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
Transparent thin films of CdO:Ce has been deposited on to glass and silicon substrates by spray pyrolysis technique for various concentrations of cerium (2, 4, and 6 Vol.%). CdO:Ce films were characterized using different techniques such as X-ray diffraction (XRD), atomic force microscopy(AFM) and optical properties. XRD analysis show that CdO films exhibit cubic crystal structure with (1 1 1) preferred orientation and the intensity of the peak increases with increasing's of Ce contain when deposited films on glass substrate, while for silicon substrate, the intensity of peaks decreases, the results reveal that the grain size of the prepared thin film is approximately (73.75-109.88) nm various with increased of cerium content. With a sur
... Show MoreThe real and imaginary part of complex dielectric constant for InAs(001) by adsorption of oxsagen atoms has been calculated, using numerical analysis method (non-linear least square fitting). As a result a mathematical model built-up and the final result show a fairly good agreement with other genuine published works.
In this research, the effect of adding two different types of reinforcing particles was investigated, which included: nano-zirconia (nano-ZrO2) particles and micro-lignin particles that were added with different volume fractions of 0.5%, 1%, 1.5% and 2% on the mechanical properties of polymer composite materials. They were prepared in this research, as a complete prosthesis and partial denture base materials was prepared, by using cold cure poly methyl methacrylate (PMMA) resin matrix. The composite specimens in this research consist of two groups according to the types of reinforced particles, were prepared by using casting methods, type (Hand Lay-Up) method. The first group consists of PMMA resin reinforced by (nano-ZrO
... Show MoreThe main goal of this work is to put a simple model of the spectral energy distribution of binary stars called WW Cha. This model is built up on the extracted data from various telescopes and archives for the target WW Cha stars and then analyzing them using a python environment. The result of the fitting proposes that there are two protoplanetary disks around the WW Cha star, with different physical properties for each disk, such as the size of the inner disk being 10 AU, while the size of the outer disk being 300 AU. The shape of the outer disk is a flaring disk not a flat disk according to the value of the power law for the surface density (1.5). The emission in the disk is caused by small amorphous olivine grains rangin
... Show MoreAn electrolytic process for the removal of Zn(II) from aqueous solution using a parallel amalgamated copper screens cathode operated in the flow through mode is proposed. The current-potential curves recorded at a rotating amalgamated copper disc electrode were used to determine diffusion coefficient of Zn(II). The performance of electrolytic reactor was investigated by using different flow rates at initial zinc ion concentration(48 mg/L). Taking into account the residential Zn(II) concentration, the best results were obtained for cathode potential of (-1.35 V vs. SCE) at flow rate (320 L/h). Zinc ion concentration was found to decrease from 48 mg/L to 1 mg/L during 120 min. of electrolysis. The experimental data are well correlate
... Show MoreInSb alloy was prepared then InSb:Bi films have been prepared successfully by thermal evaporation technique on glass substrate at Ts=423K. The variation of activation energies(Ea1,Ea2)of d.c conductivity with annealing temperature (303, 373, 423, 473, 523 and 573)K were measured, it is found that its values increases with increasing annealing temperature. To show the type of the films, the Hall and thermoelectric power were measured. The activation energy of the thermoelectric power is much smaller than for d.c conductivity and increases with increasing annealing temperature .The mobility and carrier concentration has been measured also.
This research is focusing on finding more effective polymers that leads to enhance the rheological properties of Water Base Muds. The experiments are done for different types of mud for all substances which are Polyacrylamide, Xanthan gum, CMC (Carboxyl Methyl Cellulose). This study shows the effect of add polymer to red bentonite mud, effect of add polymer to Iraqi bentonite mud, the effect of add bentonite to polymer mud. The mud properties of Iraqi bentonite blank are enhanced after adding the polymers to the blank mix, CMC gives the highest value of plastic viscosity and Gel strength than others; X-anthan gives the highest value of yield point and gel strength than others. For the red bentonite mud, Polyacrylamide ha
... Show MoreThis research includes depositionof thin film of semiconductor, CdSe by vaccum evaporation on conductor polymers substrate to the poly aniline where, the polymer deposition on the glass substrats by polymerization oxidation tests polymeric films and studied the structural and optical properties through it,s IR and UV-Vis , XRD addition to thin film CdSe, on of the glass substrate and on the substrate of polymer poly-aniline and when XRD tests was observed to improve the properties of synthetic tests as well as the semiconductor Hall effect proved to improve the electrical properties significantly