• Kyungpook Mathematical Journal
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• v.52 no.4
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• pp.459-472
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• 2012

A piecewise smooth system is characterized by non-differentiability on a curve in the phase space. In this paper, we discuss particular bifurcation phenomena in the dynamics of a piecewise smooth system. We consider a two-dimensional piecewise smooth system which is composed of a linear map and a nonlinear map, and analyze the stability of the system to determine the existence of dangerous border-collision bifurcation. We finally present some numerical examples of the bifurcation phenomena in the system.

• Journal of the Korean Mathematical Society
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• v.40 no.6
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• pp.1075-1083
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• 2003

The purpose of this paper is to investigate the piecewise wise polynomial approximation for the curved boundary. We analyze the error of an approximated solution due to this approximation and then compare the approximation errors for the cases of polygonal and piecewise polynomial approximations for the curved boundary. Based on the results of analysis, p-version numerical methods for solving Dirichlet's problems are applied to any smooth curved domain.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.49-65
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• 2006

A robust numerical method for a singularly perturbed second-order ordinary differential equation having two parameters with a discontinuous source term is presented in this article. Theoretical bounds are derived for the derivatives of the solution and its smooth and singular components. An appropriate piecewise uniform mesh is constructed, and classical upwind finite difference schemes are used on this mesh to obtain the discrete system of equations. Parameter-uniform error bounds for the numerical approximations are established. Numerical results are provided to illustrate the convergence of the numerical approximations.

• Communications for Statistical Applications and Methods
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• v.29 no.1
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• pp.127-150
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• 2022

We discuss multiple change-point estimation as edge detection in piecewise smooth functions with finitely many jump discontinuities. In this paper we propose change-point estimators using concentration kernels with Fourier coefficients. The change-points can be located via the signal based on Fourier transformation system. This method yields location and amplitude of the change-points with refinement via concentration kernels. We prove that, in an appropriate asymptotic framework, this method provides consistent estimators of change-points with an almost optimal rate. In a simulation study the proposed change-point estimators are compared and discussed. Applications of the proposed methods are provided with Nile flow data and daily won-dollar exchange rate data.

• Bulletin of the Korean Mathematical Society
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• v.46 no.3
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• pp.409-434
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• 2009

In this paper, we consider a generalized Riemann problem of the first order hyperbolic conservation laws. For the case that excludes the centered wave, we prove that the generalized Riemann problem admits a unique piecewise smooth solution u = u(t, x), and this solution has a structure similar to the similarity solution u = $U{(\frac{x}{t})}$ of the correspondin Riemann problem in the neighborhood of the origin provided that the coefficients of the system and the initial conditions are sufficiently smooth.

• Journal of Energy Engineering
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• v.23 no.2
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• pp.21-27
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• 2014

The influence of the surface roughness on the natural convection heat transfers of a vertical plate were measured experimently. Mass transfer experiments instead of heat transfer experiment were performed based on the analogy. The piecewise electrodes were adopted to measure the local-average Nusselt number. Prandtl number was 2,014 and height of the plate was 0.154m The test results for a smooth surface showed similar heat transfer rate with the Le Fevre heat transfer correlation for a vertical plate. The Nusselt number increased with the roughness Rz $0.5{\sim}14.1{\mu}m$. The test results were presented by a simple correlation.

• Journal of the Korean Data and Information Science Society
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• v.23 no.3
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• pp.595-604
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• 2012

In this article, we consider chaotic behavior happened in nonsmooth dynamical systems. To quantify such a behavior, a computation of Lyapunov exponents for chaotic orbits of a given nonsmooth dynamical system is focused. The Lyapunov exponent is a very important concept in chaotic theory, because this quantity measures the sensitive dependence on initial conditions in dynamical systems. Therefore, Lyapunov exponents can decide whether an orbit is chaos or not. To measure the sensitive dependence on initial conditions for nonsmooth dynamical systems, the calculation of Lyapunov exponent plays a key role, but in a theoretical point of view or based on the definition of Lyapunov exponents, Lyapunov exponents of nonsmooth orbit could not be calculated easily, because the Jacobian derivative at some point in the orbit may not exists. We use an algorithmic calculation method for computing Lyapunov exponents using time series for a two dimensional piecewise smooth dynamic system.

• Journal of KIISE:Computer Systems and Theory
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• v.31 no.7
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• pp.414-420
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• 2004

Among the desirable properties of a piecewise linear parameterization, guaranteeing a one-to-one mapping (i.e., no triangle flips in the parameter plane) is often sought. A one-to-one mapping is accomplished by non-negative coefficients in the affine transformation. In the Floater's method, the coefficients were computed after the 3D mesh was flattened by geodesic polar-mapping. But using this geodesic polar map introduces unnecessary local distortion. In this paper, a simple variant of the original shape-preserving mapping technique by Floater is introduced. A new simple method for calculating barycentric coordinates by using straightest geodesics is proposed. With this method, the non-negative coefficients are computed directly on the mesh, reducing the shape distortion introduced by the previously-used polar mapping. The parameterization is then found by solving a sparse linear system, and it provides a simple and visually-smooth piecewise linear mapping, without foldovers.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2004.05b
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• pp.47-53
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• 2004

The paper shows that the combination of the hardware, NI PCI 6110E board and the software, Fourier and continuous wavelet transform(CWT) can be used to implement for extracting the important features of the real-time signal. The results confirmed that CWT produces the fast computation enough for the application of the real-time signal processing except the negligible time delay. In denoising case, because of the lack of translation invariance of wavelet basis, traditional wavelet thresholding leads to pseudo-Gibbs phenomena in the vicinity of discontinuities of signal. In this paper, in order to reduce the pseudo-Gibbs phenomena, wavelet coefficients are threshold and reconstruction algorithm is implement through shift-invariant gibbs free denoising algorithm based on wavelet transform footprint. The proposed algorithm can potentially be extended to more general signals like piecewise smooth signals and represents an effective solution to problems like signal denoising.

• Journal of the Institute of Electronics and Information Engineers
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• v.53 no.6
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• pp.137-145
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• 2016

A novel tracking method is proposed to find coronary artery using high-order curve model in coronary CTA(Computed Tomography Angiography). The proposed method quickly generates numerous artificial trajectories represented by high-order curves, and each trajectory has its own cost. The only high-ranked trajectories, located in the target structure, are selected depending on their costs, and then an optimal curve as the centerline will be found. After tracking, each optimal curve segment is connected, where optimal curve segments share the same point, to a single curve and it is a piecewise smooth curve. We demonstrated the high-order curve is a proper model for classification of coronary artery. The experimental results on public data set sho that the proposed method is comparable at both accuracy and running time to the state-of-the-art methods.