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 .

Despite the principle of separation of powers brought by the French Revolution, which entrusted the task of drafting legislation and its amendment to the legislative authority and the task of settling disputes and settling them in the judiciary. However, since that date, the French judiciary has played a major role in the development of French civil law (In spite of all the economic and social developments that have taken place in French society throughout these years) since its promulgation until February of 2016, the date of the Legislative Decree No. 131 of the year 2016 A modification is the largest in the history of the French Civil Code (which was the judicial precedents in which a significant impact), was assisted by the French judic

The topic of context is one of the important topics, which was mentioned as a concept in several fields and different fields, and there were many points of view that defined that concept.
He specified the title of the research (design contexts in the design of the interior space), as the research sought to identify the concept of context in the interior design of the spaces of sewing workshops. The research was divided into four chapters:
The first chapter, which consists of the methodological framework, the problem of research and the need for it, the importance of research, the goal and limits of research for sewing workshops for vocational schools from (2020-2021).
The second chapter: consists of previous studies and the theo

Purpose: The research aims to estimate models representing phenomena that follow the logic of circular (angular) data, accounting for the 24-hour periodicity in measurement. Theoretical framework: The regression model is developed to account for the periodic nature of the circular scale, considering the periodicity in the dependent variable y, the explanatory variables x, or both. Design/methodology/approach: Two estimation methods were applied: a parametric model, represented by the Simple Circular Regression (SCR) model, and a nonparametric model, represented by the Nadaraya-Watson Circular Regression (NW) model. The analysis used real data from 50 patients at Al-Kindi Teaching Hospital in Baghdad. Findings: The Mean Circular Erro

Land use change, particularly the expansion of urban areas and associated human activities at the expense of natural and semi-natural areas, is a major ecological issue in urban areas around the world. Climate change being a very strong additional driver for changing the temperature and habitat in the cities. This also applies to Baghdad, Iraq, where urbanisation and climate change exerts a major pressure on the natural habitats of the city, and thus may affect the ability of city planners to adapt to future climate change scenarios. Here we present evidence of substantial growth in urban areas, increases in temperature, and degradation of natural vegetation within Baghdad city by using Remote Sensing techniques and an assessment for the

Field experiment was conducted to test the effect of saline water and fertilizers rate on Pisum sativum L. plants . Treatments of the experiment included two levels of water salinity (2, 7 dSm-1) as a main plot and three levels of potash fertilization K2SO4 (44%K) namely 150 control, 300 and 450 kg/Donum as a sub plot. Results indicated that irrigation of plant with saline water 7 dSm-¹ caused a significant decrease in K and P contents specially in the upper parts of the plants , the percentage of the K increased (2.80%) under 2 dSm-¹of irrigation water and 300 kg/ donum fertilizer rate in the upper leaves, However K decreased(1.10%) in lower leaves under 7 dSm-¹ and 300 kg/donum fertilizer. while P increased in pods und

Free radicals and oxidative damage caused by them have being suggested to be involved in the pathogenesis of migraine. These may result from distorted equilibrium of pro-oxidant/anti-oxidant system that continuously generates and detoxifies oxidants during normal aerobic metabolism. Escape of such system from equilibrium leads to damage of cellular elements with the depletion of cellular stores of anti-oxidants material such as glutathione and vitamin E. Therefore, free radical scavengers (vitamin E or melatonin) seems to be of potential benefit as prophylactic anti-migraine therapy by neutralizing free radicals overproduction and possibly preventing formation of highly toxic intermediates (such as nitric oxide). In addition of being pow

Present study was conducted to evaluate the different levels of energy to protein ratios (EPR) using food waste and black soldier fly larvae meal (FWBSFL) on growth performance and nutrient digestibility of broilers. A total of 160 one-day old broiler chicks were divided randomly to four groups and each group had 8 replicates with 5 chicks per replicate. The control diet was formulated using conventional feed ingredients with EPR of 154 for the starter period and 167 for the finisher period. The other treatments were diets with normal, low, and high EPR (154,143, and 166 for the starter period; 167, 155, and 177 for the finisher period) using FWBSFL. Feed consumption and body weight gain as well as digestibility of crude protein, cr

John Updike’s use of setting in his fiction has elicited different and even conflicting reactions from critics, varying from symbolic interpretations of setting to a sense of confusion at his use of time and place in his stories.  The present study is an attempt at examining John Updike’s treatment of binary settings in Pigeon Feathers and Other Stories (1962) to reveal theme, characters’ motives and conflicts.  Analyzing Updike’s stories from a structuralist’s perspective reveals his employment of two different places and times in the individual stories as a means of reflecting the psychological state of the characters, as in “The Persistence of Desire”, or expressing conflicting views on social and political is

        The research deals with the analysis of the city's commercial center using geographic information systems to solve the problem of congestion by evaluating the efficiency and adequacy of car parking lots according to local and Arab standards. Undoubtedly, the importance of car parking areas, as they are not within the desired efficiency within the city, will lead to congestion and traffic becomes very difficult. Thus, the transportation service loses its most important characteristic, which is the ease of movement. Therefore, there has become an urgent need to study and analyze it, as well as to verify the adequacy of the service, and the amount of deficit required to be provided to solve the tra