In this paper, the density of state (DOS) at Fe metal contact to Titanium dioxide semiconductor (TiO2) has been studied and investigated using quantum consideration approaches. The study and calculations of (DOS) depended on the orientation and driving energies. was a function of TiO2 and Fe materials' refractive index and dielectric constant. Attention has focused on the effect of on the characteristic of (DOS), which increased with the increasing of refractive index and dielectric constant of Fe metal and vice versa. The results of (DOS) and its relation with and values of system have been discussed. As for contact system is increased, (DOS) values increased at first, but the relation is disturbed later and transforms into an inve

This paper is concerned with the numerical solutions of the vorticity transport equation (VTE) in two-dimensional space with homogenous Dirichlet boundary conditions. Namely, for this problem, the Crank-Nicolson finite difference equation is derived.  In addition, the consistency and stability of the Crank-Nicolson method are studied. Moreover, a numerical experiment is considered to study the convergence of the Crank-Nicolson scheme and to visualize the discrete graphs for the vorticity and stream functions. The analytical result shows that the proposed scheme is consistent, whereas the numerical results show that the solutions are stable with small space-steps and at any time levels.

In this study, a new technique is considered for solving linear fractional Volterra-Fredholm integro-differential equations (LFVFIDE's) with fractional derivative qualified in the Caputo sense. The method is established in three types of Lagrange polynomials (LP’s), Original Lagrange polynomial (OLP), Barycentric Lagrange polynomial (BLP), and Modified Lagrange polynomial (MLP). General Algorithm is suggested and examples are included to get the best effectiveness, and implementation of these types. Also, as special case fractional differential equation is taken to evaluate the validity of the proposed method. Finally, a comparison between the proposed method and other methods are taken to present the effectiveness of the proposal meth

I've made extensive studies on the distribution of the electric field stable heterogeneous within intensive that contain metal rings with slope diagonal positive to a site halfway to be in its maximum value, followed by decline negative and equally to the other end of the concentrated distributed by electric stable thanking sequentially and have focused empirical studies in the pastthe molecules that you focused Pantqaúha during passage

To obtain the approximate solution to Riccati matrix differential equations, a new variational iteration approach was ‎proposed, which is suggested to improve the accuracy and increase the convergence rate of the approximate solutons to the ‎exact solution. This technique was found to give very accurate results in a few number of iterations. In this paper, the ‎modified approaches were derived to give modified solutions of proposed and used and the convergence analysis to the exact ‎solution of the derived sequence of approximate solutions is also stated and proved. Two examples were also solved, which ‎shows the reliability and applicability of the proposed approach. ‎

This paper aims to study the biosorption for removal of lead, cadmium, copper and arsenic ions using algae as a biosorbent. A series of experiments were carried out to obtain the breakthrough data in a fluidized bed reactor. The minimum fluidization velocities of beds were found to be 2.27 and 3.64 mm/s for mish sizes of 0.4-0.6 and 0.6-1 mm diameters, respectively. An ideal plug flow model has been adopted to characterize the fluidized bed reactor. This model has been solved numerically using MATLAB version 6.5. The results showed a well fitting with the experimental data. Different operating conditions were varied: static bed height, superficial velocity and particle diameter. The breakthrough curves were plotted for each metal. Pb2+ s

The aim of this research is to benefit from recycl the aircraft waste oils which is discarded in sewage network, to be used in preparation of greases for industrial purposes and to reduce the environmental pollution. In this research synthetic greases were prepared with special specifications by mixing the waste oils after treating with (silica gel as adsorbent agent, and filtration to precipitate impurities then heated to 110 C? to get rid of water) bentonite produced in Iraq which is available and cheap with existence of high density polyethylene at specific conditions of ( heating and mixing) . The best weight proportion were reached, then paraffin wax and additives were added to improve the properties of grease and give the