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
In this work, a reactive DC magnetron sputtering technique was used to prepare TiO2 thin films. The variation in argon and oxygen gases mixing ratios (4:1, 2:1, 1:1, 1:2, 1:4) was used to achieve optimal properties for gas sensing. In addition, an analysis of the optical XRD properties of TiO2 thin films is presented. High-quality and uniform nanocrystalline films were obtained at a working gas pressure of 0.25 mbar and 1:4 (Ar/O2) gas mixture. The optical properties showed a transparent thin film with uniform adherence to the substrate. The average transmission of the TiO2 films deposited on the glass substrates was higher than 95% over the range of 400 to 800 nm.
... Show MoreIn this paper, we used two monomers, 3,3',4,4'-benzophenone tetracarboxylic dianhydride (BTDA) and m,m'-diaminobenzophenone (m, m’-DABP), to produce polyamide acid and then converted it to polyimide (PI). The effects of phosphoric acid (H3PO4) molarity (1, 2, and 3 M) on the structural, thermal, mechanical, and electrical characteristics of the polyimides/polyaniline (PI/PANI) nanocomposites were studied. Two sharp reflection peaks were developed by the addition of PANI to PI. When 3 M H3PO4 is added, the crystalline sharp peak loses some of its intensity. The complex formation of PI/PANI-H3PO4 was confi
... Show MoreIn this research the effect of laser energy by using argon gas on the some physical properties of semiconductor film of TiO2, was studied used Q-Switch Nd:YAG laser in different energies (600-1000) mJ with temperature 100 0C for glass substrate under vacuum nearly 10-3 - - , and by AFM test the roughness of films increased when the energy of laser increased too. The values of roughness between (6.77-13) nm, therefore the thicknesses increased to change from (34.88 - 165.48) nm, so the absorption of film increased because of the thickness of the film increased and we can get the optical energy gap between (3.6-3.9) eV.
Background: Dental casts come into direct contact with impression materials and other items that are contaminated by saliva and blood from a patient's mouth, leaving the casts susceptible to cross-contamination. The disinfectant solutions of the impression materials cause various adverse reactions. Therefore, disinfection of dental casts may be effective in preventing cross infection. This study was carried out to evaluate the surface hardness, dimensional accuracy, reproduction of details and surface porosity of type III, type IV and type IV extra hard dental stone after immersion in and spray by using SOLO and Sodium hypochlorite disinfectant solutions. Materials and methods: 240 Stone samples were prepared in rubber rings, A total of 60
... Show MoreIn this Research, (In2O3: CdO) films were prepared using pulsed laser deposition (PLD) method on glass substrate at room temperature deposited at laser influence 500mJ/cm2with different shoots N= (200,300,400,500and600). the structural, and the optical properties and the films are studied with different annealing temperatures (523and 623) K. Optical measurements and the films were analyzed by UV-VIS absorption spectra. The structural properties of samples were investigated by x-ray diffraction patterns of the films and show that the films and polycrystalline Structure with all shoots. Transmittance spectrum found is equal to 93.17%, refractive index range is 1.635 and energy gap range is 2.75-3.15ev.
Semi-empirical methods were applied for calculating the vibration frequencies and IR absorption intensities for normal coordinates of the {mono (C56H28), di (C84H28), tri (C112H28) and tetra (C140H28)} -rings layer for (7,7) armchair single wall carbon nanotube at their equilibrium geometries which were all found to have D7d symmetry point group.
Assignment of the modes of vibration (3N-6) was done depending on the pictures of their modes by applying (Gaussian 03) program. Comparison of the vibration frequencies of (mono, di, tri and tetra) rings layer which are active in IR, and inactive in Ramman spectra. For C-H stretching vibrat
... Show MorePure and Fe-doped zinc oxide nanocrystalline films were prepared
via a sol–gel method using -
C for 2 h.
The thin films were prepared and characterized by X-ray diffraction
(XRD), atomic force microscopy (AFM), field emission scanning
electron microscopy (FE-SEM) and UV- visible spectroscopy. The
XRD results showed that ZnO has hexagonal wurtzite structure and
the Fe ions were well incorporated into the ZnO structure. As the Fe
level increased from 2 wt% to 8 wt%, the crystallite size reduced in
comparison with the pure ZnO. The transmittance spectra were then
recorded at wavelengths ranging from 300 nm to 1000 nm. The
optical band gap energy of spin-coated films also decreased as Fe
doping concentra
We studied the changing of structural and optical properties of pure and Aluminum-doped ZnO thin films prepared by thermal evaporation technique on glass substrates at thickness (800±50)nm with changing of annealing temperatures ( 200,250,300 )℃ for one hour. The investigation of (XRD) indicates that the pure and doped ZnO thin films were polycrystalline of a hexagonal wurtzite structure with preferred orientation along (002) plane. The grain size was decreased with doping before annealing, but after annealing the grain size is increasing with the increase of annealing temperature for pure film whereas for the doped films with ratios 1 %, 2 % we found that the grain size is larger than that before annealing. The grain size
... Show More