• Journal of Educational Research in Mathematics
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• v.27 no.3
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• pp.375-389
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• 2017

The purpose of this study is to analyze the difference and inter-connectivity between the definition of continuity in school mathematics and the definition of academic mathematics in four perspectives. These difference and inter-connectivity have not analyzed in previous papers. According to this study, the definition of 'continuity and discontinuity at one point' in school mathematics depends on the limit processing but in academic mathematics it depends on the topology of the domain. The target function of the continuous function in school mathematics is a function whose domain is limited to an interval or a union of intervals, but the target function of the continuous function in academic mathematics is all functions. Based on these results, the following two opinions are given in relation to the concept of continuity in school mathematics. First, since the notion of local continuity in school mathematics is based on limit processing, the contents of 2009-revised textbooks that deal with discontinuity at special point not belonging to the domain is appropriate. Here the discontinuity appears as types of infinite discontinuity, removable discontinuity, and step discontinuity. Second, the definition of a general continuous function is proposed to "if there is no discontinuity point in the domain of a function y = f(x), we call the function f a continuous function." This definition allows the discontinuity at special point in non-domain, but is consistent with the definition in academic mathematics.

• Journal of the Korean Data and Information Science Society
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• v.21 no.1
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• pp.51-59
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• 2010

In the case that the regression function has a discontinuity point in generalized linear model, Huh (2009) estimated the location and jump size using the log-likelihood weighted the one-sided kernel function. In this paper, we consider estimation of the unknown number of the discontinuity points in the regression function. The proposed algorithm is based on testing of the existence of a discontinuity point coming from the asymptotic distribution of the estimated jump size described in Huh (2009). The finite sample performance is illustrated by simulated example.

• The Bulletin of The Korean Astronomical Society
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• v.36 no.2
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• pp.91-91
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• 2011

The passage of the interplanetary discontinuity (i.e., sudden increases in the solar wind speed, density, and IMF strength) was detected by ACE near GSE (x, y, z) ~ (222, -36, 3) Re upstream of Earth around 22:48 UT on November 24, 2008. About 55 min later, this solar wind discontinuity was observed by Geotail near GSE (x, y, z) ~ (23, 18, -7) Re in front of Earth's bow shock. From the propagation time of the solar wind discontinuity between ACE and Geotail, it is expected that the discontinuity front is aligned with the Parker spiral and strikes the postnoon dayside magnetopause first. Using coordinated multi-point measurements (THEMIS and GOES) at or in geosynchronous orbit, we observed a tailward propagating sudden impulse (SI), excited by the interplanetary discontinuity, around 23:50 UT with its front retaining alignment similar to that of solar wind discontinuity. The SI event appears a negative-then-positive variation in the H component at high latitude Chokurdakh (CHD: MLAT ~ 64.7 deg) in the prenoon sector, which is opposite sense of normal SI event. During the positive deflection at CHD, the SuperDARN Hokkaido radar detected the downward motion of the ionosphere, implying westward electric field enhancement, at subauroral latitudes near CHD meridian. In our study we will discuss magnetospheric and ionospheric responses to the passage of the solar wind discontinuity using multi-point observations in space and on the ground.

• Tunnel and Underground Space
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• v.17 no.3 s.68
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• pp.165-174
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• 2007

The technique, which reproduces the figures of objects from measured data of the objects using 3-D laser scanner, is called reverse engineering. Recently, research studies into applications of reverse engineering to rock engineering are increasing in number, in the discontinuity surveys for rock slopes out of man's reach, or rapid discontinuity surveys for wide range areas. For analysis of discontinuity using reverse engineering, a program for processing point clouds data from the 3-D laser scanner, for sampling from these point clouds data, and finally analyzing the discontinuity is needed. However, existing programs rarely have sufficient functions to properly analyze the discontinuities. In this study, a program was developed, which can automatically sample discontinuities from the point clouds data which measured in a rock slope using a 3-D laser scanner, and which can also undertake statistical analysis of the discontinuities. This developed program was verified by the application of discontinuity surveys in a rock slope and a tunnel. By undertaking the discontinuity survey using a 3-D laser scanner and the developed program, the feasibility and rapidity of such surveys is expected to improve in areas out of man's reach in geotechnical surveys. Taking into consideration the fact that the international level of related techniques is at a rudimentary stage, the possibility of prior occupation of a broad market is also expected.

