• Proceedings of the KSEEG Conference
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• 2001.04a
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• pp.143-146
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• 2001

• Communications of the Korean Mathematical Society
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• v.13 no.1
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• pp.181-193
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• 1998

The Shannon sampling series is the prototype of an interpolating series or sampling series. Also the Shannon wavelet is one of the protypes of wavelets. But the coefficients of the Shannon sampling series are different function values at the point of discontinuity, we analyze the Gibbs phenomenon for the Shannon sampling series. We also find a way to go around this overshoot effect.

• Journal of the Korean Mathematical Society
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• v.60 no.3
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• pp.635-682
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• 2023

In this paper, we consider linear elliptic systems from composite materials where the coefficients depend on the shape and might have the discontinuity between the subregions. We derive a function which is related to the gradient of the weak solutions and which is not only locally piecewise Hölder continuous but locally Hölder continuous. The gradient of the weak solutions can be estimated by this derived function and we also prove the local piecewise gradient Hölder continuity which was obtained by the previous results.

• Economic and Environmental Geology
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• v.31 no.4
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• pp.339-347
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• 1998

The purpose of this study is to find P-wave crustal velocity structure and the Moho characteristics beneath Seoul (SEO) and Inchon (INCN) stations using broadband teleseismic records. The use of broadband receiver function analysis is increasing to estimate the fine-scale velocity structure of the lithosphere. The broadband receiver functions are developed from teleseismic events of P waveforms recorded at Seoul (SEO) and Inchon (INCN) stations, and are analyzed to examine the crustal structure beneath the stations. The teleseismic receiver functions are inverted in the time domain of the vertical P wave velocity structures beneath the stations. The crustal velocity structures beneath the stations are estimated using the receiver function inversion method (Ammon et al., 1990). The general features of inversion results are as follows: (1) For the Seoul station, the Conrad and Moho discontinuities exist at 22 km and 30 km depth in the south ($BAZ=180^{\circ}$) direction. (2) For the Inchon station, the Conrad discontinuity exists at 22 km depth in the direction of SE ($BAZ=145^{\circ}$) and the Moho discontinuity exists at 30~34 km depth with a 4 km thick, which consists of a laminated velocity transition layers with thickness, whereas a crust-mantle boundary beneath the Seoul station consists of a more sharp boundary compared with the Moho shape of INCN station.

• Geomechanics and Engineering
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• v.11 no.4
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• pp.515-530
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• 2016

In this paper, five different quantitative parameters were proposed for the characterization of the primary roughness which is the component of surface morphology that prevails during large strike-slip faults of more than 50 m. These parameters are mostly the anisotropic properties of rock surface morphology at various scales: (i) coefficient ($k_a$) and degree (${\delta}_a$) of apparent structural anisotropy of surface; (ii) coefficient ($k_r$) and degree (${\delta}_r$) of real structural anisotropy of surface; (iii) surface anisotropy function P(${\varphi}$); and (iv) degree of surface waviness ($W_s$). The coefficient and degree of apparent structural anisotropy allow qualifying the anisotropy/isotropy of a discontinuity according to a classification into four classes: anisotropic, moderately anisotropic/isotropic and isotropic. The coefficient and degree of real structural anisotropy of surface captures directly the actual surface anisotropy using geostatistical method. The anisotropy function predicts directional geometric properties of a surface of discontinuity from measurements in two orthogonal directions. These predicted data may subsequently be used to highlight the anisotropy/isotropy of the surface (radar plot). The degree of surface waviness allows qualifying the undulation of anisotropic surfaces. The proposed quantitative parameters allows their application at both lab and field scales.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.32 no.12C
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• pp.1149-1155
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• 2007

In this paper, we propose a new overlap and add speech synthesis method which demonstrates improved continuity performance. The proposed method uses a weighted phase error function and minimizes the wave discontinuity of the synthesis signal, rather than the phase discontinuity, to estimate the mid-point phase. Experimental results show that the proposed method improves the continuity between the synthesized signals relative to the existing method.

• 한국전산유체공학회:학술대회논문집
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• 2003.10a
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• pp.184-186
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• 2003

In order to reduce numerical dissipation in a multi-dimensional flow, a new variable interpolation method for Roe's FDS is proposed. By introducing the Mach number weighting function w, the properties at the cell-interface are interpolated and in a non flow-aligned grid system, it can give more accurate solution because of less numerical dissipation. Various test cases including oblique contact discontinuity are simulated and compared with the results of original Roe's FDS.

• Economic and Environmental Geology
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• v.52 no.3
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• pp.231-241
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• 2019

Kinematic analysis determines the stability of rock slope by analyzing the relationship between the slope face orientation and the discontinuity orientation. In this study, terrestrial LiDAR was used to obtain a large amount of discontinuity orientation data and then, the probabilistic characteristics of the orientation data obtained using terrestrial LiDAR were analyzed. Subsequently, the probabilistic kinematic analysis was carried out using the discontinuity orientations generated randomly from Fisher function in Monte Carlo simulation. In addition, the probabilistic kinematic analysis was also performed using the actual orientation data obtained from the terrestrial LiDAR to compare their results. Consequently, the results of both probabilistic analyses showed similar results. Therefore, if sufficient orientation data are provided by other means such as terrestrial LiDAR, the probabilistic analysis will show reasonable results using the actual field data without randomly generating orientation data. In addition, the deterministic kinematic analysis was also carried out using representative orientation of discontinuity sets. The analysis result of the probabilistic analysis showed similar results with the deterministic analysis because the dispersion of the discontinuity orientations in a joint set is not large.

• 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.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2001.10a
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• pp.19-26
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• 2001

Previously, an improved crack analysis technique based on Element-Free Galerkin Method (EFGM) which includes a discontinuity function and a singular basis function was presented. The technique needs neither addition of nodes nor modification of the model, but it shows some dependency on the formulation and modeling parameters such as the class of weight function, the size of compact support, dilation parameter and the range controlled by the singular basis function. For those parameters, a parametric study was performed on the calculation of a discrete error and then, a guideline for the choice of adequate parameters in the technique was proposed.