Author

# K. Kannan

Other affiliations: Nest Labs

Bio: K. Kannan is an academic researcher from Shanmugha Arts, Science, Technology & Research Academy. The author has contributed to research in topics: Closed set & Wavelet. The author has an hindex of 19, co-authored 120 publications receiving 1298 citations. Previous affiliations of K. Kannan include Nest Labs.

##### Papers

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TL;DR: An accurate and efficient Haar wavelet solution of Fisher's equation, a prototypical reaction-diffusion equation, which is found to be accurate, simple, fast, flexible, convenient, small computation costs and computationally attractive.

Abstract: In this paper, we develop an accurate and efficient Haar wavelet solution of Fisher's equation, a prototypical reaction-diffusion equation. The solutions of Fisher's equation are characterized by propagating fronts that can be very steep for large values of the reaction rate coefficient. There is an ongoing effort to better adapt Haar wavelet methods to the solution of differential equations with solutions that resemble shock waves or fronts typical of hyperbolic partial differential equations. Moreover the use of Haar wavelets is found to be accurate, simple, fast, flexible, convenient, small computation costs and computationally attractive.

140 citations

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TL;DR: A genetic algorithm-based ANN model is proposed for the turning process in manufacturing Industry that satisfies all the accuracy requirements and is found to be a time-saving model.

Abstract: Artificial intelligent tools like genetic algorithm, artificial neural network (ANN) and fuzzy logic are found to be extremely useful in modeling reliable processes in the field of computer integrated manufacturing (for example, selecting optimal parameters during process planning, design and implementing the adaptive control systems). When knowledge about the relationship among the various parameters of manufacturing are found to be lacking, ANNs are used as process models, because they can handle strong nonlinearities, a large number of parameters and missing information. When the dependencies between parameters become noninvertible, the input and output configurations used in ANN strongly influence the accuracy. However, running of a neural network is found to be time consuming. If genetic algorithm-based ANNs are used to construct models, it can provide more accurate results in less time. This article proposes a genetic algorithm-based ANN model for the turning process in manufacturing Industry. This model is found to be a time-saving model that satisfies all the accuracy requirements.

89 citations

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TL;DR: It is shown that the wavelet method is efficient and powerful in solving wide class of linear and nonlinear reaction–diffusion equations and future scope and directions involved in developing wavelet algorithm for solving reaction– Diffusion equations are addressed.

Abstract: Wavelet method is a recently developed tool in applied mathematics. Investigation of various wavelet methods, for its capability of analyzing various dynamic phenomena through waves gained more and more attention in engineering research. Starting from ‘offering good solution to differential equations’ to capturing the nonlinearity in the data distribution, wavelets are used as appropriate tools at various places to provide good mathematical model for scientific phenomena, which are usually modeled through linear or nonlinear differential equations. Review shows that the wavelet method is efficient and powerful in solving wide class of linear and nonlinear reaction–diffusion equations. This review intends to provide the great utility of wavelets to science and engineering problems which owes its origin to 1919. Also, future scope and directions involved in developing wavelet algorithm for solving reaction–diffusion equations are addressed.

82 citations

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TL;DR: An improved hybrid method for removing noise from low SNR molecular images is introduced and shows that the proposed model performs better even at higher levels of noise.

Abstract: In this paper an improved hybrid method for removing noise from low SNR molecular images is introduced. The method provides an improvement over the one suggested by Jian Ling and Alan C. Bovik (IEEE Trans. Med. Imaging, 21(4), [2002]). The proposed model consists of two stages. The first stage consists of a fourth order PDE and the second stage is a relaxed median filter, which processes the output of fourth order PDE. The model enjoys the benefit of both nonlinear fourth order PDE and relaxed median filter. Apart from the method suggested by Ling and Bovik, the proposed method will not introduce any staircase effect and preserves fine details, sharp corners, curved structures and thin lines. Experiments were done on molecular images (fluorescence microscopic images) and standard test images and the results shows that the proposed model performs better even at higher levels of noise.

73 citations

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TL;DR: In this paper, the authors developed an accurate and efficient Haar transform or Haar wavelet method for some of the well-known nonlinear parabolic partial differential equations, including the Nowell-whitehead equation, Cahn-Allen equation, FitzHugh-Nagumo equation, Fisher's equation, Burger's equation and the Burgers-Fisher equation.

Abstract: Wavelet transform or wavelet analysis is a recently developed mathematical tool in applied mathematics. In this paper, we develop an accurate and efficient Haar transform or Haar wavelet method for some of the well-known nonlinear parabolic partial differential equations. The equations include the Nowell-whitehead equation, Cahn-Allen equation, FitzHugh-Nagumo equation, Fisher’s equation, Burger’s equation and the Burgers-Fisher equation. The proposed scheme can be used to a wide class of nonlinear equations. The power of this manageable method is confirmed. Moreover the use of Haar wavelets is found to be accurate, simple, fast, flexible, convenient, small computation costs and computationally attractive.

66 citations

##### Cited by

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TL;DR: To the best of our knowledge, there is only one application of mathematical modelling to face recognition as mentioned in this paper, and it is a face recognition problem that scarcely clamoured for attention before the computer age but, having surfaced, has attracted the attention of some fine minds.

Abstract: to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.

3,015 citations

15 Feb 2016

TL;DR: Standard methods for the examination of water and wastewater: including bottom sediments and sludges, standard methods for examining water, including bottom sediment and sludge, are described in this paper.

Abstract: Standard methods for the examination of water and wastewater: including bottom sediments and sludges , Standard methods for the examination of water and wastewater: including bottom sediments and sludges , مرکز فناوری اطلاعات و اطلاع رسانی کشاورزی

613 citations

01 Sep 1976

TL;DR: In this article, the authors present a direct and systematic way of finding exact solutions and Backlund transformations of a certain class of nonlinear evolution equations, which they solve exactly using a kind of perturbational approach.

Abstract: The main purpos e of this chapter is to present a direct and systematic way of finding exact solutions and Backlund transformations of a certain class of nonlinear evolution equations. The nonlinear evolution equations are transformed, by changing the dependent variable(s), into bilinear differential equations of the following special form
$$ F\left( {\frac{\partial }{{\partial t}} - \frac{\partial }{{\partial {t^1}}},\frac{\partial }{{\partial x}} - \frac{\partial }{{\partial {x^1}}}} \right)f(t,x)f({t^1},{x^1}){|_{t = {t^1},x = {x^1}}} = 0 $$
, which we solve exactly using a kind of perturbational approach.

612 citations