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
Polyaniline Multi walled Carbon nanotubes (PANI/MWCNTs) nanocomposite thin films have been prepared by non-equilibrium atmospheric pressure plasma jet on glass substrate with different weight percentage of MWCNTs 1, 2, 3, 4%. The diameter of the MWCNTs was in the range of 8-55 nm and length - - 55 55 μm. the nanocomposite thin films were characterized by UV-VIS, XRD, FTIR, and SEM. The optical studies show that the energy band gap of PANI/MWCNTs nanocomposites thin films will be different according to the MWCNTs polyaniline concentration. The XRD pattern indicates that the synthesized PANI/MWCNTs nanocomposite is amorphous. FTIR reveals the presence of MWCNTs nanoparticle embedded into polyaniline. SEM surface images show that the MWCNT
... Show MoreThe effect of heat treatment on the optical properties of the bulk heterojunction blend nickel (II) phthalocyanine tetrasulfonic acid tetrasodium salt and Tris (8-hydroxyquinolinato) Aluminum (NiPcTs/Alq3) thin films which prepared by spin coating was described in this study. The films coated on a glass substrate with speed of 1500 rpm for 1.5 min and treated with different annealing temperature (373, 423 and 473) K. The samples characterized using UV-Vis, X ray diffraction and Fourier transform Infrared (FTIR) spectra, XRD patterns indicated the presence of amorphous and polycrystalline blend (NiPcTs/Alq3). The results of UV visible shows that the band gap increase with increasing the annealing temperature up to 373 K and decreases with
... Show MoreIn 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
Fiber 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 MoreCu X Zn1-XO films with different x content have been prepared by
pulse laser deposition technique at room temperatures (RT) and
different annealing temperatures (373 and 473) K. The effect of x
content of Cu (0, 0.2, 0.4, 0.6, 0.8) wt.% on morphology and
electrical properties of CuXZn1-XO thin films have been studied.
AFM measurements showed that the average grain size values for
CuXZn1-xO thin films at RT and different annealing temperatures
(373, 473) K decreases, while the average Roughness values increase
with increasing x content. The D.C conductivity for all films
increases as the x content increase and decreases with increasing the
annealing temperatures. Hall measurements showed that there are
two
The (NiTsPc) thin films operating by vacuum evaporation technique are high recital and good desirable for number of applications, were dumped on glass substrates at room temperature with (200±20nm) thickness and doped with Al at different percentage (0.01,0.03) besides annealing the sample with 200˚C for 1 hours . The stimuluses of aluminum dopant percentage on characterization of the dropped (Ni Ts Pc) thin films were studied through X-ray diffraction in addition from the attained results, were all the films have polycrystalline in nature, as well the fallouts of XRD aimed at film illustrations polycrystalline, depending on the Al ratio doping, the results, SEM exposed the surface is regularly homogeneous. Utilizing first-ideolog
... Show MoreThe properties of structural and optical of pure and doped nano titanium dioxide (TiO2) films, prepared using chemical spray pyrolysis (CPS) technique, with different nanosize nickel oxide (NiO) concentrations in the range (3-9)wt% have been studied. X-Ray diffraction (XRD) technique where using to analysis the structure properties of the prepared thin films. The results revealed that the structure properties of TiO2 have polycrystalline structure with anatase phase. The parameters, energy gap, extinction coefficient, refractive index, real and imaginary parts were studied using absorbance and transmittance measurements from a computerized ultraviolet visible spectrophotometer (Shimadzu UV-1601 PC) in the wavelength
... Show MoreIn drilling fluid program, selecting the drilling fluid that will reduce the lost time is the first objective, and will be economical regardless of its cost. The amount and type of solids in drilling fluid is the primary control of the rheological and filtration properties. Palygorskite clay (attapulgite) is an active solid that has the ability to reactive with its environment and form a gel structure within a fluid and due to its stability in the presence of brines and electrolytes this type of clay is preferred for use. The aim of this study is to improve properties of Iraqi palygorskite (PAL) by adding different chemical additives such as caustic soda NaOH and soda ash Na2CO3 with a different con
... Show More