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 .

The investment decision, a critical decision for each investor as it involves risks and uncertain returns, so investors should avoid cases of uncertainty associated with the final decisions they are involved, and the problem of research in individual differences and differences in the behavior of individual investors and reflect the impact of this investment decision in the Iraqi market for securities. Therefore, the research aims to understand and analyze the impact of determinants of investor behavior as an independent variable in investment decision-making as a dependent variable in the Iraqi market for securities, and the research started from two main hypotheses to explore the influence and correlation between research varia

To identify the fungi associated with water hyacinth (Eichhornia crassipes [Mart.] Solms), an aquatic weed, which presents in Tigris river from Baghdad south ward. Five regions from middle and south of Iraq (Al-Noumanya, Saeid Bin-Jubier, Al-Azizia, Al-Reyfay and Al-Hay) were selected for this study. Twelve fungal species were isolated. Alternaria alternata, Acremonium sp and Cladsporium herbarum, were the most frequently species (91.66 % ,50 % and 25 %) respectively. The fungi Alternaria alternata, Acremonium sp. and Phoma eupyrena were more aggressive to water hyacinth as (91.66%,83,33%, and 75%) in pathogenicity test.

In this study, gamma-ray spectrometry with an HPGe detector was used to measure the specific activity concentrations of ²²⁶Ra, ²³²Th, and ⁴⁰K in soil samples collected from IT1 oil reservoirs in Kirkuk city, northeast Iraq. The “spectral line Gp” gamma analysis software package was used to analyze the spectral data. ²²⁶Ra specific activity varies from 9  0.34 Bq.kg^-1 to 17  0.47 Bq.kg^-1. ²³²Th specific activity varies from 6.2  0.08 Bq.kg^-1 to 18  0.2 Bq.kg^-1. ⁴⁰K specific activity varies from 25  0.19 Bq.kg^-1 to 118  0.41 Bq.kg^-1. The radiological hazard due to the radiation emitted from natural r

Iridoid glycosides are a group of naturally occurring chemical compounds. They are a large family of compounds biosynthesized by plants, they often have pharmacological effects. The aim of this study is to isolate and identified iridoid glycoside in a newly studied, cultivated in Iraq named Gardenis jasminoides. The medicinal importance of iridoid glycoside, on one hand and absence of phytochemical investigation on leaves of Gardenia on the other hand, acquired this study its importance. Many compounds were isolated from leaves plant part one of these compounds was identified by different chemical analysis like: melting point (MP), thin layer chromatography (TLC), Fourier transforms infrared spectra (FTIR) and high performance l

This research deals with the role of quantitative (indirect) tools of monetary policy that used by the Central Bank of Iraq in order to control and manage the size of the money supply that intermediate goal through which monetary policy is able to achieve its final goals, foremost among which is to reduce inflation and raise the value of the local currency in front of foreign currency rates. The research is based on a major hypothesis stating that quantitative tools have a direct and strong influence on the money supply, especially under the circumstances of the shift towards a market economy. There has been a branching relationship with this statistically significant relationship between the money supply and the quantitative tools used

This research aims to know the role of transformational leadership in the organizational success of the College of Education at Samarra University. The researcher adopted the analytical descriptive method in analyzing the research problem. The research included two main hypotheses that resulted in four hypotheses that were subjected to statistical tests. A sample of (54) The researcher used the survey method as a main tool for collecting data and information as well as visits and structured interviews that took place during the period of application. The research reached a set of conclusions and recommendations among the conclusions that there is an art relationship There is a strong and moral impact between transformational lead

A survey of blood parasites among members of two species of Iraqi babblers Timaliidae,
Turodoides caudatus salvadori (de Fillipi, 1865) and Turdoides alterostris (Hartert, 1909)
was carried out in the middle and south of Iraq. Two species of haematozoa were recovered,
Haemoproteus turdoidus sp. nov. and Plasmodium relictum Grassi &Felleti. The description
of the new taxon is provided and discussed with pertinent literature.

Background: Trauma is one of the most common
clinical problems that confront the maxillofacial
surgeon and radiologist alike. Middle third facial
fractures are diagnosed primarily on the bases of
clinical examination and plain radiographs than can
result in much preoperative speculation.
Objective: To assess the advantages of spiral
computerized tomography over conventional
radiography in the pre-surgical evaluation of middle
third facial fractures.
Methods: Thirty patients with thirty-eight facial
fractures were studied, all patients were examined
clinically, by plain radiography and then by spiral CT.
Results: Of the 38 middle-third fractures, 16
(42.1%) were zygomatic fractures, 8 (21.1%) were

A pure posteriorly posterior communicating artery (PCoA) aneurysm represents a surgical challenge. This is mainly when there is a need for good exposure of the aneurysmal neck, sac, PCoA, and anterior choroidal arteries. Ruptured pure posteriorly directed PCoA aneurysm imposes significantly extra challenge as the surgeon undergoes dissection through a tight brain. Even with measures commonly used to attain brain relaxation like the lumbar drain and cisternal fenestration. Here, we describe a technique for posterior temporal pole mobilization (TPM) as an integrated part of microsurgical clipping of ruptured pure posteriorly directed PCoA aneurysms. This technique is implicated in twenty-three successive cases of ruptured PCoA aneurys