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
The compounding of polyvinyl chloride (PVC) with two types of fillers and some additives were studied for the manufacturing of acid resistant tile. Various concentrations of two types of fillers namely; calcium carbonate and recycled glass powder were used along with different additives generally categorized as plasticizers, stabilizers, and lubricants were mixed in the standard concentration unit parts per hundred resins (phr) with the PVC as base polymer. The effects of filler materials on acid resistant towered different acids like sulphuric, nitric and hydrochloric at different concentration were studied. Samples which passed the test were further checked for dielectric strength and mechanical properties. It was found that the recycl
... Show MoreThe (NiTsPc) thin films operating by vacuum evaporation technique are high recital and good desirable for number of applications, were dumped on glass substrates at room temperature with (200±20nm) thickness and doped with Al at different percentage (0.01,0.03) besides annealing the sample with 200˚C for 1 hours . The stimuluses of aluminum dopant percentage on characterization of the dropped (Ni Ts Pc) thin films were studied through X-ray diffraction in addition from the attained results, were all the films have polycrystalline in nature, as well the fallouts of XRD aimed at film illustrations polycrystalline, depending on the Al ratio doping, the results, SEM exposed the surface is regularly homogeneous. Utilizing first-ideolog
... Show MoreIn recent years, nano-modified asphalt has gained significant attraction from researchers in the design of asphalt pavement fields. The recently discovered Titanium dioxide nanoparticles (TiO2) are among the most exciting and promising nanomaterials. This study examines the effect of 1, 3, 5, and 7% of nano-TiO2 by weight of asphalt on some of its rheological and hardened properties. The experimental study included physical and rheological properties. The asphalt penetration, softening point, ductility, and rotational viscometer tests indicate that 5% nano-TiO2 is the ideal amount to be added to bitumen as a modifier. The
Explain in this study, thickness has an inverse relationship with electrical resistivity and a linear relationship with Grain boundary scattering. According to the (Fuchs-Sondheier, Mayadas-Shatzkces) model, grain boundary scattering leads To an Increase in electrical Resistivity. The surface scattering Coefficient of Ag, which Fuchs-Sondheier and Mayadas-Shatzkces measured at , Ag's grain boundary reflection coefficient , which Mayadas-Shatzkces measured at , If the concentration of material has an effect on metal's electrical properties, According to this silver is a good electrical conductor and is used frequently in electrical and electronic circuits.
A reseach is carried out by using Alumina material type α-Al2O3 which has partical size 63μm doped with different percentage weight of MgO (0.1%,0.3%and0.5%) and by using dry press method to prepare the samples ,A force press 50KN used and sintering to 1500oC with soaking time of 6 hours. The physical properties were studied such as "Bulk density ,Porosity and water absorption "also the mechanical properties such as (hardness,compressive strength ), the result shows that the best ratio of maginsa(MgO) added to Alumina (Al2O3)is 0.5%and this worked to improve Physical and mechanical properties .
A thermal evaporation technique was used to prepare ZnO thin films. The samples were prepared with good quality onto a glass substrate and using Zn metal. The thickness varied from (100 to 300) ±10 nm. The structure and optical properties of the ZnO thin films were studied. The results of XRD spectra confirm that the thin films grown by this technique have hexagonal wurtzite, and also aproved that ZnO films have a polycrystalline structure. UV-Vis measurement, optical transmittance spectra, showed high transmission about 90% within visible and infrared range. The energy gap is found to be between 3.26 and 3.14e.V for 100 to 300 nm thickness respectivly. Atomic Force Microscope AFM (topographic image ) shows the grain size incre
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