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 paper the definition of fuzzy anti-normed linear spaces and its basic properties are used to prove some properties of a finite dimensional fuzzy anti-normed linear space.
In this paper the definition of fuzzy normed space is recalled and its basic properties. Then the definition of fuzzy compact operator from fuzzy normed space into another fuzzy normed space is introduced after that the proof of an operator is fuzzy compact if and only if the image of any fuzzy bounded sequence contains a convergent subsequence is given. At this point the basic properties of the vector space FC(V,U)of all fuzzy compact linear operators are investigated such as when U is complete and the sequence ( ) of fuzzy compact operators converges to an operator T then T must be fuzzy compact. Furthermore we see that when T is a fuzzy compact operator and S is a fuzzy bounded operator then the composition TS and ST are fuzzy compact
... Show MoreThe traction property is one of the important mechanical properties, especially the rotary parts which are subjected to constant and variable loads There are many methods used to improve this property, and the shoot peening by metal balls is considered the most critical one. the study focuses on this characteristic of steel CK35 used in many engineering applications as the rotating shafts and railway This study shows that the fatigue strength is improved by14% after shoot peening with metal balls. The study includs the rehabilitation of damaged samples as a result of fatigue corrosion. The standard solution adopted was 36% MgCl2 with a 30 days immersion period. These samples has been improved by 6% after it decreased by18% d
... Show MoreIn this work, 332 Al alloy was prepared and reinforced with (0.5% and 1%) nano-Al2O3 particles. The prepared unreinforced and reinforced 332 Al alloy with nano-Al2O3 were solution heat treated (T6) at 510 ̊C and aged at 225 ̊C with different times (1, 3, and 5 h). Hardness test was performed on all the prepared alloys. All prepared alloys were dry slided under different applied loads (5, 10, 15, and 20 N) against steel counterface surface using pin on disk apparatus. The results showed that refinement effect was observed after addition of nano-Al2O3 particles and a change in silicon morphology after performing the solution heat treatment. The results also showed that har
... Show MoreIn this research, Haar wavelets method has been utilized to approximate a numerical solution for Linear state space systems. The solution technique is used Haar wavelet functions and Haar wavelet operational matrix with the operation to transform the state space system into a system of linear algebraic equations which can be resolved by MATLAB over an interval from 0 to . The exactness of the state variables can be enhanced by increasing the Haar wavelet resolution. The method has been applied for different examples and the simulation results have been illustrated in graphics and compared with the exact solution.
The microstructure and wear properties of 392 Al alloy with different Mg contents were studied using centrifugal casting. All melted alloys were heated to 800 ºC and poured into the preheated centrifugal casting mold (200-250 ºC) at different mould rotational speeds (1500, 1900 and 2300 r.p.m). It is clear from the results obtained that wear rate was dependent on the Mg content, applied load and mould rotational speed. Furthermore, wear test showed that the minimum wear rate was found in the inner layer of produced rings at mould rotational speed of 1900 r.p.m and Mg content of 5%.
Extraction and preparation of red organic dye from beetroot plant in different concentrations by using the solvent extraction process. Ethanol was the solvent used to prepare five different concentrations at the ratio of (Dye: Ethanol) abbreviated (D: E) 5:0,4:1, 3:2, 2:3,1:4. The optical, structural, and morphological properties are studied for the samples. The results appeared using the UV-Vis spectroscope the maximum peak of absorption (A) spectrum at wavelength Aλmax=480 nm when the transmittance (T) at the same wavelength 25% and the reflectivity 0.8%. Florescent (F) spectrum of beetroot dye is measured at wavelength Fλmax=535nm achieved to redshift about Δλ=55 nm. Also, measured the energy band gap
... Show MoreThis research includes a study of dezincification by corrosion from brass alloys in three types of media, which are acidic solution, basic and slat solution in different percentages. The study show the higher dezincification occurs in basic solution which decrease the fatigue properties where the fatigue properties are inversely proportional with dezincification.
Experiments were conducted to study axial liquid dispersion coefficient in slurry bubble column of 0.15 m inside diameter and 1.6 m height using perforated plate gas distributor of 54 holes of a size equal to 1 mm diameter and with a 0.24 free area of holes to the cross sectional area of the column. The three phase system consists of air, water and PVC used as the solid phase. The effect of solid loading (0, 30 and 60 kg/m3) and solid diameter (0.7, 1.5 and 3 mm) on the axial liquid dispersion coefficient at different axial location (25, 50 and 75 cm) and superficial gas velocity covered homogeneous-heterogeneous flow regime (1-10 cm/s) were studied in the present work. The results show that the axial liquid dispersion coeffic
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