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
This study included preparation for the unsaturated polyester samples before and after reinforced by the Alumina oxide powder of different volume fraction amounting (2%,4%,6%). And this research included the study of some of mechanical properties such as (Hardness,compressive,wear). The results showed that the increase of the hardness and compressive strength after the reinforced and the increase with the volume fraction increase. As the wear test shows that the wear rate increases with applied load increase(5,10,15) from (10.6-18.6) gm/cm befor reninforced and from(5.4-15.2)gm/cm,(4.7-12.9)gm/cm,(48.1)gm/cm,after reinforced from the different volume fraction, and t
... Show MoreThis study includes the preparation of the ferrite nano ferrite CuxAl0.3-XNi0.7Fe2O4 (where: x = 0, 0.05, 0.1, 0.15, 0.2, 0.25, 0.3) M using the auto combustion method (sol-gel), and citric acid was used as fuel for auto combustion. The ferrite samples were checked by X-ray diffraction (XRD), Field Emission Scanning Electron Microscopes (FE-SEM), and energy dispersive X-ray analyzer (EDX). They showed that the prepared compound has a face-centered cubic structure (FCC). The lattice constant increases with an increase in the percentage of doping of the copper ions, and a decrease for the aluminum ion and that the compound is porous and its grains are spherical, and there are no other
... Show MoreIn this research, the structural and optical properties were studied for Bi2O3 and Bi2O3: Al thin films with different doping ratios ( 1, 2, 3 ) % , which were prepared by thermal evaporation technique under vacuum , with thickness ( 450 ± 20 ) nm deposited on glass substrates at room temperature ( 300 ) K , Structural measurements by ( XRD) techniques demonstrated that all samples prepared have polycrystalline structure with tetragonal structure and a preferred orientation [ 201 ] the &n
... Show MoreThe work concerned with studying the effect of (SiO2) addition as a
filler on the adhesive properties of (PVA). Samples were prepared as
sheets by using casting method. The mechanical properties showed
that increase in tensile strength from (34MPa) to (68MPa) when
(SiO2) added to (PVA). The adhesive strength showed that joint
properties depend upon specific adhesive characteristic of material
(PVA) and (SiO2\PVA)composites at different concentrations (1.5%,
2.5%, 3.5%, 4.5wt%), the cohesive strength of the adhesive material,
the joint design, and adherent type (Sponge Rubber(SR), Natural
leather (NL), Vulcanized Rubber(VR), and Cartoon). The results
proved the tensile strength increased with (SiO2) ratio, so
The use of blended cement in concrete provides economic, energy savings, and ecological benefits, and also provides. Improvement in the properties of materials incorporating blended cements. The major aim of this investigation is to develop blended cement technology using grinded local rocks . The research includes information on constituent materials, manufacturing processes and performance characteristics of blended cements made with replacement (10 and 20) % of grinded local rocks (limestone, quartzite and porcelinite) from cement. The main conclusion of this study was that all types of manufactured blended cement conformed to the specification according to ASTM C595-12 (chemical and physical requirements). The percentage of the compress
... Show MoreThe aim of this research is to study the optical properties of carbon-magnesium plasma resulting from arc discharge with explosive wire technique, where the energy gap of each of carbon and magnesium and the carbon-magnesium bond for three values of the wire exploding current (50,75,100 amperes) was studied. It was found that the energy gap for each of carbon and magnesium decreases with increasing the current, the X-ray diffraction of magnesium and the carbon-magnesium suspension was studied, and FTIR of the carbon-magnesium suspended carbon was studied for three values of the exploding current (50, 75, 100 amperes) and the type of bonds for carbon and magnesium was determined. To ob
Scleral acrylic resin is widely used to synthesize ocular prosthesis. However, the properties of this material change over time, thus requiring the prosthesis to be refabricated. Many studies were conducted to improve these properties by reinforcing this material with nanoparticles. This study aims to evaluate the effect of silver nanoparticle powder on the mechanical properties (transverse flexural strength, impact strength, shear bond strength, surface microhardness, and surface roughness) of scleral acrylic resin used for ocular prostheses. Two concentrations were selected from the pilot study and evaluated for their effects on scleral acrylic resin properties. According to the pilot study, 0.01 and 0.02wt% AgNPs powder improved
... Show MoreIn this study, the ZnTe thin films were deposited on a glass substrate at a thickness of 400nm using vacuum evaporation technique (2×10-5mbar) at RT. Electrical conductivity and Hall effect measurements have been investigated as a function of variation of the doping ratios (3,5,7%) of the Cu element on the thin ZnTe films. The temperature range of (25-200°C) is to record the electrical conductivity values. The results of the films have two types of transport mechanisms of free carriers with two values of activation energy (Ea1, Ea2), expect 3% Cu. The activation energy (Ea1) increased from 29meV to 157meV before and after doping (Cu at 5%) respectively. The results of Hal
... Show MoreThe various properties of the ground and excited electronic states of coumarins 102 using density functional theory (DFT) and time-dependent density functional theory (TDDFT) was calculated by the B3LYP density functional model with 6-31G(d,p) basis set by Gaussian 09 W program. Spectral characteristics of coumarin102 have been probed into by methods of experimental UV-visible, and quantum chemistry. The UV spectrum was measured in methanol. The optimized structures, total energies, electronic states (HOMO- LUMO), energy gap, ionization potentials, electron affinities, chemical potential, global hardness, softness, global electrophilictity, and dipole moment were measured. We find good agreement between experimental data of UV spectrum and
... Show MoreSuperconducting thin films of Bi1.6Pb0.4Sr2Ca2Cu2.2Zn0.8O10 system were prepared by depositing the film onto silicon (111) substrate by pulsed laser deposition. Annealing treatment and superconducting properties were investigated by XRD and four probe resistivity measurement. The analysis reveals the evolution of the minor phase of the films 2212 phase to 2223 phase, when the film was annealed at 820 °C. Also the films have superconducting behavior with transition temperature ≥90K.