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
The performance of asphalt pavements is crucial due to heavy traffic loads from civil and industrial developments. Various additives and modifiers are used in flexible roads to improve their resistance to deterioration caused by climatic changes. From this context, modifying the asphalt binder with polymers is popular in asphalt pavement construction. The present research investigates the effect of Polyethylene (PE) polymers in powder form on the characteristics of asphalt mixtures since these polymers are composed of hydrocarbons. It is similar to asphalt binders, making them very effective in enhancing the performance of neat asphalt produced from the oil refinery. To confirm this, two types of PE, High-Density PE (HDPE) and Low-Density P
... Show MoreTo learn how the manner of preparation influences film development, this study examined film expansion under a variety of deposition settings. To learn about the membrane’s properties and to ascertain the optimal pretreatment conditions, which are represented by ambient temperature and pressure, Laser pressure of 2.5[Formula: see text]m bar, the laser energy density of 500[Formula: see text]mJ, distortion ratio ([Formula: see text]) as a function of laser pulse count, all achieved with the double-frequency Nd: YAG laser operating in quality-factor mode at 1064[Formula: see text]nm. MgxZn[Formula: see text] films of thickness [Formula: see text][Formula: see text]nm were deposited on glass substrates at pulse
... Show MoreBulk polycrystalline samples have been prepared by the two-step solid state reaction process. It has been observed that as grown Tl2-xHgxSr2Ca2Cu3O10+δ (with x = 0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.8, 1) corresponds to the 2223 phase. It has been found that Tc varies with Hg content .The optimum Tc is about 120K for the composition Tl1.6Hg0.4Sr2Ca2Cu3O10+δ.The microstructure for Tl1.6Hg0.4Sr2Ca2Cu3O10+δ observed to be most dense and this phase exhibits the highest stability.
In this work, the structure properties of nano Lead sulfide PbS thin films are studied. Thin samples were prepared by pulse laser deposition and deposited on glass substrates at wavelength 1064nm wavelength with a various laser energies (200,300,400,500)nm. The study of atomic force microscope (AFM) and X-ray diffraction as well as the effect of changing the laser energy on the structural properties has been studied. It has been observed that the membrane formed is of the polycrystalline type and the predominant phase is the plane (111) and (200). The minimum grain size obtained was 16.5 nm at a laser energy about 200 mJ. The results showed that thin films of average granular sizes (75 nm) could be prepared.As for the optical properties,
... Show MoreThin a-:H films were grown successfully by fabrication of designated ingot followed by evaporation onto glass slides. A range of growth conditions, Ge contents, dopant concentration (Al and As), and substrate temperature, were employed. Stoichiometry of the thin films composition was confirmed using standard surface techniques. The structure of all films was amorphous. Film composition and deposition parameters were investigated for their bearing on film electrical and optical properties. More than one transport mechanism is indicated. It was observed that increasing substrate temperature, Ge contents, and dopant concentration lead to a decrease in the optical energy gap of those films. The role of the deposition conditions on value
... Show MoreIn this work, pure and doped Vanadium Pentoxide (V2O5) thin films with different concentration of TiO2 (0, 0.1, 0.3, 0.5) wt were obtained using Pulse laser deposition technique on amorphous glass substrate with thickness of (250)nm. The morphological, UV-Visible and Fourier Transform Infrared Spectroscopy (FT-IR) were studied. TiO2 doping into V2O5 matrix revealed an interesting morphological change from an array of high density pure V2O5 nanorods (~140 nm) to granular structure in TiO2-doped V2O5 thin film .Transform Infrared Spectro
... Show MorePolycrystalline ingots of cadmium telluride have been synthesized using the direct
reaction technique, by fusing initial component consisting from pure elements in
stoichiometric ratio inside quartz ampoule is evacuated 10-6 torr cadmium telluride has
been grown under temperature at (1070) oC for (16) hr. was used in this study, the phases
observed in growing CdTe compound depend on the temperature used during the growth
process. Crystallography studies to CdTe compound was determined by X-ray diffraction
technique, which it has zinc blend structure and cubic unit cell, which lattice constants is
a=6.478
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