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 the current study, the definition of mapping of fuzzy neutrosophic generalized semi-continuous and fuzzy neutrosophic alpha has generalized mapping as continuous. The study confirmed some theorems regarding such a concept. In the following, it has been found relationships among fuzzy neutrosophic alpha generalized mapping as continuous, fuzzy neutrosophic mapping as continuous, fuzzy neutrosophic alpha mapping as continuous, fuzzy neutrosophic generalized semi mapping as continuous, fuzzy neutrosophic pre mapping as continuous and fuzzy neutrosophic γ mapping as continuous.
Natural fibers and particles reinforced composites are being broadly used due to their bio and specific properties such as low density and easy to machine and production with low cost. In this work, water absorption and mechanical properties such as tensile strength, flexural strength and impact strength of recycled jute fibers reinforced epoxy resin were enhanced by treating these fibers with alkaline solution. The recycled jute fibers were treated with different concentration of (NaOH) solution at (25 0C) for a period of (24) hours. From the obtained results, it was found that all these properties are improved when fibers treated with (7.5wt% NaOH) related to untreated fibers. Conversely, the mentioned properties of composit
... Show MoreIn this research, damping properties for composite materials were evaluated using logarithmic decrement method to study the effect of reinforcements on the damping ratio of the epoxy matrix. Three stages of composites were prepared in this research. The first stage included preparing binary blends of epoxy (EP) and different weight percentages of polysulfide rubber (PSR) (0%, 2.5%, 5%, 7.5% and 10%). It was found that the weight percentage 5% of polysulfide was the best percentage, which gives the best mechanical properties for the blend matrix. The advantage of this blend matrix is that; it mediates between the brittle properties of epoxy and the flexible properties of a blend matrix with the highest percentage of PSR. The second stage
... Show MoreIn this work, we first construct Hermite wavelets on the interval [0,1) with it’s product, Operational matrix of integration 2^k M×2^k M is derived, and used it for solving nonlinear Variational problems with reduced it to a system of algebric equations and aid of direct method. Finally, some examples are given to illustrate the efficiency and performance of presented method.
The photo-electrochemical etching (PECE) method has been utilized to create pSi samples on n-type silicon wafers (Si). Using the etching time 12 and 22 min while maintaining the other parameters 10 mA/cm2 current density and HF acid at 75% concentration.. The capacitance and resistance variation were studied as the temperature increased and decreased for prepared samples at frequencies 10 and 20 kHz. Using scanning electron microscopy (SEM), the bore width, depth, and porosity % were validated. The formation of porous silicon was confirmed by x-ray diffraction (XRD) patterns, the crystal size was decreased, and photoluminescence (PL) spectra revealed that the emission peaks were centered at 2q of 28.5619° and 28.7644° for et
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This research aims to study and improve the passivating specifications of rubber resistant to vibration. In this paper, seven different rubber recipes were prepared based on mixtures of natural rubber(NR) as an essential part in addition to the synthetic rubber (IIR, BRcis, SBR, CR)with different rates. Mechanical tests such as tensile strength, hardness, friction, resistance to compression, fatigue and creep testing in addition to the rheological test were performed. Furthermore, scanning electron microscopy (SEM)test was used to examine the structure morphology of rubber. After studying and analyzing the results, we found that, recipe containing (BRcis) of 40% from th
... Show MoreAg2O (Silver Oxide) is an important p-type (in chasm to most oxides which were n-type), with a high conductivity semiconductor. From the optical absorbance data, the energy gap value of the Ag2O thin films was 1.93 eV, where this value substantially depends on the production method, vacuum evaporation of silver, and optical properties of Ag2O thin films are also affected by the precipitation conditions. The n-type and p-type silicon substrates were used with porous silicon wafers to precipitate ±125 nm, as thick Ag2O thin film by thermal evaporation techniques in vacuum and via rapid thermal oxidation of 400oC and oxidation time 95 s, then characterized by measurement of
... Show MoreCopper selenide (Cu2Se) thin films were prepared by thermal evaporation at RT with thickness 500 nm. The heat-treating for (400 &500) K for the absorber layer has been investigated. This research includes, studying the structural properties of X-ray diffraction (XRD) that show the Cu2Se thin film (Cubic) and has a polycrystalline orientation prevalent (220). Moreover, studying the effect of annealing on their surface morphology properties by using Atomic Force Microscopy AFM. Optical properties were considered using the transmittance and absorbance spectra had been recorded when wavelength range (400 - 1000) nm in order to study the absorption coefficient and energy gap. It was found that these films had allowed direct transitio
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