• Journal of Advanced Research in Ocean Engineering
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• v.1 no.3
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• pp.157-167
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• 2015

In order to provide simple and accurate wave theory in design of offshore structure, an analytical approximation is introduced in this paper. The solution is limited to flat bottom having a constant water depth. Water is considered as inviscid, incompressible and irrotational. The solution satisfies the continuity equation, bottom boundary condition and non-linear kinematic free surface boundary condition exactly. Error for dynamic condition is quite small. The solution is suitable in description of breaking waves. The solution is presented with closed form and dispersion relation is also presented with closed form. In the last century, there have been two main approaches to the nonlinear problems. One of these is perturbation method. Stokes wave and Cnoidal wave are based on the method. The other is numerical method. Dean's stream function theory is based on the method. In this paper, power series method was considered. The power series method can be applied to certain nonlinear differential equations (initial value problems). The series coefficients are specified by a nonlinear recurrence inherited from the differential equation. Because the non-linear wave problem is a boundary value problem, the power series method cannot be applied to the problem in general. But finite number of coefficients is necessary to describe the wave profile, truncated power series is enough. Therefore the power series method can be applied to the problem. In this case, the series coefficients are specified by a set of equations instead of recurrence. By using the set of equations, the nonlinear wave problem has been solved in this paper.

• Journal of KIISE:Computing Practices and Letters
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• v.16 no.3
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• pp.356-360
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• 2010

Recently, there have been many research efforts on privacy-preserving data mining. In privacy-preserving data mining, accuracy preservation of mining results is as important as privacy preservation. Random perturbation privacy-preserving data mining technique is known to well preserve privacy. However, it has a problem that it destroys distance orders among time-series. In this paper, we propose a notion of the noise averaging effect of piecewise aggregate approximation(PAA), which can be preserved the clustering accuracy as high as possible in time-series data clustering. Based on the noise averaging effect, we define the PAA distance in computing distance. And, we show that our PAA distance can alleviate the problem of destroying distance orders in random perturbing time series.