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, the emission spectra and atomic structure of the aluminum target had been studied theoretically using Cowan code. Cowan code was used to calculate the transitions of electrons between atomic configuration interactions using the mathematical method called (Hartree-Fock). The aluminum target can give a good emission spectrum in the XUV region at 10 nm with oscillator strength of 1.82.
The hydrodynamic properties of laser produced plasma (LPP) were investigated for the purpose of creating a light source working in the EUV region. Such a light source is very important for lithography (semiconductor manufacturing). The improved MEDUSA (Med103) code can calculate the plasma hydrodynamic properties (velocity, electron density,
When the depth of stressed soil is rather small, Plate Load Test (PLT) becomes the most efficient test to estimate the soil properties for design purposes. Among these properties, modulus of subgrade reaction is the most important one that usually employed in roads and concrete pavement design. Two methods are available to perform PLT: static and dynamic methods. Static PLT is usually adopted due to its simplicity and time saving to be performs in comparison with cyclic (dynamic) method. The two methods are described in ASTM standard.
In this paper the effect of the test method used in PLT in estimation of some mechanical soil properties was distinguished via a series of both test methods applied in a same site. The comparison of
... Show MoreIn this study, two active galaxies (NGC4725, NGC4639) have been chosen to study their morphological and photometric properties, by using the IRAF ISOPHOTE ELLIPS task with griz-filters. Observations are obtained from the Sloan Digital Sky Survey (SDSS) which reaches now to the DATA Release (DR14). The data reduction of all images (bias and flat field) has been done by SDSS Pipeline. The surface photometric investigation was performed like the magnitude. Together with isophotal contour maps, surface brightness profiles and a bulge/disk decomposition of the images of the galaxies, although the disk position angle, ellipticity, and inclination of the galaxies have been done. Also, the color of galaxies was studied, where chromatic distribution
... Show MorePolycrystalline ingots of cadmium telluride have been synthesized using the direct
reaction technique, by fusing initial component consisting from pure elements in
stoichiometric ratio inside quartz ampoule is evacuated 10-6 torr cadmium telluride has
been grown under temperature at (1070) oC for (16) hr. was used in this study, the phases
observed in growing CdTe compound depend on the temperature used during the growth
process. Crystallography studies to CdTe compound was determined by X-ray diffraction
technique, which it has zinc blend structure and cubic unit cell, which lattice constants is
a=6.478
oA
Nanocomposite was prepared using unsaturated polyester (UP) resin as a matrix and graphene nanoparticles as a reinforcement material in six percentage weights (0, 0.1, 0.2, 0.3, 1 and 1.5%). Mechanical, calorimetric and thermal studies were performed on the (UP) resin/graphene nanocomposite. All tests showed a clear improvement of all mechanical properties examined (hardness, flexural strength (F.S), impact strength (I.S) and tensile strength (T.S)) with increasing graphene percentage. In addition, the temperature of glass transition and thermal conductivity of this composite increased with increasing graphene content.
There is no doubt that optical fiber technology is one of the most important stages of the communications revolution at all and it is of utmost importance in our daily life. In this work, five fibers with core radii 2.5, 4.5 and 6.5–8.5 μm were designed. The properties of all guided modes have been calculated at a wavelength of 1550 nm by using RP Fiber Calculator. A single-mode fiber is obtained when the core radius approaches the wavelength. As the core radius is increased, the fiber becomes a multimode. The percentage power in the core increases with increasing core radius. The modes profiles were illustrated and compared with the modern references.