• Geophysics and Geophysical Exploration
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• v.25 no.4
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• pp.242-251
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• 2022

Automatic differentiation automatically calculates the derivatives of a function using the chain rule once the forward operation of a function is defined. Given the recent development of computing libraries that support automatic differentiation, many researchers have adopted automatic differentiation techniques to solve geophysical inverse problems. We analyzed the advantages, disadvantages, and performances of automatic differentiation techniques using the gradient calculations of seismic full waveform inversion objective functions. The gradients of objective functions can be expressed as multiplications of the derivatives of the model parameters, wavefields, and objective functions using the chain rule. Using numerical examples, we demonstrated the speed of analytic differentiation and the convenience of complex gradient calculations for automatic differentiation. We calculated derivatives of model parameters and objective functions using automatic differentiation and derivatives of wavefields using analytic differentiation.

• 주택과사람들
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• s.222
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• pp.66-69
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• 2008

경기 침체와 미분양 급증으로 유동성 위기에 처한 건설 업체들이 늘면서 미분양 아파트 '땡처리' 시장이 확대되고 있다. 지난해 10월부터 시장 회복을 위해 주택공사가 미분양 아파트를 매입 중이지만, 매입을 완료했거나 올해까지 매입할 미분양 분량은 총 5000가구(약 1조 원)에 달한다. 게다가 미분양 아파트 펀드를 준비 중인 부동산 자산 운용사에 매입 의뢰가 들어온 미분양 물량 규모만 해도 2조 원에 이른다. 결국 3조원대 상당의 아파트 땡처리 시장이 열린 셈이다.

• 한국신재생에너지학회:학술대회논문집
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• 2009.06a
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• pp.852-855
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• 2009

고압 미분탄 공급 기술은 건식 석탄가스화기 시스템의 안정적인 연속운전을 위한 핵심이 되는 기술로서, 본 연구에서는 스크류피더 방식 및 기류수송 방식의 pilot급 고압 미분탄 공급장치를 이용한 미분탄 공급량 제어 기술 개발을 진행하였다. 그리고, 일반적으로 dense phase 형태로 다량의 미분탄을 공급하는 기류수송 방식 고압 미분탄 공급장치에서 가스화기로 공급되는 미분탄의 공급량을 감소시키기 위하여 다공 chamber를 통하여 가압 질소를 공급할 경우, 차압이 증가함에 따라 미분탄의 공급량이 증가하기는 하지만 lean 또는 medium phase 형태로 미분탄 공급량 제어가 가능함을 확인할 수 있었다.

• Communications of Mathematical Education
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• v.6
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• pp.383-407
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• 1997

가환다원환의 대수적 미분에 관한 성질들은 많은 연구의 대상이 되어 왔다. 본 논문은 가환 다원환에서 정의된 대수적 미분의 일반화로써 가환일 필요가 없는 일반다원환의 대수적 미분의 성질을 연구한 것이다. 비가환다원환의 미분정의를 바탕으로 하여 가환다원환에서 연구되어 온 보편적 미분가군의 성질을 일반다원환 의 미분가군에 적용하려고 노력하였다. 이 논문에서 사용한 정리의 증명과정이나 기본개념은 가환다원환의 미분개념에서 나타난 성질들을 바탕으로 하였다.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.36 no.7
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• pp.634-641
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• 2008

Automatic Differentiation(AD) is a tool for generating sensitivities, such as gradient or Jacobian, automatically. AD tools provide mathematically exact sensitivities for the given source code. In this paper applications of automatic differentiation are studied. Derivative codes are generated with AD tools for structural analysis code and flow analysis code. How to apply AD tools is explained and the accuracy of sensitivities is compared with the finite difference. Sensitivities of generated derivative code accord well with finite difference, but the calculation time of derivative code increases. It was found that the calculation time can be decreased by additional modification of derivative code.

• Communications of the Korean Mathematical Society
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• v.20 no.3
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• pp.411-426
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• 2005

본 논문에서는 상미분방정식, 지연미분방정식, 중립형 지연미분방정식, 그리고 차분방정식 의 안정성에 관한 연구방법과 최근의 연구동향들을 간략하게 소개하였다.

• 주택과사람들
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• s.210
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• pp.20-23
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• 2007

미분양 아파트가 정부 통계9만 가구 이상이고, 시장 분위기는 20만 가구가 넘어선 가운데 정부는 미분양 아파트를 임대 주택으로 활용하는 방안을 발표했으나 시장은 냉담하기만 하다. 지방의 미분양 아파트는 적체된 지 오래고, 남양주 진접지구 등 수도권 지역도 미분양에서 더 이상 자유롭지 못하다. 각 지역별 미분양 현황을 살펴보고, 부동산 경기 활성화를 위한 대책에 대해 알아본다

• Journal of the Korean School Mathematics Society
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• v.15 no.2
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• pp.331-348
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• 2012

With a gradual increase in research on teaching and learning calculus, there have been various studies about students' thinking about the derivative. This paper reviews the results of the existing empirical studies published in Korean and English. These studies mainly have shown that how students think about the derivative is related to their understanding of the related concepts and the representations of the derivative. There are also recent studies that emphasize the importance of how students learn the derivative including different applications of the derivative in different disciplines. However, the current literature rarely addressed how students think about the derivative in terms of the language differences, e.g., in Korean and English. The different terms for the derivative at a point and the derivative of a function, which shows the relation between concepts, may be closely related to students' thinking of the derivative as a function. Future study on this topic may expand our understanding on the role language-specific terms play in students' learning of mathematical concepts.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.17 no.2 s.119
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• pp.185-193
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• 2007

This paper deals with the application of the numerical differentiation using the differential quadrature(DQ) in the curved member-like structural analysis. Derivative values of the geometry of structure are definitely needed for analyzing the structural behavior. For verifying the numerical differentiation using DQ, free vibration problems of arch are selected. Terms of curvature composed with the derivatives of arch geometry obtained herein are agreed quite well with exact values obtained explicitly. Natural frequencies subjected to terms of curvature obtained by DQ are agreed quite well with those in the literature. The numerical differentiation using DQ can be practically utilized in the structural analysis.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.25 no.4
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• pp.501-507
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• 2021

Neural networks with differentiable activation functions are differentiable with respect to input variables. We improve the approximation capability of neural networks by using the gradient and Hessian of neural networks to satisfy the differential equations of the problems of interest. We apply differential neural networks to the pricing of financial options, where stochastic differential equations and the Black-Scholes partial differential equation represent the differential relation of price of option and underlying assets, and the first and second derivatives of option price play an important role in financial engineering. The proposed neural network learns - (a) the sample paths of option prices generated by stochastic differential equations and (b) the Black-Scholes equation at each time and asset price. Experimental results show that the proposed method gives accurate option values and the first and second derivatives.