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.

Braces in straight bridge systems improve the lateral-torsional buckling resistance of the girders by reducing the unbraced length, while in horizontally curved and skew bridges, the braces are primary structural elements for controlling deformations by engaging adjacent girders to act as a system to resist the potentially large forces and torques caused by the curved or skewed geometry of the bridge. The cross-frames are usually designed as torsional braces, which increase the overall strength and stiffness of the individual girders by creating a girder system that translates and rotates as a unit along the bracing lines. However, when they transmit the truck’s live load forces, they can produce fatigue cracks at their connection

In this research, the problem of multi- objective modal transport was formulated with mixed constraints to find the optimal solution. The foggy approach of the Multi-objective Transfer Model (MOTP) was applied. There are three objectives to reduce costs to the minimum cost of transportation, administrative cost and cost of the goods. The linear membership function, the Exponential membership function, and the Hyperbolic membership function. Where the proposed model was used in the General Company for the manufacture of grain to reduce the cost of transport to the minimum and to find the best plan to transfer the product according to the restrictions imposed on the model.

Background: The prevention of the enamel demineralization at the periphery of the brackets is a significant challenge to orthodontic professionals. The aim of this clinical study was to compare the Streptococcus mutants count in the plaque surrounding two orthodontic adhesive types, Fuji Ortho LC and Enlight (Ormco). Materials and methods: A total of 13 patients (7 male and 6 female) needing fixed orthodontic appliance therapy were participated. A split mouth technique was followed with appliances bonded by two orthodontic adhesive types, Fuji Ortho LC and Enlight (Ormco). Saliva was collected before placement of appliances (T0) and again at three weeks (T1) and six weeks (T2) after placement of appliances. Plaque was collected from areas a

This study was conducted to examine the discharge capacity of the reach of the Tigris River between Kut and Amarah Barrages of 250km in length. The examination includes simulation the current capacity of the reach by using HEC-RAS model. 247cross sections surveyed in 2012 were used in the simulation. The model was calibrated using observed discharges of 533, 800, 1025 and 3000m³/s discharged at Kut Barrage during 2013, 1995, 1995 and 1988, respectively, and its related water level at three gauge stations located along the reach. The result of calibration process indicated that the lowest Root Mean Square Error of 0.095 can be obtained when using Manning’s n coefficient of 0.026, 0.03 for th

Epoxy (EP) – Silica (SiO2) composites are well known composites used in microelectronic industry . So it is important to study their dielectric behavior under different conditions such as
the presence carbon black (UV absorber) and immersion in the water for 30 days .
Dielectric properties were calculated over the frequency range 102 – 106 Hz for epoxy composites with different weight % of micrometer 1.5μm SiO2 particles (60%, 65% and 70wt%) modified with 0.5wt% silane coupling agent to improve adhesion between EP and SiO2 phases .

Background: Understanding the morphological characteristics between the floor of the maxillary sinus and the tips of the maxillary posterior roots is crucial in orthodontics involving diagnosis and treatment planning. The aim of this study was to evaluate the distances from the maxillary posterior root apices to the inferior wall of the maxillary sinus, thickness and density of maxillary sinus floor using cone-beam computed tomography images and the relationships between roots and maxillary sinus according to gonial angle and skeletal pattern. Materials and methods: Three-dimensional images of each root were checked, and the distances were measured along the true vertical axis from the apex of the root to the sinus floor, and the thickne

This research aims to find how three different types of mouthwashes affect the depth of artificial white spot lesions. Teeth with various depths of white spot lesions were immersed in either splat mouthwash, Biorepair mouthwash, Sensodyne mouthwash, or artificial saliva (control)twice daily for one minute for 4 weeks and 8 weeks at 37°C. After this immersion procedure, lesion depth was measured using a diagnosed pen score. A one-way analysis of variance, Dunnett T3 and Tukey's post hoc α = .05 were used to analyze the testing data. Splat mouthwash enhanced the WSL remineralization and made the lowest ΔF compared with other mouthwashes in shallow and deep enamel after 4 and 8 weeks of treatment. In the repair groups, after 4 weeks

In this paper, Pentacene based-organic field effect transistors (OFETs) by using different layers (monolayer, bilayer and trilayer) for three different gate insulators (ZrO2, PVA and CYEPL) were studied its current–voltage (I-V) characteristics by using the gradual-channel approximation model. The device exhibits a typical output curve of a field-effect transistor (FET). Source-drain voltage (Vds) was also investigated to study the effects of gate dielectric on electrical performance for OFET. The effect of capacitancesemiconductor in performance OFETs was considered. The values of current and transconductance which calculated using MATLAB simulation. It exhibited a value of current increase with increasing source-drain voltage.