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 .

This study came to discuss the subject of industries dependent on petrochemical industries in Iraq (plastic as a model) during the period 2005–2020, and the study concluded that the plastic industries contribute to areas of advancement and progress and opportunities to deal efficiently with the challenges posed by the new variables, the most important of which is the information revolution. communications and trade liberalization, and this is what contributes to the competitiveness of these industries. And because the petrochemical industry in Iraq has an active role in establishing plastic industrial clusters and clusters of micro, small, and medium industries by providing the necessary feedstock for these industries in various fields

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

يشهد المسرح الدولي قضايا مستجدة ومستحدثة مثل تعدد الفاعلين من الدول ومن غير الدول وتزايد مساحات نفوذهم وتأثيرهم ،ومن جانب اخر أثرت جائحة كورونا على البيئة والمناخ بشكل ملموس على جوانب عدة. فضلا عن ذلك تأثرت جميع المجتمعات البشرية بالإرهاب والهجمات الالكترونية وغيرها ومن بينها دول والمجتمع الدولي بإفراده مؤسسات وكيان اقتصادي وسياسي وقانوني وأمني وامتداد اثاره واسبابه الكثيرة والمتداخلة وما يثيره من خلق حا

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.

In 1908 , the American poet Ezra Pound (1885-1972) , the central figure in the modern movement who was the driving force behind several movements , notably Imagism and Vorticism , met the Irish poet W. B. Yeats in London . Pound was employed as his secretary and the two soon became close friends . He found Yeats a realist, symbolist and a metaphysical poet with an uncanny power over words and regarded him the greatest living poet .The poetical style and the occult beliefs of the Irish poet drew the attention of the American Imagist .During the war, Pound and Yeats lived together at Stone Cottage in Sussex studying Japanese literature .Speaking of Yeats , T. S. Eliot described him as "one of those few whose history is the history of their

     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

The applications of herbal medicine have recently acquired growing interest in range of the prophylaxis and treatment of diseases. Olibanum has been used since ancient eras and several reports studied the pharmacological characteristics of boswellic acid, particularly their effect on the inflammatory response, analgesic properties, and anti-arthritic activity mostly in cell lines, but new approaches include animal models to assess these natural derivatives effects taking into consideration of being safer than synthetic preparations.  The impact of olibanum oil on several parameters was studied in rats during this study. These included white blood cell (WBC) count, lactate dehydrogenase (LDH), and C reactive protein (CRP), as well a

Background: Generally, genetic disorders are a leading cause of spontaneous abortion, neonatal death, increased morbidity and mortality in children and adults as well. They a significant health care and psychosocial burden for the patient, the family, the healthcare system and the community as a whole. Chromosomal abnormalities occur much more frequently than is generally appreciated. It is estimated that approximately 1 of 200 newborn infants had some form of chromosomal abnormality. The figure is much higher in fetuses that do not survive to term. It is estimated that in 50% of first trimester abortions, the fetus has a chromosomal abnormality. Aim of the study: This study aims to shed some light on the results of chromosomal studies per

This research examines aspects of Imam Al-Qurtubi's efforts in matters related to the topics of faith that he dealt with in his interpretation (the provisions of the provisions of the Qur’an); and it has been shown that Imam Al-Qurtubi in most of the doctrinal issues dealt with in his interpretation approximates the doctrine of the Sunnis of Ash'aris, Maturids and people of impact. He had responses to some of the teams, such as stereoscopic, karami, and Mu'tazilite, reinforcing the responses with transfer and mental evidence.
    It was found that Imam Al-Qurtubi says that there is an increase in faith and a decrease in it, that the increase is through actions (so obedience increases and decreases in sin) and that the