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 .

During the last few years, the greener additives prepared from bio-raw materials with low-cost and multifunctional applications have attracted considerable attention in the field of lubricant industry. In the present work, copolymers derived from sunflower and linseed oils with decyl methacrylate were synthesized by a thermal method using benzoyl peroxide (BPO) as a radical initiator. Direct polymerization of fatty acid double bonds in the presence of a free radical initiator results in the development of environmentally friendly copolymeric additives (Co-1 and Co-2). Fourier Transform Infrared (FTIR) and Proton Nuclear Magnetic Resonance (1H-NMR) were used to characterize the resulting copolymers. Thermal decomposition of copolymers was de

An International Publisher for Academic and Scientific Journals The mucilage of white and black chia seeds were extracted and determining their contents of bioactive compounds such as tannins, glycosides, flavonoids, phenols, and studying their activity as anti-filamentary and anticancer. Results showed that tannins exist in white chia seeds with 35%while it is 38% in black seeds, flavonoids represent 0.98mg/ml in white chia seeds and 1.5 mg/ml for black seeds. Both kinds of seeds showed anti-filamentaryactivity, the inhibition ratio was 86.5% for white seeds and 97.3% for black seeds. Chia black seeds showed anticancer activity and the inhibition of the tumor muscle cell line ratio (GI%) was 34.8% at 50mg/ml concentration and 88.4%

Prepositions have a key function, which is to associate parts of a sentence, called letters In addition, it adds the meanings of the verbs to the names, ie reached by them, and called by the coffin characters Qualities..

          I chose to search for the meaning of the preposition "from" in Surat Maryam to know its meanings in terms of originality and expansion, so the title of the research (the meanings of preposition "from" in terms of originality and expansion in Surat Maryam model(

Atheists have spread in the modern era, so that atheism has become a bad phenomenon in the world in general and in Islamic societies in particular, so the research aims to study the individual and social effects left by atheism on the atheists themselves, and the research included multiple axes: atheism linguistically and idiomatically, atheism in the Qur’an Noble and Modern (and Contemporary) Atheism Statistics: and the reasons for atheism: Studying the phenomenon of atheism in Iraq as a model, then studying the effects of atheism: on the individual first, then atheism and its impact on society, then the conclusion, recommendations, sources and references

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

Understanding, promoting, and teaching media literacy is an important societal challenge. STEM educators are increasingly looking to incorporate 21st century skills such as media literacy into core subject education. In this paper we investigate how undergraduate Computer Science (CS) students can learn media literacy as a by-product of collaborative video tutorial production. The paper presents a study of 34 third-year CS undergraduates who, as part of their learning, were each asked to produce three video tutorials on Raspberry Pi programming, using a collaborative video production tool for mobile phones (Bootlegger). We provide results of both quantitative and qualitative analysis of the production process and resulting video tutorials,

Objectives: Serratia marcescens is a gram-negative pathogen of many species. The ability of S. marcescens to form biofilms and its potent innate resistance to antimicrobials and cleaning solutions are both essential for its pathogenicity and survival. The present study was conducted to investigate the effect of glyceryl trinitrate (GTN) on the biofilm of S. marcescens, as an alternative for antibiotic therapy. Methods: Different specimens, including ear swabs, burns, mid-stream urine, wound swabs, and sputum, were collected from patients who were brought to Al-Ramadi Hospital, Iraq. All samples were cultured, and the colonies that were obtained were detected using the VITEK® 2 compact. The ability of biofilms to develop was e

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