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
Nano TiO2 thin films on glass substrates were prepared at a constant temperature of (373 K) and base vacuum (10-3 mbar), by pulsed laser deposition (PLD) using Nd:YAG laser at 1064 nm wavelength. The effects of different laser energies between (700-1000)mJ on the properties of TiO2 films was investigated. TiO2 thin films were characterized by X-ray diffraction (XRD) measurements have shown that the polycrystalline TiO2 prepared at laser energy 1000 mJ. Preparation also includes optical transmittance and absorption measurements as well as measuring the uniformity of the surface of these films. Optimum parameters have been identified for the growth of high-quality TiO2 films
... Show MoreMicrowave heating is caused by the ability of the materials to absorb microwave energy and convert it to heat. The aim of this study is to know the difference that will occur when heat treating the high strength aluminum alloys AA7075-T73 in a microwave furnace within different mediums (dry and acidic solution) at different times (30 and 60) minutes, on mechanical properties and fatigue life. The experimental results of microwave furnace heat energy showed that there were variations in the mechanical properties (ultimate stress, yielding stress, fatigue strength, fatigue life and hardness) with the variation in mediums and duration times when compared with samples without treatment. The ultimate stress, yielding stress and fatigue streng
... Show MorePreviously many properties of graphene oxide in the field of medicine, biological environment and in the field of energy have been studied. This diversity in properties is due to the possibility of modification on the composition of this Nano compound, where the Graphene oxide is capable of more modification via addition other functional groups on its surface or at the edges of the sheet. The reason for this modification possibility is that the Sp3 hybridization (tetrahedral structure) of the carbon atoms in graphene oxide, and it contains many oxygenic functional groups that are able to reac with other groups. In this research the effect of addition of some amine compounds on electrical properties of graphene oxide has been studied by the
... Show MoreIn the present work we prepared heterojunction not homogenous CdS/:In/Cu2S) by spray and displacement methods on glass substrate , CdS:In films prepared by different impurities constration. Cu2S prepared by chemical displacement method to improve the junction properties , structural and optical properties of the deposited films was achieved . The study shows that the film polycrystalline by XRD result for all film and the energy gap was direct to 2.38 eV with no effect on this value by impurities at this constration .
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
... Show MoreThin films of pure tin mono-sulfide SnS and tin mono-sulfide for (1,2,3,4)% fluorine SnS:F with Thicknesses of (0.85 ±0.05) ?m and (0.45±0.05) ?m respectively were prepared by chemical spray pyrolysis technique. the effect of doping of F on structural and optical properties has been studied. X-Ray diffraction analysis showed that the prepared films were polycrystalline with orthorhombic structure. It was found that doping increased the intensity of diffraction peaks. Optical properties of all samples were studied by recording the absorption and transmission spectrum in range of wave lengths (300-900) nm. The optical energy gap for direct forbidden transi
... Show MoreUndoped and Co-doped zinc oxide (CZO) thin films have been prepared by spray pyrolysis technique using solution of zinc acetate and cobalt chloride. The effect of Co dopants on structural and optical properties has been investigated. The films were found to exhibit maximum transmittance (~90%) and low absorbance. The structural properties of the deposited films were examined by x-ray diffraction (XRD). These films, deposited on glass substrates at (400? C), have a polycrystalline texture with a wurtzite hexagonal structure, and the grain size was decreased with increasing Co concentration, and no change was observed in lattice constants while the optical band gap decreased from (3.18-3.02) eV for direct allowed transition. Other parameters
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