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
Abstract:
In this study a type of polymeric composites from melting poly propylene as a basic substance with Palm fronds powder were prepared. Evaluation of polymeric composites was done by studying some of it is mechanical properties, which included:Yong modulus (E), Impact Strength (I.S), Brinell hardness (B.H) and Compression Strength (C.S). The polymeric composites were studied before and after reinforcment by comparing between them. There was an increase in resistance of Yong modulus (E), Impact Strength (I.S), Brinell hardness (B.H) and compression Strength (C.S). Also, the effect of some acids were studied such as (HCl, H2
In this work, a composite material was prepared from Low-density polyethylene (LDPE) with different weight percent of grain and calcinations kaolin at temperature of (850oC) using single screw extruder and a mixing machine operated at a temperature between (190-200oC). Some of mechanical and physical properties such as tensile strength, tensile strength at break, Young modulus, and elongation at break, shore hardness and water absorption were determined at different weight fraction of filler (0, 2, 7, 10 and 15%). It was found that the addition of filler increases the modulus of elasticity, elongation at break, shore hardness and impact strength; on other hand, it decreases the tensile strength and tensile strength
... 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
... 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 work, The effect of annealing treatment at different temperatures (373, 423 and 473) K and chemical treatment with talwen at different immersion time (40, 60 and 80) min on structural and optical properties of the bulk heterojunction (BHJ) blend copper phthalocyanine tetrasulfonic acid tetrasodium salt/poly dioxyethylenethienylene doped with polystyrenesulphonic acid (CuPcTs/PEDOT:PSS) thin films were investigated. The films were fabricated using spin coating technique. X-ray diffraction (XRD) measurements displayed only one peak at 2θ =4.5o corresponding to (001) direction which has dhkl larger than for standard CuPcTs. The dhkl increase then decrease with increasing annealing temperature and
the time of chemical treatment w
Nuclear 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 MorePurepolyaniline 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 study the as-deposited and heat treated at 423K of conductive blende graphene oxide (GO) / poly(3,4-ethylenedioxythiophene)-poly(styrenesulfonate) (PEDOT:PSS) thin films was prepared with different PEDOT:PSS concentration (0, 0.25, 0.5, 0.75 and 1.0)wt% on pre-cleaned glass substrate by spin coating technique. The energy dispersive X-ray Analysis (EDX) show the existence of higher amount of carbon and oxygen related to hydroxyl and carbonyl groups. X-ray diffraction (XRD) analysis of the as-deposited and annealed GO/PEDOT:PSS thin films blend indicated that the film prepared show broad peak around 8.24 corresponding to the (001) level refers to GO, this peak shifted to the lower 2θ with increasing PEDOT:PSS concentr
... 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 MoreThe present study included the use of the approximate semi-experimental method, the time-independent density function theory (unrestricted), the time-dependent density function theory, and Hartree-Fock method to calculate the reaction pathway of the anti-inflammatory drug diclofenac with its common ionic carriers (sodium and potassium). The basis sets used were STO-3G, 3-21G, 6-31G, and 6-311G. The drug was studied with two new proposed carrier ions (lithium and calcium) which were compared with common carriers. The calculations included the optimized geometrical structure and some physical properties such as standard heat of formation, dipole moment, total energies, and analytical spectra of IR, UV-VIS and 1H NMR. The biologi
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