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
This study was conducted in an orchard pomegranate's Department of Horticulture College of Agriculture, University of Baghdad for two seasons 1999-2000 on cultivars pomegranate Salimi and narrators seedless to study the effect spraying Nizant growth in sex ratio of flowers and recipes flowering and winning was selected 27 trees per class 15 years old planted
Unsaturated polyester was used as a matrix which was filled with different percentages of cobalt ferrite using hand lay-up method. Cobalt ferrite was synthesized using solid state ceramic method with reagent of CoO and Fe2O3. Mechanical properties such tensile strength, Young's modulus and shore D hardness of the composite have been studied. All these properties have increased by 10% with increasing cobalt ferrite contents. Also the thermal properties such thermal conductivity and specific heat capacity are highly increased as the ferrite content increased, while the thermal diffusivity increased by 22 %. On the other hand dielectric strength of composite has been measured which increased by 50% by increasing the cobalt ferrite content.&
... Show MoreThe effect of annealing on the structural and optical properties of Antimony trisulfide (Sb2S3) is investigated. Sb2S3 powder is vaporized on clean glass substrates at room temperature under high vacuum pressure to form thin films. The structural research was done with the aid of X-ray diffraction (XRD) and atomic force microscopy (AFM). The amorphous to the polycrystalline transformation of these thin films was shown by X-ray diffraction analysis after thermal annealing. These films' morphology is explained. The absorption coefficient and optical energy gap of the investigated films are calculated using transmission spectra. Both samples have strong absorption in the visible spectrum, according to UV-visible absorption spectra. The optical
... Show Moreby in situ polymerization of aniline monomer, conducting polyaniline (PANI) nanocomposites containing various concentrations of carboxylic acid functionalized multi-walled carbon nanotubes (f-MWCNT) were synthesized. The morphological and electrical properties of pure PANI and PANI /MWCNT nanocomposites were examined by using Fourier transform- infrared spectroscopy (FTIR), X-ray diffraction (XRD) and Atomic Force Microscopy (AFM) respectively. FTIR spectra shows that the carboxylic acid groups formed at the both ends of the sidewalls of the MWCNTs. The aniline monomers were polymerized on the surface of MWCNTs, depending on the -* electron interaction between aniline monomers and MWCNTs and hydrogen bonding into interaction between t
... Show MoreOne of the major problems facing the road construction engineer is the collapsible granular soil which may be used for embankment construction. Problems appears when such compacted soil come in touch with water, it exhibits cracking and uncontrolled settlement. Collapsible soils are defined as any unsaturated soil that goes through a radical rearrangement of practice and great loss of volume upon wetting, with or without additional loading. An attempt has been made in this investigation to stabilize the collapsible soil of Nasiriya with asphalt emulsion. Specimens of pure and asphalt emulsion stabilized soil have been prepared using optimum fluid content and tested. The first group of specimens of (60x60x20) cm have been tested for direct s
... Show Morein this paper sufficient conditions of oscillation of all of nonlinear second order neutral differential eqiation and sifficient conditions for nonoscillatory soloitions to onverage to zero are obtained
Refractories are mineral and chemical-, based, materials with excellent heat resistance, making them ideal for use in the construction of ovens, furnace walls industries. According to this our research is concerned to study the effect of addition of (4% CaO) and (5% graphite) on the silica brick properties. Different amounts of CaO and Graphite were included in the white sand (raw ingredients) of silica bricks as a binder to prepare the composition then the composition were sintered using Different sintering temperatures ranging from (1000–1400)𝛐C under static air. Density, thermal conductivity, porosity, and water absorption Compression there was power tested after sintering. XRD analysis was used to identify raw materials’
... Show MoreThe recent development in statistics has made statistical distributions the focus of researchers in the process of compensating for some distribution parameters with fixed values and obtaining a new distribution, in this study, the distribution of Kumaraswamy was studied from the constant distributions of the two parameters. The characteristics of the distribution were discussed through the presentation of the probability density function (p.d.f), the cumulative distribution function (c.d.f.), the ratio of r, the reliability function and the hazard function. The parameters of the Kumaraswamy distribution were estimated using MLE, ME, LSEE by using the simulation method for different sampling sizes and using preli
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