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 industrial production sector has an important role in the national economy of the advanced countries as well as the developing ones to get higher levels for their economy . We in Iraq , just like most of the develpoing countries , our economy still suffers of great shortage in this active sector in spite of the repeated statements about the desire of activating the contribution of this sector in the national economy . The industrial sector in Iraq suffers in general of many problems , especially the public industrial sector (manufacturing) . These problems have been  existed because of the unnatural conditions that Iraq has passed during the previous decades especially in the political and security sides . which reflecte

Maximum likelihood estimation method, uniformly minimum variance unbiased estimation method and minimum mean square error estimation, as classical estimation procedures, are frequently used for parameter estimation in statistics, which assuming the parameter is constant , while Bayes method assuming the parameter is random variable and hence the Bayes estimator is an estimator which minimize the Bayes risk for each value the random observable and for square error lose function the Bayes estimator is the posterior mean. It is well known that the Bayesian estimation is hardly used as a parameter estimation technique due to some difficulties to finding a prior distribution.

The interest of this paper is that

It was Aristotle who first drew attention to the superior quality of literature to the other factual fields of knowledge. Contradicting his predecessor Plato on the issue of „truth,‟ Aristotle believed that „poetry is more philosophical and deserves more serious attention than history: for while poetry concerns itself with universal truths, history considers only particular facts.‟ (1) The critical attention to the disparity between the literary truth and the historical truth grew up throughout ages to flourish in the Renaissance and after with a bunch of distinctive views on this subject. Sir Philip Sidney (1554-1586), for example, found that literature does not offer a literal description of reality but rather a heightened vers

The present study was conducted to evaluate the effect of fungi Gigaspora margarita and Glomus desriticola in stimulating the resistance of the capsicum annuum L. towards the chromium and lead after 60 days, planting and using the pots in the glass house. The highest concentration of chromium and lead in the root was found in the presence of the mycorrhizal mixture (194.93, 150.40) μg / g, respectively, compared to the lowest concentration (90.69, 79.37) μg / g respectively, while the highest concentration of chromium and lead in the shoot was found in the presence of the mycorrhizal mixture (94.63, 79.33) μg / g respectively, compared with the lowest concentration in the control treatment (72.58, 60.70) μg / g respectively. The results

Celery (Apium graveolens L. ; family : Apiaceae) was often used as a spice in daily food. However, this plant contains many antioxidant compounds useful for attenuating neurodegenerative disorders including Parkinson's disease. Planting celery in the form of microgreens harvested 15 days was expected to increase the content of bioactive compounds. In the current study, we intended to evaluate the neuromodulatory potential of methanol extract of celery microgreens on fruit flies (Drosophila melanogaster Meigen : family Drosophilidae ; ordo : Diptera) which were exposed to paraquat. Neuroprotective capacity was assessed by survival rate, locomotor performance, lipid peroxidation and dopamine content after being treated wi

The research aims to shed light on the internet and how to employ them and to take advantage of applications in scientific research among faculty members, from a survey the opinions of professors at the University of Alanbar and Almustansiriah, to see the reality of use of the Internet and ways to invest in the service of scientific research.
The follow descriptive analysis approach , which is appropriate to the nature of this study concerned with exploring the views on the uses of the Internet. The study reached the field the following results:
1- There are(60) % of respondents use the Internet on an ongoing basis to see new information and keep pace with scientific developments in the field of specialty and the average use of the

Background: The use of electronic apex locators for working length determination eliminates many of the problems associated with the radiographic measurements (interference of anatomical structures, errors in projection such as elongation or shortening, and lack of three-dimensional representation). Its most important advantage over radiography is that it measures the length of the root canal to the apical constriction, not to the radiographic apex. The aim of this study was to assess the accuracy of a new fifth generation apex locator (Joypex 5) in recording the apical constriction and comparing it with a third generation apex locator (Root ZX) in vitro. Materials and method: Twenty four single-rooted sound human premolars, extracted for t

Background: Sonographic examination is an important tool in assessment of normal and abnormal cervical lymph nodes. The aim of the study is to assess the distribution and the characteristic features of normal cervical lymph nodes in a sample of Syrian population. Materials and Methods: Fifty healthy Syrian subjects (25 men and 25 women) with an age of 20 -60years old, who had their cervical lymph nodes examined by ultrasound. Three hundred and two lymph nodes were detected. Lymph nodes were evaluated for their number, size, site, echogenic hilus, shape, as well as for the border sharpness. The subjects were categorized by age into four groups, (20 -30, 31 - 40 , 41 - 50 , 51- 60 years ). Statistical analysis of data was done using SP