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 .

Ureteric obstruction is rarely noted in cases of gastric cancer. Its involvement by distant metastasis from gastric adenocarcinoma without direct invasion is an exceptionally unusual occurrence. This is the story of a 58-year-old man who arrived at the emergency department with acute flank pain and fever. He was initially diagnosed with obstructive pyelonephritis after the discovery of a new onset, complete ureteric obstruction on the left side. Subsequent investigations and follow-up revealed the presence of gastric adenocarcinoma with possible ureteric metastasis bilaterally, flank pain and hydronephrosis were the first and only presentations of gastric cancer. The rarity of the condition and the unusual presentation encouraged us to r

To investigate the efficacy of polyether‐ether‐ketone (PEEK) wire as a fixed orthodontic retainer, by comparing its performance to other retainer wires and optimizing its adhesion to composite bonding materials.

     The research aimed to identify the extent to which the media offices in the ministries depend on the website of the Iraqi Council of Ministers as a source of information. Such goal includes a set of sub-goals: Knowing the reasons for media offices' reliance on the information provided by the Cabinet's website; and revealing the benefit derived from relying on the Cabinet's website.

The researcher used the survey method to screen and comprehend the extent to which the media offices in the ministries depend on the website of the Iraqi Council of Ministers as a source of information.

The mechanism of comprehensive account of the limits of research wa

This research aims at know the position of Al-Jassas Al- Hanafi (D. 370 AH) of  "As-Sifat Al- Khbriya", through his interpretation: (the provisions of Qur'an), by studying his interpretation of the verses related to this issue.

The most significant results of this study that Al-Jassas did not consider the words that called: "As-Sifat Al- Khbriya" as adjectives to Allah almighty, but he consider them contained an inappropriate meaning to Allah almighty, thus it must be referred to the perfect arbitrator, so he was believe in opinion of interpretation. and interpretations of Al-Jassas for the related of the Qur'an verses relat

The construction project is a very complicated work by its nature and requires specialized knowledge to lead it to success. The construction project is complicated socially, technically and economically in its planning, management and implementation aspects due to the fact that it has many variables and multiple stakeholders in addition to being affected by the surrounding environment. Successful projects depend on three fundamental points which are cost-time, performance and specifications. The project stakeholder's objective to achieve best specifications and the cost-time frame stipulated in the contract.

The question is, was the optimum implementation accomplished? The provision for the success of the project

Purpose: The research aims to determine the relationship between E-Learning and Total Quality Management (TQM) in Educational institutions in Nineveh Governorates.

Methodology / Design: The researchers distributed (30) questionnaires to employees (teachers and administrators) of Nineveh Governorate education who represent the community of the research sample, as they were analyzed using the SPSS V.20

The importance of research: The importance of the research in the fact that it focuses on one of the educational methods represented in integrating the traditional method and relying on modern technologies using computers and the Internet in the field of education to improve the reali

Background: Studying and investigating the transverse strength(Ts), impact strength(Is), hardness (Hr) and surface roughness(Ra) of conventional and modified autopolymerizing acrylic resin with different weight percentages of biopolymer kraftlignin, after curing in different water temperatures; 40°C and 80°C. Material and Methods: Standard acrylic specimens were fabricated according to ADA specification No.12 for transverse strength, ISO 179 was used for impact testing, Shore D for hardness and profilometerfor surface roughness. The material lignin first dispersed in the monomer, then the powder PMMA is immediately added. Ligninadded in different weight percentages. Then cured using pressure pot (Ivomet) in two temperatures;40°C a

The study aims to know the nature of the expected relationship between market share management strategies and the variation in the performance of the shares of a number of Iraqi industrial companies listed in the Iraqi Stock Exchange. For the period (2005-2018) in the light of both the monthly closing prices and sales volume during the research period, the (Panel Data) method was relied on through a stylistic test (fixed effects model and random effects model), and the results determined the need to adopt the fixed effects model method for sample data and test Assumptions, the results showed the positive impact of market share according to its strategies on the performance of stocks according to its studied indicators (Treynor index