected to represent the transmitter station and many different communication points which are located in different directions around the transmitter station have been represented as receiving stations.

In this research the relation between skin resistances and standard penetration test of over consolidated
clay soils has been studied. The research includes doing boreholes at Babil governorate in Iraq to get
undisturbed samples and standard penetration test. Determination skin friction from direct shear test between
smooth concrete and soil was explored in laboratory for design purposes and correlated with standard
penetration test values. In many foundation design problems, the shear strength between soil and
foundation materials were estimated or correlated without any direct methods for measurement.
Twelve strain controlled direct shear tests were performed simulate the shear strength interaction
between smooth c

     The use of multifunction additives in the lubricant sector has attracted great interest due to their ability to simultaneously improve and add multiple functions. This work describes the preparation and evaluation of over-based magnesium stearate detergent as a multifunction additive by the reaction of stearic acid with carbon dioxide gas in the presence of magnesium oxide nanoparticles and ammonia. The prepared over-based magnesium stearate was evaluated as a multifunction additive through blending it in various concentrations of 1-5 wt/wt% with sixty stock lubricating oils. The American Society for Testing and Materials (ASTM) and the Institute of Petroleum (IP) were used to determine the total base number (TBN), viscosity ind