In a connected graph , the distance function between each pair of two vertices from a set vertex  is the shortest distance between them and the vertex degree  denoted by  is the number of edges which are incident to the vertex  The Schultz and modified Schultz polynomials of  are have defined as:

 respectively, where the summations are taken over all unordered pairs of distinct vertices in  and  is the distance between  and  in  The general forms of Schultz and modified Schultz polynomials shall be found and indices of the edge – identification chain and ring – square graphs in the present work.

In order to improve the students’ performance level in some of the skills that are implemented on the mat device of ground movements, including the front and rear rolling, it is necessary to study the most important indicators that have a clear impact on the performance of those rolls. Among the objectives of the research: To identify the percentage of the contribution of flexibility of the hip joint, the angle of the knees and the muscular strength of the arms in the performance of the front and rear rolling skills, an opening of the research sample. The researchers used the descriptive method in the survey method for its suitability to the nature of the work, and the research community was represented by students of the third st

Background: The main aim of the present study is to qualify and quantify voids formation of root canals obturated with GuttaCore (GC) and experimental Hydroxyapatite polyethylene (HA/PE) as new carrier-based root canal fillings by using micro computed tomography scan. Materials and methods: In the present study, eight straight single-rooted human permanent premolar teeth are selected and disinfected, then stored in distilled water. The teeth decoronated leaving a root length of 12mm each. The root canals instrumented by using crown down technique and the apical diameter of the root canal prepared to a size # 30/0.04 for achieving standardized measurements. A 5mL of 17% EDTA used to remove the smear layer followed by 5mL of 2.5% NaOCl and r

The present study aims to investigate the various request constructions used in Classical Arabic and Modern Arabic language by identifying the differences in their usage in these two different genres. Also, the study attempts to trace the cases of felicitous and infelicitous requests in the Arabic language. Methodologically, the current study employs a web-based corpus tool (Sketch Engine) to analyze different corpora: the first one is Classical Arabic, represented by King Saud University Corpus of Classical Arabic, while the second is The Arabic Web Corpus “arTenTen” representing Modern Arabic. To do so, the study relies on felicity conditions to qualitatively interpret the quantitative data, i.e., following a mixed mode method

Multi-walled carbon nanotubes (MWCNTs) were functionalized by hexylamine (HA) in a promising, cost-effective, rapid and microwave-assisted approach. In order to decrease defects and remove acid-treatment stage, functionalization of MWCNTs with HA was carried out in the presence of diazonium reaction. Surface functionality groups and morphology of chemically-functionalized MWCNTS were characterized by FTIR, Raman spectroscopy, thermogravimetric analysis (DTG), and transmission electron microscopy (TEM). To reach a promising dispersibility in oil media, MWCNTs were functionalized with HA. While the cylindrical structures of MWCNTs were remained reasonably intact, characterization results consistently confirmed the sidewall-functionalization o

A Strength Pareto Evolutionary Algorithm 2 (SPEA 2) approach for solving the multi-objective Environmental / Economic Power Dispatch (EEPD) problem is presented in this paper. In the past fuel cost consumption minimization was the aim (a single objective function) of economic power dispatch problem. Since the clean air act amendments have been applied to reduce SO2 and NOX emissions from power plants, the utilities change their strategies in order to reduce pollution and atmospheric emission as well, adding emission minimization as other objective function made economic power dispatch (EPD) a multi-objective problem having conflicting objectives. SPEA2 is the improved version of SPEA with better fitness assignment, density estimation, an