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
Poly(L-lactic acid) (PLLA)/poly(caprolactone) (PCL) and two types of organoclay (OMMT) including a fatty amide and ocatdecylamine montmorillonite (FA-MMT and ODA-MMT) were employed to produce polymer nanocomposites by melt blending. Materials were characterized using X-ray diffraction (XRD), Fourier transform infrared (FTIR) spectroscopy, thermogravimetric analysis (TGA), elemental analysis, scanning electron microscopy (SEM) and transmission electron microscopy (TEM). Mechanical properties were also investigated for these nanocomposites. The nanocomposites showed increasing mechanical properties and thermal stability. XRD results indicated that the materials formed nanocomposites. SEM morphology showed that increasing content of OMMT reduc
... Show MoreIn this paper, we introduce and study the essential and closed fuzzy submodules of a fuzzy module X as a generalization of the notions of essential and closed submodules. We prove many basic properties of both concepts.
The effects of reinforcing polymers with glass and graphite particles on enhancing their flexural properties are investigated. Five composites were fabricated using the same polymer matrix material with different volume fractions of reinforcement particles. They comprise glass particles and graphite particles each having volume fractions of 20% and 30% as well as a hybrid composite having 10% glass and 10% graphite. Three-point bending tests using a Universal Testing Machine were carried out on specimens of the above mentioned composites, as well as specimens of the polymer matrix material to determine their flexural properties. The experimental test results indicate that the flexural stiffness of all the composites wer
... Show MoreLead selenide PbSe thin films of different thicknesses (300, 500, and 700 nm) were deposited under vacuum using thermal evaporation method on glass substrates. X-ray diffraction measurements showed that increasing of thickness lead to well crystallize the prepared samples, such that the crystallite size increases while the dislocation density decreases with thickness increasing. A.C conductivity, dielectric constants, and loss tangent are studied as function to thickness, frequency (10kHz-10MHz) and temperatures (293K-493K). The conductivity measurements confirm confirmed that hopping is the mechanism responsible for the conduction process. Increasing of thickness decreases the thermal activation energy estimated from Arhinus equation is
... 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 MoreThe study area soils suffer from several problems appear as tkhesvat and cracks in the roads and waterlogging which reduces the susceptibility of soil to withstand pressure, this study was conducted on the soil of the Karkh district based on field study that included (6) samples of soil physical analyses contain different ratios of (mud, sand, silt) as percentages (52%, 45%, 3 #) respectively, and liquidity limit rate (39%) Stroke rate plasticity was (20.6%) The rate coefficient of plasticity total (19.2%)0
This 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 MoreIndium doped CdTe polycrystalline films of thickness equals to 300nm were grown on corning glass substrates at temperature equals to 423K by thermal co-evaporation technique. The structural and electrical properties for these films were studied as a function of heat treatment (323,373,423)K. The x-ray analysis showed that all samples are polycrystalline and have the cubic zincblende structure with preferential orientation in the [111] direction, no diffraction peaks corresponding to metallic Cd, Te or other compounds were observed. It was found that the electrical resistivity drops and the carrier concentration increases when the CdTe film doped with 1.5% indium and treated at different annealing temperatures.