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

The toughening of epoxy resins with the addition of organic or inorganic compounds is of great interest nowadays, considering their large scale of applications. In the present work, composites of epoxy are synthesized with kaolin particles having different particle sizes as reinforcement. Composites of epoxy with varying concentration (0 to 40 weight %) of kaolin was prepared by using hand lay method. The variation of mechanical properties such as modulus of elasticity, yield, tensile, and compressive strength with filler content was evaluated. The composite showed improved modulus of elasticity and compressive properties on addition of filler. In contrast, the tensile and yield strength of the composite

Background: Chronic hyperplastic candidiasis is the least common type of oral candidiasis. The diagnosis, long-term treatment, and prognosis of this potentially malignant oral condition are still currently unclear. Objective: the aim of this study is to analyze the demographic features and clinical characteristics of oral chronic hyperplastic candidiasis. Materials and Methods: A retrospective analysis was performed on blocks and case sheets of patients who were diagnosed with chronic hyperplastic candidiasis in the archives of Oral and Maxillofacial Pathology at the College of Dentistry/University of Baghdad. Demographic and clinical characteristics were analyzed. Results: twenty-one cases with chronic hyperplastic candidiasis were coll

Reinforcing asphalt concrete with polyester fibers considered as an active remedy to alleviate the harmful impact of fatigue deterioration. This study covers the investigation of utilizing two shapes of fibers size, 6.35 mm by 3.00 mm and 12.70 mm by 3.00 mm with mutual concentrations equal to 0.25 %, 0.50 % and 0.75 % by weight of mixture. Composition of asphalt mixture consists of different optimum (40-50) asphalt cement content, 12.50 mm nominal aggregate maximum size with limestone dust as a filler. Following the traditional asphalt cement and aggregate tests, three essential test were carried out on mixtures, namely: Marshall test (105 cylindrical specimens), indirect tensile strength test (21 cylindrical specimens)

Concerns about the environment, the cost of energy, and safety mean that low-energy cold-mix asphalt materials are very interesting as a potential replacement for present-day hot mix asphalt. The main disadvantage of cold bituminous emulsion mixtures is their poor early life strength, meaning they require a long time to achieve mature strength. This research work aims to study the protentional utilization of waste and by-product materials as a filler in cold emulsion mixtures with mechanical properties comparable to those of traditional hot mix asphalt. Accordingly, cold mix asphalt was prepared to utilize paper sludge ash (PSA) and cement kiln dust (CKD) as a substitution for conventional mineral filler with percentages ranging fro

Rutting has a significant impact on the pavements' performance. Rutting depth is often used as a parameter to assess the quality of pavements. The Asphalt Institute (AI) design method prescribes a maximum allowable rutting depth of 13mm, whereas the AASHTO design method stipulates a critical serviceability index of 2.5 which is equivalent to an average rutting depth of 15mm. In this research, static and repeated compression tests were performed to evaluate the permanent strain based on (1) the relationship between mix properties (asphalt content and type), and (2) testing temperature. The results indicated that the accumulated plastic strain was higher during the repeated load test than that during the static load tests. Notably, temperatur

Nanocomposite was prepared using unsaturated polyester (UP) resin as a matrix and graphene nanoparticles as a reinforcement material in six percentage weights (0, 0.1, 0.2, 0.3, 1 and 1.5%). Mechanical, calorimetric and thermal studies were performed on the (UP) resin/graphene nanocomposite. All tests showed a clear improvement of all mechanical properties examined (hardness, flexural strength (F.S), impact strength (I.S) and tensile strength (T.S)) with increasing graphene percentage. In addition, the temperature of glass transition and thermal conductivity of this composite increased with increasing graphene content.