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
Abstract
Locally natural occurring Iraqi rocks of Bauxite and Porcelanite (after pre calcinations at 1000oC for 1hr) were used, with the addition of different proportions of MgO and Al2O3, to prepare refractory materials. The effects of these additives on the physical and thermal properties of the prepared refractories were investigated.
Many batches of Bauxite/MgO, Bauxite/Al2O3, Bauxite/MgO/Al2O3, and Porcelanite/ MgO/Al2O3 were prepared. The mixture is milled and classified into different size fractions; fine (less than 45μm) 40%, middle (45-75μm) 40%, and coarse (75-106μm) 20% .
... Show MoreGallium arsenide diamondoids structural and vibrational properties are investigated using density functional theory at the PBE/6-31(d) level and basis including polarization functions. Variation of energy gap as these diamondoids increase in size is seen to follow confinement theory for diamondoids having nearly equiaxed dimensions. Density of energy states transforms from nearly single levels to band structure as we reach larger diamondoids. Bonds of surface hydrogen with As atoms are relatively localized and shorter than that bonded to Ga atoms. Ga-As bonds have a distribution range of values due to surface reconstruction and effect of bonding to hydrogen atoms. Experimental bulk Ga-As bond length (2.45 Å) is within this distribu
... Show MoreIn this paper, A.C conductivity of micro and nano grain size- TiO2 filled epoxy composites is measured. The dielectric material used is epoxy resin, while micro and nano-sized titanium dioxide (TiO2) of grain size (1.5μm, and 50nm) was used as filler at low filler concentrations by weight (3%, and 5%). Additionally the effect of annealing temperature range (293-373)º K and at a frequency range of 102-106 Hz on the A.C conductivity of the various specimens was studied.
The result of real permittivity for micro and nanocomposite show that the real permittivity increases with decreasing frequency at range of 102-106Hz. The micron-filled material has a higher real relative permittivity than the nano-filled this is true at all the temper
In this work, the superconducting CuBa2LaCa2Cu4O11+δ compound was prepared by citrate precursor method and the electrical and structural properties were studied. The electrical resistivity has been measured using four probe test to find the critical temperature Tc(offset) and Tc(onset). It was found that Tc (offset) at zero resistivity has 101 K and Tc (onset) has 116 K. The X-ray diffraction (XRD) analysis exhibited that a prepared compound has a tetragonal structure. The crystal size and microscopic strain due to lattice deformation of CuBa2LaCa2Cu4O11+δ were estimated by four methods, namely Scherer(S), Halder-Wagner(H-W), size-strain plot (SSP) and Williamson-Hall, (W-H) methods. Results of crystal sizes obtained by these meth
... Show MoreZinc Oxide (ZnO) is probably the most typical II-VI
semiconductor, which exhibits a wide range of nanostructures. In
this paper, polycrystalline ZnO thin films were prepared by chemical
spray pyrolysis technique, the films were deposited onto glass
substrate at 400 °C by using aqueous zinc chloride as a spray
solution of molar concentration of 0.1 M/L.
The crystallographic structure of the prepared film was analyzed
using X-ray diffraction; the result shows that the film was
polycrystalline, the grain size which was calculated at (002) was
27.9 nm. The Hall measurement of the film studied from the
electrical measurements show that the film was n-type. The optical
properties of the film were studied using
A series of liquid crystals comprising a heterocyclics dihydro pyrrole and 1,2,3-triazole rings [VII]-[X] were synthesized by many steps starting from a reaction of 3,3'-dimethyl-[1,1'-biphenyl]- 4,4'-diamine with chloroacetyl chloride in a mixture of solutions DMF and TEA to synthesise the compounds [I], then the compounds [I] reacted with malononitrile in 1,4-dioxane and TEA solutions to produce compounds [II], then the first step is repeated with compound [II] where it reacted with chloroacetyl chloride in mixture of DMF and TEA to give compound [III], this compound reacted with sodium azide in the presence of sodium chloride and DMF as solvent to produce the compound [IV], which reacted with acrylic acid by a 1.3 dipolar reaction in sol
... Show MoreThe electrical properties of CdO/porous Si/c-Si heterojunction prepared by deposition of CdO layer on porous silicon synthesized by electrochemical etching were studied. The structural, optical, and electrical properties of CdO (50:50) thin film prepared by rapid thermal oxidation were examined. X-ray diffraction (XRD) results confirmed formation of nanostructured silicon layer the full width half maximum (FWHM) was increased after etching. The dark J-V characteristics of the heterojunction showed strong dependence on etching current density and etching time. The ideality factor and saturation current of the heterojunction were calculated from J-V under forward bias. C-V measurements confirmed that the prepared heterojunctions are abrupt
... Show MoreThe synthesis of conducting polyaniline (PANI) nanocomposites containing various concentrations of functionalized single-walled carbon nanotubes (f-SWCNT) were synthesized by in situ polymerization of aniline monomer. The morphological and electrical properties of pure PANI and PANI/SWCNT nanocomposites were examined by using Fourier transform- infrared spectroscopy (FTIR), and Atomic Force Microscopy (AFM) respectively. The FTIR shows the aniline monomers were polymerized on the surface of SWCNTs, depending on the -* electron interaction between aniline monomers and SWCNTs. AFM analysis showed increasing in the roughness with increasing SWCNT content. The AC, DC electrical conductivities of pure PANI and PANI/SWCNT nanocomposite h
... Show MoreMortar of ordinary Portland cement was blended with cockles shell
powder at different weight ratios to investigate the effect of powder
admixture on their strength and thermal conductivity. Results showed
that addition of cockles shell powder at 50% of mortar weight
improves hardness and compressive strength notably and reduces the
thermal conductivity of the end product. Results suggest the
possibility to incorporate cockles shell powders as constituents in
cement mortars for construction and plastering applications.