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 Invar effect in 3D transition metal such as Ni and Mn, were prepared on a series composition of binary Ni1-xMnx system with x=0.3, 0.5, 0.8 by using powder metallurgy technique. In this work, the characterization of structural and thermal properties have been investigated experimentally by X-ray diffraction, thermal expansion coefficient and vibrating sample magnetometer (VSM) techniques. The results show that anonymously negative thermal expansion coefficient are changeable in the structure. The results were explained due to the instability relation between magnetic spins with lattice distortion on some of ferromagnetic metals.
In the present work a modification was made on three equations to represent the
experiment data which results for Iraqi petroleum and natural asphalt. The equations
have been developed for estimating the chemical composition and physical properties
of asphalt cement at different temperature and aging time. The standard deviations of
all equations were calculated.
The modified correlation related to the aging time and temperature with penetration
index and durability index of aged petroleum and natural asphalts were developed.
The first equation represents the relationship between the durability index with aging
time and temperature.
loge(DI)=a1+0.0123(2loge T
... Show MoreThe Silver1Indium1Selenide (AgInSe2) (AIS) thin1films of (3001±20) nm thickness have been1prepared2from the compound alloys2using thermal evaporation2 technique onto the glass2substrate at room temperature, with a deposition rate2(3±0.1) nm2sec-1.
The2structural, optical and electrical3properties have been studied3at different annealing3temperatures (Ta=450, 550 and 650) K.
The amount3or (concentration) of the elements3(Ag, In, Se) in the prepared alloy3was verified using an
... Show MoreAir pollution is a major environmental problem, due to the increasing number of vehicles in Baghdad city streets and their direct impact on the process of air pollution resulting from an exhaust and non-exhaust pollutants (brake, clutch, tire wear, road surface wear and corrosion of vehicle components).
The aim of this study is to detect the chemical and physical properties of brake pad particles as well as the concentrations of heavy metals found in these pad particles. This study included, a collection of eleven (11) samples of brake pads belong to different types of cars, most of these cars were used commonly in Baghdad city streets. The size of break pads particles was examined under Scanning El
... Show MoreIn this work, the fine structure macro-porous silicon (macroPS) substrate was prepared by photo-electro-chemical etching of n-type silicon wafer. Ultraviolet illumination condition of wavelength 360nm wavelength and intensity of about 100mW/cm2 with etching current density of about 50 mA/cm2 and etching time 5
min was employed. The Hybrid device gold nanoparticles /macroPorous Silicon (AuNPs/macroPS) was fabricated by deposition AuNPs into mPS substrate Via immersion plating process of macroPS in the solution of HAuCl4 with the (10-3M) concentration and 2min immersion time. The characteristics of PS before and after
immersion process were investigated by scanning electron microscopy (SEM), EDS,&nb
Environmental pollutions and resources depletion motivates scientific research to innovate technologies for sustainable productive systems. To develop gas sensing substance with optimized performance a perovskite compound of HoxFe1-x FeO3 (where x= 0, 0.01, 0.03 and 0.05) were prepared by standard solid state reaction technique. The crystal structure was studied by XRD, which confirmed the formation of polycrystalline orthorhombic structure with space group Pbnm type perovskite. The preferred crystal growth of the main peak was (211). The structural parameters were also calculated and it was found that the lattice constants and particle size increased with the Ho doping ratio. The electrical properties were studied using the Hall effect,
... Show MoreIndium antimony (InSb) alloy were prepared successfully. The InSb films were prepared by flash thermal evaporation technique on glass and Si p-type substrate at various substrate temperatures (Ts= 423,448,473, and 498 K). The compounds concentrations for prepared alloy were examined by using Atomic Absorption Spectroscopy (AAS) and X-ray fluorescence (XRF). The structure of prepared InSb alloy and films deposited at various Ts were examined by X-ray diffraction (XRD).It was found that all prepared InSb alloy and films were polycrystalline with (111) preferential direction . The electrical properties of the films are studied with the varying Ts. It is found that
... Show MoreThe goal of this research is to use optical emission spectroscopy to investigate the parameters of exploding silver wire plasma. The silver discharge plasma's emission spectra were recorded and studied. For silver wire of diameter 0.4 mm and different currents 75,100, and 125A in deionized water, the plasma electron temperature ( ) was calculated by Boltzmann plot and container plasma medium temperature by thermal camera, and the electron density ( ) was computed by Stark broadening using the hydrogen (H line) at 656.279 nm With increasing current from 75 to 125 A, the electron density (ne) increased from 3.160× to 8.762× , while electron temperatures increased from 0.571 to 1.334 eV under the same conditions.
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