The goal of this research is to solve several one-dimensional partial differential equations in linear and nonlinear forms using a powerful approximate analytical approach. Many of these equations are difficult to find the exact solutions due to their governing equations. Therefore, examining and analyzing efficient approximate analytical approaches to treat these problems are required. In this work, the homotopy analysis method (HAM) is proposed. We use convergence control parameters to optimize the approximate solution. This method relay on choosing with complete freedom an auxiliary function linear operator and initial guess to generate the series solution. Moreover, the method gives a convenient way to guarantee the convergence of series solutions via the control parameter curve graphical method to rate the convergence and obtain the best solution. Decoding and analyzing potential Korteweg-de-Vries, Benjamin, and Airy equations, followed by convergence analysis to demonstrate the applicability of the method. By using the programs Mapel and Mathematica, the obtained results are very effective, accurate, and convergent to the exact solution after a few iterations, as shown in the tables and figures of this work.
This paper describes the synthesis of ?- Fe2O3 nanoparticles by sol-gel route using carboxylic acid(2-hydroxy benzoic acid) as gelatin media and its photo activity for degradation of cibacron red dye . Hematite samples are synthesized at different temperatures: 400, 500, 600, 700, 800 and 900 ?C at 700 ?C the ?-Fe2O3 nanoparticles are formed with particle size 71.93 nm. The nanoparticles are characterized by XRD , SEM, AFM and FTIR . The 0.046 g /l of the catalyst sample shows high photo activity at 3x10-5M dye concentration in acidic medium at pH 3.
This work addressed the assignment problem (AP) based on fuzzy costs, where the objective, in this study, is to minimize the cost. A triangular, or trapezoidal, fuzzy numbers were assigned for each fuzzy cost. In addition, the assignment models were applied on linguistic variables which were initially converted to quantitative fuzzy data by using the Yager’sorankingi method. The paper results have showed that the quantitative date have a considerable effect when considered in fuzzy-mathematic models.
This article studied some linear and nonlinear optical characteristics of different pH solutions from anthocyanin dye extract at 180 oC from red cabbage. First, the linear spectral characteristics, including absorption and transmittance in the range 400-800 nm for anthocyanin solution 5% v/v with different pHs, were achieved utilizing a UV/VIS spectrophotometer. The experimental results reveal a shift in the absorption toward the longer wavelength direction as pH values increment. Then, the nonlinear features were measured using the Z-scan technique with a CW 532 nm laser to measure the nonlinear absorption coefficient through an open aperture. A close aperture (diameter 2 mm) calculates the nonlinear refractive index. The open Z-scan sh
... Show MoreIn this paper we present the first ever measured experimental electron momentum density of Cu2Sb at an intermediate resolution (0.6 a.u.) using 59.54 keV 241Am Compton spectrometer. The measurements are compared with the theoretical Compton profiles using density function theory (DFT) within a linear combination of an atomic orbitals (LCAO) method. In DFT calculation, Perdew-Burke-Ernzerhof (PBE) scheme is employed to treat correlation whereas exchange is included by following the Becke scheme. It is seen that various approximations within LCAO-DFT show relatively better agreement with the experimental Compton data. Ionic model calculations for a number of configurations (Cu+x/2)2(Sb-x) (0.0≤x≤2.0) are also performed utilizing free a
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This study investigated the optimization of wear behavior of AISI 4340 steel based on the Taguchi method under various testing conditions. In this paper, a neural network and the Taguchi design method have been implemented for minimizing the wear rate in 4340 steel. A back-propagation neural network (BPNN) was developed to predict the wear rate. In the development of a predictive model, wear parameters like sliding speed, applying load and sliding distance were considered as the input model variables of the AISI 4340 steel. An analysis of variance (ANOVA) was used to determine the significant parameter affecting the wear rate. Finally, the Taguchi approach was applied to determine
... Show MoreA mathematical method with a new algorithm with the aid of Matlab language is proposed to compute the linear equivalence (or the recursion length) of the pseudo-random key-stream periodic sequences using Fourier transform. The proposed method enables the computation of the linear equivalence to determine the degree of the complexity of any binary or real periodic sequences produced from linear or nonlinear key-stream generators. The procedure can be used with comparatively greater computational ease and efficiency. The results of this algorithm are compared with Berlekamp-Massey (BM) method and good results are obtained where the results of the Fourier transform are more accurate than those of (BM) method for computing the linear equivalenc
... Show MoreZnS nanoparticles were prepared by a simple microwave irradiation method under mild condition. The starting materials for the synthesis of ZnS quantum dots were zinc acetate (R & M Chemical) as zinc source, thioacetamide as a sulfur source and ethylene glycol as a solvent. All chemicals were analytical grade products and used without further purification. The quantum dots of ZnS with cubic structure were characterized by X-ray powder diffraction (XRD), the morphology of the film is seen by scanning electron microscopy (SEM). The particle size is determined by field effect scanning electron microscopy (FESEM), UV-Visible absorption spectroscopy and XRD. UV-Visible absorption spectroscopy analysis shows that the absorption peak of the as-prep
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This work is considered the first study for the components of the Iraqi Leucaena leucocephala plant, where the different phytochemical compounds that present in the aerial parts were identified by using the gas chromatography/mass spectrometry technique (GC/MS). The type of the components and their concentration will differ according to the part of the plant used and the method of extraction (hot and cold). This study made a comparison in lupeol concentration that was identified and isolated from petroleum ether fractions of Leucaena leucocephala by using Gas Chromatography/Mass Spectrometry (GC/MS), High-performance thin-layer chromatography (HPTLC), and Preparative High-Performance Li
... Show MoreThe fuzzy assignment models (FAMs) have been explored by various literature to access classical values, which are more precise in our real-life accomplishment. The novelty of this paper contributed positively to a unique application of pentagonal fuzzy numbers for the evaluation of FAMs. The new method namely Pascal’s triangle graded mean (PT-GM) has presented a new algorithm in accessing the critical path to solve the assignment problems (AP) based on the fuzzy objective function of minimising total cost. The results obtained have been compared to the existing methods such as, the centroid formula (CF) and centroid formula integration (CFI). It has been demonstrated that operational efficiency of this conducted method is exquisitely deve
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