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
Preparation of superposed thin film (CdTe)1-xSex / ZnS) with concentration of (x= 0.1, 0.3, 0.5) at a temperature of substrate (Ts= 80 0C) by using Thermal Vacuum Evaporation System. The measurement of X-ray diffraction shows that the compounds CdTe, ZnS, (CdTe)1-xSex and (CdTe)1-xSex / ZnS have a polycrystalline structure, the C-V characteristic shows that the capacitance degrease by increasing the concentration (x) in reverse bias, while the I-V characteristic shows the current dark (Id) increase in forward and reverse bias by increasing (x) and the photocurrent (Iph) increase in reverse bias by increasing the concentration (x), the values of photocurrent are greater than from the values of the dark current for all concentrations
... Show MoreBackground: The mechanical and physical properties of Polymethyl methacrylate (PMMA) don’tfulfill the entire ideal requirements of denture base materials. The purpose of this study was to produce new modified polymer nanocomposite (PMMA /ZrO2-TiO2) andassess itsimpact strength, transverse strength and thermal conductivity in comparison to the conventionalheat polymerized acrylic resin. Materials and Methods: Both ZrO2 and TiO2nano fillers were silanized with TMSPM (trimethoxysilyl propyl methacrylate) silane coupling agent before beingdispersed by ultrasonication with the methylmethacrylate (monomer) and mixed with the polymer by means of 2% by weight in (1:1) ratio, 60 specimens were constructed by conventional water bath processing
... Show Moremixtures of cyclohexane + n-decane and cyclohexane + 1-pentanol have been measured at 298.15, 308.15, 318.15, and 328.15 K over the whole mole fraction range. From these results, excess molar volumes, VE , have been calculated and fitted to the Flory equations. The VE values are negative and positive over the whole mole fraction range and at all temperatures. The excess refractive indices nE and excess viscosities ?E have been calculated from experimental refractive indices and viscosity measurements at different temperature and fitted to the mixing rules equations and Heric – Coursey equation respectively to predict theoretical refractive indices, we found good agreement between them for binary mixtures in this study. The variation of th
... Show MoreFlexible pavements are subjected to three main distress types: fatigue crack, thermal crack, and permanent deformation. Under severe climate conditions, thermal cracking particularly contributes largely to a considerable scale of premature deterioration of pavement infrastructure worldwide. This challenge is especially relevant for Europe, as weather conditions vary significantly throughout the year. Hydrated lime (HL) has been recognized as an effective additive to improve the mechanical properties of asphalt concrete for pavement applications. Previous research has found that a replacement of conventional limestone dust filler using hydrated lime at 2.5% of the total weight of aggregates generated an optimum improvement in the mec
... Show MoreSpray pyrolysis technique was subjected to synthesized (SnO2)1-x (TiO2: CuO) x Thin films on different substrates like glass and single crystal silicon using. The structure of the deposited films was studied using x-ray diffraction. A more pronounced diffraction peaks of SnO2 while no peaks of (CuO , TiO2 ) phase appear in the X-ray profiles by increasing of the content of (TiO2 , CuO) in the sprayed films. Mixing concentration (TiO2 , CuO) influences on the size of the crystallites of the SnO2 films ,the size of crystallites of the spray paralyzed oxide films change in regular manner by increasing of (TiO
... Show MoreSilver selenide telluride Semiconducting (Ag2Se0.8Te0.2) thin films were by thermal evaporation at RT with thickness350 nm at annealing temperatures (300, 348, 398, and 448) °K for 1 hour on glass substrates .using X-ray diffraction, the structural characteristics were calculated as a function of annealing temperatures with no preferential orientation along any plane. Atomic force microscopy (AFM) and X-ray techniques are used to analyze the Ag2SeTe thin films' physical makeup and properties. AFM techniques were used to analyze the surface morphology of the Ag2SeTe films, and the results showed that the values for average diameter, surface roughness, and grain size mutation increased with annealing temperature (116.36-171.02) nm The transm
... Show MoreFadak farm project was selected to conduct this study in and to evaluate the state of quality and health indices in term of soil physical properties, where this farm is located in Holly Najaf Governorate. Some physical properties (soil texture, mean weight diameter, bulk density, porosity, infiltration rate, saturated hydraulic conductivity and available water) were selected to assess the quality then health indices, Results showed that classes of moderate and poor soil health were dominated in lands of this farm for physical properties It was noted that the class good of soil health wasnot collaterally appeared in areas for the physical characteristics.
Objective This study aimed to evaluate the effects of disinfectant solutions, namely, the alcoholic extract of Salvadora persica L. (A1 = 10% and A2 = 15%) and chlorhexidine digluconate (A3 = 2%), on the tear strength and hardness of room temperature vulcanizing (RTV) VST50F and heat temperature vulcanizing (HTV) Cosmesil M511 silicone elastomers before and after reinforcement with nanofillers (TiO2) and intrinsic pigment. Materials and Methods: A total of 320 specimens were prepared, with 160 specimens each for RTV and HTV silicone. Forty specimens were evaluated before disinfection and divided into two equal groups, namely, control (without additive) and experimental (with ad
In this study, plastic wastes named (PET and PVC) were used to prepare polymer matrix composite (PMC) which can be used in different applications. Composite materials were prepared by mixing unsaturated polyester resin (UP) with plastic wastes, two types of plastic waste were used in this work included polyethylene-terephthalate (PET) and Polyvinyl chloride (PVC) with various weight fractions (0, 5,10,15, 20 and 25%) added as a filler in flakes form. In this work, some of the tests that were carried out included (tensile, bending, and compressive strength) as mechanical tests, in addition to (thermal conductivity and water absorption) as physical tests. The values of tensile, compressive strength and Young's modulus of UP increased after
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