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 this work, nanostructure porous silicon surface was prepared using electrochemical etching method under different current densities. I have studied the surface morphology and photoluminescence (PL) of three samples prepared at current densities 20, 30 and 40 mA/cm2 at fixed etching time 10 min. The atomic force microscopy (AFM) images of porous silicon showed that the nanocrystalline silicon pillars and voids over the entire surface has irregular and randomly distributed. Photoluminescence study showed that the emission peaks centered at approximately (600 – 612nm) corresponding energies (2.06 – 2.02eV).
While current-voltage characteristics shows, as the current density increase the current flow in the forward bias is decreasi
A colloidal indium oxide (In2O3) nanoparticles (NPs) were synthesized pulsed laser ablation (PLA) of indium plate placed on the bottom of the quartz vessel containing (3ml) of pure ethanol. The influence laser energy on the properties of the formed nano-particles were characterized by using atomic force microscopy (AFM), X-ray diffraction (XRD), Ultraviolet Visible (UV-Vis) technique, and electrical properties measurements. The XRD revealed the crystallization structure of In2O3 nanoparticles and all the films having preferential orientation along (222) plane and intensity increases with increasing laser energy, The UV–Visible spect
... Show MoreThe need for optical fibers has emerged for its ability to transmit information with less attenuation and over long distances. In this work, four optical fibers with core radii from 1 μm to 4.75 μm in steps of 1.25 μm and a numerical aperture of 0.17 were studied and their modes properties have been calculated at a wavelength of 633 nm by using RP Fiber Calculator (free version 2022). Also, the effect of increasing the core radius on these properties has been studied. Multimode fibers can be obtained when the radius of the fiber core is large compared to the operating wavelength of the fiber which is less than the cutoff wavelength of the mode. Otherwise, a single-mode fiber is obtained. It has been concluded that all the calculated p
... Show MoreUtilizing first principles calculations within PW91 exchange-correlation method, we investigated a boron sheet that exhibits related electronic properties. The 2-dimensional boron sheet is flattened and has an atomic structure where the pair cores of every three ordered hexagons within the hexagonal network are loaded up by extra atoms, which saves the triangular lattice symmetry. The boron sheet takes possession of intrinsic metal properties and the electronic bands are comparable to the bands of the graphene that are close to the Fermi level. The real and imaginary parts of the dielectric function show a metallic or semiconductor behaviour, depending on the electric field direction.
In this work, the electrical properties and optimum conditions of the plasma sputtering system have been studied. The electrical properties such as Paschen's curve, current-voltage, current pressure relations, the strength of magnetic field as a function of inter-electrode distance, the influence of gas working pressure and argon-oxygen ratio on the electrical characterization were studied to determine the basic optimum condition of the system operation. the discharge current as a function of discharge voltage showed high discharge current at 2.5 cm. These parameters represent the basic conditions to operate any plasma sputtering system which are the right behavior to build up and design the discharge an el
... Show MoreThe performance grading system (superpave) has provided means to incorporate binder characteristics with
pavement failure types. It’s a comprehensive system that relates climate, traffic conditions and aging with
critical pavement distress. The objective of this paper is to develop an improved asphalt binder grading
system for Iraq based on the principal of superpave. The country was divided into different zones according
to the highest and lowest temperature ranges and traffic loading. The Performance graded binder proposed
for each zone was compared with some States of USA that have same hot weather of Iraq by using Long
Term Pavement Performance (LTPP v3.1) software. Iraqi asphalt samples were tested using the Supe
Petrophysical properties of Mishrif Formation at the Tuba field determined from interpretation of open log data of(Tu-2,3,4,5,6,12,24,and 25) wells. These properties include total (effected) and secondary porosity, as well as moveable and residual oil saturation into invaded and uninvaded zones. According to Petrophysical properties it is possible to divided Mishrif Formation into three reservoir units (RU1,2,and 3) separated by four cap rocks (Bar1,2,3,and 4) . Three-dimension reservoir model is established by used (Petrel, 2009) Software for each reservoir units. Result shows that the second and third reservoir units represent important reservoir units of Mishrif Formation. Thickness and reservoir properties enhanced toward middle and
... Show MoreIn this work, pure and doped Vanadium Pentoxide (V2O5) thin films with different concentration of TiO2 (0, 0.1, 0.3, 0.5) wt were obtained using Pulse laser deposition technique on amorphous glass substrate with thickness of (250)nm. The morphological, UV-Visible and Fourier Transform Infrared Spectroscopy (FT-IR) were studied. TiO2 doping into V2O5 matrix revealed an interesting morphological change from an array of high density pure V2O5 nanorods (~140 nm) to granular structure in TiO2-doped V2O5 thin film .Transform Infrared Spectro
... Show MoreBaTiO3 thin films have been deposited on Si (111) and glass substrates by using pulsed laser deposition technique. The films were characterized by using X-ray diffraction, atomic force microscope and optical transmission spectra. The films growth on Si after annealing at 873K showed a polycrystalline nature, and exhibited tetragonal structure, while on glass substrate no growth was noticed at that temperature. UV-VIS transmittance measurements showed that the films are highly transparent in the visible wavelength region and near-infrared region for sample annealing on glass substrate. The optical gap of the film were calculated from the curve of absorption coefficient (αhν) 2 vs. hν and was found tobe 3.6 eV at substrate temperature 5
... Show MoreIn recent decades, tremendous success has been achieved in the advancement of chemical admixtures for Portland cement concrete. Most efforts have concentrated on improving the properties of concrete and studying the factors that influence on these properties. Since the compressive strength is considered a valuable property and is invariably a vital element of the structural design, especially high early strength development which can be provide more benefits in concrete production, such as reducing construction time and labor and saving the formwork and energy. As a matter of fact, it is influenced as a most properties of concrete by several factors including water-cement ratio, cement type and curing methods employed.
Because of acce