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
Overlapped have been prepared from epoxy resin material added to carbon Nanotube and percentages weight (0.1, 0.05, 0.01) % Studied the mechanical properties of the composite (bending, tensile an d hardness) has been found that the Flexural and tensile modulus of the composites were higher than the pure epoxy resin this may be due to the high mechanical strength of carbon nano tube (CNT). The hardness of the epoxy carbon Nanotube composites increased and the reason is due to increased overlap and stacking between the additives and material basis, which reduces the movement of polymer molecules leading to increased resistance to scratching material and cutting, will become more resistance to plastic deformation.
The optical energy gap and optical constants such as the reflective index, dielectric constant have been evaluated due to The optical transmission and UV-VIS absorption spectra have been recorded in the wavelength (200 - 1100 nm) for PVA/PANI polymer blends and PVA/PANI/ZnO nanocomposites with different concentrations of ZnO (0.02, 0.05, 0.07, 0.1and 0.2) wt %. The results indicate that the materials have allowed direct transition. The reflection index and dielectric constant are increase with wavelength
The eff ect of partial substitution for lanthanum (La) on the structural properties of the compound Y1-xLaxBa4Cu7O15+δ were studied. The variation of (x) are x=0.1, 0.2 and 0.3, which was synthesized by solid state reaction method. The mixed powder was pressed with pressure (7 ton / cm2) as a disc (1.5 cm) diameter and a thickness of (0.25 to 0.3 cm). The samples were sintering by 120 °C / hour with a changing rate from room temperature to 850 ° C through 72 hours. XRD analysis using to calculate crystal size, strain and degree of crystallinity. It was found all samples have orthorhombic structure and change of structure with increasing lanthanum concentration. It was shown that the change lanthanum concentrations of all our samp
... Show MoreA calculation have been carried out for determination some of the spectroscopic properties of Hydrogen Iodide HI molecules such as, the intensity of the absorption spectrum as a function of the variation of the temperature ranging from 10 to 1000 K. This study shows that the populations and hence intensity of the molecule increased as the temperature increased. Another determination of the maximum rotational quantum number Jmax of N2 , CO , BrF AgCl and HI molecules has been carried out.
The huge magnetic fields of neutron star cause the nuclei of the stellar surface to form a tightly bound condensed layer. In this research some characteristics of polar gap and magnetosphere enclosed the star according to Sturrock Model were illustrated, positrons move out along the open field lines, and electrons flow to the stellar surface as in the related to Sturrock model. The magnetic field within polar gap areas, which is defined by the Irvin Radius (RL) decreases due to the expansion of the polar, resulting from the physical motion of the accreted material. The values of height gap at different distances from the star were estimated. The obtained results improve the most energetic positrons those with E? Emax radiate away their ener
... Show MoreIn this research, the geotechnical properties of the soil profile in Hilla city within Babylon Governorate in the middle parts of Iraq are described. The geotechnical data at the specific sites were collected from some geotechnical investigation reports performed at some selected locations. This article is devoted to studying the distribution of soil properties (the physical and mechanical) in the horizontal and vertical directions. Moreover, a correlation between different physical and mechanical properties is performed. The correlation is executed using statistical analysis by Microsoft Excel Software (2016). From the regression results, it was found that the nature of the soil is c
The effects of BaCl2 dopant on the optical properties of poly (vinyl alcohol) have been investigated. Pure and BaCl2 doped PVA films were prepared using solvent casting method. These films were characterized using UV/VIS technique in order to estimate the kind of transition which was found to be indirect transition. The value of the optical energy gap was decrease with increasing dopant concentration.
Refractive index, extinction coefficient and Urbach tail have been also investigated; it was found that all the above parameters affects by doping.
The research’s main goal is to investigate the effects of using magnetic water in concrete mixes with regard to various mechanical properties such as compressive, flexural, and splitting tensile strength. The concrete mix investigated was designed to attain a specified cylinder compressive strength (30 MPa), with mix proportions of 1:1.8:2.68 cement to sand to crushed aggregate. The cement content was about 380 kg/m3, with a w/c ratio equal to 0.54, sand content of about 685 kg/m3, and gravel content of about 1,020 kg/m3. Magnetic water was prepared via passing ordinary water throughout a magnetic field with a magnetic intensity of 9,000 Gauss. The strength test
Cowpea is a very important legume in Nigeria that is being utilized to Substitute high-cost animal protein for low-income people. The knowledge of some physical properties of various moisture contents is of utmost importance in the design of its handling and processing equipment and machinery, which is the aim of this work, which studied the physical properties of IT99K-573-1-1 (SAMPEA14) variety of Cowpea within 8.77 to 21.58 % db moisture content. The properties studied include Major, Intermediate, and Minor diameters, Sphericity, Surface area, Specific gravity, Volume, Bulk density, 50-tap density, 100-tap density, 1250-tap density, seed mass, Angle of repose, Geometric mean diameter, and Arithmetic mean diameter. The
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