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.

This research includes the synthesis of some new different heterocyclic derivatives of 5-Bromoisatin. New sulfonylamide, diazine, oxazole, thiazole and 1,2,3-triazole derivatives of 5-Bromoisatin have been synthesized. The synthesis process started by the reaction of 5-Bromoisatin with different reagents to obtain schiff bases of 5-Bromoisatin intermediate compounds(1, 8, 19) by using glacial acetic acid as a catalyst in three routes. The first route, 5-Bromoisatin reacted with p-aminosulfonylchloride to product compound(1), then converted to sulfonyl amide derivatives(2-7) by the reaction of compound(1) with different substituted primary aromatic amine in absolute ethanol. The second route includes the reaction of 5-Bromoisatin rea

The current research aims to :
•know the level of the chaotic behavior of the sample as a whole .
•Know the differences with statistical significance in disorderly behavior between the
disadvantaged and non-disadvantaged peers .
To achieve these objectives, the selected sample of Talbhalmrahlh medium and specifically
students of the second grade average, were chosen randomly stratified's (360) students
included sex (male, female) and (deprived of the Father and the non-deprived) for the
academic year (2013-2014) to the province Baghdad on both sides (Rusafa-Karkh (
As applied to them measurements of disorderly behavior, which is prepared by the researcher,
having achieved _khasaúsma of psychometric (valid

In all process industries, the process variables like flow, pressure, level, concentration
and temperature are the main parameters that need to be controlled in both set point
and load changes.
A control system of propylene glycol production in a non isothermal (CSTR) was
developed in this work where the dynamic and control system based on basic mass
and energy balance were carried out.
Inlet concentration and temperature are the two disturbances, while the inlet
volumetric flow rate and the coolant temperature are the two manipulations. The
objective is to maintain constant temperature and concentration within the CSTR.
A dynamic model for non isothermal CSTR is described by a first order plus dead
time (FO

Sulfamethoxazole (SMX) is the most significant antibiotic in the sulfonamide family. It was chosen as the representative of this category because of its widespread use. Starting with sulfamethoxazole, a new series of 2-Azetidinone (M1-M6) was synthesized, the structure of these new derivatives was confirmed using spectral methods, starting with the synthesis of Schiff’s bases by reflux of different aromatic benzaldehydes, separately, with Sulfamethoxazole in ethanol with few drops of acetic acid. The final compounds were obtained by ketene-imine synthesis of β-lactam using chloroacetyl chloride. The designed chemicals’ synthesis has been completed successfully. Physical parameters (melting points and Rf values), Fourier transfo

In this paper, third order non-polynomial spline function is used to solve 2nd kind Volterra integral equations. Numerical examples are presented to illustrate the applications of this method, and to compare the computed results with other known methods.

Background: Optimal root canal retreatment was required safe and efficient removal of filling material from root canal. The aim of this in vitro study was to compare the efficacy of reciprocating and continuous motion of four retreatment systems in removal of root canal filling material. Materials and Methods: Forty distal roots of the mandibular first molars teeth were used in this study, these roots were embedded in cold clear acrylic,roots were instrumented using crown down technique and rotary ProTaper systemize Sx to size F2 ,instrumentation were done with copiousirrigation of 2.5% sodium hypochlorite and 17% buffered solution of EDTA was used as final irrigant followed by distilledwater, roots were obturated with AH26 sealer and Prota

Background: Optimal root canal retreatment was required safe and efficient removal of filling material from root canal. The aim of this in vitro study was to compare the efficacy of reciprocating and continuous motion of four retreatment systems in removal of root canal filling material. Materials and Methods: Forty distal roots of the mandibular first molars teeth were used in this study, these roots were embedded in cold clear acrylic,roots were instrumented using crown down technique and rotary ProTaper systemize Sx to size F2 ,instrumentation were done with copiousirrigation of 2.5% sodium hypochlorite and 17% buffered solution of EDTA was used as final irrigant followed by distilledwater, roots were obturated with AH26 sealer and Prota