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

New N2O2 donor kind Schiff basehas been destined and structured by reaction Ampyrone with O-hydroxyacetophenone and Anthranilic acid. The metal complexes of the Schiff base with Mn(II), Hg(II), Ni(II), Cu(II), and Co(II) metal ions were designed and characterized by magnetic susceptibility, elemental analyses, molar conduction, IR, and 1H NMR,UV-Vis spectral metrics.The UV-Vis. and magnetic susceptibility data of the complexes suggest a square-planar, tetrahedraland octahedral geometries around the central metal ions. All elaborations were accomplished after determination the optimum molar concentration and pH which followed law of Lambert-Beer's in the researches pH scopes. The composition of these complexes were conclude dapprobating to t

It was known that every left (?,?) -derivation is a Jordan left (?,?) – derivation on ?-prime rings but the converse need not be true. In this paper we give conditions to the converse to be true.

To evaluate the bioactivity and the cytocompatibility of experimental Bioglass-reinforced polyethylene-based root-canal filling materials. The thermal properties of the experimental materials were also evaluated using differential scanning calorimetry, while their radiopacity was assessed using a grey-scale value (GSV) aluminium step wedge and a phosphor plate digital system. Bioglass 45S5 (BAG), polyethylene and Strontium oxide (SrO) were used to create tailored composite fibres. The filler distribution within the composites was assessed using SEM, while their bioactivity was evaluated through infrared spectroscopy (FTIR) after storage in simulated body fluid (SBF). The radiopacity of the composite fibres and their thermal properties were

Abstract: This study aims to investigate the effects of solvents of various polarities on the electronic absorption and fluorescence spectra of RhB and Rh6G. The singlet‐state excited dipole moments (me) and ground state dipole moments (mg) were estimated from the equations of Bakshiev -Kawski and Chamma‐ Viallet using the variation of Stokes shift along with the solvent’s dielectric constant (e) and refractive indexes (n). The observed singlet‐state excited dipole moments were found to be larger than the ground‐state ones. Moreover, the obtained fluorescence quantum yield values were influenced by the environment of the fluorescing molecule. Consequently, the concentration of the dye solution, excited singlet state absorption and

This work is devoted to study the properties of the ground states such as the root-mean square ( ) proton, charge, neutron and matter radii, nuclear density distributions and elastic electron scattering charge form factors for Carbon Isotopes (9C, 12C, 13C, 15C, 16C, 17C, 19C and 22C). The calculations are based on two approaches; the first is by applying the transformed harmonic-oscillator (THO) wavefunctions in local scale transformation (LST) to all nuclear subshells for only 9C, 12C, 13C and 22C. In the second approach, the 9C, 15C, 16C, 17C and 19C isotopes are studied by dividing the whole nuclear system into two parts; the first is the compact core part and the second is the halo part. The core and halo parts are studied using the

Both traditional and novel techniques were employed in this work for magnetic shielding evaluation to shed new light on the magnetic and aromaticity properties of benzene and 12 [n]paracyclophanes with n = 3–14. Density functional theory (DFT) with the B3LYP functional and all-electron Jorge-ATZP and x2c-TZVPPall-s basis sets was utilized for geometry optimization and magnetic shielding calculations, respectively. Additionally, the 6-311+G(d,p) basis set was incorporated for the purpose of comparing the magnetic shielding results. In addition to traditional evaluations such as NICS/NICSzz-Scan, and 2D-3D σiso(r)/σzz(r) maps, two new techniques were implemented: bendable grids (BGs) and cylindrical grids (CGs) of ghost atoms (Bqs). BGs a

In this paper, Bayes estimators of the parameter of Maxwell distribution have been derived along with maximum likelihood estimator. The non-informative priors; Jeffreys and the extension of Jeffreys prior information has been considered under two different loss functions, the squared error loss function and the modified squared error loss function for comparison purpose. A simulation study has been developed in order to gain an insight into the performance on small, moderate and large samples. The performance of these estimators has been explored numerically under different conditions. The efficiency for the estimators was compared according to the mean square error MSE. The results of comparison by MSE show that the efficiency of Bayes est

In this paper, a least squares group finite element method for solving coupled Burgers' problem in   2-D is presented. A fully discrete formulation of least squares finite element method is analyzed, the backward-Euler scheme for the time variable is considered, the discretization with respect to space variable is applied as biquadratic quadrangular elements with nine nodes for each element. The continuity, ellipticity, stability condition and error estimate of least squares group finite element method are proved.  The theoretical results  show that the error estimate of this method is . The numerical results are compared with the exact solution and other available literature when the convection-dominated case to illustrate the effic

In this work, a numerical study is performed to predict the solution of two – dimensional, steady and laminar mixed convection flow over a square cylinder placed symmetrically in a vertical parallel plate. A finite difference method is employed to solve the governing differential equations, continuity, momentum, and energy equation balances. The solution is obtained for stream function, vorticity and temperature as dependent variables by iterative technique known as successive over relaxation. The flow and temperature patterns are obtained for Reynolds number and Grashof number at (Re= -50,50,100,-100) (positive or negative value refers to aidding or opposing buoyancy , +1 assisting flow, -1 opposing flow) and (102 to 105) , respective