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
A revolution called information revolution has recently invaded the world. It is Currently considered one of the most important properties of development to the countries of the world The criteria provided by computers such as accuracy, speed, time saving Storage and restore have led them to be widely used in economy, industry, agriculture, communications, etc., as well as being the major finder of reengineering the operations of innovation. The use of computers in the preparation of budgets will lead to achieve accuracy. Since, the operation draws upon the statistic and quantity estimations about budget items, the computerized balance sheet may save time and effort of preparing mathematical equations annually. According to the problem o
... Show MoreChanges in mechanical properties of material as a result of service in different conditions can be provided by mechanical testing to assist the estimation of current internal situation of these materials, or the degree of deterioration may exist in furnaces serviced at high temperature and exceed their design life. Because of the rarity works on austenitic stainless steel material type AISI 321H, in this work, ultimate tensile strength, yield strength, elongation, hardness, and absorbed energy by impact are evaluated based on experimental data obtained from mechanical testing. Samples of tubes are extracted from furnace belong to hydrotreaterunit, also samples from un-used tube material are used to make comparisons between these properti
... Show MoretA novel synthesis procedure is presented for preparing triethanolamine-treated graphene nanoplatelets(TEA-GNPs) with different specific areas (SSAs). Using ultrasonication, the covalently functionalizedTEA-GNPs with different weight concentrations and SSAs were dispersed in distilled water to prepareTEA-GNPs nanofluids. A simple direct coupling of GNPs with TEA molecules is implemented to synthesizestable water-based nanofluids. The effectiveness of the functionalization procedure was validated by thecharacterization and morphology tests, i.e., FTIR, Raman spectroscopy, EDS, and TEM. Thermal conduc-tivity, dispersion stability, and rheological properties were investigated. Using UV–vis spectrometer, ahighest dispersion stability of 0.876
... Show MoreDenture bases are fabricated routinely using Poly(methyl methacrylate) (PMMA) acrylic resin. Yet, it is commonly known for its major drawbacks such as insufficient strength and ductility. The purpose of this study was to improve the performance of PMMA acrylic resin as a denture base material by reinforcement with surface treated lithium disilicate glass ceramic powder. The ceramic powder was prepared by grinding and sieving IPS e.max CAD MT blocks. Then, the powder was surface treated with an organosilane coupling agent (TMSPM) and added to PMMA in amount of 1%, 3%, 5% and 7% by weight. Characterizations of the powder was done by particle size analysis, XRD and FTIR. Transverse strength, Impact strength, Shore D hardness and surface roughn
... Show MoreThe nonlinear optical properties response of nematic liquid crystal (6CHBT) and the impact of doping with two kinds of nanoparticles; Fe3O4 magnetic nanoparticles and SbSI ferroelectric nanoparticles have been studied using the non-linear dynamic method through z-scan measurement technique. This was achieved utilizing CW He-Ne laser. The pure LC and magnetic LC nanoparticle composite samples had a maximum absorption while the ferroelectric LC nanoparticle composite had a minimum absorption of the incident light. The nonlinear refractive index was positive for the pure LC and the rod-like ferronematic LC composite samples, while it was negative for the ferroelectric LC composite. The studying of the nonlinear optical
... Show MoreAluminum doped zinc selenide ZnSe/n-Si thin films of (250∓20 nm) thickness with (0.01, 0.02 and 0.03), are depositing on the two type of substrate (glass and n-Si) to manufacture (ZnSe/n-Si) solar cell through using thermal vacuum evaporation procedure. physical and optoelectronic properties were examined for the samples. X-Ray and AFM techniques are using to study the structure properties. The energy band gap of as-deposited ZnSe thin films for changed dopant ratio were ranging from (2.6-2.68 eV). The results of Hall effect show that pure and doping films were (p-type), and the concentration carriers and the carriers mobility increases with increase Al-dopant ratio. The (C-V) have shown that the heterojunction were of abrupt type. In add
... Show MoreIn this research the hard chromium electroplating process, which is one of the common methods of overlay coating was used, by using chromium acid as source of chromium and sulphuric acid as catalyst since the ratio between chromic acid and sulphuric acid is (100 : 1) consequently. Plating process was made by applying current of density (40 Amp / dm2) and the range of solution temperature was (50 – 55oC) with different time periods (1-5 hr). A low carbon steel type (Ck15) was used as substrate for hard chromium electroplating. Solid carburization was carried out for hard chromium plating specimen at temperature (925oC) with time duration (2 hr) to be followed with quenching and tempering
... Show MoreGlass Ionomer Cement (GIC) is one of the important dental temporary filing materials. The aim of this study is to evaluate the effect of adding 3, 5 and 7 wt. % of TiO2 microparticles to conventional GIC powder (Riva Self Cure) on mechanical properties and its effect on absorption and solubility processes. TiO2 particles additives improved compressive strength and biaxial flexural strength, where the compressive strength increased with increasing in the added ratio, while the highest value of the biaxial flexural strength was at 3 wt.%. The addition of TiO2 particles improved the surface Vickers microhardness values, with highest value at 5 wt. %. On other hand TiO2 addition im
... Show MorePresent study was conducted in order to assess Slabiaat water quality by measuring some physical and chemical factors of river water, the study included a choice of three stations along of Slabiaat River in Samawa city, water samples collected a monthly during the period from September 2013 August 2014. The study involved measuring the Air & water temperatures, pH, Electrical conductivity, Total dissolved solids, Dissolved oxygen, Total hardness, calcium hardness, magnesium, turbidity, and some types of bacteria in River water. The study results showed that the values of air & water temperatures have ranged between (20.1-36.6)?C , (10-21.8) in Slabiaat River, respectively . pH values ranged between (6.6-8.7). Electrical conductivity in
... Show MoreA numerical model for Polypropylene 575 polymer melts flow along the solid conveying screw of a single screw extruder under constant heat flux using ANSYS-FLUENT 17.2 software has been conducted. The model uses the thermophysical properties such as Viscosity, thermal conductivity, Specific heat and density of polypropylene 575 that measured as a function of temperature, and residence time data for process simulation. The numerical simulation using CFD models for single screw extruder and the polymer extrusion was analysed for parameters such as (thermal conductivity, specific heat, density and viscosity) reveals a high degree of similarity to experimental data measured. The most important outcome of this study is that geometrical, parame
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