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
Cu 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
In this study, Laser Shock Peening (LSP) effect on the polymeric composite materials has been investigated experimentally. Polymeric composite materials are widely used because they are easy to fabricate and have many attractive features. Unsaturated polyester resin as a matrix was selected and Aluminum powder with micro particles as a reinforcement material was used with different volume fraction (2.5%, 5% and 7.5%). Hand lay-up process was used for preparation the composites. Fatigue test with constant amplitude with stress ratio (R =-1) was carried out before and after LSP process with two levels of energy (1Joule and 2Joule). The result showed an increase in the endurance strength of 25.448% at 7.5% volume fraction when peened is 1J
... Show MoreIn this study, condensation polymerization was used to synthesize a number of novel liquid crystal polymers with 1,3,4-oxadiazole rings based on melamine. The new synthesized polymers were characterized by Fourier transform infrared (FTIR) and proton nuclear magnetic resonance (1HNMR) spectroscopy. Differential scanning calorimetry (DSC) and optical polarization microscopy (OPM) were used to investigate their liquid crystalline properties. The results demonstrated that throughout a wide temperature range, most of the polymers exhibited columnar (CohX) and nematic (N) liquid crystalline phases.
The structural, optical properties of cupper indium gallium selenite (CuIn1-xGaxSe) have been studied. CuIn1-xGaxSe thin films for x=0.6 have been prepared by thermal evaporation technique, of 2000±20 nm thickness, with rate of deposition 2±0.1 nm/sec, on glass substrate at room temperature. Heat treatment has been carried out in the range (373-773) K for 1 hour. It demonstrated from the XRD method that all the as-deposited and annealed films have polycrystalline structure of multiphase. The optical measurement of the CIGS thin films conformed that they have, direct allowed energy gap equal to 1.7 eV. The values of some important optical parameters of the studied films such as (absorption coefficient, refractive index, extinction coeffici
... Show MoreResilient polymeric materials such as silicone elastomers are currently used for maxillofacial prostheses construction but the strength of these materials and their clinical performance need to be optimized with the addition of reinforcing fillers. This study investigates the effect of zirconia nanopowder addition on tear strength, tensile strength, elongation at break, Shore A hardness, surface roughness and cytotoxicity of VST-50 maxillofacial silicone. Silicone base was mixed with different amounts (1%, 2% and 3%) of zirconia nanopowder using a vacuum mixer. Silicone without filler was used as control for comparison. Scanning Electron Microscopy and Atomic Force Microscopy were utilized to assess the efficiency of high-shear vacuum mixin
... 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 MoreThe aim of this work is to enhance the mechanical properties of the glass ionomer cement GIC (dental materials) by adding Zirconium Oxide ZrO2 in both micro and nano particles. GIC were mixed with (3, 5 and 7) wt% of both ZrO2 micro and nanoparticles separately. Compressive strength (CS), biaxial flexural strength (BFS), Vickers Microhardness (VH) and wear rate losses (WR) were investigated. The maximum compression strength was 122.31 MPa with 5 wt. % ZrO2 micro particle, while 3wt% nanoparticles give highest Microhardness and biaxial flexural strength of 88.8 VHN and 35.79 MPa respectively. The minimum wear rate losses were 3.776µg/m with 7 wt. % ZrO2 nanoparticle. GIC-contai
... 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 MorePolyaniline 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 D phase polyamide (PA6)on the rheological properties, Young Modulus and the thermal expansion coefficient of two blends groups (bitumen-polyamide) were tested. The first group was for bitumen-PA6 blends and the second group for bitumen blended with polymer resulted from the crystallization of PA6-formic acid solution in water(PAFW).The obtained results proved that adding both types of polyamide has led to a rise in toughness and softening point temperature while the penetration Index approached -3 after adding the polyamide. So, all these changes make bitumen-polyamide blends more suitable for use in hot climate regions. The blends properties were explained according to the reaction that takes place between the polyamide and
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