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

Due to the continuing demand for larger bandwidth, the optical transport becoming general in the access network. Using optical fiber technologies, the communications infrastructure becomes powerful, providing very high speeds to transfer a high capacity of data. Existing telecommunications infrastructures is currently widely used Passive Optical Network that apply Wavelength Division Multiplexing (WDM) and is awaited to play an important role in the future Internet supporting a large diversity of services and next generation networks. This paper presents a design of WDM-PON network, the simulation and analysis of transmission parameters in the Optisystem 7.0 environment for bidirectional traffic. The sim

Purpose This study investigated periodontal ligament (PDL) restoration in osseointegrated implants using stem cells. Methods Commercial pure titanium and zirconium oxide (zirconia) were coated with beta-tricalcium phosphate (β-TCP) using a long-pulse Nd:YAG laser (1,064 nm). Isolated bone marrow mesenchymal cells (BMMSCs) from rabbit tibia and femur, isolated PDL stem cells (PDLSCs) from the lower right incisor, and co-cultured BMMSCs and PDLSCs were tested for periostin markers using an immunofluorescent assay. Implants with 3D-engineered tissue were implanted into the lower right central incisors after extraction from rabbits. Forty implants (Ti or zirconia) were subdivided according to the duration of implantation (healing period: 45 o

The new, standard molecular biologic system for duplicating DNA enzymatically devoid of employing a living organism, like E. coli or yeast, represents polymerases chain reaction (PCR). This technology allows an exponential intensification of a minor quantity of DNA molecule several times. Analysis can be straightforward with more DNA available. A thermal heat cycler performs a polymerization chain reaction that involves repeated cycles of heating and cooling the reactant tubes at the desired temperature for each reaction step. A heated deck is positioned on the upper reaction tube to avoid evaporating the reaction mixture (normally volumes range from 15 to 100 l per tube), or an oil layer can be placed on a reaction mixture su

This paper aims to propose a hybrid approach of two powerful methods, namely the differential transform and finite difference methods, to obtain the solution of the coupled Whitham-Broer-Kaup-Like equations which arises in shallow-water wave theory. The capability of the method to such problems is verified by taking different parameters and initial conditions. The numerical simulations are depicted in 2D and 3D graphs. It is shown that the used approach returns accurate solutions for this type of problems in comparison with the analytic ones.

The concept of deficit in public budget becomes a chronic economic phenomenon in most of the world, whether the advanced countries or developing countries. Despite  the difference in the visions of the economic schools to accept or reject the deficit in public budget but the opinion that prevailed is the necessity of the state to reduce the public spending which led to a continuous deficits in the public budget which consequently increased the government borrowing ,increase income taxes and wealth, consequently this weakened the in motivation in private investment which contributed to the increase of in factionary stagnation , so that governments have to cover the lack of local funding sources which become difficult to be eq

Al-Huweizah Marsh is considered as the largest in Iraq. This research aims to maintain thesustainability of Al-Huweizah Marsh under all circumstances and within the limits of the
available natural resources from the Iraqi side and the absence of feeding from the Iranian sidedue to the recent Iranian separation dike along the international boundaries within the marsh.
Twelve scenarios have been suggested as a first step to restore the whole marsh. But the
uncontrolled Iranian feeders and exiguity of their discharges recently, it was necessary to studyonly the northern part of the marsh as an alternative case to ensure reasonable amounts of waterfor the purpose of maintaining and restore the marsh. Hydrological routing model was