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
Heterocyclic compounds are employed in many applications, and numerous researchers have created liquid crystals by adding heterocyclic to the structures of these molecules. This work includes the synthesis and characterization of new compounds that contain 5H-thiazolo [4,3-b][1,3,4] thiadiazol united in multiple steps, starting with the synthesis of the aldehyde compound [I] by reaction chloro ethyl acetate with 4-hydroxybenzaldehyde in the presence of ethanol and potassium carbonate, followed by reactions with thiosemicarbazide, mercapto acetic acid in sulphuric acid to produce compound [II] then reflux compound [II] with hydrazine hydrate to product compound [III], after that reaction the later compound with nalkoxybenzaldehyde [IV]n and
... Show MoreGypseous soils are spread in several regions in the world including Iraq, where it covers more than 28.6% [1] of the surface region of the country. This soil, with high gypsum content causes different problems in construction and strategic projects. As a result of water flow through the soil mass, permeability and chemical arrangement of these soils vary over time due to the solubility and leaching of gypsum. In this study the soil of 36% gypsum content, is taken from one location about 100 km (62 mi) southwest of Baghdad, where the sample is taken from depth (0.5 - 1) m below the natural ground surface and mixed with (3%, 6%, 9%) of Copolymer and Styrene-butadiene Rubber to improve t
The refractive indices, nD densities 𝜌, and viscosities of binary mixtures of sulfolane + n -butanol + sec- butanol + iso- butanol + tert – butanol + n-propanol and iso- propanol were measured at 298.15K. Form experimental data, excess molar volum VE , excess molar refractivity ∆nD, excess molar viscosity E and excess molar Gibbs free energy of activation of viscous flow G *E were calculated. From n-propanol – sulfolane and iso- propanol sulfolane mixtures showed negative ∆nD, n-butanol – sulfolane, sec-butanal – sulfolane, iso-butanol – sulfolane and tert- butanol sulfolane , nD was positive over the whole mole fraction rang , while VE , E and G *E show a negative deviation. The
... Show MoreIn this study, the investigation of Local natural Iraqi rocks kaolin with the addition of different proportions of bauxite and its effect on the physical and mechanical properties of the produced refractories was conducted. Kaolin/bauxite mixture was milled and classified into various size fractions, the kaolin (less than 105 μm) and the bauxite (less than 70μm). The specimens were mixed from kaolin and bauxite in ranges B1 (95+5)%, B2 (90+10)%, B3(85+15)%, and B4 (80+20)% respectively. The green specimens were shaped by the semi-dry method using a hydraulic press and a molding pressure of 7 MPa with the addition of (9-12) %wt. of PVA ratio. After molding and drying, the specimens were fired at (1100, 1200 and 13
... Show MoreBulk polycrystalline samples have been prepared by the two-step solid state reaction process. It has been observed that as grown Tl2-xHgxSr2Ca2Cu3O10+δ (with x = 0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.8, 1) corresponds to the 2223 phase. It has been found that Tc varies with Hg content .The optimum Tc is about 120K for the composition Tl1.6Hg0.4Sr2Ca2Cu3O10+δ.The microstructure for Tl1.6Hg0.4Sr2Ca2Cu3O10+δ observed to be most dense and this phase exhibits the highest stability.
Mechanical rock properties are essential to minimize many well problems during drilling and production operations. While these properties are crucial in designing optimum mud weights during drilling operations, they are also necessary to reduce the sanding risk during production operations. This study has been conducted on the Zubair sandstone reservoir, located in the south of Iraq. The primary purpose of this study is to develop a set of empirical correlations that can be used to estimate the mechanical rock properties of sandstone reservoirs. The correlations are established using laboratory (static) measurements and well logging (dynamic) data. The results support the evidence that porosity and sonic travel time are consistent i
... Show MoreIn this work, the structure properties of nano Lead sulfide PbS thin films are studied. Thin samples were prepared by pulse laser deposition and deposited on glass substrates at wavelength 1064nm wavelength with a various laser energies (200,300,400,500)nm. The study of atomic force microscope (AFM) and X-ray diffraction as well as the effect of changing the laser energy on the structural properties has been studied. It has been observed that the membrane formed is of the polycrystalline type and the predominant phase is the plane (111) and (200). The minimum grain size obtained was 16.5 nm at a laser energy about 200 mJ. The results showed that thin films of average granular sizes (75 nm) could be prepared.As for the optical properties,
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