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 effect of thermal treatment on optical constants of pure PMMA and with addition (15 and 35) ml of coumarin at different temperatures (100, 110 and 120) C0 for 1 hour were investigated. Cast method used to prepares films of pure PMMA and PMMA with (15 and 35) of coumarin. UV/VIS spectrometer technique used to measure the absorption spectra for these films. The optical constant (absorption spectra and absorption coefficient) don’t changes after applied temperatures in pure PMMA film but the optical constant (absorption spectra and absorption coefficient) in PMMA with (15 and 35) ml of coumarin increased with applied temperatures. The optical energy gap of pure PMMA and PMMA with (15 and 35) ml of coumarin sl
... Show MoreChemical bath deposition was used to synthesize ZnO nanorods (NRs) on glass and fluorine_doped tin oxide (FTO) substrates. X-ray diffraction was performed to examine the crystallinity of ZnO nanorod. Results showed that ZnO NRs had a wurtzite crystal structure. Field emission scanning electron microscopy images showed that glass sample had rod-like structure distribution with (50 nm) diameter and average length of approximately (700 nm), whereas the FTO-coated glass sample had 25 nm diameter and average length of approximately 950 nm. The direct optical transition band gaps of the glass and FTO_coated glass samples were( 4 and 4.43 eV), respectively. The structural and optical properties of the synthesized ZnO p
... Show MoreIn the present work, nanocomposite of poly (vinyl alcohol) (PVA) incorporated with functionalized graphene oxide (FGO) were fabricated using casting method. PVA was dispersed by varying content of FGO (0.3, 0.5, 0.8, 1 wt %). The PVA- FGO nanocomposite was characterized by FT‐IR, FE-SEM and XRD. Frequency dependence of real permittivity (ε’), imaginary (ε’’) and a.c conductivity of PVA/FGO and PVA/GO nanocomposite were studied in the frequency range 100 Hz- 1 MHz. The experimental results showed that the values of real (ε’) and imaginary permittivity (ε’’) increased dramatically by increasing the FGO content in PVA matrix. PVA/ FGO (1 wt %) nanocomposite revealed higher electrical conductivity of 6.4×10-4 Sm-1 compared to
... Show MoreIn the present work, pulsed laser deposition (PLD) technique was applied to a pellet of Chromium Oxide (99.999% pure) with 2.5 cm diameter and 3 mm thickness at a pressure of 5 Tons using a Hydraulic piston. The films were deposited using Nd: YAG laser λ= (4664) nm at 600 mJ and 400 number of shot on a glass substrate, The thickness of the film was (107 nm). Structural and morphological analysis showed that the films started to crystallize at annealing temperature greater than 400 oC. Absorbance and transmittance spectra were recorded in the wavelength range (300-
4400) nm before and after annealing. The effects of annealing temperature on absorption coefficient, refractive index, extinction coefficient, real and imaginary parts of d
In the present work, the focusing was on the study of the x-ray diffraction, dielectric constant, loses dielectric coefficient, tangent angle, alter- natively conductivity and morphology of PET/BaTio3. The PET/BaTio3 composite was prepared for polyethylene terephthalate PET polymer composite containing 0, 10, 20, 30, 40, 50, and 60 wt. % from Barium titanate BaTi03 powder. The composite of two materials leads to form mixing solution and hot-pressing method. The effect of BaTio3 on the structure and dielectric properties with morphology was studied on PET matrix polymer using XRD, LCR meter and SEM.
The aim of present work is to improve mechanical and fatigue properties for Aluminum alloy7049 by using Nano composites technique. The ZrO2 with an average grain diameter of 30-40 nm, was selected as Nano particles, to reinforce Aluminum alloy7049 with different percentage as, 2, 4, 6 and 7 %. The Stir casting method was used to fabricate the Nano composites materials due to economical route for improvement and processing of metal matrix composites. The experimental results were shown that the adding of zirconium oxide (ZrO2) as reinforced material leads to improve mechanical properties. The best percentage of improvement of mechanical properties of 7049 AA was with 4% wt. of ZrO2 about (7.76% ) for ultim
... Show MoreBiodiesel define as the mono-alkyl esters of vegetable oil and animal fats is an alternative diesel fuel that is steadily gaining attention because the combustion of fossil fuels such as coal, oil and natural gas has been identify as a major cause of the increase in the concentration of carbon dioxide in the earth’s atmosphere and causing global warming.
The present work concerns with estimating the physical properties experimentally such as kinematic viscosity, density, flash point and carbon residue of biodiesel that produced by the esterification reaction of methanol and oleic acid with homogeneous catalysts H2SO4 in a lab-scale packed reactive distillation column using the best operating conditions of methanol to oleic acid 8:1,