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 elements of theater formation that fall within the spatial experience of the scenography of the show, which the directors work in in the imaginary theater, are important and have an aesthetic, intellectual and cognitive dimension, working to highlight reality in an aesthetic image surrounding space and space. And its relationship to the distinct, multiple and variable spaces above the stage, to produce theatrical signals and endless meanings through the possibility of infinite reconfiguration of the theater's space and its public and private space through the distribution of a group of blocks within the scenic image.
I dealt with in the first chapter (the methodological framework), which includes the research problem identified

In this work, two different structures are proposed which is fuzzy real normed space (FRNS) and fuzzy real Pre-Hilbert space (FRPHS). The basic concept of fuzzy norm on a real linear space is first presented to construct  space, which is a FRNS with some modification of the definition introduced by G. Rano and T. Bag. The structure of fuzzy real Pre-Hilbert space (FRPHS) is then presented which is based on the structure of FRNS. Then, some of the properties and related concepts for the suggested space FRN such as -neighborhood, closure of the set  named , the necessary condition for separable, fuzzy linear manifold (FLM) are discussed. The definition for a fuzzy seminorm on  is also introduced with the prove that a fuzzy seminorm on

Blades of gas turbine are usually suffered from high thermal cyclic load which leads to crack initiated and then crack growth and finally failure. The high thermal cyclic load is usually coming from high temperature, high pressure, start-up, shut-down and load change. An experimental and numerical analysis was carried out on the real blade and model of blade to simulate the real condition in gas turbine. The pressure, temperature distribution, stress intensity factor and the thermal stress in model of blade have been investigated numerically using ANSYS V.17 software. The experimental works were carried out using a particular designed and manufactured rig to simulate the real condition that blade suffers from. A new cont

Background: Orthodontic therapy often causes external root resorption. Serum vitamin D (VD) level is important for tooth mineralization and bone remodeling. This study aimed to test the impact of vitamin D (VD) supplements on bone and root remodelling in a vitamin D (VD) deficient rat model following orthodontic retention. Methods and Material: 30 male Wistar rats were divided into three groups: a control group of 10 rats and two experimental groups of 10 rats each with vitamin D deficiency (VDD) induced by a VD-free diet for 21 days. And a third group with VD supplementAll groups received orthodontic active treatment using a modified orthodontic appliance that applied 50 gm of force for 14 days to move the maxillary right first mol

Storage of rainwater within the root depth zone is one of the modern ways to increase plant production. Subsurface water retention technology was applied to assess improving values of crop yield and crop water use efficiency, applying a membrane made of low-density polyethylene trough installed below the crop root zone. The goal of this paper is to assess that the retention of rainwater above the membrane can improve the crop yield and crop water use efficiency values for winter wheat. The experiment was conducted in open field, within Joeybeh Township, located in east of the Ramadi City, in Anbar Province, in winter growing season 2018-2019. Two plots T1 (with membrane trough) and T2 (without membrane) were used for the

ABSTRACT
Threw this research to the following:
1 - Know the impact of strategy Puglia in the collection of the rules of the Arabic language
students at the Institute of preparation parameters .
2 - Know the impact of the retention strategy in Puglia collection rules Arabic language
students at the Institute of preparation parameters .
To verify the status Mmermaa Find researcher Elsafreeten following two hypotheses :
1 - There is no statistically significant difference between the average score for the collection
of the fourth grade students at the Institute for the preparation of material parameters who
were studying grammar strategy Puglia and average grades collectible fourth grade
students at the Institu

Background: Fixed orthodontic appliances impede the maintenance of oral hygiene and result in plaque accumulation leads to enamel demineralization caused by acids produced by bacteria. Studies on plaque control strategies in orthodontic populations are limited. This might be caused by difficulties in the quantitative evaluation of dental plaque because the teeth have various levels of bracket coverage, and different tooth sizes and malocclusions, making the traditional categorical indices complex. The present study aims to evaluate the effect of different hygiene protocols on plaque quantity on bands with different attachments. Materials and method: Twenty patients had four bands within the orthodontic appliance. Then randomly divided into