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
Purepolyaniline and doped with hydrochloric acid was prepared in different molarities at room temperature. The a.c electrical properties were stadied.AC conductivityσac (ω), is found to vary as ωS in the frequency range (100Hz-10MH), S< 1and decreases indicating a dominate hopping process. Thedielectric constant ε1and dielectric loss ε2 have been determined for bulk polyaniline. ε1 decrease with the increase frequency. Electrical conductivity measurements increase with the increases both of the amount of HCl and the dose of radiation. The dielectric investigations show decrease with dose radiation.
In this investigation, metal matrix composites (MMCs) were manufactured by using powder technology. Aluminum 6061 is reinforced with two different ceramics particles (SiC and B4C) with different volume fractions as (3, 6, 9 and 12 wt. %). The most important applications of particulate reinforcement of aluminum matrix are: Pistons, Connecting rods etc. The specimens were prepared by using aluminum powder with 150 µm in particle size and SiC, B4C powder with 200 µm in particle size. The chosen powders were mixed by using planetary mixing setup at 250 rpm for 4hr.with zinc stearate as an activator material in steel ball milling. After mixing process the powders were compacted by hydraulic
... Show MoreThe pure and Sb doped GeSe thin films have been prepared by thermal flash evaporation technique. Both the structural and optical measurement were carried out for as deposited and annealed films at different annealing temperatures.XRD spectra revealed that the all films have one significant broad amorphous peak except for pure GeSe thin film which annealed at 573 K, it has sharp peak belong to orthorhombic structure nearly at 2θ=33o . The results of the optical studies showed that the optical transition is direct and indirect allowed. The energy gap in general increased with increasing annealing temperature and decreased with increase the ratio of Sb dopant. The optical parameters such as refractive index, extinction coefficient and r
... Show MoreThis study was aimed to study the effect of adding transglutaminase (TGase) on the mechanical and reservation properties of the edible films manufactured from soybean meal protein isolate (SPI) and whey protein isolate(WPI). The results showed an improvement in the properties with increase in the WPI ratios. Thickness of the SPI films amounted 0.097 mm decreased to 0.096 mm for the WPI: SPI films at a ratio of 2:1, when TGase was added decreased to 0.075 mm. While the tensile strength increased from 7.64 MPa for SPI films to eight MPa for the WPI: SPI films at a ratio of 2:1, when TGase was added increased to 11.04 MPa. Also, the elongation of the WPI: SPI films at a ratio of 2:1 presence of the TGase decreased to 40.6% compared wit
... Show MoreNuclear structure of 29-34Mg isotopes toward neutron dripline have been investigated using shell model with Skyrme-Hartree–Fock calculations. In particular nuclear densities for proton, neutron, mass and charge densities with their corresponding rms radii, neutron skin thicknesses and inelastic electron scattering form factors are calculated for positive low-lying states. The deduced results are discussed for the transverse form factor and compared with the available experimental data. It has been confirmed that the combining shell model with Hartree-Fock mean field method with Skyrme interaction can accommodate very well the nuclear excitation properties and can reach a highly descriptive and predictive power when investiga
... Show MoreThe pure and Sb doped GeSe thin films have been prepared by thermal flash evaporation technique. Both the structural and optical measurement were carried out for as deposited and annealed films at different annealing temperatures.XRD spectra revealed that the all films have one significant broad amorphous peak except for pure GeSe thin film which annealed at 573 K, it has sharp peak belong to orthorhombic structure nearly at 2θ=33o. The results of the optical studies showed that the optical transition is direct and indirect allowed. The energy gap in general increased with increasing annealing temperature and decreased with increase the ratio of Sb dopant. The optical parameters such as refractive index, extinction coefficient and real and
... Show MoreThis work aims to enhance acoustic and thermal insulation properties for polymeric composite by adding nanoclay and rock wool as reinforcement materials with different rations. A polymer blend of (epoxy+ polyester) as matrix materials was used. The Hand lay-up technique was used to manufacture the castings. Epoxy and polyester were mixed at different weight ratios involving (50:50, 60:40, 70:30, 80:20, and 90:10) wt. % of (epoxy: polyester) wt. % respectively. Impact tests for optimum sample (OMR), caustic and thermal insulation tests were performed. Nano clay (Kaolinite) with ratios ( 5 and 7.5% ) wt.% , also hybrid reinforcement materials involving (Kaolite 5 & 7.5 % wt.% + 10% volume fraction of rockwool ) were added as reinforcem
... Show MoreIn this study, pure SnO2 Nanoparticles doped with Cu were synthesized by a chemical precipitation method. Using SnCl2.2H2O, CuCl2.2H2O as raw materials, the materials were annealed at 550°C for 3 hours in order to improve crystallization. The XRD results showed that the samples crystallized in the tetragonal rutile type SnO2 stage. As the average SnO2 crystal size is pure 9nm and varies with the change of Cu doping (0.5%, 1%, 1.5%, 2%, 2.5%, 3%),( 8.35, 8.36, 8.67, 9 ,7, 8.86)nm respectively an increase in crystal size to 2.5% decreases at this rate and that the crystal of SnO2 does not change with the introduction of Cu, and S
... Show MoreObjective Advantageous properties of silicone elastomer made it one of the favorable materials in maxillofacial prosthesis construction, but these properties may change after months of usage or after pigments addition. This study aimed to define the optimum concentration for a mixture of two types of intrinsic pigments that added to VST-50 maxillofacial silicone material and study their effects on mechanical properties before and after artificial aging. Methods After the pilot study was conducted, 0.1% by weight of rayon flocking and 0. 2% by weight of burnt sienna intrinsic pigment concentration was selected because of improvement in tested mechanical properties of VST-50 maxillofacial silicone. A total of one hundred and eighty samples we
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