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.
Praise be to God, Lord of the Worlds, who has made His way for His servants who know in the depths and who are devoted to Him at all times and times, so He has delivered to Himself their pain from two exiles, and His prayers and peace are the perfect trust in the presence of the pearl of charity of existence. Possessor of great intercession and praiseworthy status until the day of meeting and eternity, and upon his family and companions, the people of tomorrow, steadfastness, generosity, and generosity, and after that
For a long period of time, I have been asking myself: Why did he attack so many contemporary books, especially Sufism? Why this unlimited financial expenditure on printing, binding, beautifying and enticing readers?
... Show MoreThe interest of many companies has become dealing with the tools and methods that reduce the costs as one of the most important factors of successful companies, and became the subject of the attention of many economic units because of the impact on the profits of company, and since the nineties of the last century the researchers and writers gave great attention to this subject, especially in light of the large competition and rapid developments in cost management techniques, as well as the wide and significant change in production methods that have been directed towards achieving customer satisfaction, all this and more driven by economic units in all sectors whether it is service or productivity to find methods that would reduc
... Show MoreThe current study aimed to isolate and diagnose Candida spp yeasts that cause candidiasis with a PCR device from patients reviewed for some hospitals in Baghdad city and by 190 samples, the study recorded 123 isolates and the total percentage of infection was 64.7% .Samples were taken from different clinical cases of the vagina, blood and mouth and the Candida spp were (70.37%, 41.26%, 86.95%) respectively. Five types of yeasts were isolated and diagnosed, namely C. albicans, C. tropicalis, C. parapsilosis, C. krusei and C.glabarta. They were confirmed by PCR device and the most notable were yeast C. albicans, where 91 isolates were found, 73.98%, while the lowest infection was recorded. C.glabartawith 3 isolates, at 2.43%, significant diff
... Show MoreThe banking sector of all kinds is the backbone of the economy in all countries, as it is the main financier of most economic projects in order to achieve economic development and achieve stability, which contributes to providing the necessary resources in return for obtaining a profit margin in exchange for giving up his money and bearing credit risks. Among the aforementioned banking sectors are: Islamic banks that invest their capital in several forms in order to obtain profits that enable them to continue and grow, and the most important of these formulas is the Murabaha formula, which is summarized by the bank selling a commodity after owning it and then selling it to the applicant for this commodity based on a prior request
... Show MoreTo achieve the goals, the researcher followed the design of equal and independent groups of partial control and post-test . The research has chosen the Institute of Fine Arts in the area Almansour area as deliberate sample where three sections of students have been chosen and the number of students is (69) students. The researcher conducted equivalence in the variables (age, and IQ , and the overall rate for grade III). in diagnostic phase, (21) concepts of alternative image out of (46) concepts have been identified in addition to the goals of formulation of acquisition concepts according to the three processes (definition, discrimination and application). Achievement test has been
... Show MoreDesulfurization of a simulated diesel fuel by different adsorbents was studied in a fixed-bed adsorption process operated at ambient temperature and pressure. Three different adsorption beds were used, commercial activated carbon, Cu-Y zeolite, and layered bed of 15wt% activated carbon followed by Cu-Y zeolite.Initially Y-zeolite was prepared from Iraqi rice husk and then impregnated with copper. In general, the adsorbents tested for total sulfur adsorption capacity at break through followed the order Ac/Cu-Y zeolite>Cu-Y zeolite>Ac. The best adsorbent, Ac/Cu-Y zeolite is capable of producing more than 30 cm3 of simulated diesel fuel per gram of adsorbent with a weighted average content of 5 ppm-S, while Cu-Y zeolite producing of
... Show MoreThe intensification of competition among all companies and at different levels has become necessary for every company need to continue to improve its performance in order to be able to face the competition and stay in the market. To achieve this, we must rely on the company's accounting information more accurate and appropriate and provided in a timely manner, for the purpose of use in planning and decision making.
So there must be information systems that help the administration to continuous development and improvement of the performance of companies in general, and this is what you need Jordanian companies, especially after the accession of Jordan to the field
... Show MoreThe estimation of recharge to ground water is the important basics to improve the use of ground water with other available resources, and to save ground water resource from depletion, especially when using large quantity of ground water during a long time such as for agricultural purposes. Al-Wand River Basin in Iraq suffers from water shortage of its requirement of Blajo–Al-Wand Project, and to cover this shortage, the ground water plays a good role to overcome this problem. In this study, three methods were used to estimate the recharge and ground water storage for Al-Wand Basin, these methods are: Water Table Fluctuation (WTF), Water Balance of Climatic for Basin, and Water Table Balance for Basin. The results showe
... Show MoreThe research aims to identify the role of the dimensions of financial inclusion in achieving the competitive advantage by An exploratory research of the views of a sample of customers of the 20 Algerian commercial banks, And the relationship between its dimensions (Access dimension, Usage dimension, Quality) And competitive advantage. This research is based on the analytical descriptive approach. The questionnaire was adopted as a main tool in collecting data and information on the sample of 377.
The The research showed several results, the most important of which is a strong correlation between the dimensions of the three financial inclusion combined and the competitive advantage of the Algerian commercial banks, and explained t
... Show MoreThe research aims at evaluating the illustrations images and determining the availability of good image standards in the illustrations images of the content of the second intermediate stage computer's book for the academic year (2019-2020) as seen by computer teachers. The sample was randomly selected, (30) teachers who are actually teaching the subject in schools within the geographical area of the province of Baghdad (Karkh III). To achieve this goal, ten standards were identified: scientific accuracy, suitability for the level of students, image clarity, image freshness, quality of coloring, suitability of its location of the subject, Matching their content glimpsed, The subject matter is appropriate in terms of area, matching its tit
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