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
Polyaniline (PANI) has been prepared by the oxidation method in order to fabricate it with various concentrations of copper nanoparticles (CuNPs) which produced using the reduction method. Various techniques have characterized pure PANI and PANI doped CuNPs composites, such as fourier transform infrared spectroscopy (FT-IR), X-ray diffraction spectroscopy (XRD), field emission scanning electron microscopy (FE-SEM) and energy dispersive X-ray spectroscopy (EDS), which were provided important information about the structure and morphology of the fabricated polymer nanocomposites. The properties of dielectric permittivity (έ), dielectric loss (ἔ) and electrical conductivity (σ_AC) properties were studied at room temperature versus a range
... Show MoreResults of a study of alloys and films with various Pb content have been reported and discussed. Films of of thickness 1.5
In this paper, ceramic water filters were produced by using ten mixtures of different ratios of red clay and sawdust under different production conditions. The physical properties of these filters were tested. The production conditions include five press pressures ranged from 10 to 50MPa and a firing schedule having three different final temperatures of 1000, 1070, and 1100˚C. The tests results of the physical properties were used to obtain best compatibility between the hydraulic and the mechanical properties of these filters. Results showed that as the press pressure and the firing temperature are increased, the bulk density and the compressive and bending strengths of the produced filters are increased, while, the porosity and absorp
... Show MoreHot mix recycling of asphalt pavements is increasingly being used as one of the major rehabilitation methods by various highway agencies. Besides general savings in costs and energy expended, it also saves our natural resources and environment. Recycling process presents a sustainable pavement by using the old materials that could be reclaimed from the pavement; these materials could be mixed with recycling agents to produce recycled mixtures. The important expected benefits of recycling process are the conservation of natural resources and reduction of environmental impact. The primary objectives of this work are evaluating the Tensile and Shear Properties of recycled asphalt concrete mixtures, In addition to the
... Show MoreThis research involves studying the mechanical properties and corrosion behavior of “low carbon steel” (0.077wt% C) before and after welding using Arc, MIG and TIG welding. The mechanical properties include testing of microhardness, tensile strength, the results indicate that microhardness of TIG, MIG welding is more than arc welding, while tensile strength in arc welding more than TIG and MIG.
The corrosion behavior of low carbon weldments was performed by potentiostat at scan rate 3mV.sec-1 in 3.5% NaCl to show the polarization resistance and calculate the corrosion rate from data of linear polarization by “Tafel extrapolation method”. The results indicate that the TIG welding increase the corrosion current d
... Show MoreIn this work, zinc oxide nanoparticles (ZnONPs) and sawdust/epoxy composite (20:80) were mixed using a simple molding method with different ZnONPs concentrations of (0.1, 0.3, 0.5, 0.7, and 1.0 %). The samples of the nanocomposites were characterized by the Scanning Electron Microscopy (SEM) technique to demonstrate the homogeneity of the prepared ZnONPs/nanocomposites. The photocatalytic activity of the samples was examined using the methylene blue (MB) dye as a pollutant solution, through evaluation of the efficiency of the prepared compound in the treatment of organic pollutants under illumination by sunlight. The photocatalytic results showed that after 240 minutes of exposure to sunlight, the sample prepared using (0.5 vol.% of ZnON
... Show MoreThe study effect Graphene on optical and electrical properties of glass prepared on glass substrates using sol–gel dip-coating technique. The deposited film of about (60-100±5%) nm thick. Optical and electrical properties of the films were studied under different preparation conditions, such as graphene concentration of 2, 4, 6 and 8 wt%. The results show that the optical band gap for glass-graphene films decreasing after adding the graphene. Calculated optical constants, such as transmittance, extinction coefficient are changing after adding graphene. The structural morphology and composition of elements for the samples have been demonstrated using SEM and EDX. The electrical properties of films include DC electrical conductivity; we
... Show MoreIn this work, two different structures are proposed which is fuzzy real normed space (FRNS) and fuzzy real Pre-Hilbert space (FRPHS). The basic concept of fuzzy norm on a real linear space is first presented to construct space, which is a FRNS with some modification of the definition introduced by G. Rano and T. Bag. The structure of fuzzy real Pre-Hilbert space (FRPHS) is then presented which is based on the structure of FRNS. Then, some of the properties and related concepts for the suggested space FRN such as -neighborhood, closure of the set named , the necessary condition for separable, fuzzy linear manifold (FLM) are discussed. The definition for a fuzzy seminorm on is also introduced with the prove that a fuzzy seminorm on
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