A graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense related. The objects correspond to mathematical abstractions called vertices (also called nodes or points) and each of the related pairs of vertices is called an edge (also called link or line). A directed graph is a graph in which edges have orientation. A simple graph is a graph that does not have more than one edge between any two vertices and no edge starts and ends at the same vertex.  For a simple undirected graph G with order n, and let  denotes its complement. Let δ(G), ∆(G) denotes the minimum degree and maximum degree of G respectively. The complement degree polynomial of G is the polynomial CD[G,x]= , where C

Adsorption studies were carried out to test the ability of the Iraqi rice bran (Amber type) to adsorb some metals divalent cations (Cd2+, Co2+, Cu2+, Fe2+, Ni2+, Pb2+, and Zn2+) as an alternative tool to remove these pollutants from water. The Concentrations of these ions in water were measured using flame and flamless atomic absorption spectrophotometry techniques. The applicability of the adsorption isotherm on Langmuir or Freundlisch equation were tested and found to be dependent on the type of ions. The results showed different adsorptive behavior and different capacities of the adsorption of the ions on the surface of the bran. The correlation between the amounts adsorbed and different cation parameters including (electronegativity, io

The performance of asphalt pavements is crucial due to heavy traffic loads from civil and industrial developments. Various additives and modifiers are used in flexible roads to improve their resistance to deterioration caused by climatic changes. From this context, modifying the asphalt binder with polymers is popular in asphalt pavement construction. The present research investigates the effect of Polyethylene (PE) polymers in powder form on the characteristics of asphalt mixtures since these polymers are composed of hydrocarbons. It is similar to asphalt binders, making them very effective in enhancing the performance of neat asphalt produced from the oil refinery. To confirm this, two types of PE, High-Density PE (HDPE) and Low-Density P

Two homopolymeric and three copolymeric additives for base oil were synthesized using octyl acrylate (OA) and tert-butyl acrylamide (TBA) monomers. The two additives named P1 and P2 are the homopolymers of TBA and OA, respectively, whereas copolymeric additives named Co1, Co2, and Co3 were synthesized by varying the ratios of TBA:OA as 1:3, 3:1 and 1:1, respectively. The prepared polymers were characterized by Fourier Transform Infrared (FTIR). Based on the solubility of synthesized polymers in base oil and reactivity ratios of TBA/OA copolymer (0.222, 0.434) calculated by Fineman-Ross method, P2, Co1, Co2 and Co3 were selected to evaluate their performance as pour point depressant (PPD), viscosity improver (VII), and anticorrosion addit

In this paper Hermite interpolation method is used for solving linear and non-linear second order singular multi point boundary value problems with nonlocal condition. The approximate solution is found in the form of a rapidly convergent polynomial. We discuss behavior of the solution in the neighborhood of the singularity point which appears to perform satisfactorily for singular problems. The examples to demonstrate the applicability and efficiency of the method have been given.

We demonstrate a behavior of laser pulse grows through fiber laser inside and output cavity with a soliton fiber laser based on the multi-wall carbon nanotube saturable absorber (SA), we investigate the effects of a saturable absorber parameter on the mode-locking of a realistic Erbium fiber ring laser. Generalized nonlinear Schrodinger equation including the nonlinear effects as gain dispersion, second anomalous group velocity dispersion (GVD), self phase modulation (SPM), and two photon absorption used to describe pulse evolution. An analytical method has been used to understand and to quantify the role of the SA parameter on the propagation dynamics of pulse laser. We compute the chirp, power, width and phase of the soliton for range

The aim of this research is to employ starch as a stabilizing and reducing agent in the production of CdS nanoparticles with less environmental risk, easy scaling, stability, economical feasibility, and suitability for large-scale production. Nanoparticles of CdS have been successfully produced by employing starch as a reducing agent in a simple green synthesis technique and then doped with Sn in certain proportions (1%, 2%, 3%, 4%, and 5%).According to the XRD data, the samples were crystallized in a hexagonal pattern, because the average crystal size of pure CdS is 5.6nm and fluctuates in response to the changes in doping concentration 1, 2, 3, 4, 5 %wt Sn, to become   4.8, 3.9, 11.5, 13.1, 9.3 nm respectively. An increase in crystal

In this work, nanostructure zinc sulfide (ZnS) thin films at temperature of substrate 450 oC and thickness (120) nm have been produced by chemical spray pyrolysis method. The X-Ray Diffraction (XRD) measurements of the film showed that they have a polycrystalline structure and possessed a hexagonal phase with strong crystalline orientation of (103). The grain size was measured using scanning electron microscope (SEM) which was approximately equal to 80 nm. The linear optical measurements showed that ZnS nanostructure has direct energy gap. Nonlinear optical properties experiments were performed using Q-switched 532 nm Nd:YAG laser Z-scan system. The nonlinear refractive index (n2) and nonlinear absorption coefficient (β) estimated for Z

This research include synthesized and characterization the compound [I] by reaction terephthaldehyde , mercaptoacetic acid and thiosemicarbazide with concentrated sulfuric acid then this compound reaction with ethyl chloroacetate and sodium acetate to product ester compound [II],the latter compound reaction with hydrazine hydrate to synthesized acid hydrazide [III] after that reaction with 4-alkoxy benzaldehyde[IV]n to synthesized Schiff bases compounds [V]n, the compound [VI] synthesized via reaction compound [I] with chloroacetic acid and sodium acetate then the compound[VI] reaction with 2-phenylenediamine in 4 N hydrochloric acid to product benzimidazole compound[VII]. The compounds characterized by melting points, FTIR and 1HNMR spectr