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: Dental stone casts come into contact with impression materials and becomes susceptible to cross contamination from saliva and blood. This study was done to evaluate the physical and mechanical properties of dental stone type IV after treatments with various disinfecting agents and regimes (methods). Materials and Methods: Type IV dental stone and different types of disinfecting agents were used and divided into seven groups: G1: dental stone without disinfection (control group), G2: dental stone mixed with silver nitrate powder 0.5% , G3: dental stone mixed with silver nitrate powder 1%, G4: dental stone mixed with copper sulfate powder 0.5%, G5: dental stone mixed with copper sulfate powder 1% ,G6: dental stone immersed in prop
... Show MoreIn the present work, the focusing was on the study of the x-ray diffraction, dielectric constant, loses dielectric coefficient, tangent angle, alter- natively conductivity and morphology of PET/BaTio3. The PET/BaTio3 composite was prepared for polyethylene terephthalate PET polymer composite containing 0, 10, 20, 30, 40, 50, and 60 wt. % from Barium titanate BaTi03 powder. The composite of two materials leads to form mixing solution and hot-pressing method. The effect of BaTio3 on the structure and dielectric properties with morphology was studied on PET matrix polymer using XRD, LCR meter and SEM.
The Nano compound (Ba1-xSrxTiO3) as (X=0,0.26,0.28,0.30,0.32,0.34) was synthesized by using sol-gel method, the structural properties of result compound were studied by using xray diffraction test (XRD) and scanning electron microscope (SEM). the results were exhibited and by using software indexing to x-ray diffraction pattern that all prepared samples possess tetragonal phase and there is not any other phases were existed. also the substitution process didn't change the phase of compound and increase in (Sr+2) ion concentration leads to decrease lattice parameters (a,c) then the unite cell volume was decreased, as the particle size calculated from Debye-Scherrer and Williamson-Hall equations , and the calculated dens
... Show MoreFiber reinforced polymer composite is an important material for structural application. The diversified application of FRP composite has taken center of attraction for interdisciplinary research. However, improvements on mechanical properties of this class of materials are still under research for different applications. In this paper we have modified the epoxy matrix by Al2O3, SiO2 and TiO2 nano particles in glass fiber/epoxy composite to improve the mechanical and physical properties. The composites are fabricated by hand lay-up method. It is observed that mechanical properties like flexural strength, hardness are more in case of SiO2 modified epoxy composite compare to other nano
... Show MoreIn the present work, pulsed laser deposition (PLD) technique was applied to a pellet of Chromium Oxide (99.999% pure) with 2.5 cm diameter and 3 mm thickness at a pressure of 5 Tons using a Hydraulic piston. The films were deposited using Nd: YAG laser λ= (4664) nm at 600 mJ and 400 number of shot on a glass substrate, The thickness of the film was (107 nm). Structural and morphological analysis showed that the films started to crystallize at annealing temperature greater than 400 oC. Absorbance and transmittance spectra were recorded in the wavelength range (300-
4400) nm before and after annealing. The effects of annealing temperature on absorption coefficient, refractive index, extinction coefficient, real and imaginary parts of d
Oil well drilling fluid rheology, lubricity, swelling, and fluid loss control are all critical factors to take into account before beginning the hole's construction. Drilling fluids can be made smoother, more cost-effective, and more efficient by investigating and evaluating the effects of various nanoparticles including aluminum oxide (Al2O3) and iron oxide (Fe2O3) on their performance. A drilling fluid's performance can be assessed by comparing its baseline characteristics to those of nanoparticle (NPs) enhanced fluids. It was found that the drilling mud contained NPs in concentrations of 0,0.25, 0. 5, 0.75 and 1 g. According to the results, when drilling fluid was used without NPs, the coeff
... Show MoreThe effect of thermal annealing on some structural and optical properties of ZnSe thin films was studied which prepared by thermal evaporation method with (550±20) nm thickness and annealing at (373,473)K for (2h), By using X-ray diffraction technique structural properties studied and showed that the films are crystalline nature and have ( cubic structure ) .From the observed results after heating treatment, We found that the annealing to perform decreases in grain size and increases in dislocation and observed the optical properties increase in absorption and decrease in transmission. From absorption spectra optical energy gap calculated about (2.66,2.68)eV which decreases value after heating treatment
The aim of present work is to improve mechanical and fatigue properties for Aluminum alloy7049 by using Nano composites technique. The ZrO2 with an average grain diameter of 30-40 nm, was selected as Nano particles, to reinforce Aluminum alloy7049 with different percentage as, 2, 4, 6 and 7 %. The Stir casting method was used to fabricate the Nano composites materials due to economical route for improvement and processing of metal matrix composites. The experimental results were shown that the adding of zirconium oxide (ZrO2) as reinforced material leads to improve mechanical properties. The best percentage of improvement of mechanical properties of 7049 AA was with 4% wt. of ZrO2 about (7.76% ) for ultim
... Show MoreBiodiesel define as the mono-alkyl esters of vegetable oil and animal fats is an alternative diesel fuel that is steadily gaining attention because the combustion of fossil fuels such as coal, oil and natural gas has been identify as a major cause of the increase in the concentration of carbon dioxide in the earth’s atmosphere and causing global warming.
The present work concerns with estimating the physical properties experimentally such as kinematic viscosity, density, flash point and carbon residue of biodiesel that produced by the esterification reaction of methanol and oleic acid with homogeneous catalysts H2SO4 in a lab-scale packed reactive distillation column using the best operating conditions of methanol to oleic acid 8:1,
In this research study Hardness (shore D), Water absorption,
Flexural, Impact Test, and Fracture Toughness of polymer nano
composites. The polymer nano composites based on unsaturated
polyester resin reinforced with Kevlar fibers (K.F). The samples are
attended by hand lay – up method according to (Rule mixture) for
various volume fractions of unsaturated polyester resin, fiber and
carbon nanotube. The polyester resin was matrix strengthened with
3% volume fraction from Kevlar fiber and (0.5%, 1%, 1.5%, 2%)
volume fractions of carbon nanotube. The water absorption, hardness
(shore D), flexural test, impact test and toughness fracture properties
were studied. Results showed that the water absorption increas