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
Gypseous soils are common in several regions in the world including Iraq, where more than 28.6% of its surface is covered with this type of soil. This soil, with high gypsum content, causes different problems for construction and strategic projects. As a result of water flow through the soil mass, the permeability and chemical arrangement of these soils varies with time due to the solubility and leaching of gypsum. In this study, the soil of 36% gypsum content, was taken from one location about 100 km southwest of Baghdad, where the samples were taken from depths (0.5 - 1) m below the natural ground and mixed with (3%, 6%, 9%) of Copolymer and Novolac polymer to improve the engineering properties that include: collapsibility, perm
... Show MoreThe effects of BaCl2 dopant on the optical properties of poly (vinyl alcohol) have been investigated. Pure and BaCl2 doped PVA films were prepared using solvent casting method. These films were characterized using UV/VIS technique in order to estimate the kind of transition which was found to be indirect transition. The value of the optical energy gap was decrease with increasing dopant concentration.
Refractive index, extinction coefficient and Urbach tail have been also investigated; it was found that all the above parameters affects by doping.
The eff ect of partial substitution for lanthanum (La) on the structural properties of the compound Y1-xLaxBa4Cu7O15+δ were studied. The variation of (x) are x=0.1, 0.2 and 0.3, which was synthesized by solid state reaction method. The mixed powder was pressed with pressure (7 ton / cm2) as a disc (1.5 cm) diameter and a thickness of (0.25 to 0.3 cm). The samples were sintering by 120 °C / hour with a changing rate from room temperature to 850 ° C through 72 hours. XRD analysis using to calculate crystal size, strain and degree of crystallinity. It was found all samples have orthorhombic structure and change of structure with increasing lanthanum concentration. It was shown that the change lanthanum concentrations of all our samp
... Show MoreSeveral schottky diodes were fabricated from polyaniline/ Carbon nanotube (single and multiwalled) composites. These composites were synthesized with different concentration and two carbon nanotubes types, Single and Multi-Walled Carbon Nanotubes (SWCNT & MWCNT). Aluminum and silver paste were chosen as schottky and ohmic contact respectively. physical and electrical were used to studied these composite by using Atomic Force Microscopy (AFM) and electrical measurements. The Root Mean Square RMS surface roughness of the composite samples was found to be around 4nm. The currentvoltage characteristic were measurements for all samples in the bias range ±15V at room temperature. The results shows the increasing in carbon nanotubes concentration
... Show MoreThe aim of this research is to develop mechanical properties of a new aluminium-lithium-copper alloy. This alloy prepared under control atmosphere by casting in a permanent metal mould. The microstructure was examined and mechanical properties were tested before and after heat treatment to study the influence of heat treatment on its mechanical properties including; modulus of elasticity, tensile strength, impact, and fatigue. The results showed that the modulus of elasticity of the prepared alloy is higher than standard alloy about 2%. While the alloy that heat treated for 6 h and cooled in water, then showed a higher ultimate tensile stress comparing with as-cast alloy. The homogenous heat treatment gives best fatigue
... Show MoreThis study investigates the possibility of using waste plastic as one of the components of expired lead-acid batteries to produce lightweight concrete. Different percentages of lead-acid battery plastic were used in the production of lightweight concrete. The replacements were (70, 80 and 100%) by volume of the fine and coarse aggregate. Results demonstrated that a reduction of approximately 23.6% to 35% in the wet density was observed when replacement of 70% to 100% of the natural aggregate by lead-acid battery plastic. Also, the compressive strength decreased slightly with the increase in plastic content at different curing ages of 7, 28, 60, 90, 120 days. The lowest value of compressive strength was (20.7 MPa) for (wa
... Show MoreCowpea is a very important legume in Nigeria that is being utilized to Substitute high-cost animal protein for low-income people. The knowledge of some physical properties of various moisture contents is of utmost importance in the design of its handling and processing equipment and machinery, which is the aim of this work, which studied the physical properties of IT99K-573-1-1 (SAMPEA14) variety of Cowpea within 8.77 to 21.58 % db moisture content. The properties studied include Major, Intermediate, and Minor diameters, Sphericity, Surface area, Specific gravity, Volume, Bulk density, 50-tap density, 100-tap density, 1250-tap density, seed mass, Angle of repose, Geometric mean diameter, and Arithmetic mean diameter. The
... Show MorePVA:PEG/MnCl2 composites have been prepared by adding (MnCl2) to the mixture of the poly vinyl alcohol (PVA) and poly ethylene glycol (PEG) with different weight percentages (0, 2, 4, 6, 8 and 10) wt.% by using casting method. The type of charge carriers, concentration (nH) and Hall mobility (μH) have been estimated from Hall measurements and show that the films of all concentration have a negative Hall coefficient. In D.C measurement increase temperature leads to decrease the electrical resistance. The D.C conductivity of the composites increases with the increasing of the concentration of additive particles and temperature. The activation energy decreases for all composites with increasing the concentration of the additive particles.
... Show MoreThis research deals with study of the effect of additives on rheological properties (yield point, plastic viscosity ,and apparent viscosity) of emulsions. Twenty seven emulsion samples were prepared; all emulsions in this investigation are invert emulsions when water droplets are dispersed in diesel oil. The resulting emulsions are called water-in-oil (W/O) emulsions. The rheological properties of these emulsions were investigated using a couett coaxial cylinder rotational viscometer (Fann-VG model 35 A), by measuring shear stress versus shear rate. It was found that the effect of additives on rheological properties of emulsions as follow: the increase in the concentration of asphaltic material tends to increase the rheological propertie
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