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.

Abstract

This study aims at clarifying the current performance appraisal system in government units and the extent to which they contribute to the development of the performance of these units by evaluating and measuring the performance of these units on an ongoing basis to subject their services to an assessment and measurement process in order to improve the efficiency of these units to reach their objectives efficiently and effectively. (Iraqi hospitals) by trying to determine the possibility of the government accounting system in the process of evaluating performance, through the comparison of financial performance for successive years and different hospitals using the financial and non-financial model of the evaluati

Diabetes mellitus is a common health problem worldwide counting about 1.2 million cases in Iraq in 2015. Taking in account of the patient’s beliefs about the prescribed medication had been reported to be one of the most important factors that affects adherence where holding positive beliefs about medications is a prerequisite for intentional adherence. The aim of the current study was to investigate and assess beliefs about medicines among type 2 diabetic patients and to determine possible association between this belief and glycemic control as well as some patient-specific factors. This study is a cross-sectional study carried out on 380 (mean age 56.58± 10.06 years) already diagnosed T2DM patients who attended the National Diabetes

Quantum key distribution (QKD) provides unconditional security in theory. However, practical QKD systems face challenges in maximizing the secure key rate and extending transmission distances. In this paper, we introduce a comparative study of the BB84 protocol using coincidence detection with two different quantum channels: a free space and underwater quantum channels. A simulated seawater was used as an example for underwater quantum channel. Different single photon detection modules were used on Bob’s side to capture the coincidence counts. Results showed that increasing the mean photon number generally leads to a higher rate of coincidence detection and therefore higher possibility of increasing the secure key rate. The secure key rat

Among several separation processes, the air flotation distinguish as remarkably high potential separation process related to its high separation efficiency and throughput, energy-efficient, simple process, cost-effective, applicable to a wide range of oily wastewater and no by-products. The current study aimed to investigate the effect of the type and concentration of surfactant on the stability of oil-water emulsion and efficiency of the separation process. For this purpose, three types of surfactant where used (anionic SDS, mixed nonionic Span 85/Tween 80, and cationic CTAB). The results demonstrated that the Span 85/Tween 80 surfactant has the best stability, and it increases with the surfactant concentration augmentation. The removal ef

Diverting river flow during construction of a main dam involves the construction of cofferdams, and tunnels, channels or other temporary passages. Diversion channels are commonly used in wide valleys where the high flow makes tunnels or culverts uneconomic. The diversion works must form part of the overall project design since it will have a major impact on its cost, as well as on the design, construction program and overall cost of the permanent works. Construction costs contain of excavation, lining of the channel, and construction of upstream and downstream cofferdams. The optimization model was applied to obtain optimalchannel cross section, height of upstream cofferdam, and height of downstream cofferdamwith minimum construction cost

A twisted-fin array as an innovative structure for intensifying the charging response of a phase-change material (PCM) within a shell-and-tube storage system is introduced in this work. A three-dimensional model describing the thermal management with charging phase change process in PCM was developed and numerically analyzed by the enthalpy-porosity method using commercial CFD software. Efficacy of the proposed structure of fins for performing better heat communication between the active heating surface and the adjacent layers of PCM was verified via comparing with conventional longitudinal fins within the same design limitations of fin material and volume usage. Optimization of the fin geometric parameters including the pitch, numb

Background: Diabetes mellitus is a chronic metabolic disorder of the carbohydrate, protein and fat metabolism, resulting in increased blood glucose levels. Various complications of diabetes have been described with periodontitis being added as the sixth complication of diabetes mellitus. Matrix metalloproteinase-8 (MMP-8) has been identified as major tissue-destructive enzyme in periodontal disease. MMP-8 is released from neutrophils in a latent, inactive pro form and becomes activated during periodontal inflammation by independent and/or combined actions of host-derived inflammatory mediators .C-reactive protein is a systemic marker released during the acute phase of an inflammatory response. Subjects, materials and methods: Total samples

There are many varied studies that dealt with the dramatic construction, especially books and studies that addressed drama in its construction and the method of writing it, that no textbook or a general cultural content is void of tackling the dramatic text in its construction and how the dramatic action develops in it. Therefore, a question occurs to the mind about the feasibility of dealing with the dramatic construction in this time, where many contemporary studies of dramatology and its relation and the contemporary critical directions are accumulating. This question many have two realistic aspects, yet the novelty and originality that this research shows lie in addressing a refined linguistic text in its style and connotations, such