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: Intramedullary astrocytomas
account for about 1% of all CNS tumors and
6–8% of spinal cord tumors. The vast majority
of intramedullary astrocytomas are slowgrowing
lesions.
Objectives: The goal in this study was to
review a series of patients who underwent
surgical removal of intramedullary high-grade
astrocytomas, focusing on the functional
outcome and the effect of multimodality
treatment on the survival of patients with high
grade intramedullary astrocytoma.
Methods: Between June 1999 and June 2004,
22 patients underwent removal of
intramedullary high-grade astrocytomas in four
neurosurgical hospital in Baghdad/ Iraq
(Neurosurgical hospital, Al Shaheed Adnan
Hospital for
Let be a non-trivial simple graph. A dominating set in a graph is a set of vertices such that every vertex not in the set is adjacent to at least one vertex in the set. A subset is a minimum neighborhood dominating set if is a dominating set and if for every holds. The minimum cardinality of the minimum neighborhood dominating set of a graph is called as minimum neighborhood dominating number and it is denoted by . A minimum neighborhood dominating set is a dominating set where the intersection of the neighborhoods of all vertices in the set is as small as possible, (i.e., ). The minimum neighborhood dominating number, denoted by , is the minimum cardinality of a minimum neighborhood dominating set. In other words, it is the
... Show MoreGypseous soil is a collapsible soil, which causes large deformations in buildings that are constructed on it. Various methods have been used to minimise this effect, such as replacing the gypseous soil or using soil stabilisation (grouting or soil improvement). This study was carried out on four types of gypseous soils that have different properties and various gypsum contents. The testing was carried out on remoulded samples to evaluate the compressibility of gypseous soil under different conditions. The samples were grouted with acrylate liquid. The relationships between the injection pressure and the radius of flow, between time of injection and radius of flow, and between time and quantity of acrylate liquid are investigated on
... Show MoreThis study aims to examine the sources of organizational power prevailing among the academic leaders at the University of Tabuk from the faculty members’ viewpoint. The purposes behind such an aim are: to reveal the level of administrative and technical institutional creativity, the nature of the relationship between the reality of organizational power and the level of institutional creativity, and to disclose statistically the significant differences between the averages of faculty members’ responses attributed to the demographic variables (gender, years of experience, academic degree). The study used the descriptive approach, both survey and correlational. A questionnaire was used to collect data from a simple random sample o
... Show MoreThe practice of art is an inevitable result imposed by the circumstances surrounding the human being, as he needs some knowledge associated with raw materials, tools and methods to develop skills in the formation of elements of the work of art in new ways that give a decent artistic appearance to the work of art. Through the exploratory study carried out by the researcher, which included asking the following question to the third grade students, Department of Art Education:
What types of materials are used in handicrafts and from which sources are they obtained? Through the answers, the problem of research was founded as follows:
-Are the products of students of the Department of Art Education in the handicraft material d
... Show MoreIn this study, the effects of blending the un-branched acrylate polymer known as Poly (n-decyl acrylate), and the branched acrylate polymer known as Poly (iso-octyl acrylate), on the viscosity index (VI), and the pour point of the Iraqi base stocks 40, and 60 respectively, were investigated. Toluene was used as a carrier solvent for both polymer types. The improvement level of oils (VI, & pour point) gained by blending the oil with the acrylate derived polymers was compared with the values of (VI, and pour point) gained by blending the oil with a commercial viscosity index, and pour point improver. The commercial lubricant additive was purchased and used by Al-Daura Refineries. It consisted of an un-known olefin copolymer dissolved i
... Show MoreThe research sought to identify the objective trends of postgraduate students at the College of Political Science - University of Baghdad for the period from 2000-2012 through the objective trends of university theses and dissertations and what are the most and least studied topics, with a re-adjustment of previously studied topics towards topics that serve issues of concern to society and avoiding topics that have been studied a lot to avoid repetition. The research came out with the following results, the most prominent of which are: The total number of what was accomplished in this college is 401 theses and dissertations, and the dissertations had the largest share of them, as their percentage reached 69%, with 275 theses compared to 126
... Show MoreThe research included four topics: the definition of Imam al-Bazzazi, his scientific life, his sheikhs, his students, his writings, his death, and selected issues of his weight in the book of prayer. The Imam al-Bazazi is the son of Muhammad ibnShihabibn Yusuf. He is known as al-Khardizi al-Khawarizmi. The author did not adopt the definitions of language and terminology, and rarely mention the legal evidence adopted by the scholars in their opinions, and only to mention the views only, and the author, may God have mercy on him in his book on the sources of m The Prophet (peace and blessings of Allaah be upon him) said: "The Prophet (peace and blessings of Allaah be upon him) And fall down the order, the third issue, which is to leave the
... Show MoreThis research aims to measure the discrepancy between the accounting income which is prepared according to generally accepted accounting principles and the tax income that is being prepared according to the rules and tax laws, and find out the most important differences that arise between incomes.The research found the most important to the following conclusions:1.Faces determining the tax base for companies subject to income challenges related to the weakness of the efficiency and the possibility of technical angel tax and its ability to examine the financial statements submitted to the tax administration tax.2.That the tax system in Iraq does not comply with accepted accounting principles generally accepted.The research recommends the
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