• Journal of applied mathematics & informatics
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• 제4권2호
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• pp.529-534
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• 1997

Even though the Shannon wavelet is a prototype of wavelets are assumed to have. By providing a sufficient condition to compute the size of Gibbs phe-nomenon for the Shannon wavelet series we can see the overshoot is propotional to the jump at discontinuity. By comparing it with that of the Fourier series we also that these two have exactly the same Gibbs constant.

• 대한수학회지
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• 제36권1호
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• pp.159-171
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• 1999

We formulate and study a finite element method for a linearized steady state, compressible, viscous Navier-Stokes equations in 2D, based on the discontinuous Galerkin method. Dislike the standard discontinuous galerkin method, we do not assume that the triangle sides be bounded away from the characteristic direction. the unique stability follows from the inf-sup condition established on the finite dimensional spaces for the (incompressible) Stokes problem. An error analysis having a jump discontinuity for pressure is shown.

• Journal of the Korean Statistical Society
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• 제35권1호
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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.

• 응용통계연구
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• 제30권2호
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• pp.259-269
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• 2017

분산함수가 불연속점을 가지는 경우, 대부분의 비모수적 함수 추정 연구에서 분산함수가 음수 값을 갖지 않기에 잔차제곱을 이용한 Nadaraya-Watson 추정량인 국소상수항추정량을 이용하였다. 한편, Huh (2014, 2016a)는 Chen 등 (2009)과 Yu와 Jones (2004)의 연구를 바탕으로 불연속 분산함수를 로그 변환한 로그분산함수를 추정 대상으로 삼아 잔차제곱이나 로그잔차제곱으로 경계점 문제를 가지지 않는 국소선형추정량을 이용하여 비모수적으로 추정하였다. Huh (2016b)는 불연속점에서 점프크기추정량을 활용하여 잔차제곱을 분산함수가 연속인 회귀모형에서 얻어진 잔차제곱인 것처럼 수정한 후 이들을 이용하여 불연속 분산함수의 추정을 연구하였다. 본 연구에서는 불연속 로그분산함수의 점프크기추정량을 이용하여 로그잔차제곱을 수정하고 불연속 로그분산함수를 국소선형추정량을 이용하여 추정하고자 한다. 제안된 추정량의 우수성을 모의실험을 통하여 Chen 등 (2009)의 로그분산함수 추정량을 이용한 Huh (2014)의 불연속 로그분산함수 추정량과 비교하고 실제자료에 적용하고자 한다.

• Computers and Concrete
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• 제5권4호
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• pp.375-388
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• 2008

Crack opening governs many transfer properties that play a pivotal role in durability analyses. Instead of trying to combine continuum and discrete models in computational analyses, it would be attractive to derive from the continuum approach an estimate of crack opening, without considering the explicit description of a discontinuous displacement field in the computational model. This is the prime objective of this contribution. The derivation is based on the comparison between two continuous variables: the distribution if the effective non local strain that controls damage and an analytical distribution of the effective non local variable that derives from a strong discontinuity analysis. Close to complete failure, these distributions should be very close to each other. Their comparison provides two quantities: the displacement jump across the crack [U] and the distance between the two profiles. This distance is an error indicator defining how close the damage distribution is from that corresponding to a crack surrounded by a fracture process zone. It may subsequently serve in continuous/discrete models in order to define the threshold below which the continuum approach is close enough to the discrete one in order to switch descriptions. The estimation of the crack opening is illustrated on a one-dimensional example and the error between the profiles issued from discontinuous and FE analyses is found to be of a few percents close to complete failure.

