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 paper discusses the Sums of Squares of “m” consecutive Woodall Numbers. These discussions are made from the definition of Woodall numbers. Also learn the comparability of Woodall numbers and other special numbers. An attempt to communicate the formula for the sums of squares of ‘m’ Woodall numbers and its matrix form are discussed. Further, this study expresses some more correlations between Woodall numbers and other special numbers.

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 .

Polyacrylamide Solutions of different concentrations (0.2, 0.4, 0.6, 0.8, 1.0 %) of Ag nanoparticles and ZnO nanoparticles were prepared, the viscosities and surface tension were measured for all solutions, where measurements indicated an increase in these properties with increased concentration, where the relative viscosity of polyacrylamide/zinc nanoparticles increased from 1.275 to 2.243, and the relative viscosity of polyacrylamide/silver nanoparticles increased from 1.178 to 1.934. Viscosity is significant parameters during electrospinning process. While the surface tension of the polyacrylamide/zinc nanoparticles has changed from 0.0343 Nm-1 to .0.0.0 Nm-1 and changed from .0.000Nm-1 to.0.0.0 Nm-1. Also the constants KH and KK were

Praise be to God, Lord of the worlds, and prayers and peace be upon our master and beloved Muhammad, the wise guide and great teacher, the guide to a straight path, the one sent as a mercy to the worlds, and upon his good and chosen family, his chosen companions, the working scholars, and those who follow them in righteousness until the Day of Judgment.

And after:

One of the important controversial topics shared between the sciences of the Noble Hadith and the Fundamentals of God is the issue of the innovator in terms of accepting and rejecting his narration and testimony, and the difference in it leads to disagreement in many branches of jurisprudence that were based on texts narrated by innovated narrators or those accu

The research aims to identify the digital repository of the University of Baghdad, explain its features, how to register, explaining the mechanism for adding and retrieving research. In addition to identifying the number of people registered in and the number of intellectual outputs stored in it. The descriptive approach and survey methods were adopted by visiting the repository's website and the websites of the University of Baghdad's formations during the period (1-6/4/2024). The theoretical framework included an explanation of the concept of the digital repository, the importance of repositories, their features, and types, with reference to models of Iraqi, Arab, and foreign university digital repositories. The practical framework of the

High frequency (HF) communications have an important role in long distances wireless communications. This frequency band is more important than VHF and UHF, as HF frequencies can cut longer distance with a single hopping. It has a low operation cost because it offers over-the-horizon communications without repeaters, therefore it can be used as a backup for satellite communications in emergency conditions. One of the main problems in HF communications is the prediction of the propagation direction and the frequency of optimum transmission (FOT) that must be used at a certain time. This paper introduces a new technique based on Oblique Ionosonde Station (OIS) to overcome this problem with a low cost and an easier way. This technique uses the

China's economic policy and its huge capabilities operate according to an expansion strategy, especially in investing foreign projects, as the past ten years have witnessed a major development in the elements of comprehensive strength, especially in the economic field, in 2014 China launched the largest initiative in the world, represented by the Belt and Road Project (BRI), which links nearly 70 countries, through this project, a very important region has emerged, which is (the port of cadres) in Pakistan, as China has headed towards that region and given the highest importance that is in its interest in the first place regardless of the great Pakistani interest, This is consistent with its future aspirations, especially after breaking

أستهدفت الدراسة اختبار أثر التوجه السوقي والتزام العاملين على أداء المنظمة المسوقة لخدمات النقل الجوي. حيث تم اختيار شركة الخطوط الجوية الملكية الأردنية كمجال تطبيقي.وقد اعتمدت الدراسة في قياس المتغيرات على مقاييس مختبرة وقد تأكد صحتها وثباتها لقياس المتغيرات في البيئة الحالية.  وقد بينت نتائج التحليل الإحصائي الذي استخدمت فيه أساليب إحصائية مختلفة بالاستعانة ببرنامج SPSS))

المقدمة

تتعامل الجهات الضريبية في مختلف دول العالم بأساليب عديدة لجباية الضرائب من المكلفين بغض النظر عن فئات وأصناف هؤلاء المكلفين،وفي العراق تم اعتماد العديد من الأساليب لجباية الضرائب على امتداد المدد الزمنية المتعاقبة،وكان لأسلوب التقدير الذاتي وهو أحد تلك الأساليب مجالاً للتطبيق خلال مدة زمنية معينة،حيث جرى تطبيق هذا الأسلوب على وحدات اقتصادية معينة، وبالرغم من المساوئ التي قد ترافق تطبيق