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
Background: One of the most common problem associated with the used of soft denture lining material is microorganisms and fungal growth especially Candida albicans, which can result in chronic mucosal inflammation. The aim of this study was to evaluate the influence of chlorhexidine diacetate (CDA) salt Incorporation into soft denture lining material on antifungal activity; against Candida albicans, and the amount of chlorhexidine di-acetate salt leached out of soft liner/CDA composite. Furthermore, evaluate shear bond strength and hardness after CDA addition to soft liner Materials and methods: chlorhexidine diacetate salt was added to soft denture lining material at four different concentrations (0.05%, 0.1% and 0.2% by weight). Four hund
... Show MorePremature degradation is the problem of maxillofacial silicones, significantly affected by ultraviolet exposure, contributing to silicones photodegradation. Degradation necessitates frequent replacement of prostheses that increase the total cost of rehabilitation.
This study evaluated the effect of bisoctrizole on the ultraviolet absorption properties of silicone material and the stability of this absorption over time. Also, the bisoctrizole effect on the surface roughness of silicone was evaluated.
This paper presents the effect of Cr doping on the optical and structural properties of TiO2 films synthesized by sol-gel and deposited by the dip- coating technique. The characteristics of pure and Cr-doped TiO2 were studied by absorption and X-ray diffraction measurement. The spectrum of UV absorption of TiO2 chromium concentrations indicates a red shift; therefore, the energy gap decreases with increased doping. The minimum value of energy gap (2.5 eV) is found at concentration of 4 %. XRD measurements show that the anatase phase is shown for all thin films. Surface morphology measurement by atomic force microscope (AFM) showed that the roughness of thin films decrease with doping and has a minimum value with 4 wt % doping ratio.
In this work, Titanium oxide thin films doped with different concentration of CuO (0,5,10, 15,20) %wt were prepared by pulse laser deposition(PLD) technique on glass substrates at room temperature with constant deposition parameter such as : pulse (Nd:YAG), laser with λ=1064 nm, constant energy 800 mJ , repetition rate 6 Hz and No. of pulse (500). The structure , optical and electrical properties were studied . The results of X-ray diffraction( XRD) confirmed that the film grown by this technique have good crystalline tetragonal mixed anatase and rutile phase structure, The preferred orientation was along (110) direction for Rutile phase. The optical properties of the films were studied by UV-VIS spectrum in the range of (360-1100)
... Show MoreIn this work, excess properties (eg excess molar volume (VE), excess viscosity (ȠE), excess Gibbs free energy of activation of viscos flow (ΔG* E) and molar refraction changes (ΔnD) of binary solvent mixtures of tetrahydrofurfuryl alcohol (THFA) with aromatic hydrocarbons (benzene, toluene and p-xylene) have been calculated. This was achieved by determining the physical properties including density ρ, viscosity Ƞ and refraction index nD of liquid mixtures at 298.15 K. Results of the excess parameters and deviation functions for the binary solvent mixtures at 298.15 K have been discussed by molecular interactions that occur in these mixtures. Generally, parameters showed negative values and have been found to fit well to Redlich-Kister
... Show MoreThis work aimed to study the effect of laser surface treatment on the mechanical characteristics and corrosion behaviour of grey cast iron type A159. Many technical applications used conventional surface treatment, but laser surface hardening has recently been used to enhance the surface properties of many alloys. The mechanical characteristics, including microstructure, microhardness, and wear resistance of A159 grey cast iron, were studied, in addition to corrosion behaviour. The experimental laser parameters in this work were 0.9, 1.2, and 1.5 KW power with continuous wave carbon dioxide lasers with scanning speeds of 10 and 12 mm/s were used. The results found that phase-transitional alterations in microstructure were influenced by lase
... Show MoreThe aim of this work is to evaluate some mechanical and physical
properties (i.e. the impact strength, hardness, flexural strength,
thermal conductivity and diffusion coefficient) of
(epoxy/polyurethane) blend reinforced with nano silica powder (2%
wt.). Hand lay-up technique was used to manufacture the composite
and a magnetic stirrer for blending the components. Results showed
that water had affected the bending flexural strength and hardness,
while impact strength increased and thermal conductivity decreased.
In addition to the above mentioned tests, the diffusion coefficient
was calculated using Fick’s 2nd law.