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.

We propose a novel strategy to optimize the test suite required for testing both hardware and software in a production line. Here, the strategy is based on two processes: Quality Signing Process and Quality Verification Process, respectively. Unlike earlier work, the proposed strategy is based on integration of black box and white box techniques in order to derive an optimum test suite during the Quality Signing Process. In this case, the generated optimal test suite significantly improves the Quality Verification Process. Considering both processes, the novelty of the proposed strategy is the fact that the optimization and reduction of test suite is performed by selecting only mutant killing test cases from cumulating t-way test ca

The largest use of x-ray in medical by dentists, employers or persons that needed by patients with specific conditions, lead to higher exposure of x-ray that may cause many diseases. In the present work radiography films have been used in evaluating the efficiency of using unsaturated polyester polymer reinforced with lead oxide (PbO) as shield material for medical x-ray devices, many parameters studied like concentration and thickness that they are increasing the attenuation of x-ray in them. The results show that the attenuation of X-ray increasing with concentration of reinforced material and with thickness, and the optical density decreases with increasing concentration from 0% to 50%, we chose 30% as suitable concentration to increase

Oil recovery could be impacted by the relation between vertical permeability (K_v) and horizontal permeability (K_h) (K_v/K_h). 4816 plugs that have been getting hold of 18 wells of Mishrif formation in the West Qurna oilfield were used. K_v/K_h data provided some scatter, but the mean is ~1. K_v/K_h =1 was used for the Petrel model before upscaling according to the heterogeneity of each layer.

K_v/K_h values for Mishrif Formation in West Qurna Oilfield are 0.8 for relatively homogeneous, 0.4 for heterogeneous rock, and 0.1 for cap rocks (CRII).

   Eclipse ^TM was used for reservoir simulation. PVT and SCAL data e

The study of the validity and probability of failure in solids and structures is highly considered as one of the most incredibly-highlighted study fields in many science and engineering applications, the design analysts must therefore seek to investigate the points where the failing strains may be occurred, the probabilities of which these strains can cause the existing cracks to propagate through the fractured medium considered, and thereafter the solutions by which the analysts can adopt the approachable techniques to reduce/arrest these propagating cracks.In the present study a theoretical investigation upon simply-supported thin plates having surface cracks within their structure is to be accomplished, and the applied impact load to the

 This research aims at forecasting the public budget of Iraq (surplus or deficit) for 2017 & 2018 through using two methods to forecast. First: forecast budget surplus or deficit by using IMF estimations average oil price per barrel adopted in the public federal budget amounted to USD 44 in 2017 & USD 46 in 2018; Second: forecast budget surplus or deficit by using MOO actual average oil price in global markets amounted to USD 66 in 2018 through applying Dynamic Model & Static Model. Then analyze the models to reach the best one. The research concluded that those estimations of dynamic forecasting model of budget surplus or deficit for 2017 & 2018 gives good reliable results for future periods when using the a

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