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 zeolite's textural properties have a significant effect on zeolite's effectiveness in the different industrial processes. This research aimed to study the textual properties of the NaX and FeX zeolites using the nitrogen adsorption-desorption technique at a constant low temperature. According to the International Union of Pure and Applied Chemistry, the adsorption-desorption isotherm showed that the studied materials were mixed kinds I/II isotherms and H3 type hysteresis. The Brunauer-Emmett-Teller isotherm was the best model to describe the nitrogen adsorption-desorption better than the Langmuir and Freundlich isotherms. The obtained adsorption capacity and Brunauer-Emmett-Teller surface area values for NaX were greater than FeX. Ac
... Show MoreEight soil samples were selected around Najaf governorate at depth levels 40-50 cm. X-Ray Fluorescence (XRF) was used to determine the concentrations of major and trace elements. Liner and mass attenuation coefï¬cient (µ, µÏ) have been determined at gamma energies (662, 1172,1332) keV using NaI (Tl) detector. The range of linear attenuation coefficients for calculated samples were (0.553-1.163) cm-1, (0.122-0.178) cm-1 and (0.049-0.105) cm-1 at (662, 1172,1332) keV respectively. The range of mass attenuation coefficients obtained (0.39-0.76) cm2/gm, (0.087-0.117) cm2/gm and (0.0336-0.074) cm2/gm at (662, 1172,1332) keV respectively. The result
... Show MoreIn the present work, lead silicate glasses have been prepared with
different amount of lead oxide content. Structure properties such as
X-ray diffraction, AFM, and FTIR analyses have been done. The
exceeding of PbO content more than 25wt% revealed a decreasing in
density. The X- ray revealed that the strongest peak related to
Hexagonal silica dioxide and the other crystal phases formed were
related to silica oxide (SiO2) and lead oxide (PbO). Growth and
decayed phases in X-ray have been observed with changing lead
oxide content. Homogeneous surface was obtained using AFM
analyzer with an average diameter around 100 nm. Infrared spectrum
is characterized by the presence of large absorption band between
120
The change in the optical properties for samples of pure PVA and PVA /K2CrO4composite have been studied .The samples were prepared with different percentage (1,3,5,and 7)%wt of K2CrO4 by casting method technique .In this work ,we are study the absorption ,reflectance spectra ,absorption coefficient, energy gap ,extinction coefficient ,and transmittance spectra as a function of wavelength range (200-800)nm ,Also real and imaginary part of dielectric constant have been studied in the range of wave length .The results exhibit the optical properties change by the increase of K2CrO4 concentration, and the values of energy gap for indirect transitions decrease by the increase of the concentration of K2CrO4
... Show MoreThe local asphalt concrete fracture properties represented by the fracture energy, J-integral, and stress intensity factor are calculated from the results of the three point bending beam test made for pre notches beams specimens with deformation rate of 1.27 mm/min. The results revealed that the stress intensity factor has increased by more than 40% when decreasing the testing temperature 10˚C and increasing the notch depth from 5 to 30mm. The change of asphalt type and content have a limited effect of less than 6%.
Cadmium Oxide thin films were deposited on glass substrate by spray pyrolysis technique at different temperatures (300,350,400, 500)oC. The optical properties of the films were studied in this work. The optical band-gap was determined from absorption spectra, it was found that the optical band-gap was within the range of (2.5-2.56)eV also width of localized states and another optical properties.