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.

The necessary optimality conditions with Lagrange multipliers  are studied and derived for a new class that includes the system of Caputo–Katugampola fractional derivatives to the optimal control problems with considering the end time free. The formula for the integral by parts has been proven for the left Caputo–Katugampola fractional derivative that contributes to the finding and deriving the necessary optimality conditions. Also, three special cases are obtained, including the study of the necessary optimality conditions when both the final time  and the final state  are fixed. According to convexity assumptions prove that necessary optimality conditions are sufficient optimality conditions.

The 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

The current research aims to find out ( the effectiveness of the structural model of learning in the acquisition of geographical concepts at the first grade average students ) , and achieving the goals of research has been formulating the null hypothesis of the following :

    " There is no difference statistically significant when Mistoi (0.5 ) between the mean scores of the collection of students in the experimental group that is studying the general geographical principles " Bonmozj constructivist learning " and the mean scores of the control group , which is considering the same article ," the traditional way " to acquire concepts.

The researcher adopted th

The research section tagged (Aesthetics of Abstract Expressionism and its Representations in the Artistic Products of Students of the Department of Art Education) into four chapters and it included in..
The first chapter: (the methodological framework) for the research, and the research problem is summarized through the question (what are the aesthetics of abstract expressionism and its representations in the artistic productions of the students of the Department of Art Education). In the products of students of the Department of Art Education).
The aim of the research was (discovering the aesthetics of abstract expressionism and its representations in the artistic products of the students of the Department of Art Education). As we

In this research we been estimated the survival function for data suffer from the disturbances and confusion of Iraq Household Socio-Economic Survey: IHSES II 2012 , to data from a five-year age groups follow the distribution of the Generalized Gamma: GG. It had been used two methods for the purposes of estimating and fitting which is the way the Principle of Maximizing Entropy: POME, and method of booting to nonparametric smoothing function for Kernel, to overcome the mathematical problems plaguing integrals contained in this distribution in particular of the integration of the incomplete gamma function, along with the use of traditional way in which is the Maximum Likelihood: ML. Where the comparison on the basis of the method of the Cen

Football has progressed from being a ritual and a celebration to become an amateur sport, a professional sport, and now, increasingly, a commercial sport. In the analysis of football business model, the systemic approach should be adopted. If sport is regarded as one of the business sectors, then the application of business system methodology can be fully justified. The interest to create strong football business system calls for the search of the ways of popularizing football business model and boosting the economic potential of its participants. In the research literature tend to ignore the business processes within the sports business. Besides, the systemic approach in football business is usually limited to p

Occupies total quality management applications play a key role in the development of institutions of higher education performance and achieve its strategic objectives through the commitment of senior management and their employees to continuous improvement of the quality of performance in the various areas of work, and can be integrated knowledge management processes, which means identifying information of value and how to take advantage. The data were collected using the style of the questionnaire for the purpose of analyzing their results on a sample composed of 83 member of the administrative leadership in colleges as representing the decision-making centers in those colleges . 

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Background: The ideal maxillofacial prosthesis should have fine and thin boundaries that bindwith the surrounding facial structures and possess high tear strength.This study aims to determinethe best percentages of nanofiller (TiO2) and intrinsic pigment (silicone functional intrinsic) thatcould be mixed in as additives to improve the tear strength of Cosmesil M511 andVST50F siliconeelastomers with the least effect on their hardness.Materials and Methods: In this in vitro experimental study, a total of 80 samples, 40 for eachelastomer, were fabricated. Each elastomer sample was split into two equal groups to test for tearstrength and Shore A hardness. Each group consisted of 20 samples, including 10 control sampleswithout additives and 10 e

In 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