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 purpose of this research is to recognize the relationship between the dimensions of  banking service quality and customer's satisfaction , through customer's evaluation of the level of service quality offered to them by Al – Rasheed bank. Also to determine the proportional importance of different dimensions of service quality. In addition to examine the relationship between banking service quality in its dimensions  and customer's satisfaction. (150 ) samples were distributed among the bank customers , only (130 ) samples were collected and good for analysis.

The results were analyzed and examined the hypothesis through a group of statistical methods. The most important results is the positive evaluation of the ba

  The life insurance marketing faces many difficulties because it is not a current tangible commodity, so it needs a planning for promotional activities and data about prospective applicants according to many factors such as age and residence area ​​, marital status and profession to determine the group wich need insurance covers.                                                                    &nb

This research aims to studying and analyzing the theoretical
framework of the environmental auditing in industrial environment to its a broad and danger environmental effects . It aims to contribute in setting and testing a proposed procedure framework for environmental auditing in that vital activity .The practical aspect focused on testing a proposed framework within practice it in a one Iraqi industrial company that has a huge effect on environmental activity, represented by Iraqi state company

Biodiesel production from microalgae depends on the biomass and lipid production. Both biomass and lipid accumulation is controlled by several factors. The effect of various culture media (BG11, BBM, and Urea), nutrients stress [nitrogen (N), phosphorous (P), magnesium (Mg) and carbonate (CO₃)] and gamma (γ) radiation on the growth and lipid accumulation of   Dictyochloropsis splendida were investigated. The highest biomass and lipid yield of D. splendida were achieved on BG11 medium. Cultivation of D. splendida in a medium containing 3000 mg L⁻¹ N, or 160 mg L⁻¹ P, or 113 mg L⁻¹ Mg, or 20 mg L^-1 CO_3, led to enhanced growth rate. While u

Tirzepatide is a revolutionary and promising medication with a high impact in the treatment of Obesity and T2DM with their complications. Its efficacy was proven through different trials in achieving favorable weight loss and a significant reduction in glycemic index. It also treated a large diversity of related co-morbidities, including fatty liver, cardiovascular disease, dyslipidemia, and more. Tirzepatide is well tolerated, has a good safety profile, and is highly reliable and suitable for use in a population.

Lorraine Hansberry’s A Raisin in the Sun (1959) appeared at the beginning of renewed political activity on the part of the blacks; it is a pamphlet about the dream of recognition of black people and the confusion of purposes and means to reach such recognition. It embodies ideas that have been uncommon on the Broadway stage in any period. Situations such as a black family moving into an all-white neighborhood were not familiar before this time; they were just beginning to emerge. In depicting this so realistically, Hansberry depends more on her personal experience as an African American embittered by social prejudices and discrimination. 

  In this paper, we investigate the connection between the hierarchical models and the power prior distribution in quantile regression (QReg). Under specific quantile, we develop an expression for the power parameter ( ) to calibrate the power prior distribution for quantile regression to a corresponding hierarchical model. In addition, we estimate the relation between the  and the quantile level via hierarchical model. Our proposed methodology is illustrated with real data example.

Suffer most of the facilities of the high cost of inventory , which affects the high cost of the product and thus affects many administrative decisions , as well as suffer the facilities of the systems developed by the provisions of inventory control , and this problem is exacerbated in the construction sector where the inventory in the form of Construction spin of the Year for another it becomes difficult to control the cost effectively , and is the research problem in question follows: What are the implications of the use of the system in time inventory accounting system for the contracting company does kills Alrkaah to the provisions of the cost of inventory and what is the optimal approach to inventory control ? Find assumed

The research deals with analyzing the influencing role of trade policies in the growth and development of productive economic sectors and their contribution to GDP and its reflection on workforce employment. Studies have proven the success of the Malaysian experience in stimulating the productive economic sectors to grow and their contribution to the gross domestic product with an increase in the growth of local markets and access to international markets for national products. The research also deals with the ineffectiveness of Iraqi trade policies after 2003 in stimulating the productive economic sectors (agricultural and industrial) on economic growth, as most of the increase in Iraqi GDP growth throughout the study period was