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
In past years, structural pavement solution has been combined with destructive testing; these destructive methods are being replaced by non-destructive testing methods (NDT). Because the destructive test causes damage due to coring conducted for testing and also the difficulty of adequately repairing the core position in the field. Ultrasonic pulse velocity was used to evaluate the strength and volumetric properties of asphalt concrete, of binder course. The impact of moisture damage and testing temperature on pulse velocity has also been studied. Data were analyzed and modeled. It was found that using non-destructive testing represented by pulse velocity could be useful to predict the quality of asphalt c
... Show MoreThe scarcity of irrigation water requires procedures of specific. One of these procedures is the implementation of the rationing system (a period of the irrigation followed by a period of the dry). This system can have an impact on the properties of irrigation channels. Therefore, the study of rationing system for irrigation channels is important in both water resources and civil engineering, especially if they are constructed with gypseous soil. In order to assess the rationing system on gypseous canals stabilized with a specific ratio of cement, practical experiments were conducted to detect the effect of wetting and drying cycles on the physical and hydraulic behavior of this soil and calculation of some properties of soil such a
... Show MoreThe research is concerned about studying the absorption spectrum of the solution coumarin dye C47. The chloroform solvent was used with C47 dye in three different concentrations 10-4, 10-5 and 10-6 M. The laser dye solution was prepared by dissolving the required amount of dye in chloroform alcohol, while studying absorption spectrum before and after irradiation with gamma ray by cobalt-60 source 60Co at exposure time, which are 0, 4, 6 and 18 hours with different absorbed doses 0, 136, 204 and 612 Gy. The results show that red shift in the absorption spectrum was increased by increasing the concentration of laser dye solutions , while the increase of gamma dose led to increase the red shift after irradiation, as the exposure period and irr
... Show Morepriorities of materials research due to their promising properties, especially in the field of thermoelectricity. The efficiency or performance of thermoelectric devices is expressed in terms of the thermoelectric figure-of-merit (ZT) – a standard indicator of a material’s thermoelectric properties for use in cooling systems. The evaluation of ZT is principally determined by the thermoelectric characteristics of the nanomaterials. In this paper, a set of investigative computations was performed to study the thermoelectric properties of monolayer TMDCs according to the semiclassical treatment of the Boltzmann transport equation. It was confirmed that the thermoelectric properties of 2D materials can be greatly improved compared with thei
... Show Moreon this research is to study the effect of nickel oxide substitution on the pure phases superconductor Tl0.5Pb0.5Ba2Can-1Cun-xNixO2n+3-δ (n=3) where x=(0,0.2,0.4,0.6,0.8.and 1.0). The specimens in this work were prepared with used procedure of solid state reaction with sintering temperature 8500C for 24 h .we used technical (4-prob)to calculated and the critical temperature Tc . The results of the XRD diffraction analysis showed that the structure for pure and doped phases was tetragonal with phases high-Tc phase (1223),(1212) and low-Tc phase (1202) and add
... Show MoreA pulsed (TEA-0O2) laser was used to dissociate molecules of silane ethylene (C2I-14) and ammonia (NH3) gases, through collision assisted multiple photon dissociation (MPD) to deposit(SiC i_xNx) thin films, where the X-values are 0, 0.13 and 0.33, on glass substrate at T,----648 K. deposition rate of (0.416-0.833) nm/pulse and thickness of (500-1000)nm .Fourier transform infrared spectrometry (FT-IR) was used to study the nature of the chemical bonds that exist in the films. Results revealed that these films contain complex networks of the atomic (Si, C, and N), other a quantity of atomic hydrogen and chemical bonds such as (Si-N, C-N, C-14 and N-H).Absorbance and Transmittance spectra in the wavelength range (400-1100) nm were used to stud
... Show MoreThe research targets study of influence of additives on sand mold’s properties and, consequently, on
that of carbon steel CK45 casts produced by three molds. Three materials were selected for addition
to sand mix at weight percentages. These are sodium carbonates, glycerin and oat flour. Sand molds
of studied properties were produced to get casts from such molds. The required tests were made to
find the best additives with respect to properties of cast. ANSYS software is used to demonstrate
the stresses distribution of each produced materials. It is shown that the mechanical properties of
casts produced is improved highly with sodium carbonates and is less with oat flour and it is seem a
few with glycerin additives