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
Different additives are used in drilling fluids when the demanded properties cannot be gotten with clays. Drilling muds needs several additives and materials to give good characteristics. There are local alternatives more suitable for enhancing the rheology and filtration of drilling fluids. An experimental work had been conducted to assess the suitability of using potato starch to enhance rheological properties and filtration in drilling mud. This study investigated the potato starch as a viscosifier and fluid losses agent in drilling fluid. Results from this study proved that rheological properties of potato starch mud increased when pH of drilling fluid is increased. Potato starch could be used to enhance gel strength at low pH
... Show MoreGround state energies and other properties of 2S shell for some atoms as Be(Z=4), B(Z=5), C(Z=6) and N(Z=7) were calculated by using Hartree-Fock wave function. We found the values of potential energies in hartree unit (3.8369, 6.78565, 10.18852 and 14.41089) respectively and the other proprieties like expectation values of the position < r1m > were in agreement with the published results. All the studied atomic properties were normalized.
Expansive soil spreads in Iraq and some countries of the world. But there are many problems can be occurred to the structures that built on, so we must study the characteristics of these soils due to the problems that may be caused to these structures which built on these kinds of soil and then study the methods of treatment. The present study focuses on improving the geotechnical properties of expansive soils by treating it Metakaolin(M). Metakaolin (M) has never been used before as an improvement material for stabilizing the expansive soil . Metakaolin is a pozzolanic material. It’s obtained by calcination of kaolinite clay at temperatures from 700°C to 800°C. Kaolin chemical composition is
... Show MoreEpoxy resin has many chemical features and mechanical properties, but it has a small elongation at break, low impact strength and crack propagation resistance, i.e. it exhibits a brittle behavior. In the current study, the influence of adding kaolin with variable particle size on the mechanical properties (flexural modulus E, toughness Gc, fracture toughness Kc, hardness HB, and Wear rate WR) of epoxy resin was evaluated. Composites of epoxy with varying concentrations (0, 10, 20, 30, 40 weights %) of kaolin were prepared by hand-out method. The composites showed improved (E, Gc, Kc, HB, and WR) properties with the addition of filler. Also, similar results were observed with the decrease in particle size. In addition, in this study, mult
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Oil is considered a commodity and is still an important and prominent role in drawing and shaping the Iraqi economic scene. The revenues generated from the export of oil are considered the main source of the general budget in cash flows.
Since the revenues consist of quantity and price and the latter is an external factor which is difficult to predict, The effect of any commodity on its price, which is proven in the theory of micro-economic, but it is observed through the research that the response is slow, which means not to take advantage of the rise in prices, by increasing the quantity exported, the result of several facto
... Show MoreNanoparticles of copper sulfide have been prepared by simple reaction between using copper nitrate with different concentrations ratio 0.1, 0.3, and 0.5 mM, thiourea by a simple chemical route. The prepared Nano powders have been deposited onto glass substrates by casting method at 60°C. The structure of the product Nano- films has been studied by x-ray diffraction, where the patterns showed that all the samples have a hexagonal structure of covellite copper sulfide with the average crystalline sizes 14.07- 16.51 nm. The morphology has been examined by atomic force microscopy, and field emission scan electron microscopy. The AFM images showed particles with almost spherical and rod shapes with average diameter sizes of 49.11- 90.64 nm.
... Show MoreThe fabricated Photodetector n-CdO /-Si factory thin films Altboukaraharara spatial silicon multi- crystallization of the type (n-Type) the deposition of a thin film of cadmium and at room temperature (300K) and thickness (300 ± 20nm) and the time of deposition (1.25sec) was antioxidant thin films cadmium (Cd) record temperature (673k) for one hour to the presence of air and calculated energy gap optical transitions electronic direct ( allowed ) a function of the absorption coefficient and permeability and reflectivity by recording the spectrum absorbance and permeability of the membrane record within the wavelengths (300 1100nm). was used several the bias ranged between 1-5 Volts. The results showed that this
... Show MoreThe main objectives of this study were investigating the effects of the maximum size of coarse Attapulgite aggregate and micro steel fiber content on fresh and some mechanical properties of steel fibers reinforced lightweight self-compacting concrete (SFLWSCC). Two series of mixes were used depending on maximum aggregate size (12.5 and 19) mm, for each series three different steel fibers content were used (0.5 %, 1%, and 1.5%). To evaluate the fresh properties, tests of slump flow, T500 mm, V funnel time, and J ring were carried out. Tests of compressive strength, splitting tensile strength, flexural tensile strength, and calculated equilibrium density were done to evaluate mechanical properties. For reference mixes, the
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