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
Chalcogenide glasses SeTe have been prepared from the high purity constituent elements .Thin films of SeTe compound have been deposited by thermal evaporation onto glass substrates for different values of film thickness . The effect of varying thickness on the value of the optical gap is reported . The resultant films were in amorphous nature . The transmittance spectra was measured for that films in the wavelength range (400-1100) nm . The energy gap for such films was determined .
The change in the optical properties for samples of pure PVA and PVA /K2CrO4composite have been studied .The samples were prepared with different percentage (1,3,5,and 7)%wt of K2CrO4 by casting method technique .In this work ,we are study the absorption ,reflectance spectra ,absorption coefficient, energy gap ,extinction coefficient ,and transmittance spectra as a function of wavelength range (200-800)nm ,Also real and imaginary part of dielectric constant have been studied in the range of wave length .The results exhibit the optical properties change by the increase of K2CrO4 concentration, and the values of energy gap for indirect transitions decrease by the increase of the concentration of K2CrO4
... Show MoreCadmium Oxide thin films were deposited on glass substrate by spray pyrolysis technique at different temperatures (300,350,400, 500)oC. The optical properties of the films were studied in this work. The optical band-gap was determined from absorption spectra, it was found that the optical band-gap was within the range of (2.5-2.56)eV also width of localized states and another optical properties.
High Alumina Glasses "Alumina Silicate Glasses" was prepared by utilizing powder technology technique. The starting materials are wasted soda-lime glass from an industrial site, Iraqi Duekhla raw kaolin and small amounts of potassium carbonates.
X-ray Diffraction and FTIR analysis show complete vitreous glasses are obtained. Increasing Alumina content plays an obvious role in improving physical and mechanical properties of the prepared high alumina glass. In addition, the increased alumina content enhanced the dielectric constant and reduced dielectric loss. These results may be interpreted as du
... Show MoreThe local asphalt concrete fracture properties represented by the fracture energy, J-integral, and stress intensity factor are calculated from the results of the three point bending beam test made for pre notches beams specimens with deformation rate of 1.27 mm/min. The results revealed that the stress intensity factor has increased by more than 40% when decreasing the testing temperature 10˚C and increasing the notch depth from 5 to 30mm. The change of asphalt type and content have a limited effect of less than 6%.
Unsaturated polyester toughened Epoxy was developed. Epoxy resin had toughened by weight fraction of 10, 20, 30, and 40 wt. % unsaturated polyester. FTIR spectroscopy has been used to investigating the intermolecular hydrogen bonding. Unsaturated polyester–epoxy matrices were characterized for their thermal properties. The FTIR test detected a peak shift of the functional groups which can explain cross-linking occurs between the two resins. The crosslinking between epoxy and unsaturated polyester confirmed via the existence of the stretching asymmetrical C-C band and contraction of the C-O band. The DSC test demonstrated that glass transition temperature value decreases with epoxy strengthening. The specific heat capacity and the
... Show MoreThe Asphalt cement is produced as a by-product from the oil industry; the asphalt must practice further processing to control the percentage of its different ingredients so that it will be suitable for paving process. The objective of this work is to prepare different types of modified Asphalt cement using locally available additives, and subjecting the prepared modified Asphalt cement to testing procedures usually adopted for Asphalt cement, and compare the test results with the specification requirements for the modified Asphalt cement to fulfill the paving process requirements. An attempt was made to prepare the modified Asphalt cement for pavement construction in the laboratory by digesting each of the two penetration grade Asphalt c
... Show MoreIn the present work, lead silicate glasses have been prepared with
different amount of lead oxide content. Structure properties such as
X-ray diffraction, AFM, and FTIR analyses have been done. The
exceeding of PbO content more than 25wt% revealed a decreasing in
density. The X- ray revealed that the strongest peak related to
Hexagonal silica dioxide and the other crystal phases formed were
related to silica oxide (SiO2) and lead oxide (PbO). Growth and
decayed phases in X-ray have been observed with changing lead
oxide content. Homogeneous surface was obtained using AFM
analyzer with an average diameter around 100 nm. Infrared spectrum
is characterized by the presence of large absorption band between
120
Silver sulfide and the thin films Ag2Se0.8Te0.2 and Ag2Se0.8S0.2 created by the thermal evaporation process on glass with a thickness of 350 nm were examined for their structural and optical properties. These films were made at a temperature of 300 K. According to the X-ray diffraction investigation, the films are polycrystalline and have an initial orthorhombic phase. Using X-ray diffraction research, the crystallization orientations of Ag2Se and Ag2Se0.8Te0.2 & Ag2Se0.8S0.2 (23.304, 49.91) were discovered (XRD). As (Ag2Se and Ag2Se0.8Te0.2 & Ag2Se0.8S0.2) absorption coefficient fell from (470-774) nm, the optical band gap increased (2.15 & 2 & 2.25eV). For instance, the characteristics of thin films made of Ag2Se0.8Te0.2 and Ag2Se0.8S0.2
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