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.

The Planning and Resource Development Department of the Iraqi Ministry of Health is very interested in improving medical care, health education, and village training programs. Accordingly, and through the available capabilities of the ministry, itdesires to allocate seven health centers to four villages in Baghdad, Iraq therefore the ministry needs to determine the number of health centers allocated to each of these villages which achieves the greatest degree of the overall effectiveness of the seven health centers in a fuzzy environment. The objective of this study is to use a fuzzy dynamic programming(DP) method to determine the optimal allocation of these centers, which allows the greatest overall effectiveness of these health centers

Radiation therapy plays an important role in improving breast cancer cases, in order to obtain an appropriateestimate of radiation doses number given to the patient after tumor removal; some methods of nonparametric regression werecompared. The Kernel method was used by Nadaraya-Watson estimator to find the estimation regression function forsmoothing data based on the smoothing parameter h according to the Normal scale method (NSM), Least Squared CrossValidation method (LSCV) and Golden Rate Method (GRM). These methods were compared by simulation for samples ofthree sizes, the method (NSM) proved to be the best according to average of Mean Squares Error criterion and the method(LSCV) proved to be the best according to Average of Mean Absolu

Over the years, the issue of inclusion of students with special educational needs (SEN) in mainstream schools is controversial worldwide. Evidence from research argues that without a positive teachers’ attitude towards the inclusion of students with SEN in mainstream schools, the successful implementation of inclusion is most likely doubtable. The aim of this paper is to understand teachers’ attitudes towards the inclusion of students with SEN in mainstream schools from different perspectives and from different contexts. The conclusion drawn in this review can be that teachers’ attitude is the most important key towards the appropriate inclusion implementation in mainstream schools. The disparity of teachers’ attitudes towards th

In this paper, we define some generalizations of topological group namely -topological group, -topological group and -topological group with illustrative examples. Also, we define grill topological group with respect to a grill. Later, we deliberate the quotient on generalizations of topological group in particular -topological group. Moreover, we model a robotic system which relays on the quotient of -topological group.

This research aims to improve the radiation shielding properties of polymer-based materials by mixing PVC with locally available building materials. Specifically, two key parameters of fast neutron attenuation (removal cross-section and half-value layer) were studied for composite materials comprising PVC reinforced with common building materials (cement, sand, gypsum and marble) in different proportions (10%, 30% and 50% by weight). To assess their effectiveness as protection against fast neutrons, the macroscopic neutron cross-section was calculated for each composite. Results show that neutron cross-section values are significantly affected by the reinforcement ratios, and that the composite material PVC + 50% gypsum is an effect

Purpose This study was design to investigate of Purpose This study was design to investigate of P. aeruginosa, an example of Gram-negative bacteria, in seven primary and secondary schools of Baghdad city, and the effects of Ethanol and Dettol of P. aeruginosa biofilm. Design/methodology/approach Seventy swabs were collected from seven primary and secondary schools of Baghdad city, Iraq, during November -December 2022. Swabs were collected from classes desk, doors handles, students hands and water taps. Standard microbiological testing methods were used on the samples for isolation and identification. The ability of bacteria to form biofilm and the effects of Ethanol and Dettol on “preformed” biofilms was examined by microtiter plate wi

E-learning is a lifeline for the educational process, which contributed to the sustainability of working educational organizations and prevented them from stopping, so the study came to measure the compatibility between E-learning quality dimensions (information technology, educational curricula, teaching methods, and intellectual capital of educational institution) as an independent variable, and educational services quality dimensions represented by (safety, tangibility, reliability and Confidence) as a dependent variable. The sample was 150 teachers was drawn from the College of Administration and Economics community of 293 teachers through the use of several statistical methods to measure the degree of correlation and impact between the