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
This study reports the fabrication of tin oxide (SnO2) thin films using pulsed laser deposition (PLD). The effect of 60Co (300, 900, and 1200 Gy) gamma radiation on the structural, morphological, and optical features is systematically demonstrated using X-ray diffraction (XRD), field emission scanning electron microscopy (FE-SEM), atomic force microscopy (AFM), and ultraviolet-visible light analysis (UV-Vis), respectively In XRD tests, the size of the crystallites decreased from 45.5 to 40.8 nm for the control samples and from 1200 Gy to 60Co for the irradiated samples. Using FESEM analysis, the particle diameter revealed a similar trend to that attained using XRD; in particular, the average diameters were 93.8 and
... Show Morewell log analysis is used to determine the rock properties like porosity, water saturation, and shale volume. Archie parameters in Archie equation, which sometimes considered constants greatly affect the determination of water saturation, also these parameters may be used to indicate whether the rocks are fractured or not so they should be determined. This research involves well logging analysis for Zubair formation in Luhais field which involves the determination of Archie parameters instead of using them as constant.
The log interpretation proved that the formation is hydrocarbon reservoir, as it could be concluded from Rwa (high values) and water saturation values (low values), the lithology of Zubair from cro
... Show MoreBackground: 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 MoreThe electronic properties (such as energy gap HOMO levels. LUMO levels, density of state and density of bonds in addition to spectroscopic properties like IR spectra, Raman spectra, force constant and reduced masses as a function of frequency) of coronene C24 and reduced graphene oxide C24OX , where x=1-5, were studied.. The methodology employed was Density Functional Theory (DFT) with Hybrid function B3LYP and 6-311G** basis sets. The energy gap was calculated for C24 to be 3.5 eV and for C24Ox was from 0.89 to 1.6862 eV for x=1-5 ,respectively. These energy gaps values are comparable to the measured gap of Graphene (1-2.2 eV). The spectroscopic properties were compared with experimental measurements, specificall
... Show MorePolycrystalline Cadmium Oxide (CdO) thin films were prepared using pulsed laser deposition onto glass substrates at room temperature with different thicknesses of (300, 350 and 400)nm, these films were irradiated with cesium-137(Cs-137) radiation. The thickness and irradiation effects on structural and optical properties were studied. It is observed by XRD results that films are polycrystalline before and after irradiation, with cubic structure and show preferential growth along (111) and (200) directions. The crystallite sizes increases with increasing of thickness, and decreases with gamma radiation, which are found to be within the range (23.84-4.52) nm and (41.44-4.974)nm before and after irradiation for thickness 350nm and 4
... Show MoreIn this research, A thin film of Rhodamine B dye and TiO2 Nanoparticles doped in PMMA Polymer has been prepared by a casting method. The sample was spectrum absorption by UV-Vis. The nonlinear optical properties were measured by Z- scan technique using Nd:YAG laser with (1064 nm) wavelength. The nonlinear refractive index (n2) and nonlinear absorption coefficient (β) were estimated for the thin film for different energies of the laser, n2 and β were decreased with increasing intensity of incident laser beam. Also, the type of β was two-photon absorption and n2 negative nonlinear reflective.
A polycrystalline PbxS1-x alloys with various Pb content ( 0.54 and 0.55) has been prepared successfully. The structure and composition of alloys are determined by X-ray diffraction (XRD), atomic absorption spectroscopy (AAS) and X-ray fluorescence (XRF) respectively. The X-ray diffraction results shows that the structure is polycrystalline with cubic structure, and there are strong peaks at the direction (200) and (111), the grain size varies between 20 and 82 nm. From AAS and XRF result, the concentrations of Pb content for these alloys were determined. The results show high accuracy and very close to the theoretical values. A photoconductive detector as a bulk has been fabricated by taking pieces of prepared alloys and polished chemic
... Show MorePolycrystalline Cadmium Oxide (CdO) thin films were prepared
using pulsed laser deposition onto glass substrates at room
temperature with different thicknesses of (300, 350 and 400)nm,
these films were irradiated with cesium-137(Cs-137) radiation. The
thickness and irradiation effects on structural and optical properties
were studied. It is observed by XRD results that films are
polycrystalline before and after irradiation, with cubic structure and
show preferential growth along (111) and (200) directions. The
crystallite sizes increases with increasing of thickness, and decreases
with gamma radiation, which are found to be within the range
(23.84-4.52) nm and (41.44-4.974)nm before and after irradiation for