• Journal of the Korean Mathematical Society
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• v.35 no.3
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• pp.559-574
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• 1998

Let the Gel'fand triple (E)$_{\beta}$/ ⊂ ( $L^2$) ⊂ (E)＊$_{\beta}$/ be the framework of white noise distribution theory constructed by Kon-dratiev and Streit. A new class of continuous multiplicative products on (E)$_{\beta}$/ is introduced and associated continuous derivations on (E)$_{\beta}$/ are discussed. Algebraic characterizations of first order differential operators on (E)$_{\beta}$/ are proved. Some applications are also discussed. $\beta$/ are proved. Some applications are also discussed.

• Journal of the Korea Convergence Society
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• v.4 no.4
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• pp.41-48
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• 2013

Observer design for system with unknown input was carried out. First, Kalman filter was considered to estimate system state with White noise. With the results of Kalman filter design, state observer, controller properties, including controllability and observability, and the Kalman filter structure and algorithm were also studied. Kalman filter algorithm was applied to Position and velocity measurement based on Kalman filter with white noise, and it was constructed and achieved by programming based on Matlab programming. Finally, observer for system with unknown input was constructed with the help of Gershgorin's disc theorem. With the designed observer, system states was constructed and applied to system with unknown input. By simulation results, estimation performance was verified. In this project, state feedback control theory, observer theory and relevant design procedure, as well as Kalman filter design were understood and used in practical application.

• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.781-802
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• 2011

Of concern in the paper is a Holling-Tanner predator-prey model with modified version of the Leslie-Gower functional response. Dynamical behaviours such as stability, permanence and Hopf bifurcation have been carried out deterministically. Using the normal form theory and center manifold theorem, the explicit formulae determining the stability and direction of Hopf bifurcation have been derived. The deterministic model is extended to a stochastic one by perturbing the growth equation of prey and predator by white and colored noises and finally the mean square stability of the stochastic model systems is investigated analytically. An extensive quantitative analysis has been performed based on numerical computation so as to validate the applicability of the proposed mathematical model.

• Ocean Systems Engineering
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• v.1 no.3
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• pp.249-261
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• 2011

The stochastic nonlinear dynamic behavior and probability density function of ship rolling are studied using the nonlinear dynamical systems approach and probability theory. The probability density function of the rolling response is evaluated through solving the Fokker Planck Equation using the path integral method based on a Gauss-Legendre interpolation scheme. The time-dependent probability of ship rolling restricted to within the safe domain is provided and capsizing is investigated from the probability point of view. The random differential equation of ships' rolling motion is established considering the nonlinear damping, nonlinear restoring moment, white noise and colored noise wave excitation.

• Transactions on Control, Automation and Systems Engineering
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• v.2 no.1
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• pp.24-30
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• 2000

The aim of this paper is to describe an advanced method of the fault diagnosis using Control Theory with reference to a crack detection, a new way to localize the crack position under influence of the plant disturbance and white measurement noise on a rotating shaft. As the first step, the shaft is physically modelled with a finite element method as usual and the dynamic mathematical model is derived from it using the Hamilton-principle and in this way the system is modelled by various subsystems. The equations of motions with a crack are established by the adaption of the local stiffness change through breathing and gaping[1] from the crack to the equation of motion with an undamaged shaft. This is supposed to be regarded as a reference system for the given system. Based on the fictitious model of the time behaviour induced from vibration phenomena measured at the bearings, a nonlinear state observer is designed in order to detect the crack on the shaft. This is the elementary NL-observer(EOB). Using the elementary observer, an Estimator(Observer Bank) is established and arranged at the certain position on the shaft. In case, a crack is found and its position is known, the procedure, fro the estimation of the depth is going to begin.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.14 no.6
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• pp.2634-2648
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• 2020

