• Honam Mathematical Journal
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• v.33 no.3
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• pp.341-346
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• 2011

We deal with a kind of impossible decomposition of some entire functions in terms of a certain form.

• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1157-1169
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• 2010

This paper presents the analytical solution of the fractional Fokker-Planck equation by Adomian decomposition method. By using initial conditions, the explicit solution of the equation has been presented in the closed form and then the numerical solution has been represented graphically. Two different approaches have been presented in order to show the application of the present technique. The present method performs extremely well in terms of efficiency and simplicity.

• The Korean Journal of Applied Statistics
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• v.24 no.6
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• pp.995-1006
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• 2011

A time series can be decomposed into simple components with a multiscale method. Empirical mode decomposition(EMD) is a recently invented multiscale method in Huang et al. (1998). It is natural to apply a classical prediction method such a vector autoregressive(AR) model to the obtained simple components instead of the original time series; in addition, a prediction procedure combining a classical prediction model to EMD and Hilbert spectrum is proposed in Kim et al. (2008). In this paper, we suggest to adopt principal component analysis(PCA) to the prediction procedure that enables the efficient selection of input variables among obtained components by EMD. We discuss the utility of adopting PCA in the prediction procedure based on EMD and Hilbert spectrum and analyze the daily worm account data by the proposed PCA adopted prediction method.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.4
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• pp.585-592
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• 2003

Among various sensitivity evaluation techniques, semi-analytical method(SAM) is quite popular since this method is more advantageous than analytical method(AM) and global finite difference method(FDM). However, SAM reveals severe inaccuracy problem when relatively large rigid body motions are identified fur individual elements. Such errors result from the numerical differentiation of the pseudo load vector calculated by the finite difference scheme. In the present study, an iterative method combined with mode decomposition technique is proposed to compute reliable semi-analytical design sensitivities. The improvement of design sensitivities corresponding to the rigid body mode is evaluated by exact differentiation of the rigid body modes and the error of SAM caused by numerical difference scheme is alleviated by using a Von Neumann series approximation considering the higher order terms for the sensitivity derivatives.

• International Journal of Naval Architecture and Ocean Engineering
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• v.7 no.2
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• pp.301-314
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• 2015

Aiming at accurately distinguishing modeless component and natural vibration mode terms from data series of nonlinear and non-stationary processes, such as Vortex-Induced Vibration (VIV), a new empirical mode decomposition method has been developed in this paper. The key innovation related to this technique concerns the method to decompose modeless component from non-stationary process, characterized by a predetermined 'maximum intrinsic time window' and cubic spline. The introduction of conceptual modeless component eliminates the requirement of using spurious harmonics to represent nonlinear and non-stationary signals and then makes subsequent modal identification more accurate and meaningful. It neither slacks the vibration power of natural modes nor aggrandizes spurious energy of modeless component. The scale of the maximum intrinsic time window has been well designed, avoiding energy aliasing in data processing. Finally, it has been applied to analyze data series of vortex-induced vibration processes. Taking advantage of this newly introduced empirical decomposition method and mode identification technique, the vibration analysis about vortex-induced vibration becomes more meaningful.

• Asia-Pacific Journal of Atmospheric Sciences
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• v.54 no.4
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• pp.611-622
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• 2018

Observed climate data are processed under the assumption that their time series are stationary, as in multi-step temperature and precipitation prediction, which usually leads to low prediction accuracy. If a climate system model is based on a single prediction model, the prediction results contain significant uncertainty. In order to overcome this drawback, this study uses a method that integrates ensemble prediction and a stepwise regression model based on a mean-valued generation function. In addition, it utilizes empirical mode decomposition (EMD), which is a new method of handling time series. First, a non-stationary time series is decomposed into a series of intrinsic mode functions (IMFs), which are stationary and multi-scale. Then, a different prediction model is constructed for each component of the IMF using numerical ensemble prediction combined with stepwise regression analysis. Finally, the results are fit to a linear regression model, and a short-term climate prediction system is established using the Visual Studio development platform. The model is validated using temperature data from February 1957 to 2005 from 88 weather stations in Guangxi, China. The results show that compared to single-model prediction methods, the EMD and ensemble prediction model is more effective for forecasting climate change and abrupt climate shifts when using historical data for multi-step prediction.

• The Korean Journal of Applied Statistics
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• v.19 no.2
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• pp.319-330
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• 2006

A signal in real world usually composes of multiple signals having different scales of frequencies. For example sun-spot data is fluctuated over 11 year and 85 year. Economic data is supposed to be compound of seasonal component, cyclic component and long-term trend. Decomposition of the signal is one of the main topics in time series analysis. However when the signal is subject to nonstationarity, traditional time series analysis such as spectral analysis is not suitable. Huang et. at(1998) proposed data-adaptive method called empirical mode decomposition (EMD) . Due to its robustness to nonstationarity, EMD has been applied to various fields. Huang et. at, however, have not considered denoising when data is contaminated by error. In this paper we propose efficient denoising method utilizing cross-validation.

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1265-1277
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• 2009

In this paper, we apply a new decomposition method for solving initial and boundary value problems, which is due to Noor and Noor [18]. The analytical results are calculated in terms of convergent series with easily computable components. The diagonal Pade approximants are applied to make the work more concise and for the better understanding of the solution behavior. The proposed technique is tested on boundary layer problem; Thomas-Fermi, Blasius and sixth-order singularly perturbed Boussinesq equations. Numerical results reveal the complete reliability of the suggested scheme. This new decomposition method can be viewed as an alternative of Adomian decomposition method and homotopy perturbation methods.

• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.525-531
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• 2007

We newly introduce the concept of summable in measure and investigate on some its properties. In addition to this, we consider a size of given series by means of we are giving Lebesgue measure to an associated series.

• Kyungpook Mathematical Journal
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• v.51 no.2
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• pp.233-239
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• 2011

In this article we study the noton of I-monotonic sequences. We prove the decomposition theorem and generalize some of the results on monotonic sequences. We also introduce I-convergent series and studied some results.