• Journal for History of Mathematics
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• v.24 no.2
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• pp.1-15
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• 2011

Approximation is a very useful approach in mathematics research. It was the same in traditional Chinese and Chosun mathematics. This study derived five characteristics from approximation approaches which were found in Chinese and Chosun mathematical books: improvement of approximate values, common and inevitable use of approximate values, recognition of approximate values and their reasons, comparison of their exactness, application of approximate principles. Through these characteristics, we can infer what Chinese and Chosun mathematicians recognized approximate values and how they manipulated them. They took approximate approaches by necessity or for the sake of convenience in mathematical study and its applications. Also, they tried to improve the degree of exactness of approximate values and use the inverse calculations to check them.

• The Korean Journal of Applied Statistics
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• v.13 no.1
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• pp.71-80
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• 2000

본 논문에서는 이변량 분포함수의 위치모수에 대한 교대위치이동 대립가설에 대한 비모수적 검정법을 제안하였다. 소표본의 경우 실제 자료에 대해 순열원리에 기초한 근사적 검정법을 제시하였다. 모의실험을 통하여 Bhattacharyya와 Johnson(1970)의 층계순위(layer ranks)에 기초한 검정법과 검정력을 비교하였다.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.27 no.1C
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• pp.78-83
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• 2002

Reachability analysis of finite state machines is very useful for many computer-aided design applications such as communication protocol or microprecessor design. We present new techniques to improve approximate reachability analysis. The key idea is to used an iterative approximate reachability analysis technique in which don't care sets derived from previous iterations are used to improve the approximation in subsequent iterations. Experimental results show that the new techniques can improve reachability analysis significantly compared to existing analysis techniques.

• Proceedings of the Korean Statistical Society Conference
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• 2005.05a
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• pp.31-36
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• 2005

EDF에 근거한 Cramer-von Mises 형태의 통계량을 합교원리를 이용하여 다변량으로 일반화한다. 그리고 제안된 통계량의 귀무가설에서의 극한분포를 적절한 공분산함수를 가진 가우스 과정의 적분의 형태로 표현하고 통계량의 근사적인 계산방법을 고려한다.

• Korean Journal of Optics and Photonics
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• v.13 no.1
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• pp.38-43
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• 2002

Simple principles of self-imaging in Multi-Mode Interference (MMI) devices are based on the approximation of propagation constants. The analysis of the basic nature of the self-imaging principle reveals the problems of previous optimization methods, and provides a new scheme to optimize the external variables for the reconciliation of approximation problems by considering two different tendencies of approximation effects. Furthermore, the representative mode method is proposed to make the application easy. This optimization method provides an essential method for stable design and fabrication of MMI devices with improved characteristics.

• Proceedings of the Korea Institute of Convergence Signal Processing
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• 2000.08a
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• pp.125-128
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• 2000

가상적인 검출잡음을 가정하고 칼만 필타(Kalman Filter)를 고려하여 근사적 최적 레귤레이터의 특성에 가깝게 함으로써 견실 안정성을 회복할 수 있는 제어 시스템의 설계에 관하여 검토한다. 본 연구에서는 관측기를 이용한 최적 레귤레이터 계에 적분기를 결합한 견실제어계의 설계법을 나타내고 견실성을 회복할 수 있는 제어기의 파라미터 설정법을 나타낸다. 제어대상의 파라미터 변동에 의해서 생기는 등가인 외란을 억제하고 과도특성이 변하지 않는 제어 시스템을 모델 매칭의 원리에 기초하여 설계한다.

• Nuclear Engineering and Technology
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• v.21 no.1
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• pp.56-61
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• 1989

A simple, approximate method for determining the two-group adjoint flux based on the Borresen's coarse-mesh 1.5 group diffusion theory scheme is proposed. With the principle of the 1.5 group diffusion theory scheme, the method describes the thermal leakage term of the adjoint flux approximately by the geomerical buckling determined from the fast adjoint flux. The accuracy of the adjoint flux is investigated tv the comparison of the adjoint flux constructed from this method with a fine-mesh finite-difference KIDD computations. It is shown that the proposed method can predict the adjoint flux as good as the KIDD results. Possible applications of the present method are then suggested in conjunction with the application of the perturbation theory.

• The Transactions of the Korea Information Processing Society
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• v.7 no.1
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• pp.286-295
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• 2000

We present a novel statistically adaptive method using the Minimum Description Length(MDL) principle for unsupervised segmentation of magnetic resonance(MR) images. In the method, Markov random filed(MRF) modeling of tissue region accounts for random noise. Intensity measurements on the local region defined by a window are modeled by a finite Gaussian mixture, which accounts for image inhomogeneities. The segmentation algorithm is based on an iterative conditional modes(ICM) algorithm, approximately finds maximum ${\alpha}$ posteriori(MAP) estimation, and estimates model parameters on the local region. The size of the window for parameter estimation and segmentation is estimated from the image using the MDL principle. In the experiments, the technique well reflected image characteristic of the local region and showed better results than conventional methods in segmentation of MR images with inhomogeneities, especially.

• Solar Energy
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• v.15 no.2
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• pp.25-37
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• 1995

This paper presents an approximate analytical solution to one-dimensional model of the charging process for stratified thermal storage tanks, in which variation of the inlet temperature as well as the momemtum-induced mixing is taken into accout. The mixing is incorporated into the model as a constant-depth perfectly mixed layer above the plug flow region. Based on the superposition principle, the variable inlet temperature is approximated by a number of step functions. Temperature distributions for the thermocline corresponding to three types of interfacial condition arr successfully derived in terms of well-defined functions, so that a linear combination of them constitutes the final solution. Validity and utility of this work is examined through the comparison of the approximate solution with an exact solution available for the case of linearly increasing inlet temperature. With increasing the number of steps, the present solution asymptotically approaches to the exact one. Even with a limited number of steps, the present results favorably agree with those by the exact solution for a wide range of the mixing depth. Also, it is revealed that fewer steps are needed for meaningful predictions as the mixing. depth becomes larger.

• Tunnel and Underground Space
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• v.31 no.6
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• pp.480-493
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• 2021

Since the generalized Hoek-Brown criterion (GHB) provides an efficient way of identifying its strength parameter values with the consideration of in-situ rock mass condition via Geological Strength Index (GSI), this criterion is recognized as one of the standard rock mass failure criteria in rock mechanics community. However, the nonlinear form of the GHB criterion makes its mathematical treatment inconvenient and limits the scope of its application. As an effort to overcome this disadvantage of the GHB criterion, the explicit approximate analytical equations for the minimum principal stress, which is associated with the maximum principal stress at failure, are formulated based on the Taylor polynomial approximation of the original GHB criterion. The accuracy of the derived approximate formula for the minimum principal stress is verified by comparing the resulting approximate minimum principal stress with the numerically calculated exact values. To provide an application example of the approximate formulation, the equivalent friction angle and cohesion for the expected plastic zone around a circular tunnel in a GHB rock mass are calculated by incorporating the formula for the approximate minimum principal stress. It is found that the simultaneous consideration of the values of mi, GSI and far-field stress is important for the accurate calculation of equivalent Mohr-Coulomb parameter values of the plastic zone.