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, yttrium oxide particles (powder) reinforced AL-Si matrix composites (Y2O3/Al-Si) and Chromium oxide particles reinforced AL-Si matrix composites (Cr2O3/AL-Si) were prepared by direct squeeze casting. The volume percentages of yttrium oxide used are (4, 8.1, 12.1, 16.1 vol %) and the volume percentages of the chromium oxide particles used are (3.1, 6.3, 9.4, 12.5 vol. %). The parameters affecting the preparation of Y2O3/Al-Si and Cr2O3/AL-Si composites by direct squeeze casting process were studied. The molten Al-Si alloy with yttrium oxide particles or with chromium oxide particles was stirred again using an electrical stirrer at speed 500 rpm and the molten alloy was poured into the squeeze die cavity. Th
... Show MoreThis investigation was conducted to examine some physical and chemical properties of sand dunes collected from Basrah (1 '2 and 3) 'Nassiriya (4 and 5) and Amara (6) provinces that situated in lower Mesopotamia plain.
The results indicate clearly that the dominant particles in the samples were sand that were ranging from (81) % to (97) %, however the aggregated size of (0.1 - 0.25) mm were predominates in the investigated sand dunes of the region . Also the study shows that the content of the organic matter and potassium ions were very low (0.1- 0.4% '0.02 -0.22 meq I 100 gm soil. Further more the current result shows high a percentage of calcium carbonate (20.3 - 42.5%). In addition, the study has found a
... Show MoreIn this research we studied the structural and optical properties of (CdTe) thin films which have been prepared by thermal evaporation deposition method on the glass substrate at R.T with thickness (450  25) nm., as a function of doping ratio with copper element in (1,3,5) % rate .The structure measurement by X-ray diffraction (XRD) analyses shows that the single phase of (CdTe) with polycrystalline structure with a preferred orientation [111]. The optical measurement shows that the (CdTe) films have a direct energy gap, and they decrease with the increase of doping ratio reaching to 5% . The optical constants are investigated and calculated, such as absorpti
... Show MoreZnO nanostructures were synthesized by hydrothermal method at different temperatures and growth times. The effect of increasing the temperature on structural and optical properties of ZnO were analyzed and discussed. The prepared ZnO nanostructures were characterized by X-ray diffraction (XRD), UV–Vis. absorption spectroscopy (UV–Vis.), Photoluminescence (PL), and scanning electron microscopy (SEM). In this work, hexagonal crystal structure prepared ZnO nanostructures was observed using X-ray diffraction (XRD) and the average crystallite size equal 14.7 and 23.8 nm for samples synthesized at growth time 7 and 8 hours respectively. A nanotubes-shaped surface morphology was found using scanning electron microscopy (SEM). The optic
... Show MoreThis thesis aims to study the effect of addition polymer materials on mechanical properties of self-compacting concrete, and also to assess the influence of petroleum products (kerosene and gas oil) on mechanical properties of polymer modified self-compacting concrete (PMSCC) after different exposure periods of (30 ,60 ,90 ,and 180 days).
Two type of curing are used; 28 days in water for SCC and 2 days in water followed 26 days in air for PMSCC.
The test results show that the PMSCC (15% P/C ratio) which is exposed to oil products recorded a lower deterioration in compressive strength's values than reference concrete. The percentages of reduction in compressive strength values of PMSCC (15% P/C ratio) was
... Show MoreIn this work, we are Study the effect of annealing temperature on the structure of a-Ge films doped with Sb and the electrical properties of a-Ge:Sb/c-Si heterojunction fabricated by deposition of a-Ge:Sb film on c-Si by using thermal evaporation. Electrical properties of aGe:Sb/c-Si heterojunction include I-V characteristics in dark at different annealing temperatures and C-V characteristics and with the C-V characteristics suggest that the fabricated heterojunction was abrupt type, built in potential determined by extrapolation from 1/C2-V curve and show that the built - inpotential (Vbi) for the Ge:Sb/Si system increases with the increase of annealing temperatures
The building of the Babylonian theater is considered as one of the distinctive buildings where its foundations have remained steadfast in the face of geographical changes, social's erosion and groundwater that threatened almost all traces of Babylon despite the destruction of the outer structure of the building. The general directorate of antiques performed prospection for those foundations (the ground map), and then the building was completed by new bricks over the original scheme. It became clear when examining the building; its components and foundations, that the building is unique in comparison with the old buildings of the world throughout Iraq. There are similar buildings in other places like Jordan and North Africa such as
Some of the characters of the Staphylolysin A and D enzymes purified from Pseudomonas aeruginosa P16 and P5 respectively were studied, the molecular weights of Staphylolysin A and D were 20.417 kilo dalton and 23.988 kilo Dalton respectively by SDS- polyacryl amide gel electrophoresis. The optimum pH for staphylolysin A activity was found to be 8 which gives higher activity reaches 150 unit/ml, and for enzyme stability was 7.5-8.5 in which the enzyme nearly retained its full activity, while it was 9.5 for staphylolysin D that gives higher activity of 16 unit/ml,and 8.5-9.5 for enzyme stability in which the enzyme nearly retained its full activity, Maximum activity of two enzymes was obtained at 40C in which the specific activity for st
... Show MoreThe effect of doping by methyl red and methyl blue on the absorption spectra and the optical energy gap of poly (methyl methacrylat) PMMA film have been studied. The optical transmission (T%) in the wavelength range 190-900 nm for films deposited by using solvent casting method were measured. The Absorptance data reveals that the doping affected the absorption edge as a red and blue shift in its values. The films show indirect allowed interband transitions that influenced by the doping. Optical constants; refractive index, extinction coefficient and real and imaginary part of dielectric constant were calculated and correlated with doping.
This work used the deposition method to synthesize nickel oxide nanoparticles. The materials mainly used in this study were nickel sulfate hexahydrate (as a precursor) and NaOH (as a precipitant). The properties of the nanopowder were characterized by XRD, FE-SEM, EDX, and VSM. The obtained results confirmed the presence of nickel oxide nanoparticles with a face-centered cubic (FCC) structure with a lattice constant (a=4.17834 Å). Scherer and Williamson-Hall equations were used to calculate the crystallite size of about (30.5-35.5) nm. The FE-SEM images showed that the particle shape had a ball-like appearance with a uniform and homogeneous distribution and confirmed that the particles were within the nanoscale. The presence of oxygen a
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