• Journal of the Korean Data and Information Science Society
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• v.18 no.3
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• pp.669-678
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• 2007

An algorithm to detect the number of discontinuity points of the variance function in regression model is proposed. The proposed algorithm is based on the left and right one-sided kernel estimators of the second moment function and test statistics of the existence of a discontinuity point coming from the asymptotic distribution of the estimated jump size. The finite sample performance is illustrated by simulated example.

• Journal of the Korean Geotechnical Society
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• v.28 no.1
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• pp.29-39
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• 2012

The maximum unit point resistance ($q_{max}$) of rock socketed drilled shafts subjected to axial loads was investigated by a numerical analysis. A 3D Finite Difference Method (FDM) analysis and a Distinct Element Method (DEM) analysis were performed with varying rock elastic modulus (E), discontinuity spacing ($S_j$), discontinuity dip angle ($i_j$), and pile diameter (D). Based on the results of obtained, it was found that the ultimate point resistance ($q_{max}$) increased as rock elastic modulus (E) and rock discontinuity spacing ($S_j$) increased. But, it was found that $q_{max}$ decreased as pile diameter (D) increased. As for the influence of the dip angle of rock discontinuity ($i_j$), it was shown that $q_{max}$ decreased up to 50% of maximum value within the range of $0^{\circ}$ < $i_j$ < $60^{\circ}$ due to the shear failure at rock discontinuities. Furthermore, it was found that if $20^{\circ}{\leq}i_j{\leq}40^{\circ}$, influence of $i_j$ should be taken into account because $q_{max}$ tended to approach a minimum value as $i_j$ approached a value near the friction angle of the discontinuity (${\phi}_j$).

• Journal of the Korean Statistical Society
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• v.35 no.1
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• pp.1-23
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• 2006

In this paper we consider an estimation of the discontinuous variance function in nonparametric heteroscedastic random design regression model. We first propose estimators of the change point in the variance function and then construct an estimator of the entire variance function. We examine the rates of convergence of these estimators and give results for their asymptotics. Numerical work reveals that using the proposed change point analysis in the variance function estimation is quite effective.

• Journal of the Korean Data and Information Science Society
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• v.23 no.4
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• pp.765-775
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• 2012

The cross-validation is a popular method to select bandwidth in all types of kernel estimation. The maximum likelihood cross-validation, the least squares cross-validation and biased cross-validation have been proposed for bandwidth selection in kernel density estimation. In the case that the probability density function has a discontinuity point, Huh (2012) proposed a method of bandwidth selection using the maximum likelihood cross-validation. In this paper, two forms of cross-validation with the one-sided kernel function are proposed for bandwidth selection to estimate the location and jump size of the discontinuity point of density. These methods are motivated by the least squares cross-validation and the biased cross-validation. By simulated examples, the finite sample performances of two proposed methods with the one of Huh (2012) are compared.

• 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.

• Journal of Welding and Joining
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• v.18 no.3
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• pp.68-75
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• 2000

The incomplete penetration(IP) discontinuity in butt joint weld, which is detected during safety analysis of the steel bridge by nondestructive evaluation(NDE) method, is classified as unacceptable defect according to the NDE codes and standards. In fact, there are a little allowance in butt joint weld in the view point of design criterion, and also detected IP discontinuity should be classified and evaluated for the fatigue strength and residual life estimation. In this study, we performed fatigue test to evaluate the fatigue strength of high strength steel(SWS490A) containing IP discontinuities in various size, the results compared and classified according to the bridge construction standard specification which published by korea administration of construction and traffic. Experimental results could be used to evaluate and estimate the IP discontinuities considering different stress range in butt joint bridge weld during periodic safety inspection.