The discussion in this paper gives several theorems and lemmas on the Sums of Squares of consecutive Carol Numbers. These theorems are proved by using the definition of carol numbers and mathematical induction method. Here the matrix form and the recursive form of sum of squares of consecutive Carol numbers is also given. The properties of the Carol numbers are also derived.
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
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This research worked on identifying the effect of increasing the volume of indebtedness by companies listed on the Iraq Stock Exchange on the trading volume of those companies, and this research included some theoretical concepts related to both debt financing and trading volume, and it represents the research community of the joint-stock companies listed in The Iraq Stock Exchange (the banking sector). As for the research sample, it was deliberately chosen represented by companies with continuous trading without stopping, which reached 10 joint-stock companies, and the period of research was extended during the period 2011-2015, and a set of indicators and financial methods were used In measuring research v
... Show MoreThe 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
... Show MoreA program in Visual Basic language was designed to predict the type of radio storm that emitted from Jupiter at specific Local Time (LT) from two different Iraqi locations (Baghdad and Basra), such storms result from the Central Meridian Longitude (CML) of system ??? for Jupiter and phase of Io’s satellite (?Io). Some of these storms are related to position of Io (Io- A,B,C,D) and others are unrelated (non-Io-A,B,C,D) to its position. The input parameters for this program were user specified by determining the observer’s location (longitude), year, month and day. The output program results in form of tables provides the observer with information about the date and the LT of beginning and end of each type of emitted storm. Two Io-storm r
... Show MoreThis is a brief research in which I tried to briefly explain the care that the Holy Qur’an received during the era of the Prophet, may God bless him and grant him peace, from the Prophet, may God bless him and grant him peace, and all of his honorable companions, may God bless him and grant him peace. I made this research in an introduction and two chapters, the first chapter I made it entitled: About the Holy Qur’an, in which I talked about general investigations about the Holy Qur’an, such as the definition of the Holy Qur’an and the difference between it and the hadith Qudsi and the hadith of the Prophet, then I mentioned a part of the virtues of the Holy Qur’an in general and the virtues of some surahs in particular, and th
... Show MoreThe 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
... Show Moreأستهدفت 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))
This paper presents a grey model GM(1,1) of the first rank and a variable one and is the basis of the grey system theory , This research dealt properties of grey model and a set of methods to estimate parameters of the grey model GM(1,1) is the least square Method (LS) , weighted least square method (WLS), total least square method (TLS) and gradient descent method (DS). These methods were compared based on two types of standards: Mean square error (MSE), mean absolute percentage error (MAPE), and after comparison using simulation the best method was applied to real data represented by the rate of consumption of the two types of oils a Heavy fuel (HFO) and diesel fuel (D.O) and has been applied several tests to
... Show MoreMany problems are facing the installation of piles group in laboratory testing and the errors in results of load and settlement are measured experimentally may be happened due to select inadequate method of installation of piles group. There are three main methods of installation in-flight, pre-jacking and hammering methods. In order to find the correction factor between these methods the laboratory model tests were conducted on small-scale models. The parameters studied were the methods of installation (in-flight, pre-jacking and hammering method), the number of piles and in sandy soil in loose state. The results of experimental work show that the increase in the number of piles value led to increase in load carrying ca
... Show MoreThe research included (the aesthetics of the sculptural formulations of swords in the Al-Kafeel Museum) four chapters. Al-Kafeel Museum.)
Within the time period: (1240 AH / (1824 and 1825) AD - 1312 AH / (1894 and 1895) AD). The second: the types of Islamic swords. The third chapter included (research procedures), and the analysis of samples from the sample (3) as a model according to the descriptive approach, and the fourth chapter dealt with (results, conclusions, recommendations, and proposals). As well as recommendations, proposals and sources.