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Math. Comput. Appl., Volume 22, Issue 3 (September 2017)

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Research

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Open AccessArticle ICA and ANN Modeling for Photocatalytic Removal of Pollution in Wastewater
Math. Comput. Appl. 2017, 22(3), 38; doi:10.3390/mca22030038
Received: 28 June 2017 / Revised: 19 July 2017 / Accepted: 20 July 2017 / Published: 11 August 2017
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Abstract
This paper discusses the elimination of Colour Index Acid Yellow 23 (C.I. AY23) using the ultraviolet (UV)/Ag-TiO2 process. To anticipate the photocatalytic elimination of AY23 with the existence of Ag-TiO2 nanoparticles processed under desired circumstances, two computational techniques, namely artificial neural
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This paper discusses the elimination of Colour Index Acid Yellow 23 (C.I. AY23) using the ultraviolet (UV)/Ag-TiO2 process. To anticipate the photocatalytic elimination of AY23 with the existence of Ag-TiO2 nanoparticles processed under desired circumstances, two computational techniques, namely artificial neural network (ANN) and imperialist competitive algorithm (ICA) modeling are developed. A sum of 100 datasets are used to establish the models, wherein the introductory concentration of dye, UV light intensity, initial dosage of nano Ag-TiO2, and irradiation time are the four parameters expressed in the form of input variables. Additionally, the elimination of AY23 is considered in the form of the output variable. Out of the 100 datasets, 80 are utilized in order to train the models. The remaining 20 that were not included in the training are used in order to test the models. The comparison of the predicted outcomes extracted from the suggested models and the data obtained from the experimental analysis validates that the performance of the ANN scheme is comparatively sophisticated when compared with the ICA scheme. Full article
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Open AccessArticle A Novel Method of Offset Approximation along the Normal Direction with High Precision
Math. Comput. Appl. 2017, 22(3), 39; doi:10.3390/mca22030039
Received: 3 July 2017 / Revised: 17 August 2017 / Accepted: 21 August 2017 / Published: 4 September 2017
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Abstract
A new algorithm is proposed for polynomial or rational approximation of the planar offset curve. The best rational Chebyshev approximation could be regarded as a kind of geometric approximation along the fixed direction. Based on this idea, we developed a wholly new offset
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A new algorithm is proposed for polynomial or rational approximation of the planar offset curve. The best rational Chebyshev approximation could be regarded as a kind of geometric approximation along the fixed direction. Based on this idea, we developed a wholly new offset approximation method by changing the fixed direction to the normal directions. The error vectors follow the direction of normal, and thus could reflect the approximate performance more properly. The approximation is completely independent of the original curve parameterization, and thus could ensure the stability of the approximation result. Experimental results show that the proposed algorithm is reasonable and effective. Full article
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Review

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Open AccessReview Analytical Solution to Normal Forms of Hamiltonian Systems
Math. Comput. Appl. 2017, 22(3), 37; doi:10.3390/mca22030037
Received: 10 June 2017 / Revised: 12 July 2017 / Accepted: 26 July 2017 / Published: 27 July 2017
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Abstract
The idea of the normalisation of the Hamiltonian system is to simplify the system by transforming Hamiltonian canonically to an easy system. It is under symplectic conditions that the Hamiltonian is preserved under a specific transformation—the so-called Lie transformation. In this review, we
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The idea of the normalisation of the Hamiltonian system is to simplify the system by transforming Hamiltonian canonically to an easy system. It is under symplectic conditions that the Hamiltonian is preserved under a specific transformation—the so-called Lie transformation. In this review, we will show how to compute the normal form for the Hamiltonian, including computing the general function analytically. A clear example has been studied to illustrate the normal form theory, which can be used as a guide for arbitrary problems. Full article
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