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 .

It is known that the oral administration of ibuprofen caused an irritation of stomach as a side effect due to its carboxylic moiety. Ibuprofen ester was synthesized by linking the carboxylic moiety of ibuprofen and the hydroxylic group of paracetamol to reduce its side effect. Study the kinetic hydrolysis of prepared ester was examined at different values of physiological pH (1.0, 5.8, 6.4 and 7.4) at 37 ± 0.1 of 1 hour period. Measurements of absorbance were carried out by UV-Visible spectrophotometer to follow the stability of ester, it showed Pseudo first order hydrolysis. The pH- apparent rate profiles of ester was exhibited a good stability at pH 1.0 and pH 5.8. Pharmacological activity in vivo of prepared ester was evaluated in re

One of the main causes for concern is the widespread presence of pharmaceuticals in the environment, which may be harmful to living things. They are often referred to as emerging chemical pollutants in water bodies because they are either still unregulated or undergoing regulation. Pharmaceutical pollution of the environment may have detrimental effects on ecosystem viability, human health, and water quality. In this study, the amount of remaining pharmaceutical compounds in environmental waters was determined using a straightforward review. Pharmaceutical production and consumption have increased due to medical advancements, leading to concerns about their environmental impact and potential harm to living things due to their increa

Deontic modality expresses what is necessary or possible according to the norms of morality and laws of community. It is a cover term for those cases where modal auxiliaries used to express notions like ''obligation'', ''prohibition'' and, ''permission''. Deontic modals are basically performatives, having the ''so-be-it'' component of directives in that the speaker directs the behavior of the addressee to get things done. The present study identifies the use of deontic models in international contracts to prove that there are major pragmatic strategies employed in writing them. To achieve the aim of the study, a modified model of Danet’s (1980) and Trosborg’s (1995) in accordance to Searle (1969) is used to analyze 16 texts selected fro

The species Vitex agnus-castus is an important medicinal plants and it is one of the cultivated and dicotyledon plants in Iraq. The anatomical of stem, petiole, midrib area, epidermis, veins, type of leaf stomata and seeds were studied by light microscope. In this research, shows the knowledge of anatomical characteristics of the studied plant, showing its importance as taxonomic characteristics through the sections of the stem, petiole, the midrib and the petals.

Background: Impacted teeth are frequent problem and one of the most affected teeth is the maxillary canine. The early diagnosis of impacted canines by radiographic evaluation is imperative. The aim of this study was to determine the prevalence of impacted maxillary canines in patients attending the Oral diagnosis and Radiology clinic in College of Dentistry, University of Al-Basrah. Materials and Methods: 1280 patients attending the Oral Diagnosis and Radiology clinic in College of Dentistry University of Al-Basrah, between October 2013 and March 2015 were examined for the study. The age of the patients ranged from 15 to 55 years, with a mean age of 22.2 years. Results: The prevalence for maxillary impacted canines in all the cases was fo

Abstract:The optimum design of the magnetic deflector with the lowest values of the radial and spiral distortion aberration coefficients was computed. The optimized calculations were made using three models, Glaser bell-shaped, Grivet-lenz and exponential models. By using the optimum axial field distribution, the pole pieces shape which gave rise to those field distributions was found by using the reconstruction method. The calculations show that the results of the three models coincide at the lower values of the excitation parameter. In general the Glaser- bell shaped model gives the optimum results at the whole range of the excitation parameter under investigation.The negative values of the spiral distortion aberration coefficient appears

As the process of  estimate for model and variable selection significant is a crucial process in the semi-parametric modeling At the beginning of the modeling process often At there are many explanatory variables to Avoid the loss of any explanatory elements may be important as a result , the selection of significant variables become necessary , so the process of variable selection is not intended to simplifying  model complexity explanation , and also predicting. In this research was to use some of the semi-parametric methods (LASSO-MAVE , MAVE and The proposal method (Adaptive LASSO-MAVE) for variable selection and estimate semi-parametric single index model (SSIM) at the same time .

Background: A carefully planned clinical medical education is critical for the provision of supportive clinical educational environment. The latter will ensure effective teaching, active learning and good attitudes and performance at the bedside. The aim of this study was to evaluate clinical learning environment at AL-Diwaniyah Teaching Hospital. Materials and Methods: A descripitive cross-sectional study involved resident doctors from Internal Medicine and Surgery departments who had six months or more residency training in the respective departments. Data were collected using the Postgraduate Hospital Educational Environment Measure. Data where analyzed using the Statistical Package for Social Sciences version 21.0 and presented us