• Communications for Statistical Applications and Methods
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• v.15 no.6
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• pp.899-908
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• 2008

If the regression function has jump points, nonparametric estimation method based on local smoothing is not statistically consistent. Therefore, when we estimate regression function, it is quite important to know whether it is reasonable to assume that regression function is continuous. If the regression function appears to have jump points, then we should estimate first the location of jump points. In this paper, we propose a procedure which can do both the testing hypothesis of discontinuity of regression function and the estimation of the number and the location of jump points simultaneously. The performance of the proposed method is evaluated through a simulation study. We also apply the procedure to real data sets as examples.

• Journal of the Korean Data and Information Science Society
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• v.16 no.3
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• pp.591-601
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• 2005

In this paper we consider detection of a discontinuity point in the variance function. When the mean function is discontinuous at a point, the variance function is usually discontinuous at the point. In this case, we had better estimate the location of the discontinuity point with the mean function rather than the variance function. On the other hand, the variance function only has a discontinuity point. The target function in order to estimate the location can be used the second moment function since the variance function and the second moment function have the same location and jump size of the discontinuity point. We propose a nonparametric detection method of the discontinuity point with the second moment function. We give the asymptotic results of these estimators. Computer simulation demonstrates the improved performance of the method over the existing ones.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2006.04a
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• pp.365-372
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• 2006

A new meshfree formulation is developed for material discontinuity problems. A local interfacial jump function which is defined as hyperplane function is embedded in the meshless approximation and the approximation accurately models functions with jumps in the displacement and the derivative fields. Diffuse derivative technique copes with difficulty due to complexity of derivative computation of meshfree approximation. Collocation method with diffuse derivative accelerates computing speed for numerical solution. By solving inclusion and composite material problems, the robustness and effectiveness of the method are verified.

• Proceedings of the Korean Statistical Society Conference
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• 2002.11a
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• pp.103-108
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• 2002

We consider an estimation of discontinuous variance function in nonparametric heteroscedastic random design regression model. We first propose estimators of a change point and jump size in variance function and then construct an estimator of entire variance function. We examine the rates of convergence of these estimators and give results on their asymptotics. Numerical work reveals that the effectiveness of change point analysis in variance function estimation is quite significant.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.06a
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• pp.343-346
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• 1998

This paper deals with the decision in vague knowledge, One method is a classic theory. That is to say, constraints and goals in the vague knowledge. Another method is the fuzzy catastrophe. If there exist two fuzzy variables, there may be a discontinuity which plays an important role in decision.

• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.633-641
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• 2004

In this paper we deal with functions in higher dimension. We provide several convergence theorem for approximation by convolution type delta sequence. We also give sufficient and necessary condition for Gibbs phenomenon to exist.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.38 no.2
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• pp.199-207
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• 2001

In this paper, we suggest an edge-based surface segmentation algorithm of 3D image using curvature. For the first, in this proposed method, we approximate 3D depth data to second order curves by each scan line and decide splitting points of 3D edges by curvature of the approximated curves. And finally make a group as 3D surface with the region of input image by the 3D edges. In the conventional algorithms, there are some difficulties in detecting 3D edge with the separated processes for the jump edge and the crease edge and especially, in deciding the ambiguous discontinuity of surface directions about the crease edge. The proposed algorithm decides curvature discontinuity using curvature which is simply calculated by a geometrical approximation. Furthermore, the algorithm has a cooperated process to calculate the jump and crease edges. The results of computer simulations with several 3D images show that the proposed method yields better performance as comparing with the conventional methods.

• The Journal of the Korea institute of electronic communication sciences
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• v.13 no.1
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• pp.23-28
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• 2018

We derive a gap of specific heat discontinuity of superconducting crystals theoretically at the critical temperature $T_{CH}$ as an explicit function of applied magnetic field H by using the thermodynamic relations for Gibbs free energy and the linear model for the critical magnetic field $H_{CT}$. The derived a gap of specific heat discontinuity is compared with experimental results by J. Kacmarcik et al. for superconducting MgCNi3 crystal. Our specific heat gap function well explain the jump up phenomena of the superconducting crystals.

• Proceedings of the KSME Conference
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• 2001.06e
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• pp.81-86
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• 2001

Interfacial pressure jump terms based on the physics of phasic interface and bubble dynamics are introduced into the momentum equations of the two-fluid model for bubbly flow. The pressure discontinuity across the phasic interface due to the surface tension force is expressed as the function of fluid bulk moduli and bubble radius. The consequence is that we obtain from the system of equations the real eigenvalues representing the void-fraction propagation speed and the pressure wave speed in terms of the bubble diameter. Inversely, we obtain an analytic closure relation for the radius of bubbles in the bubbly flow by using the kinematic wave speed given empirically in the literature. It is remarkable to see that the present mechanistic model using this practical bubble radius can indeed represent both the mathematical well-posedness and the physical wave speeds in the bubbly flow.

• Structural Engineering and Mechanics
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• v.4 no.6
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• pp.601-612
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• 1996

To simulate the large-scale failure evolution with current computational facilities, a simple approach, that catches the essential feature of failure mechanisms, must be available so that the routine use of failure analysis is feasible. Based on the previous research results, a simple analysis procedure is described in this paper for failure simulation. In this procedure, the evolution of localization is represented by a moving surface of discontinuity, and the transition between continuous and discontinuous failure modes are described via the moving jump forms of conservation laws. As a result, local plasticity and damage models, that are formulated based on thermodynamic restrictions, are still valid without invoking higher order terms, and simple integration schemes can be designed for the rate forms of constitutive models. To resolve localized large deformations and subsequent cracking, an efficient structural solution scheme is given for Static and dynamic problems.