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
The mechanical properties and microstructure of hot-rolled steel are critical in determining its performance in industrial applications, particularly when exposed to elevated temperatures. This study examines the effects of varying temperatures and soaking times on these properties through a series of controlled experiments. The primary objective was to optimize the key response parameters, including tensile strength, yield strength, and elongation, by analyzing the influence of temperature and time. A full factorial design approach was used, applying the desirability function theory to explore all possible combinations and identify optimal processing conditions. The experimental results showed that the soaking time played a critica
... 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 MoreThe increasing use of plastics in various aspects of modern life resulted in the availability of enormous amount of wastes, including a negative effect on the environment and humans. So it is necessary to find solutions to deal with these wastes and ensure to use them as solutions to use in concrete mix . In this research the production of concrete containing high and low density polyethylene has been used by (5, 10, 15)% as a replacement of part of the volume of sand, so as to obtain concrete good compressive strength as well as other benefits such as improved possibility of pumping concrete and reduce the loss of concrete for workability polymer is a material that is non-absorbable of water . It is also intended to dispose of these was
... Show MoreIn this research a computational simulation has been carried out on the design and properties of the electrostatic mirror and a mathematical expression has been suggested to represent the axial potential of an electrostatic mirror. The electron beam path using the Bimurzaev technique had been investigated as mirror trajectory with the aid of Runge – Kutta method. The spherical and chromatic aberration coefficients of mirror has computed and normalized in terms of the focal length. The choice of the mirror depends on the operational requirements. The Electrode shape of mirror two electrodes has been determined by using package SIMION computer program. Computations have shown that the suggested potentials giv
... Show MoreIn this research,we are studied impact strength, bending and compression strength of composites including the epoxy resin as a matrix , with gawaian red wood flour ,Russian white wood flour ,glass powder and rock wool fibers as reinforcement materials with volume fraction (20%) for all samples,and compared them in different conditions of temperatures. The results have shown that the impact strength increased with the reinforcement with (particles and fibers),and at high temperatures for all samples prepared,and also observed an increase in elasticity coefficient of epoxy composites filled with (different particles) and decreased in elasticity coefficient of epoxy com
... Show MoreChemical resistance ceramic tiles and mortar to alkali solution are prepared and characterized in this study due to the lack of this kind of publications in ceramic literature. Most of the utilized materials are readily available raw materials and the other materials are available commercially. Physical and mechanical properties are measured and indicate that the prepared ceramic tile and mortars are competitive to traditional building materials. Chemical resistance test against alkali solution is also performed by subjecting test specimens to 10%NaOH liquid for two weeks. The results give no indication of chemical attack to specimens of ceramic tile and mortar. The results are discussed and important conclusions are drawn to encourage c
... Show MoreThere 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.
Acid treatment is a widely used stimulation technique in the petroleum industry. Matrix acidizing is regarded as an effective and efficient acidizing technique for carbonate formations that leads to increase the fracture propagation, repair formation damage, and increase the permeability of carbonate rocks. Generally, the injected acid dissolves into the rock minerals and generates wormholes that modify the rock structure and enhance hydrocarbon production. However, one of the key issues is the associated degradation in the mechanical properties of carbonate rocks caused by the generated wormholes, which may significantly reduce the elastic properties and hardness of rocks. There have been several experimental and simulation studies regardi
... Show MoreHartree-Fock (HF) method relies in the calculations of nonlinear optical properties (NLO) for benzoic acid molecule. Also, another theoretical study is conducted by using the TD-DFT Density Functional Theory through B3LYP/High Base Set 6-311++G (2d,2p) on Gaussian program09. Moreover, an experimental study has been done to obtain the electrons spectrum for benzoic acid with and without ethanol. While the experimental study is done by using UV/VIS. spectrophotometer. Energy gap values of electronic transition between HOMO and LUMO is obtained from theoretical and experimental results. Consequently, the theoretical result for determining the energy gap calculated from EHOMO-LUMO wasvery close to the results of UV / VIS. spectrum. A theoretica
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