• 한국전산구조공학회논문집
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• 제24권5호
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• pp.577-588
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• 2011

본 논문은 복합 불연속면을 갖는 포텐셜 문제의 해석을 위해 확장된 MLS(Moving Least Squares) 차분법을 제시한다. 계면경계를 따라 해(solution)와 수직방향, 접선방향 미분들이 모두 불연속 특이성을 나타내는 복합 불연속면을 묘사하기 위해 계단함수, 쐐기함수, 가위함수와 같은 불연속 특이함수를 추가하여 기존의 MLS 차분법을 개선했다. 계면경계조건은 기지의 조건으로서 지배방정식의 이산화과정에서 추가의 미지계수를 발생시키지 않는다. 포아송 방정식 형태의 지배미분 방정식을 풀기 위해 내부영역과 경계에 절점을 배치하고 차분식을 구성한다. 차분식을 조립한 계 방정식을 직접 풀기 때문에 계산효율성이 매우 우수하다. 수치예제는 제시된 해석기법의 우수성을 잘 보여주며, 균열전파, 이동경계, 상호작용 문제 등 다양한 불연속 문제로의 확장이 기대된다.

• Journal of the Korean Data and Information Science Society
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• 제23권4호
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• pp.765-775
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• 2012

교차타당성은 커널추정량의 평활모수인 띠폭의 선택 방법으로 흔히 활용되고 있다. 연속인 확률밀도함수의 커널추정량의 띠폭 선택으로 널리 쓰이는 교차타당성 방법으로는 최대가능도교차타당성과 더불어 최소제곱교차타당성과 편의교차타당성이 있다. 확률밀도함수가 하나의 불연속점을 가질 때, Huh (2012)는 불연속점 추정을 위한 커널추정량의 띠폭 선택으로 최대가능도교차타당성을 이용한 방법을 제시하였다. 본 연구에서는 Huh (2012)에 의해 최대가능도교차타당성으로 제안된 띠폭선택의 방법과 같이 한쪽방향커널함수를 이용한 최소제곱교차타당성과 편의교차타당성으로 띠폭 선택 방법을 제시하고, 이들 띠폭 선택 방법들과 Huh (2012)의 최대가능도교차타당성을 이용한 띠폭 선택 방법을 모의실험을 통하여 비교연구 하고자 한다.

• Journal of the Korean Statistical Society
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• 제36권2호
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• pp.237-256
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• 2007

This paper studies the problem of option pricing in an incomplete market. The market incompleteness comes from the discontinuity of the underlying asset price process which is, in particular, assumed to be a compound Poisson process. To find a reasonable price for a European contingent claim, we first find the unique minimal martingale measure and get a price by taking an expectation of the payoff under this measure. To get a closed-form price, we use an asymptotic expansion. In case where the minimal martingale measure is a signed measure, we use a sequence of martingale measures (probability measures) that converges to the equivalent martingale measure in the limit to compute the price. Again, we get a closed form of asymptotic option price. It is the Black-Scholes price and a correction term, when the distribution of the return process has nonzero skewness up to the first order.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 1998년도 춘계학술대회논문집; 용평리조트 타워콘도, 21-22 May 1998
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• pp.407-412
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• 1998

In this work, a new time integration method is proposed using the generalized derivative concept to simulate the dynamic phenomena having sudden constraint occurring in dynamic contact/impact problems. By the adoption of the generalized derivative concept and jump assumption, discontinuity can be incorporated in time integration and as a result, the algorithm does not need any other special consideration of jumps in dynamic field variables due to sudden constraint like dynamic contact-release conditions. To observe the characteristics of the proposed time integration method, the stability and convergence analyses are carried out. In numerical tests, several dynamic contact/impact problems are analyzed by straightforward application of the proposed time integration method with the exterior penalty method.

• 한국추진공학회:학술대회논문집
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• 한국추진공학회 2011년도 제37회 추계학술대회논문집
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• pp.178-181
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• 2011

Recently, micro shock tube is being extensively used in various fields of engineering applications. The flow characteristics occurring in the micro shock tube may be significantly different from that of conventional macro shock tube due to very low Reynolds number and Knudsen number effects which are, in general, manifested in such flows of rarefied gas, solid-gas two-phase, etc. In these situations, Navier-Stokes equations cannot properly predict the micro shock tube flow. In the present study, a two-dimensional CFD method has been applied to simulate the micro shock tube, with slip velocity and temperature jump boundary conditions. The effects of wall thermal conditions on the unsteady flow in the micro shock tube were also investigated. The unsteady behaviors of shock wave and contact discontinuity were, in detail, analyzed. The results obtained show much more attenuation of shock wave, compared with macro-shock tubes.