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
Background: The purpose of this study was to evaluate the effect of addition of surface treated silicon dioxide Nano filler (SiO2) on some properties of heat cured acrylic resin denture base material (PMMA). The properties were impact strength, transvers strength, and surface hardness. Materials and methods: In addition to controlled group SiO2 powder was added to PMMA powder by weight in three different percentages 3%, 5% and 7%, mixed by probe ultra-sonication machine.120 specimens were constructed and divided into 3 groups according to the test (each group consist of 40 specimens) and each group was subdivided into 4 sub-groups according to the percentage of added SiO2 (finally each subgroup consist of 10 specimens). The tests conducte
... Show MoreThe research involves using phenol – formaldehyde (Novolak) resin as matrix for making composite material, while glass fiber type (E) was used as reinforcing materials. The specimen of the composite material is reinforced with (60%) ratio of glass fiber.
The impregnation method is used in test sample preparation, using molding by pressure presses.
All samples were exposure to (Co60) gamma rays of an average energy (2.5)Mev. The total doses were (208, 312 and 728) KGy.
The mechanical tests (bending, bending strength, shear force, impact strength and surface indentation) were performed on un irradiated and irrad
... Show MoreTo achieve sustainability, use waste materials to make concrete to use alternative components and reduce the production of Portland cement. Lime cement was used instead of Portland cement, and 15% of the cement's weight was replaced with silica fume. Also used were eco-friendly fibers (copper fiber) made from recycled electrical. This work examines the impact of utilizing sustainable copper fiber with different aspect ratios (l/d) on some mechanical properties of high-strength green concrete. A high-strength cement mixture with a compressive strength of 65 MPa in line with ACI 211.4R was required to complete the assignment. Copper fibers of 1% by volume of concrete were employed in mixes with four different aspect ratios
... Show MoreIn this research study the effect of fish on the properties optical films thickness 1200-1800 and calculated energy gap Basra direct transport permitted and forbidden to membranes and urged decreasing values ??of Optical Energy Gap increase fish included accounts optical also calculate the constants visual as factories winding down and the refractive index and reflectivity membranes also by real part and imaginarythe dielectric constant
In this paper deals with the effect laser irradiation on the optical properties of cobalt oxide (CoO2) thin films and that was prepared using semi computerized spray pyrolysis technique. The films deposited on glass substrate using such as an ideal value concentration of (0.02)M with a total volume of 100 ml. With substrate temperature was (350 C), spray rate (15 ml/min).The XRD diffraction given polycrystalline nature with Crystal system trigonal (hexagonal axes). The obtained films were irradiated by continuous green laser (532.8 nm) with power 140 mW for different time periods is 10 min,20min and 30min. The result was that the optical properties of cobalt oxide thin films affe
Bobbin friction stir welding (BFSW) is a variant of the conventional friction stir welding (CFSW); it can weld the upper and lower surface of the work-piece in the same pass. This technique involves the bonding of materials without melting. In this work, the influence of tool design on the mechanical properties of welding joints of 6061-T6 aluminum alloy with 6.25 mm thickness produced by FSW bobbin tools was investigated and the best bobbin tool design was determined. Five different probe shapes (threaded straight cylindrical, straight cylindrical with 3 flat surfaces, straight cylindrical with 4 flat surfaces, threaded straight cylindrical with 3 flat surface and threaded straight cylindrical with 4 flat surfaces) with various dimensio
... Show MoreIn this paper, we will illustrate a gamma regression model assuming that the dependent variable (Y) is a gamma distribution and that it's mean ( ) is related through a linear predictor with link function which is identity link function g(μ) = μ. It also contains the shape parameter which is not constant and depends on the linear predictor and with link function which is the log link and we will estimate the parameters of gamma regression by using two estimation methods which are The Maximum Likelihood and the Bayesian and a comparison between these methods by using the standard comparison of average squares of error (MSE), where the two methods were applied to real da
... Show MoreRandom laser gain media is synthesized with different types of dye at the same concentration (1×10-3 M) as an active material and silicon dioxide NPs (silica SiO2) as scatter centers through the Sol-Gel technique. The prepared samples are tested with UV–Vis spectroscopy, Fluorescence Spectroscopy, Field Emission Scanning Electron Microscopy (FESEM), and Energy Dispersive X-ray Diffraction (EDX). The end result demonstrates that doped dyes with silica nanoparticles at a concentration of 0.0016 mol/ml have lower absorbance and higher fluorescence spectra than pure dyes. FESEM scans revealed that the morphology of nanocrystalline silica is clusters of nano-sized spherical particles in the range (25-67) nm. It is con
... Show MoreBackground: The incorporation of rubber has not been entirely successful because it can have detrimental effects on the transverse Strength and hence the rigidity of the denture base. Materials and methods: Zirconium oxide nanoparticales were coated with a layer of trimethoxysilylpropylmethacrylate (TMSPM) before sonication in monomer (MMA) with the percentages 3% by weight then mixed with powder using conventional procedure.(100) samples were prepared and divided into five groups according to the test performed ,Each group consisted of 20 specimens and these were subdivided into 2 groupsGroup (A): control group (10 specimens of high impact acrylic resin without zirconium oxide) and Group (B):zirconium oxide group(10 specimens of high impac
... Show MoreBackground: Poly propylene fibers with and without silane treatment have been used to reinforce heat cure denture base acrylic but, some mechanical properties like transverse strength, impact strength, tensile strength, hardness, wear resistance and wettability. Which are related to the clinical use of the prosthesis are not evaluated yet. The aim of the study is to identify the influence of incorporation of treated and untreated fibers on these properties Materials and methods: Eighty four heat cure acrylic specimens were constructed by conventional flasking technique. They were divided into six groups according to the tests and each group was subdivided into two subgroups control and experimental groups (seven samples for each subgroup
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