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.
Background: Oral health is important to the quality of life of all individuals. Oral lesions can cause discomfort or pain that interferes with mastication, swallowing, and speech. Oral disease is a health problem that is not only a matter of oral hygiene and local condition, but can also be a precursor to other dangerous and potentially life threatening illnesses. The present study was designed to analyze the main clinicopathological aspects of most common oral lesions in patients who visit the Oral Diagnosis Clinic of the College of Dentistry, University of Sulaimani, Kurdistan region, Iraq. Patients and methods: This prospective study was performed on 3144 patients from July 2009-July 2010. In this study a total of 3144 patients were e
... Show MoreObjectives: The demand for orthodontic treatment is nowadays increasing significantly for aesthetic improvement and to correct various kinds of malocclusion, yet the prolonged treatment time remains the main obstacle. This review aimed to demonstrate various orthodontic techniques and highlight the evidence-based successful approaches used for acceleration of orthodontic tooth movement. Materials and Methods: Data and sources of information pertaining to accelerated orthodontic tooth movement premised on English-written articles were searched using electronic databases including Google Scholar, Scopus, PubMed and MEDLINE. Results: This review demonstrated the availability of different surgical and non-surgical methods to enhance tooth movem
... Show Morehe dairy industry is one of the industrial activities classified within the food industries in all phases of the dairy industry, which leads to an increase in the amount of wastewater discharged from this industry. The study was conducted in the Abu Ghraib dairy factory, classified as one of the central factories in Iraq, located in the west of Baghdad governorate, with a design capacity of 22,815 tons of dairy products. The characteristics of the liquid waste generated from the factory were determined for the following parameters biological oxygen demand (BOD5), Chemical oxygen demand (COD), total suspended solids (TSS), pH, nitrate, phosphate, chloride, and sulfate with an average value of (1079, 1945, 323, 9.2, 24, 2
... Show MoreI've been in this research preparation and diagnostic complexes mixed Kandat of Alcavaúan Alpiculan ion Althaaossianat with some metal ions has been reactive in ethanol solvent and distilled water by (1:1) and water complexes and lotions to the accounts of the metal in the complex
We have chosen the subject of the research (the letters at Ibn Jinnie in the lexicon of the tongue of the Arabs) in order to know the opinion of Ibn Jinnie in this range of words and compare them with the opinions of scientists who preceded him to know the personality of this linguistic world.
Sustainable development (SD) is an improvement that meets present needs but jeopardizes the ability of new populations to do the same. It is vital to acquaint EFL students with the terminology and idiomatic expressions of this discipline. Nowadays, sustainable development and the environment have been prioritized in every aspect of life. Since culture and the teaching of Foreign language English cannot be separated, the English language becomes the mean of communication in health, economics, education, and politics. Thus, integrating sustainable development goals within language learning and teaching is very important. This descriptive quantitative study aims to investigate the perception of EFL pre-service teachers of sustainable develo
... Show MoreThe study found a number of results. The most prominent were the low married during the years of the study in 1997-2012. The study also showed the level of administrative units that the percentage of widows and single rise in urban and rural decline. This is due to the different nature of urban and rural society of the behavior and social habits and traditions.As the proportion of divorced and unmarried are decreased in urban and increase proportion in the countryside, and this is due to the influence of the rural population in the urban centers. As well as the study showed that there was a significant effect of the economic and social factors and other factors on marital status on its parts in the study area.