In this paper, an adaptive sparse singular value decomposition (ASSVD) algorithm is proposed to estimate the signal matrix when only one data matrix is observed and there is high dimensional white noise, in which we assume that the signal matrix is low-rank and has sparse singular vectors, i.e. it is a simultaneously low-rank and sparse matrix. It is a structured matrix since the non-zero entries are confined on some small blocks. The proposed algorithm estimates the singular values and vectors separable by exploring the structure of singular vectors, in which the recent developments in Random Matrix Theory known as anisotropic Marchenko-Pastur law are used. And then we prove that when the signal is strong in the sense that the signal to noise ratio is above some threshold, our estimator is consistent and outperforms over many state-of-the-art algorithms. Moreover, our estimator is adaptive to the data set and does not require the variance of the noise to be known or estimated. Numerical simulations indicate that ASSVD still works well when the signal matrix is not very sparse.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.21 no.2
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• pp.135-143
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• 2008

In this study, it was investigated for dynamic nonlinear characteristics using dynamic data obtained by shaking table test. The design of Tuned Liquid Damper(TLD) has limitation to plan based on Tuned Mass Damper(TMD) analogy and linear wave theory. Also, while there are many studies regarding properties of TLD under harmonic load, there are not estimated for dynamic non-linear characteristics of TLD under the load that is not governed by particular frequency like a white noise. This paper investigated dynamic non-linear characteristics of TLD varied with load amplitude using a white noise and suggested equations that can estimate damping ratio, natural frequency ratio and effective mass ratio of TLD.

• 제어로봇시스템학회:학술대회논문집
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• 1998.10a
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• pp.301-307
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• 1998

The goal of this paper is to describe an advanced method of the fault diagnois using Control Theory with reference to a crack detection, a new way to localize the crack position under infulence of the plant disturbance and white measurement noise on a rotating shaft. As a first step, the shaft is physically modelled with a finite element method as usual and the dynamic mathematical model is derived from it using the Hamilton - principle and in this way the system is modelled by various subsystems. The equations of motion with crack is established by adaption of the local stiffness change through breathing and gaping from the crack to the equation of motion with un-damaged shaft. This is supposed to be regarded as reference for the given system. Based on the fictitious model of the time behaviour induced from vibration phenomena measured at the bearings, a nonlinear State Observer is designed in order to detect the crack on the shaft. This is elementary NL- observer(EOB). Using the elementary observer, an Estimator(Observer) Bank is established and arranged at the certain position on the shaft. In case a crack is found and its position is known, the procedure for the estimation of the depth is going to begin.

• ETRI Journal
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• v.46 no.3
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• pp.367-378
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• 2024

We propose a number-theory-based quantized mathematical optimization scheme for various NP-hard and similar problems. Conventional global optimization schemes, such as simulated and quantum annealing, assume stochastic properties that require multiple attempts. Although our quantization-based optimization proposal also depends on stochastic features (i.e., the white-noise hypothesis), it provides a more reliable optimization performance. Our numerical analysis equates quantization-based optimization to quantum annealing, and its quantization property effectively provides global optimization by decreasing the measure of the level sets associated with the objective function. Consequently, the proposed combinatorial optimization method allows the removal of the acceptance probability used in conventional heuristic algorithms to provide a more effective optimization. Numerical experiments show that the proposed algorithm determines the global optimum in less operational time than conventional schemes.

• Journal of KIISE:Computer Systems and Theory
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• v.35 no.12
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• pp.560-567
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• 2008

In this paper, we discuss a simple and straightforward binarization procedure which can generate black/white comics from the video frame image. Generally, the region of human's skin is colored white or light gray, while the dark region is filled with the irregular but regular patterns like hatching in most of the black/white comics. Note that it is not enough for simple threshold method to perform this work. Our procedure is decoupled into four processes. First, we use bilateral filter to suppress noise color variation and reserve boundaries. Then, we perform mean-shift segmentation for each similar colored pixels to be clustered. Third, the clustered regions are merged and extended by our region extension algorithm considering each color of their regions. Finally, we decide which pixels are on or off using by our dynamic binarization method based on the HSV color model. Our novel black/white cartooning procedure was so successful to render comic cuts from a well-known cinema in a resonable time and manual intervention.