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
Spray pyrolysis technique was subjected to synthesized (SnO2)1-x (TiO2: CuO) x Thin films on different substrates like glass and single crystal silicon using. The structure of the deposited films was studied using x-ray diffraction. A more pronounced diffraction peaks of SnO2 while no peaks of (CuO , TiO2 ) phase appear in the X-ray profiles by increasing of the content of (TiO2 , CuO) in the sprayed films. Mixing concentration (TiO2 , CuO) influences on the size of the crystallites of the SnO2 films ,the size of crystallites of the spray paralyzed oxide films change in regular manner by increasing of (TiO
... Show MoreFlexible pavements are subjected to three main distress types: fatigue crack, thermal crack, and permanent deformation. Under severe climate conditions, thermal cracking particularly contributes largely to a considerable scale of premature deterioration of pavement infrastructure worldwide. This challenge is especially relevant for Europe, as weather conditions vary significantly throughout the year. Hydrated lime (HL) has been recognized as an effective additive to improve the mechanical properties of asphalt concrete for pavement applications. Previous research has found that a replacement of conventional limestone dust filler using hydrated lime at 2.5% of the total weight of aggregates generated an optimum improvement in the mec
... Show MorePM3 semiempirical method and Density Functional Theory (DFT) calculations of the type (B3LYP) and a Gaussian basis set (6-311G) were carried out for fullerene C60 molecule with its construction units (5radialene, 1,2,3-trimethylene indan, and corannulene), to evaluate the geometrical structure (bond lengths, symmetry, and energetic such as heat of formation ΔH0f, total energy Etot., dipole moment μ, EHOMO (highest occupied molecular orbital energy), ELUMO (lowest unoccupied molecular orbital energy), energy gap ΔEHOMO-LUMO), the distribution of electron density and vibration frequencies, all at their equilibrium geometries. Assignment of the vibrations modes was done according to the movement of the atoms as a result of DFT calculatio
... Show MoreHigh temperature superconductors materials with composition Bi1.6-xSbxPb0.4Sr2Ca2-yCdyCu3OZ (x = 0, 0.1, 0.2 and 0.3) and (y = 0.01 and 0.02), were prepared by using the chemical reaction in solid-state ways, and test influence of partial replacement of Bi and Ca with Sb and Cd respectively on the superconducting properties, all samples were sintered at the same temperature (850 oC) and for the same time (195 h). The structural analysis of the prepared samples was carried out using X-ray diffraction (XRD) measurements performed at room temperature, scanning electron microscope (SEM) and dc electrical resistivity was measured as a function of temperature. It was found that the sample prepared by partial substitution of Sb at ratio (x= 0.2
... Show Moremixtures of cyclohexane + n-decane and cyclohexane + 1-pentanol have been measured at 298.15, 308.15, 318.15, and 328.15 K over the whole mole fraction range. From these results, excess molar volumes, VE , have been calculated and fitted to the Flory equations. The VE values are negative and positive over the whole mole fraction range and at all temperatures. The excess refractive indices nE and excess viscosities ?E have been calculated from experimental refractive indices and viscosity measurements at different temperature and fitted to the mixing rules equations and Heric – Coursey equation respectively to predict theoretical refractive indices, we found good agreement between them for binary mixtures in this study. The variation of th
... Show MoreIn this work; copper oxide films (CuO) were fabricated by PLD. The films were analyzed by UV-VIS absorption spectra and their thickness by using profilometer. Pulsed Nd:YAG laser was used for prepared CuO thin films under O2 gas environment with varying both pulse energy and annealing temperature. The optical properties of as-grown film such as optical transmittance spectrum, refractive index and energy gap has been measured experimentally and the effects of laser pulse energy and annealing temperature on it were studied. An inverse relationship between energy gap and both annealing temperature and pulse energy was observed.
The research targets study of influence of additives on sand mold’s properties and, consequently, on
that of carbon steel CK45 casts produced by three molds. Three materials were selected for addition
to sand mix at weight percentages. These are sodium carbonates, glycerin and oat flour. Sand molds
of studied properties were produced to get casts from such molds. The required tests were made to
find the best additives with respect to properties of cast. ANSYS software is used to demonstrate
the stresses distribution of each produced materials. It is shown that the mechanical properties of
casts produced is improved highly with sodium carbonates and is less with oat flour and it is seem a
few with glycerin additives
Mechanical and thermal properties of composites, consisted of unsaturated polyester resin, reinforced by different kinds of natural materials (Orange peels and Date seeds) and industrial materials (carbon and silica) with particle size 98 µm were studied. Various weight ratios, 5, 10, and 15 wt. % of natural and industrial materials have been infused into polyester. Tensile, three-point bending and thermal conductivity tests were conducted for the unfilled polyester, natural and industrial composite to identify the weight ratio effect on the properties of materials. The results indicated that when the weight ratio for polyester with date seeds increased from 10% to 15%, the maximum Young’s modulus decreased by 54%. When the weight rat
... Show MoreIn this study, plastic wastes named (PET and PVC) were used to prepare polymer matrix composite (PMC) which can be used in different applications. Composite materials were prepared by mixing unsaturated polyester resin (UP) with plastic wastes, two types of plastic waste were used in this work included polyethylene-terephthalate (PET) and Polyvinyl chloride (PVC) with various weight fractions (0, 5,10,15, 20 and 25%) added as a filler in flakes form. In this work, some of the tests that were carried out included (tensile, bending, and compressive strength) as mechanical tests, in addition to (thermal conductivity and water absorption) as physical tests. The values of tensile, compressive strength and Young's modulus of UP increased after
... Show MoreAbstract
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
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