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
Natural bitumen (NB) is a highly precious material and has drawn increasing attention due to its unique properties, especially since it is available in large quantities and has been used in limited fields. In this research, the exploitation of NB from sulfur springs as an alternative energy resource in the production of asphalt pavement is evaluated. It can be concluded from the experimental results that the chemical composition and surface morphology of NB samples are different from those of base asphalt. Besides, the rheological properties of virgin NB are not sufficient for paving work. To overcome this obstacle, NB from five different springs is modified with limestone filler (LSF) to enhance its properties. LSF is a natural material an
... Show MorePermanent deformation (rutting) of asphalt mixtures is one of the major forms of distress. Aggregate gradation is one of the most important factors affecting the permanent deformation of asphalt mixtures. Other variables are also important to understand their effects on the mixture such as temperature, binder content and compaction level. For this purpose 6 different aggregate gradations have been chosen and each one of them has been manufactured / tested with different variables. The results showed that at relatively low temperature there is little effect of aggregate packing on the permanent deformation. However, as the temperature increases the effect of gradation becomes apparent, in that the better the packing the better the resistance
... Show MoreIn this research PbS thin film have been prepared by chemical bath deposition technique (CBD).The PbS film with thickness of (1-1.5)μm was thermally treated at temperature of 100°C for 4 hours. Some Structural characteristics was studied by using X-ray diffraction (XRD)and optical microscope photograph some of chemical gas sensing measurements were carried out ,it shown that the sensitivity of (CO2) gas depend on the grain Size and deposition substrate. The grain size of PbS film deposited on on glass closed to 21.4 nm while 37.97nm for Si substrate. The result of current-voltage characterization shwon the sensitivity of prepared film deposited on Si better than film on glass.
The present paper deals with prepared of ternary Se80-xTe20Gex system alloys and thin films. The XRD analysis improved that the amorphous structure of alloys and thin films for ternary Se80-xTe20Gex (at x=10and 20at.%Ge) which prepared by thermal evaporation techniques with thickness 250 nm. The optical energy gap measurements show that the optical energy gap decreases with increasing of (Ge) content from (1.7 to 1.47 eV)
It is found that the optical constants, such as refractive
index ,extinction coefficient, real and imaginary dielectric
constant are non systematic with increasing of Ge contents
and annealing temperatures
Polyaniline polymer has been prepared by chemical oxidation
polymerization method in laboratory successfully. The PANI and
(PVA+PVP) as a polymer blends in different percentage (30%, 50%,
70%) from Polyaniline was prepared. The sample was studies as
optical properties by UV-vis spectrophotometer at (400-700) nm.
The result of optical energy gap was 2.23 eV for pure (PVA+ PVP)
and with additive was increasing with increasing PANI concentration
to become (2.49 for 30% to 2.52 for 70%) PANI. The goal of this
project is prepare triple blend polymer and study the effect when add
conductive polymer (Polyaniline) on the optical properties and
calculate optical constant as energy gap, refractive index, dielectric
Gypsum Plaster is an important building materials, and because of the availabilty of its raw materials. In this research the effect of various additives on the properties of plaster was studied , like Polyvinyl Acetate, Furfural, Fumed Silica at different rate of addition and two types of fibers, Carbon Fiber and Polypropylene Fiber to the plaster at a different volumetric rate. It was found that after analysis of the results the use of Furfural as an additive to plaster by 2.5% is the optimum ratio of addition to that it improved the flexural Strength by 3.18%.
When using Polyvinyl Acetate it was found that the ratio of the additive 2% is the optimum ratio of addition to the plaster, because it improved the value of the flexural stre
This study, establishes two stochastic monotonicity results concerning the run length of an upper one –sided Exponentially Weighted Moving Average (EWMA) control charts, based on the logarithm of the sample variance, for monitoring a process standard deviation, these properties cast interesting light on the control chart performance, and their extension to other one –sided EWMA control charts.
Lithium doped Nickel-Zinc ferrite material with chemical formula Ni0.9−2x Zn0.1LixFe2+xO4, where x is the ratio of lithium ions Li+ (x = 0, 0.01, 0.02, 0.03 and 0.04) prepared by using sol-gel auto combustion technique. X-ray diffraction results showed that the material have pure cubic spinal structure with space group Fd-3m. The experimental values of the lattice constant (aexp) were decreased from 8.39 to 8.35 nm with doped Li ions. It was found that the decreasing of the crystallite size with addition of lithium ions concentration. The radius of tetrahedral (rtet) and octahedral (roct) site were computed from cation distribution. SEM images have been taken to show the morphology of compound. The dielectric parameters [dissipation fa
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