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bsj-4152
Representation of Algebraic Integers as Sum of Units over the Real Quadratic Fields
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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 .

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Publication Date
Tue Jun 17 2025
Journal Name
Research In Social Sciences
Using Chatbot and ChatGPT as Useful Tools in Scientific Academic Writing
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This review investigates the practice and influence of chatbots and ChatGPT as employable tools in writing for scientific academic purposes. A primary collection of 150 articles was gathered from academic databases, but it was systematically chosen and refined to include 30 studies that focused on the use of ChatGPT and chatbot technology in academic writing contexts. Chatbots and ChatGPT in writing enhancement, support for student learning at higher education institutions, scientific and medical writing, and the evolution of research and academic publishing are some of the topics covered in the reviewed literature. The review finds these tools helpful, with their greatest advantages being in areas such as structuring writings, gram

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Publication Date
Sat Jul 26 2025
Journal Name
Arab World English Journal
YouTube as a Learning Tool Among EFL Learners: A Systematic Review
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This review paper examines the crucial impact of YouTube on learning English as a Foreign Language. Recently, learners’ interaction and development of their skills have been improved due to the integration of digital platforms into language education. YouTube is regarded as one of the most prevalent platforms due to its accessibility, multimodal content, and capacity to simulate real-life communication. This study tackles thirty selected research articles from various cultural and institutional backgrounds to identify the pedagogical benefits and challenges associated with using YouTube in teaching English. Conventional methods of teaching English as a foreign language encounter difficulties in improving students’ engagement and

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Publication Date
Thu Oct 01 2020
Journal Name
Journal Of Legal Sciences
Judicial Tools in Developing Civil Law Rules – France as a Model
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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

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Publication Date
Sat Jan 01 2022
Journal Name
International Journal Of Research In Social Sciences & Humanities
COLLABORATIVE WRITING AS A MEANS IN DEVELOPING EFL LEARNERS’ WRITING PERFORMANCE
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Collaborative learning is a way that prepares students practically for real-world applications. Working together as teamwork to execute various writing skills is essential in most professions since it increases the level of experience. Thus, the current study aims to identify the role collaborative writing in developing students' level of performance in writing. It is qualitative in nature since the researcher depended on the extant literature in achieving the objective of the study. The researcher touched upon related theories that addressed Collaborative learning, categories, and problems .It concluded that collaborative writing increases the students’ self-confidence, self-esteem, creativity, and motivation through the interact

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Publication Date
Mon Jun 01 2020
Journal Name
Journal Of Engineering
GIS as A Tool for Expansive Soil Detection at Sulaymaniyah City
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Geotechnical engineering like any other engineering field has to develop and cope with new technologies. This article intends to investigate the spatial relationships between soil’s liquid limit (LL), plasticity index (PI) and Liquidity index (LI) for particular zones of Sulaymaniyah City. The main objective is to study the ability to produce digital soil maps for the study area and determine regions of high expansive soil. Inverse Distance Weighting (IDW) interpolation tool within the GIS (Geographic Information System) program was used to produce the maps. Data from 592 boreholes for LL and PI and 245 boreholes for LI were used for this study. Layers were allocated into three depth ranges (1 to 2, 2 to 4 and 4 to 6)

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Publication Date
Fri Jan 01 2016
Journal Name
Journal Of Engineering
Zirconium Sulfate as Catalyst for Biodiesel Production by Using Reactive Distillation
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Production of fatty acid esters (biodiesel) from oleic acid and 2-ethylhexanol using sulfated zirconia as solid catalyst for the production of biodiesel was investigated in this work.

 

       The parameters studied were temperature of reaction (100 to 130°C), molar ratio of alcohol to free fatty acid (1:1 to 3:1), concentration of catalyst (0.5 to 3%wt), mixing speed (500 to 900 rpm) and types of sulfated zirconia (i.e modified, commercial, prepared  catalyst according to literature and reused catalyst). The results show the best conversion to biodiesel was 97.74% at conditions of 130°C, 3:1, 2wt% and 650 rpm using modified catalyst respectively. Also, modified c

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Publication Date
Sun Jun 30 2019
Journal Name
Journal Of The College Of Education For Women
(Evaluation and Mobility) As Two self-Organizing Posts for University Students
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One of the important goals in the learning process is to be effective learning through the self-direction of the learner , because it has an impact on the effort of learners , it is better to be a learner responsible for learning and independent of the acquisition of knowledge ,

اذ اكدتكثيرAs many have confirmed منFrom الدراساتStudies والادبياتAnd literature انthat فشلالكثير The failure of many منFrom الطلبةStudents فيin a تنظيمgroup المعلوماتthe information ومعالجتهاAnd processed اثناءduring عمليةProcess تعلمهمLearn them لاNo يرجعReturns الىto me انخفاضdrop فيin a درجةDegree ذكائهمTheir intelligence اوor عدمNo

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Publication Date
Wed Jun 29 2022
Journal Name
Journal Of The College Of Education For Women
Gender and Urban Studies as an Interactive Approach and Integrated Curriculum
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The integration of gender in urban studies is considered a goal and objective to build a society characterized by justice and equality. It further allows all its residents to enjoy the opportunities to live in a safe urban life. Based on the that, the limitations of the research and its field of interest related to the relationship between gender and urban studies have become clear. The insufficient knowledge in this regard considers gender as a concept that does not exist in itself, but rather overlaps and intersects with several concepts and studies, including urban studies. Thus, it has become necessary to adopt a descriptive methodology that helps reach a theoretical framework to explain the beginnings of such an interaction and inte

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Publication Date
Fri Dec 30 2011
Journal Name
Al-kindy College Medical Journal
Postprandial Hyperglycemia as a Significant Risk Factor for Coronary Heart Disease
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Background: The highest concentrations of
blood glucose during the day are usually found
postprandialy. Postprandial hyperglycemia (PPH)
is likely to promote or aggravate fasting
hyperglycemia. Evidence in recent years suggests
that PPH may play an important role in functional
& structural disturbances in different body organs
particularly the cardiovascular system.
Objective: To evaluate the effect of (PPH) as a
risk factor for coronary Heart disease in Type 2
diabetic patients.
Methods: Sixty-three type2 diabetic patients
were included in this study. All have controlled
fasting blood glucose, with HbA1c correlation.
They were all followed for five months period
(from May to October 2008)

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Publication Date
Sun Jan 01 2023
Journal Name
Materials Chemistry And Physics
BC2N nanotube as a promising anode for rechargeable calcium ion batteries
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Because of cost-effective production and abundant resources of calcium, Ca-ion batteries (CIBs) are an appropriate option to alternate Li-ion batteries (LIBs). A new category of anode materials for CIBs has emerged since the successful synthesis of carbon nanotubes, which are B and N doped derivatives of it. For high-performance CIBs, BC2N nanotube (BC2NNT) has been studied as promising anode materials. In order to comprehend electrochemical attributes, cycling stability, and adsorption behavior of BC2NNT, first-principles computations have been executed. Based on nuclear magnetic resonance computations, two types of hexagonal rings (B2C2N2 (I) and BC4N (II)) were specified that are non-aromatic. Ca has adsorption on B2C2N2 and BC4N with ad

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