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
Pure and Fe-doped zinc oxide nanocrystalline films were prepared
via a sol–gel method using -
C for 2 h.
The thin films were prepared and characterized by X-ray diffraction
(XRD), atomic force microscopy (AFM), field emission scanning
electron microscopy (FE-SEM) and UV- visible spectroscopy. The
XRD results showed that ZnO has hexagonal wurtzite structure and
the Fe ions were well incorporated into the ZnO structure. As the Fe
level increased from 2 wt% to 8 wt%, the crystallite size reduced in
comparison with the pure ZnO. The transmittance spectra were then
recorded at wavelengths ranging from 300 nm to 1000 nm. The
optical band gap energy of spin-coated films also decreased as Fe
doping concentra
Self-compacted concrete (SCC) considered as a revolution progress in concrete technology due to its ability for flowing through forms, fusion with reinforcement, compact itself by its weight without using vibrators and economic advantages. This research aims to assess the fresh properties of SCC and study their effect on its compressive strength using different grading zones and different fineness modulus (F.M) of fine aggregate. The fineness modulus used in this study was (2.73, 2.82,2.9& 3.12) for different zones of grading (zone I, zone II& marginal zone(between zone I&II)) according to Iraqi standards (I.Q.S No.45/1984).Twelve mixes were prepared, each mix were tested in fresh state with slump, V-Funnel and L-Box tests, then 72
... Show MoreElectronic properties including (bond length, energy gap, HOMO, LUMO and density of state) as well as spectroscopic properties such like infrared, Raman scattering, force constant, reduced mass and longitu- dinal optical mode as a function of frequency are based on size and concentration of the molecular and nanostructures of aluminum nitride ALN, boron nitride BN and AlxB7-XN7 as nanotubes has calculated using Ab –initio approximation method dependent on density functional theory and generalized gradient approximation. The geometrical structure are calculated by using Gauss view 05 as a complementary program. Shows the energy gap of ALN, BN and AlxB7-XN7 as a function of the total number of atoms , start from smallest molecule to reached
... Show MoreSelf-compacted concrete (SCC) considered as a revolution progress in concrete technology due to its ability for flowing through forms, fusion with reinforcement, compact itself by its weight without using vibrators and economic advantages. This research aims to assess the fresh properties of SCC and study their effect on its compressive strength using different grading zones and different fineness modulus (F.M) of fine aggregate. The fineness modulus used in this study was (2.73, 2.82,2.9& 3.12) for different zones of grading (zone I, zone II& marginal zone(between zone I&II)) according to Iraqi standards (I.Q.S No.45/1984).Twelve mixes were prepared, each mix were tested in fresh state with slump, V-Funnel and L-Box tests, t
... Show MoreThe acrylic polymer composites in this study are made up of various weight ratios of cement or silica nanoparticles (1, 3, 5, and 10 wt%) using the casting method. The effects of doping ratio/type on mechanical, dielectric, thermal, and hydrophobic properties were investigated. Acrylic polymer composites containing 5 wt% cement or silica nanoparticles had the lowest abrasion wear rates and the highest shore-D hardness and impact strength. The increase in the inclusion of cement or silica nanoparticles enhanced surface roughness, water contact angle (WCA), and thermal insulation. Acrylic/cement composites demonstrated higher mechanical, electrical, and thermal insulation properties than acrylic/silica composites because of their lowe
... Show MoreThe functional properties of the defatted powder and protein isolate of germinated mung bean seeds were studied and the estimation of the amino acids was carried out. The results showed a significant increase in the values of the amino acids leucine, lysine, phenylalanine and valine. The results of studying the functional properties of the protein isolate and defatted powder showed that there were significant differences between the sample The defatted and protein isolate, if the water absorption capacity of the defatted mung powder was 2.5% water/gm protein and the water absorption capacity of the protein isolate was 3%ml water/g protein, the fat binding capacity of the defatted powder was 0.3 ml fat/g protein and the isolate The ratio was
... Show MoreSulphated zirconia (SZ) is one of the most important solid acid catalysts was synthesize at different operating conditions, different calcination temperature and sulfonating time has been used. The prepared catalyst was distinguished by X-ray Diffraction (XRD), particle size and morphology of catalyst were checked by atomic force microscopy (AFM) and scanning electron microscopy (SEM) respectively, in addition to analysis by (DTA) Differential thermally and Energy Dispersive X-Ray (EDX). Finally, the N2 adsorption-desorption was used to measure the surface area (BET) and pore volume. High degree of tetragonal crystallinity was obtained 90 %, and surface area of 169 m2/g and pore volume of 0.39 cm3g-1 at 600°C calcination temperature for 3
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