This paper deals with testing a numerical solution for the discrete classical optimal control problem governed by a linear hyperbolic boundary value problem with variable coefficients. When the discrete classical control is fixed, the proof of the existence and uniqueness theorem for the discrete solution of the discrete weak form is achieved. The existence theorem for the discrete classical optimal control and the necessary conditions for optimality of the problem are proved under suitable assumptions. The discrete classical optimal control problem (DCOCP) is solved by using the mixed Galerkin finite element method to find the solution of the discrete weak form (discrete state). Also, it is used to find the solution for the discrete adj

Laue back reflection patterns for quartz crystal are indexed by using Orient Express- program to simulate orientation of single crystals from assignment of principle zones. An oriented quartz single crystal was used as a substrate to deposit Zn metal by controlled thermal evaporation to achieve single crystal films of Zn that are subsequently evaluated by x-ray powder diffraction.

In this article, a numerical method integrated with statistical data simulation technique is introduced to solve a nonlinear system of ordinary differential equations with multiple random variable coefficients. The utilization of Monte Carlo simulation with central divided difference formula of finite difference (FD) method is repeated n times to simulate values of the variable coefficients as random sampling instead being limited as real values with respect to time. The mean of the n final solutions via this integrated technique, named in short as mean Monte Carlo finite difference (MMCFD) method, represents the final solution of the system. This method is proposed for the first time to calculate the numerical solution obtained fo

An overall mathematical model for copper pipe corrosion in flowing water was derived based on mass transfer fundamentals where we introduced the effects of boundary layer velocity, bulk flow velocity and the surface oxide protective film on the corrosion rate. A set of experiments were conducted in a straight 10mm diameter copper pipe, flow of water include six velocities of maximum value 7.33m/sec at 200C and 350C. The good agreement between the calculated and experimental corrosion rate values were achieved , the agreement reached 92% .

Nanocomposites of polymer material based on CdS as filler
material and poly methyl methacrylate (PMMA) as host matrix have
been fabricated by chemical spray pyrolysis method on glass
substrate. CdS particles synthesized by co-precipitation route using
cadimium chloride and thioacetamide as starting materials and
ammonium hydroxide as precipitating agent. The structure is
examined by X-ray diffraction (XRD), the resultant film has
amorphous structure. The optical energy gap is found to be (4.5,
4.06) eV before and after CdS addition, respectively. Electrical
activation energy for CdS/PMMA has two regions with values of
0.079 and 0.433 eV.

The effect of annealing on the structural and optical properties of Antimony trisulfide (Sb2S3) is investigated. Sb2S3 powder is vaporized on clean glass substrates at room temperature under high vacuum pressure to form thin films. The structural research was done with the aid of X-ray diffraction (XRD) and atomic force microscopy (AFM). The amorphous to the polycrystalline transformation of these thin films was shown by X-ray diffraction analysis after thermal annealing. These films' morphology is explained. The absorption coefficient and optical energy gap of the investigated films are calculated using transmission spectra. Both samples have strong absorption in the visible spectrum, according to UV-visible absorption spectra. The optical

Optical properties of Rhodamine-B thin film prepared by PLD
technique have been investigated. The absorption spectra using
1064nm and 532 nm laser wavelength of different laser pulse
energies shows that all the curves contain two bands, B band and Q
bands with two branches, Q1 and Q2 band and a small shift in the
peaks location toward the long wavelength with increasing laser
energy. FTIR patterns for Rhodamine-B powder and thin film within
shows that the identified peaks were located in the standard values
that done in the previous researches. X-ray diffraction patterns of
powder and prepared Rhodamine-B thin film was display that the
powder has polycrystalline of tetragonal structure, while the thin film

In this research PbS and PbS:Cu films were prepered with thicknesses (0.85±0.05)?m and (0.55±0.5)?m deposit on glass and silicon substrate respectively using chemical spray pyrolysis technique with a substrate temperature 573K, from lead nitrate salt, thiourea and copper chloride. Using XRD we study the structure properties for the undoped and doped films with copper .The analysis reveals that the structure of films were cubic polycrystalline FCC with a preferred orientation along (200) plane for the undoped films and 1% doping with copper but the orientation of (111) plane is preferred with 5% doping with the rest new peaks of films and appeared because of doping. Surface topography using optical microscope were be checked, it was found

In this paper,the homtopy perturbation method (HPM) was applied to obtain the approximate solutions of the fractional order integro-differential equations . The fractional order derivatives and fractional order integral are described in the Caputo and Riemann-Liouville sense respectively. We can easily obtain the solution from convergent the infinite series of HPM . A theorem for convergence and error estimates of the HPM for solving fractional order integro-differential equations was given. Moreover, numerical results show that our theoretical analysis are accurate and the HPM can be considered as a powerful method for solving fractional order integro-diffrential equations.