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
During 9–10 September 2011 the ACE, Wind, and SOHO spacecraft measured the complex interaction between an interplanetary coronal mass ejection (ICME) and a corotating interaction region (CIR) associated with the heliospheric sector boundary. Except for a few short periods, the suprathermal electrons are unidirectional, suggesting that the ICME magnetic field has opened through interchange reconnection. Signatures of interaction are distributed throughout the event suggesting that the structures have become entangled or embedded. Since the ICME speed is relatively low, the strong forward shock must be caused by the ICME‐CIR interaction. Other interesting features are the upstream heating flux disc
In this work, MWCNT in the epoxy can be prepared at room temperature and thickness (1mm) at different concentration of CNTs powder. Optical properties of multi-walled carbon nanotubes (CNTs) reinforced epoxy have been measured in the range of (300-800)nm. The electronic transition in pure epoxy and CNT/epoxy indicated direct allowed transition. Also, it is found that the energy gap of epoxy is 4.1eV and this value decreased within range of (4.1-3.5)eV when the concentration of CNT powder increased from (0.001-0.1)% respectively.
The optical constants which include (the refractive index (n), the extinction coefficient (k), real (ε1) and imaginarily (ε2) part of dielectric constant calculated in the of (300-800)nm at different concent
Abstract
Semiconductor-based gas sensors were prepared, that use n-type tin oxide (SnO2) and tin oxide: zinc oxide composite (SnO2)1-x(ZnO)x at different x ratios using pulse laser deposition at room temperature. The prepared thin films were examined to reach the optimum conditions for gas sensing applications, namely X-ray diffraction, Hall effect measurements, and direct current conductivity. It was found that the optimum crystallinity and maximum electron density, corresponding to the minimum charge carrier mobility, appeared at 10% ZnO ratio. This ratio appeared has the optimum NO2 gas sensitivity for 5% gas concentration at 300 °C working temperat
... Show MoreIn the current study, CuAl0.7In0.3Te2 thin films with 400 nm thickness were deposited on glass substrates using thermal evaporation technique. The films were annealed at various annealing temperatures of (473,573,673 and 773) K. Furthermore, the films were characterized by X-ray Diffraction spectroscopy (XRD), field emission scanning electron microscopy (FESEM), atomic force microscopy (AFM), and Ultra violet-visible (UV–vis). XRD patterns confirm that the films exhibit chalcopyrite structure and the predominant diffraction peak is oriented at (112). The grain size and surface roughness of the annealed films have been reported. Optical properties for the synthesized films including, absorbance, transmittance, dielectric constant, and refr
... Show MoreZnxNi1-x-yCuyFe2O4 spinel ferrite were prepared using solid state reaction method with (y=0.1, x=0.2, 0.3, 0.4, 0.5, 0.6 ) . X-ray diffraction with diffractometer CuKα analysis have been carried out and studied showing single phase spinel cubic with space group FDÍž 3m for all prepared samples . Lattice parameters and crystallite grain size and x-ray density(Ïx-ray) bulk density and porosity ratio's were calculated and showed good agreement with the international data reported in the scientific research's.
We investigated at the optical properties, structural makeup, and morphology of thin films of cadmium telluride (CdTe) with a thickness of 150 nm produced by thermal evaporation over glass. The X-ray diffraction study showed that the films had a crystalline composition, a cubic structure, and a preference for grain formation along the (111) crystallographic direction. The outcomes of the inquiry were used to determine these traits. With the use of thin films of CdTe that were doped with Ag at a concentration of 0.5%, the crystallization orientations of pure CdTe (23.58, 39.02, and 46.22) and CdTe:Ag were both determined by X-ray diffraction. orientations (23.72, 39.21, 46.40) For samples that were pure and those that were doped with
... Show MoreIn this study, a double frequency Q-switching Nd:YAG laser beam (1064 nm and λ= 532 nm, repetition rate 6 Hz and the pulse duration 10ns) have been used, to deposit TiO2 pure and nanocomposites thin films with noble metal (Ag) at various concentration ratios of (0, 10, 20, 30, 40 and 50 wt.%) on glass and p-Si wafer (111) substrates using Pulse Laser Deposition (PLD) technique. Many growth parameters have been considered to specify the optimum condition, namely substrate temperature (300˚C), oxygen pressure (2.8×10-4 mbar), laser energy (700) mJ and the number of laser shots was 400 pulses with thickness of about 170 nm. The surface morphology of the thin films has been studied by using atomic force microscopes (AFM). The Root Mean Sq
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