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
Flexible pavements are subjected to three main distress types: fatigue crack, thermal crack, and permanent deformation. Under severe climate conditions, thermal cracking particularly contributes largely to a considerable scale of premature deterioration of pavement infrastructure worldwide. This challenge is especially relevant for Europe, as weather conditions vary significantly throughout the year. Hydrated lime (HL) has been recognized as an effective additive to improve the mechanical properties of asphalt concrete for pavement applications. Previous research has found that a replacement of conventional limestone dust filler using hydrated lime at 2.5% of the total weight of aggregates generated an optimum improvement in the mec
... Show MoreSpray pyrolysis technique was subjected to synthesized (SnO2)1-x (TiO2: CuO) x Thin films on different substrates like glass and single crystal silicon using. The structure of the deposited films was studied using x-ray diffraction. A more pronounced diffraction peaks of SnO2 while no peaks of (CuO , TiO2 ) phase appear in the X-ray profiles by increasing of the content of (TiO2 , CuO) in the sprayed films. Mixing concentration (TiO2 , CuO) influences on the size of the crystallites of the SnO2 films ,the size of crystallites of the spray paralyzed oxide films change in regular manner by increasing of (TiO
... Show MoreHigh temperature superconductors materials with composition Bi1.6-xSbxPb0.4Sr2Ca2-yCdyCu3OZ (x = 0, 0.1, 0.2 and 0.3) and (y = 0.01 and 0.02), were prepared by using the chemical reaction in solid-state ways, and test influence of partial replacement of Bi and Ca with Sb and Cd respectively on the superconducting properties, all samples were sintered at the same temperature (850 oC) and for the same time (195 h). The structural analysis of the prepared samples was carried out using X-ray diffraction (XRD) measurements performed at room temperature, scanning electron microscope (SEM) and dc electrical resistivity was measured as a function of temperature. It was found that the sample prepared by partial substitution of Sb at ratio (x= 0.2
... Show MoreTin dioxide doped silver oxide thin films with different x content (0, 0.03, 0.05, 0.07) have been prepared by pulse laser deposition technique (PLD) at room temperatures (RT). The effect of doping concentration on the structural and electrical properties of the films were studied. Atomic Force Measurement (AFM) measurements found that the average value of grain size for all films at RT decrease with increasing of AgO content. While an average roughness values increase with increasing x content. The electrical properties of these films were studied with different x content. The D.C conductivity for all films increases with increasing x content. Also, it found that activation energies decrease with increasing of AgO content for all films.
... Show MoreMechanical and thermal properties of composites, consisted of unsaturated polyester resin, reinforced by different kinds of natural materials (Orange peels and Date seeds) and industrial materials (carbon and silica) with particle size 98 µm were studied. Various weight ratios, 5, 10, and 15 wt. % of natural and industrial materials have been infused into polyester. Tensile, three-point bending and thermal conductivity tests were conducted for the unfilled polyester, natural and industrial composite to identify the weight ratio effect on the properties of materials. The results indicated that when the weight ratio for polyester with date seeds increased from 10% to 15%, the maximum Young’s modulus decreased by 54%. When the weight rat
... Show More