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Generalized Abel Inversion Using Homotopy Perturbation Method

Applied Mathematics 2011年第2期2卷 254-257页

作者： Sunil Kumar Om P. Singh sandeep dixit 不详

Many problems in physics like reconstruction of the radially distributed emissivity from the line-of-sight projected intensity, the 3-D image reconstruction from cone beam projections in computerized tomography, etc. lead naturally, in the case of radial symmetry, to the study of Abel’s type integral equation. Obtaining the physically relevant quantity from the measured one requires, therefore the inversion of the Abel’s integral equation. The aim of this letter is to present a user friendly algorithm to invert generalized Abel integral equation by using homotopy perturbation method. The stability of the algorithm is analysed. The validity and applicability of this powerful technique is illustrated through various particular cases which demonstrate its efficiency and simplicity in solving these types of integral equations.

关键词： Generalized Abel Integral Equation Homotopy Perturbation Method Noise Term Stability

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Solution of the Generalized Abel Integral Equation by Using Almost Bernstein Operational Matrix

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American Journal of Computational Mathematics 2011年第4期1卷 226-234页

作者： sandeep dixit Rajesh K. Pandey Sunil Kumar Om P. Singh 不详

A direct almost Bernstein operational matrix of integration is used to propose a stable algorithm for numerical inversion of the generalized Abel integral equation. The applicability of the earlier proposed methods was restricted to the numerical inversion of a part of the generalized Abel integral equation. The method is quite accurate and stable as illustrated by applying it to intensity data with and without random noise to invert and compare it with the known analytical inverse. Thus it is a good method for applying to experimental intensities distorted by noise.

关键词： Abel Inversion Bernstein Polynomials Almost Bernstein Operational Matrix Of Integration Noise Resistance

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Comparison of Radial Basis Function Neural Network and Response Surface Methodology for Predicting Performance of Biofilter Treating Toluene

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Journal of Software Engineering and Applications 2012年第8期5卷 595-603页

作者： Sharvari C. Deshmukh J. Senthilnath Rashmi M. dixit Sameena N. Malik Ram A. Pandey Atul N. Vaidya Subbaramajois N. Omkar sandeep N. Mudliar Department of Aerospace Engineering Indian Institute of Sciences Bangalore India Environmental Biotechnology Division National Environmental Engineering and Research Institute Nagpur India Solid Waste Management Division National Environmental Engineering and Research Institute Nagpur India

Biofiltration is emerging as a promising cost effective technique for the Volatile Organic Compounds (VOCs) removal from industrial waste gases. In the present investigation a comparative modeling study has been carried out using Radial Basis Function Neural Network (RBFN) and Response Surface Methodology (RSM) to predict and optimize the performance of a biofilter system treating toluene (a model VOC). Experimental biofilter system performance data collected over a time period by daily measurement of inlet VOC concentration, retention time, pH, temperature and packing moisture content was used to develop the mathematical model. These independent variables acted as the inputs to the mathematical model developed using RSM and RBFN, while the VOC removal efficiency was the biofilter system performance parameter to be predicted. The data set was divided into two parts: 60% of data was used for training phase and remaining 40% of data was used for the testing phase. The average % error for RSM and RBFN were 7.76% and 3.03%, and R2 value obtained were 0.8826 and 0.9755 respectively. The results indicated the superiority of RBFN in the prediction capability due to its ability to approximate higher degree of nonlinearity between the input and output variables. The optimization of biofilter parameters was also done using RSM to optimize the biofilter performance. RSM being structured in nature enabled the study of interaction effect between the independent variables on biofilter performance.

关键词： VOC Toluene Biofilter Response Surface Methodology Radial Basis Function Neural Network

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