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
Introduction: This study was performed to compare the effect of Fractional CO2 laser or Q switched Nd:YAG laser of surface treatment on the shear bond strength of zirconia-porcelain interface. Methods: Fractional CO2 laser at 30 W, 2 ms, time interval 1 ms, distance between spots 0.3 mm, and number of scans is (4) or Q switched Nd:YAG laser at 30 J/mm2 and 10 Hz were used to assess the shear bond strength of zirconia to porcelain. Pre-sintered zirconia specimens were divided into three groups (n = 10) according to the surface treatment technique used: (a) untreated (Control) group; (b) CO2 group; (c) Nd:YAG group. All samples were then sintered and veneered with porcelain according to the manufacturer’s instructions. Surface morph
... Show MoreUnsaturated soil can raise many geotechnical problems upon wetting and drying resulting in swelling upon wetting and collapsing (shrinkage) in drying and changing in the soil shear strength. The classical principles of saturated soil are often not suitable in explaining these phenomena. In this study, expansive soil (bentonite and sand) were tested in different water contents and dry unit weight chosen from the compaction curve to examine the effect of water content change on soil properties (swelling pressure, expansion index, shear strength (soil cohesion) and soil suction by the filter paper method). The physical properties of these soils were studied by conducting series of tests in laboratory. Fitting methods
... Show MoreIn this research, the effect of reinforcing epoxy resin composites with a filler derived from chopped agriculture waste from oil palm (OP). Epoxy/OP composites were formed by dispersing (1, 3, 5, and 10 wt%) OP filler using a high-speed mechanical stirrer utilizing a hand lay-up method. The effect of adding zinc oxide (ZnO) nanoparticles, with an average size of 10-30 nm, with different wt% (1,2,3, and 5wt%) to the epoxy/oil palm composite, on the behavior of an epoxy/oil palm composite was studied with different ratios (1,2,3, and 5wt%) and an average size of 10-30 nm. Fourier Transform Infrared (FTIR) spectrometry and mechanical properties (tensile, impact, hardness, and wear rate) were used to examine the composites. The FTIR
... Show MoreThe aim of this study was to evaluate tensile properties of low and medium carbon ferrite -martensite dual phase steel, and the effect cryogenic treatment at liquid nitrogen temperature (-196 ºC) on its properties. Low carbon steel (C12D) and medium carbon steels (C32D & C42D) were used in this work. For each steel grade, five groups of specimens were prepared according to the type of heat treatment. The first group was normalized, the second group was normalized and subsequently subjected to cryogenic treatment then tempered at (200 ºC) for one hour, the third group was quenched from intercritical annealing temperature of (760 ºC) to obtain dual phase (DP) steel, the fourth and fifth groups were both quenched from (760 ºC), but
... Show MoreTo enlighten the extent of crude oil pollution effects on some anatomical characteristics of olive plant (Olea europaea ). Two years - old seedlings were chosen to grow under 5 levels of pollution (0.0, 0.5, 1.0, 2.0, and 3.0, liter/ plant). The experiment has been conducted in the experimental field of Natural History Research Center and Museum, University of Baghdad. It was designed as CRD experiment. Testing wood specimens were prepared after 2.5 years of growth. Fiber length, width, wall thickness, and wood specific gravity were measured. Results showed that olive plants could not resist the highest level ( 3 liters / plant ) of pollution .Fiber length was the most affected property by treatment. All fiber dimensions wer
... Show MoreIn this paper, thermal properties were performed by using semi-empirical theoretical calculations to study the molecular structure of a nonlinear molecular system, the (S2F2) molecule in the infrared region, by using semi-empirical quantum programs in the (MNDO / PM3) method. This study is under the condition of obtaining the stable structure of the molecule in which the molecule obtains the minimum value of the total energy. The thermodynamic properties were also calculated, including the heat of formation, whose value was (-61.002kcal / mol), the entropy and its value (78.2916 cal / mol.k), as well as the heat capacity (15.9454 cal / mol.k) and the enthalpy (3763.434 cal /mol), Gibbs F
... Show MoreThe current research aimed to investigate the psychometric characteristics of the Arabic version of the Nomophobia scale for the Omani youth. The scale was administered to a random sample of students from public and private universities and colleges in Oman. The research sample consisted of 2507 students, of whom 868 males and 1639 females. The validity of the measure was first checked by presenting the scale to a group of experts in this field. Then the exploratory and confirmatory factor analysis was carried out. The exploratory factor analysis revealed the existence of three main factors: the fear of connectivity loss, the fear of communication loss with others, and the fear of network outages. These factors accounted for 65.6% of the
... Show MoreIn this study ZnS thin film was prepared by using thermal evaporation vacuum technique under the pressure (10-6) Torr on glass substrate at room temperature and annealing at 523 K Samples were irradiated to CO2 laser of power (1 watt) and wave length (10.6) μm at distance 10 cm from the source during (5 sec). The absorbance spectra was recorded by using UV-visible spectrophotometer and used to calculated some of optical properties investigated including their transmittance, reflectance spectra, energy gap, and extinction coefficient. From the result of thin films samples at room temperature and at 523 K, we conclude that the irradiation by laser causes a decrease in the transmittance and increasing in reflection and extinction coeffic
... Show MoreIn the current study, CuAl0.7In0.3Te2 thin films with 400 nm thickness were deposited on glass substrates using thermal evaporation technique. The films were annealed at various annealing temperatures of (473,573,673 and 773) K. Furthermore, the films were characterized by X-ray Diffraction spectroscopy (XRD), field emission scanning electron microscopy (FESEM), atomic force microscopy (AFM), and Ultra violet-visible (UV–vis). XRD patterns confirm that the films exhibit chalcopyrite structure and the predominant diffraction peak is oriented at (112). The grain size and surface roughness of the annealed films have been reported. Optical properties for the synthesized films including, absorbance, transmittance, dielectric constant, and refr
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