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The Representaion of Algebraic Integers as Sum of Units over the Real Quadratic Fields: REPRESENTAION 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
Wed Mar 29 2023
Journal Name
Journal Of The College Of Education For Women
The Counselor Brent Scowcroft and his Role in Achieving the Requirements of the American National Security
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       Despite the multiplicity of institutions contributing to the decision-making process in the United States of America, they interact to crystallize positions regarding international and strategic situations. The formulation of the national security policy depends on a number of institutions that complement each other in order to achieve an advanced security situation. Thus, the decision reflects the process of interaction of the existing regulatory institutions. This is because the essence of the national security and achieving its requirements also stems from the existence of a coherent system of shared beliefs and principles in the American society. Besides, these elements are the bases for achieving

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Publication Date
Thu Aug 08 2019
Journal Name
Iop Conference Series: Materials Science And Engineering
A Study of poly4-oxo-4-(4-sulfamoylphenylamino) but-2-enoic acid as a good anti – Corrosion of 316L stainless steel in 0.2M hydrochloric acid solution.
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Publication Date
Wed Sep 14 2016
Journal Name
Journal Of Baghdad College Of Dentistry
Immunohistochemical Expression of MMP2, VEGF and D2-40 as Biological Markers of Local Invasion Potential, Angiogenesis and Lymphangiogenesis in Oral Squamous Cell Carcinoma and Verrucous Carcinoma
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Background: Verrucous carcinoma (VSCC) is considered as a rare well differentiated carcinoma variant of SCC with no metastatic potential. The aim of this study is to evaluate the Immunohistochemical expression MMP-2, VEGF and D2-40 expression in OSCC and VSCC. Materials and methods: Thirty formalin fixed paraffin embedded tissue blocks of OSCC and another twelve VSCC were collected and Four micrometer thick sections were cut from each block and mounted on positively charged slides and stained immunohistochemically with monoclonal antibodies to MMP-2, VEGF and D2-40. Results: there is no statistical difference between SCC and VSCC regarding the immunoexpression of MMP-2 and VEGF. While the lymphatic vessels density were higher in SCC than V

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Publication Date
Sun Jul 01 2012
Journal Name
American Journal Of Veterinary Research
Effect of brachycephalic, mesaticephalic, and dolichocephalic head conformations on olfactory bulb angle and orientation in dogs as determined by use of in vivo magnetic resonance imaging
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Abstract<p><bold>Objective</bold>—To determine the effect of head conformation (brachycephalic, mesaticephalic, and dolichocephalic) on olfactory bulb angle and orientation in dogs by use of in vivo MRI.</p><p><bold>Animals</bold>—40 client-owned dogs undergoing MRI for diagnosis of conditions that did not affect skull conformation or olfactory bulb anatomy.</p><p><bold>Procedures</bold>—For each dog, 2 head conformation indices were calculated. Olfactory bulb angle and an index of olfactory bulb orientation relative to the rest of the CNS were determined by use of measurements obtained from sagittal T2-weighted MRI images.</p><p><bold>R</bold></p> ... Show More
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Publication Date
Sun Jan 25 2026
Journal Name
Journal Of Baghdad College Of Dentistry
Evaluation of olive oil as a separating medium and its effect on some physical properties of processed acrylic resin denture base (A comparative study). Part one
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Back ground: During acrylic resin processing, the mold must be separated from the surface of the gypsum to prevent liquid resin from penetrating into the gypsum, and water from the gypsum seeping into the acrylic resin. For many years, tin foil was the most acceptable separating medium, and because it's difficult to apply, a tin-foil substitute is used. In this study, olive oil is used as an alternative to tin foil separating medium for first time, so the aim of the study was to evaluate its effect as a separating medium on some physical properties such as (surface roughness, water sorption and solubility) of acrylic resins denture base comparing it with those processed using tin-foil and tin foil substitute such as (cold mold seal) separat

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Publication Date
Wed Apr 01 2020
Journal Name
Journal Of Economics And Administrative Sciences
The role of the effectiveness of self-managed teams in improving the quality of services / an applied study in Ramadi municipality
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This research aims to identify the effective role of self-managed teams in the quality of service performance in the directorate of Ramadi municipality. The problematic nature of our research involves this main question of the effective role of self-managed teams in the Municipality of Ramadi in improving the services of performance quality to the beneficiaries from the Directorate service. The importance of this study lies in the role played by the work teams in the organizations that excel in their field, the attendant of the changes in the leadership, administrative roles of the institutions, and teams leaders, will be achieved by the self-managed teams in improving the quality of the service provided by the institution to whi

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Publication Date
Wed Dec 19 2018
Journal Name
Journal Of Planner And Development
معوقات تنفيذ المخططات الأساسية بأبعادها التشريعية والقانونية حالة دراسية - مدينة الكوت
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Publication Date
Wed Dec 29 2021
Journal Name
Modern Sport
Effect of rehabilitation exercises in improving the motor range of people with partial rupture of the anterior cruciate ligament of the knee joint by ages (30-35) men
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The study aimed to prepare rehabilitation exercises using some rubber ropes for people with partial rupture of the anterior cruciate ligament, to recognize their effect on the recovery of motor tides and to reduce the pain of those with partial rupture of the anterior cruciate ligament of the knee joint, and adopted the experimental method by designing the experimental and controlled groups on a sample of those with partial rupture of the anterior cruciate ligament of men (30-35) One year of those who attend the Physiotherapy Center/Rafidain University College of 12 injured were deliberately selected from their community of origin by (100%), and after determining the measuring tools and preparation of exercises applied with rubber r

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Publication Date
Tue Nov 24 2015
Journal Name
Iraqi Journal Of Market Research And Consumer Protection
The Impact of External Environment Factors on the Quality of Educational Services (An Empirical Study): The Impact of External Environment Factors on the Quality of Educational Services (An Empirical Study)
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This research aims to identify the role of external environment factors on the quality of educational services, from the academic point of view, where the distribution of a questionnaire to a random sample of (100) university professors, and then analyzing a model, and test the validity of this model using structural modeling (SEM) (Structural Equation Modeling).
And then test the relationships between variables using the software of Statistical Package for Social Sciences (SPSS V.18), the research found a number of conclusions, the most important conclusion is: the external environment factors has significant impact on the quality of educational services.

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Publication Date
Sun Dec 31 2023
Journal Name
College Of Islamic Sciences
Bibliography of books (jurisprudence) available in the References Department of the Central Library at Al-Mustansiriya University)
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The research included making a bibliography of the jurisprudential books available in the reference section of the central library at the University of Al-Mustansiriya. From this research, and I also saw that one of its objectives was to classify these books scientifically according to what was included in the Contemporary Islamic Fiqh Library of sections that were classified on its basis, according to what has settled in the custom of contemporary jurists, and according to the researcher’s view and his humble diligence, so the research was organized into an introduction and three topics. Each topic contained approximately five demands that included the sections of the contemporary jurisprudential lib

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