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
Tin oxide films (SnO2) of thickness (1 ?m) are prepared on glass substrate by post oxidation of metal films technique. Films were irradiated with Nd:YAG double frequency laser of wavelength (532 nm) pulses of three energies (100, 500, 1000) mJ. The optical absorption, transmission, reflectance, refractive index and optical conductivity of these films are investigated in the UV-Vis region (200-900) nm. It was found that the average transmittance of the films is around (80%) at wavelength (550 nm) and showed high transmission (? 90 %) in the visible and near infrared region. The absorption edge shifts towards higher energies, which is due to the Moss-Burstien effect and it lies at (4 eV). The optical band gap increased with increasing of ene
... Show MoreThe long – term behaviour of polyethylene products used out doors is affected by weathering. In the present work,
weathering test was carried out to find the effect of the environment conditions on the mechanical properties of
HDPE/LLDPE blends with different weight percents (0, 15, 30, and 45 %) relative to the LLDPE by increasing the
exposure times to (100, 150, 200, 250, 300) hr.
A series of tests (destructive), tensile, impact and hardness were carried out on the prepared samples, the results
obtained declare the changes on the material behaviour from ductile to brittle and the polymer shows a decline in the
mechanical properties with increasing the exposure times.
In the present work empirical equations were r
Objective: The approximate life span of a silicone maxillofacial prosthesis is as short as1.5–2 years of clinical service, then a new prosthesis should be fabricated. The most common reasonfor re-making the prosthesis is silicone mechanical properties degradation. The aim of this studywas to assess some mechanical properties of VST-30 silicone for maxillofacial prostheses after addi-tion of intrinsic pigments.Methods: Two types of intrinsic pigments (rayon flocking and burnt sienna); each of them wasincorporated into silicone. One hundred and twenty samples were prepared and split into 4 groupsaccording to the conducted tests (tear strength, hardness, surface roughness, and tensile strengthand elongation percentage) with 30 samples for ea
... Show MoreLighting is a very important element of treatment if the color contains many imaging system (digital cameras) and the unit of light and the light within these units are not strong , but usefel when the light is low , in different lighting intensities conditions image quality will not persist good enough and image may become dark or slightly exposed to light which leads to lower the details in image where we can not modify contrast or light ness to compensate thr decrease without losing the light and dark deatials . So we went in this research to study the variation colored texts written on the painting and lighting cases of non –regular ( a few) and different distances . As the diversity of these texts written on the board a
... Show MoreThe Hartha Formation reservoir was evaluated to be produced in the near future in Y oil and J fields, West of the Tigris River in northern Iraq. Due to geological data analysis of the Hartha facies and diagenesis could enhance oil production with minimized risks, this research tried to deal with data to support the oil production. The Hartha reservoir is subdivided into five-rock units, Har-1, 2, 3, 4 and 5. It is of Heterogenic facies limestone, dolomite, dolomitic limestone and argillaceous dolomite. The Hartha Formation is a clean carbonate; it has an effective porosity. It consists of lime mudstone-packstone skeletal grain. This conclusion is based on the lithology, core microfacies, cutting, thin section and log interpret
... Show MoreIn this work, varying compositions of SiO2 micro filler were added
with the Polyvinyl Chloride (PVC) and samples have been prepared
using film casting technique. The results have been analyzed and
compared for PVC samples with (1 wt%, 3 wt%, 5 wt% and 10 wt%)
SiO2 micro filler. Mechanical characteristics such as tensile strength,
elongation at break and Young`s modulus were measured for all the
samples, where the tensile strength was increased from 8.39 Mpa for
purified PVC to 16 Mpa for 3% SiO2/PVC composite. Also, thermal
conductivity measurement values illustrated that composite materials
have a good thermal insulation at 10 wt. %, thermal conductivity was
decreased from 0.1684 W/m.
Background: Polymethyl methacrylate (PMMA) is used in denture fabrication and considered as the most reliable material for the construction of removable prosthodontic appliances. The material is far from ideal in fulfilling the mechanical requirements and the effect of autoclave processing has not been fully determined. The purpose of this study was to evaluate the effect of addition of salinized (ZrO2) Nano fillers in percentages 3%, 5% and 7% by weight on some properties of heat cured acrylic processed the by autoclave and compare it with 0% (control) group . Materials and methods: The silanized(ZrO2) Nano-particles was added to PMMA powder by weight in three different percentages 3%, 5% and 7%, mixed by probe ultra-sonication machine.
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