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 .

Analytical Hierarchy Process (AHP) belongs to the family of Multiple Criteria Decision Making (MCDM)  and has, recently, received a wide popularity in decision making regarding supplier selection.  The objective of this study is to apply the methodology of AHP on selecting suppliers to supply materials for the  Geological Survey and Mining  Company (GSMC).  Criteria for rating the suppliers and pairwise comparisons were identified by the members of the Tenders Analysis Committee (TAC). In order to judge the internal validity of the AHP, it was applied manually on a sample of fourteen tenders that were analyzed  and executed between 2004-2007, then an interactive computerized  package was developed 

A field experiment was carried out at the research station of the College of Agriculture - Wasit University / Kut, during the fall season 2021 in soil with texture (sandy mixture) using the RCBD design in the arrangement of splintered plates and with three replications, to study the effect of spraying different combinations of organic emulsion (Appetizer) and NPK nano fertilizer with urea fertilizer on the growth of synthetic cultivars of yellow corn. The main panels included three synthetic varieties of yellow corn (Fajr1, Sumer and Baghdad3), which symbolized by (V1,V2,V3) in sequence, while the secondary panels included five fertilization treatments in which mineral fertilizer (urea) was used 46% nitrogen with the full recomme

ان شركات التأمين وبسبب طبيعة نشاطها التأميني تتجمع لديها أموال ضخمة عن الأقساط التي تحصلها من المؤمن لهم, ولغرض عدم ترك هذه الاموال عاطلة, فأنه يتم استثمارها في مجالات وأدوات استثمار متنوعة لتحقيق عوائد منها. هذا ولغرض تحديد وتوجيه هذه الاموال في مجال أو أداة الاستثمار المناسبة أو تحديد مدى جدوى هذه الاستثمارات, فانه يتم تقييمها, وهناك عدة نماذج رياضية لتقييم بدائل الاستثمار في شركات التأمين, إلا أنه لا

planning is among the most significant in the field of robotics research.  As it is linked to finding a safe and efficient route in a cluttered environment for wheeled mobile robots and is considered a significant prerequisite for any such mobile robot project to be a success. This paper proposes the optimal path planning of the wheeled mobile robot with collision avoidance by using an algorithm called grey wolf optimization (GWO) as a method for finding the shortest and safe. The research goals in this study for identify the best path while taking into account the effect of the number of obstacles and design parameters on performance for the algorithm to find the best path. The simulations are run in the MATLAB environment to test the

Abstract:

   Witness the current business environment changes rapidly reflected on the performance of the facility wishing to stay , which is no longer style reaction enough to handle installations with their environment , and quickly began to lose its luster with the emergence of a message and the vision of contemporary business environment from a set of parts interacting with each other and the concept of behavioral includes all dimensions of performance, it is imperative to adopt a system installations influence variables and positive interaction through the development of strategic plans and the use of implementation and follow-up strategies to ensure the effectiveness of the method for meas

المستخلص     ان الغرض من موضوع اعادة تصميم الوظائف هو توفير أمكانية قيام الأفراد بأداء عدة مهام في المنظمة الصحية في الوقت نفسه واكتساب الخبرات والمهارات المتنوعة وتحقيق التوافق الانسب بين متطلبات الوظيفة والمنظمة من ناحية وحاجات ورغبات الفرد ودوافعه من ناحية اخرى ،ومن هنا انبثقت فكرة دراسة اعادة تصميم الوظائف لشعبة خدمات نقل الدم في دائرة صحة بغداد الرصافة من اجل تغيير الاساليب التقليدية المتبعة ف

تتقصى هذه الدراسة الاساليب التداولية للتأنيب لدى لطلبة العراقيين الجامعيين متعلمي اللغة الانكليزية لغة اجنبية من كلا الجنسين (ذكورا واناث) وتحديد الاساليب التداولية التي يفضلها كل منهما. تم اختبار اربعين طالبا مقسمين بالتساوي من كلا الجنسين تحريريا بأستخدام فرض اكمال النص. أظهرت النتائج بأن الطلبة العراقيين من كلا الجنسين يفضلون اسلوب التأزرعلى التمايز وتفضيل استخدام الالفة والصداقة من دون الاخلال با