This paper is concerned with introducing an explicit expression for orthogonal Boubaker polynomial functions with some important properties. Taking advantage of the interesting properties of Boubaker polynomials, the definition of Boubaker wavelets on interval [0,1) is achieved. These basic functions are orthonormal and have compact support. Wavelets have many advantages and applications in the theoretical and applied fields, and they are applied with the orthogonal polynomials to propose a new method for treating several problems in sciences, and engineering that is wavelet method, which is computationally more attractive in the various fields. A novel property of Boubaker wavelet function derivative in terms of Boubaker wavelet themselves is also obtained. This Boubaker wavelet is utilized along with a collocation method to obtain an approximate numerical solution of singular linear type of Lane-Emden equations. Lane-Emden equations describe several important phenomena in mathematical science and astrophysics such as thermal explosions and stellar structure. It is one of the cases of singular initial value problem in the form of second order nonlinear ordinary differential equation. The suggested method converts Lane-Emden equation into a system of linear differential equations, which can be performed easily on computer. Consequently, the numerical solution concurs with the exact solution even with a small number of Boubaker wavelets used in estimation. An estimation of error bound for the present method is also proved in this work. Three examples of Lane-Emden type equations are included to demonstrate the applicability of the proposed method. The exact known solutions against the obtained approximate results are illustrated in figures for comparison
In this study, mixing of zinc oxide (ZnO) nanoparticles with iron oxide(Fe2O3) at (0, 0.1, 0.3, 0.5 and 1)%wt., are deposited on glass substrates by pulsed laser deposition (PLD) technique for study characterization ZnO:Fe2O3 as solar cell electrode. The profound effect of mixed film on the structural and optical of ZnO: Fe2O3 thin films was observed. Meanwhile, the films have polycrystalline Hexagonal structures for ZnO, Rhombohedra and cubic structure for Fe2O3, and as indicated by the X-ray diffraction patterns of the films. The mean crystallite size of ZnO increase with increasing mixed ratio. The direct energy
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Poly ethylene oxide PEO / Poly vinyl alcohol PVA blends were prepared by cast method at different ratios of (25%PEO/75%PVA, 30%PEO/70%PVA, 35%PEO/65%PVA, 40%PEO/60%PVA, and 50%PEO/505PVA). Samples miscibility ,and thermal stability were studied by using differential scanning calorimetry(DSC),and thermo gravimetric analysis (TGA) analysis. The results proved that there was one glass transition temperature (Tg=160°C) at 25%PEO\PVA ratio
)that was attributed to its miscibility. This miscibility associated with (Hydrogen bonds) between (Hydroxyl group) in PVA, and PEO, whereas there were two glass transition temperature for the blends ratio more than 30%PEO,that was due its immisc
In this research, the effect of electrode material on the parameters of the produced DBD plasma was investigated. First, a non-thermal plasma was created by applying a 15 kV AC voltage between two electrodes and using a glass plate as a dielectric barrier in the design Dielectric Barrier Discharge (DBD) plasma system. The obtained plasma spectrum was analyzed using optical emission spectroscopy to calculate plasma parameters by the Boltzmann plot method. Electrodes made of copper, aluminium, and stainless steel were employed in this research. Electron temperature ( ) for copper, aluminium, and stainless steel was found to be (1.398 eV), (1.093 eV) and (1.009 eV), respectively.
In this work, the photoluminescence spectra (PL) of porous silicon (PS) have been modified by adding gold nanoparticles (AuNPs) to PS layer. PS was produced via Photo electro-chemical etching (PECE) method of n-type Si wafer with resistivity of about (10 Ω.cm) and (100) orientation. Laser wavelength of (630 nm) and illumination intensity of about (30 mW/cm2), etching current density of (10mA/cm2), and etching time of (4 min) were used during the etching process. The bare PS before metallic deposition process and porous silicon/gold nanoparticles (PS/AuNPs) structures were investigated by X-Ray Diffraction (XRD), scanning electron microscopy (SEM), and energy dispersive X-Ray (EDX). The photoluminescence spectra were investigated as a fu
... Show MoreGypsum is one of the important construction materials in Iraq in plastering surfaces and gypsum board , the ability of gypsum to give a comfortable an aesthetic ambiance as a construction material increase the need of gypsum , The particle size , total surface area and particle size distribution were factors affecting plaster properties used for construction properties . In this study gypsum paste was used with different mixing ratios of particle size and studied the physical properties of these types of pastes named (standard consistency ,setting time ,density) and compressive strength . The results showed that the water to gypsum ratio increased with increasing the fineness of the gypsum to (0.75%) and the setting time to the maxi
... Show MoreThe aim of the current study is to determine the elastic properties of carbonate rocks using ultrasonic method. Forty rock samples of Anah formation were collected at different depths from four wells drilled at the study area . The relationship between wave velocities and elastic properties of rocks was defined. Regression analyses to define these relations were applied. The results indicate that the elastic properties of the rocks show a linear relationship with both P- and S-wave velocities. The best relationship was obtained between both Young's modulus and Shear modulus with Vs in the determination of the coefficient ( R2 ), with values of 0.91 and 0.94, respectively.&n
... Show MoreIn this research a bilateral tin oxide (SnO2) thin films was prepared by Sol-
Gel method, flow coating technique which is considered a simple and cheap
technique. The horizontal sample preparation with and without the use of
installed, and also with installed to vertical sample. Results of optical
spectroscopy that the biggest values of the transmittance T was for horizontal
films with an installed, as for the absorbance A was the biggest values of the
vertical sample. For the reflectivity R was value in the horizontal films with
installed, less than a horizontal films without Sticky as well as for films
vertical. The results of the energy gap Eg for that direct allowed and forbidden
transitions and for the ind
We have studied the synthesis environment of ambient pressure silica aerogels influence on their resulting morphological and optical properties. Transparent nanoporous silica aerogel was synthesized at ambient pressure using tetraethylorthosilicate precursor via a sol-gel process. Effect of drying control chemical additives and catalyst on physical properties was investigated. Trimethylchlorolsilane was employed as a hydrophobic reagent in the surface modification process. All aerogel samples were prepared utilizing a subcritical procedure under reactant pH fixed at 8.3, using just ammonium hydroxide or together with ammonium fluoride as catalyst. The effects catalyst types as well as drying control chemical additives on the physical pro
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