• 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.

• Proceedings of the Korean Vacuum Society Conference
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• 2016.02a
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• pp.339.2-339.2
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• 2016

본 연구에서는 Ti/Al/Ti 금속 배선의 Electro-Migration(EM) 현상을 분석했다. Van der Pauw, Greek Cross bridge, Straight line linear line bridge를 결합한 패턴을 제작하여, 온도 변화에 따른 EM의 발생 시간(Failure Time)을 측정했다. 측정 조건은 W/L=3.5/300 um 소자에 전류 밀도(current density)를 $J=10^4A/cm^2$로 고정하고, 온도를 300 K, 350 K, 400 K로 가변 시켰다. 측정된 Cumulative Failure의 50 % 되는 지점(Median Time To Failure; MTTF)은 각각 22.3시간, 18.46시간, 15.4시간으로 온도가 300 K에서 400 K로 증가함에 따라 MTTF가 6.9시간 감소했다. 이 결과를 통해 Black방정식에서 온도 변수가 $t_{50}$에 영향을 주는 것을 확인했다. 온도가 증가함에 따라 더 많은 전자들이 원자에 충돌하면서 운동량을 전달하고, 더 많은 원자들이 이주되면서 EM 발생 시간이 감소했다.

• Publications of The Korean Astronomical Society
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• v.18 no.1
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• pp.11-14
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• 2003

In the earlier papers we analyzed the axisymmetric, nonstationary electrodynamics of the central black hole and a surrounding thin accretion disk in an active galactic nucleus. Based on those papers we analyze the axisymmetric, nonstationary force-free black hole magnetosphere and the motion of the plasma. We concentrate on deriving the totally new equations for the entropy incrrease and the angular momentum, energy extraction of the black hole.

• Publications of The Korean Astronomical Society
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• v.18 no.1
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• pp.15-20
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• 2003

In the earlier papers we analyzed the axisymmetric, nonstationary electrodynamics of the central black hole and a surrounding thin accretion disk in an active galactic nucleus. Based on those papers we analyze the axisymmetric, nonstationary black hole magnetosphere in this paper. We concentrate on deriving the ‘Grad-Shafranov equations’; both in the force-free and non-force-free cases. In the time-independent limit our equations naturally coincide with stationary equations as they should.

• Journal of the Korean Home Economics Association
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• v.39 no.1
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• pp.103-111
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• 2001

This study was attempted to investigate the effect of partial replacement of rice flour with black or brown rice flour on texture properties and retrogradation of Julpyun(Korean rice cake). In sensory evaluation, the Julpyuns replaced black or brown rice flour 20% had high score in color, flavor and overall acceptability not including mouthfeel. As the result of the measurement with texture analyzer, hardness, gumminess and chewiness of Julpyuns tended to decrease in proportion to the amount of black and brown rice flour in the formula. These resets implied that the degree of retrogradation of black and brown rice Julpyuns might be low. Julpyuns replaced with black rice were a little lower than those of brown rice in the hardness. In the retrogradation speed by Avrami,s equation, the rate constants of Julpyun replaced black and brown rice flour was lower than that of milled rice, restating in delay in firming.

• Publications of The Korean Astronomical Society
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• v.17 no.1
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• pp.1-6
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• 2002

In this review article the famous 'jet equation' of the neutron stars and black holes will be fully derived for the pedagogical purposes.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2004.05a
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• pp.738-741
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• 2004

최근 다양한 금융 데이터를 신경망 이론을 비롯한 최적화 기법을 통해 모델링 하려는 시도가 증가하고 있다. 이러한 시도는 블랙숄즈 모델이 가지고 있는 몇 가지 비현실적인 가정들을 극복할 수 있다는 점에서 성공적이다. 그러나 각각의 최적화 기법의 고유한 특성을 고려하지 못한 채 적용하여 성능면에서 큰 향상을 보이지 못하고 있다. 따라서 이론과 기법의 적용에 있어 금융데이터의 특성에 맞는 명확한 절차의 정의가 필요하다. 본 논문에서는 옵션의 가격결정에 적용 가능한 신경망 기법들을 제시하고 절차를 정의, 분석하고 그 성능을 블랙-숄즈 방정식과 비교한다. 비교 분석 결과는 블랙-숄즈 방정식에 의한 가격 오차와 최적화 기법을 통한 가격오차가 통계적으로 유의한 차이가 있는지 여부를 분석함으로써 유의성을 검증하였다.

• Publications of The Korean Astronomical Society
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• v.14 no.2
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• pp.57-60
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• 1999

We derive the Grad-Shafranov equation in the Macdonald-Thorne magnetosphere of the super-massive black hole in an active galactic nucleus. Our major assumption is that the plasma velocity is not only toroidal but also poloidal. As a result, we get the correction terms which are related to the poloidal motion of plasma like electrodynamic jets.

• Journal for History of Mathematics
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• v.15 no.3
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• pp.59-64
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• 2002

This paper investigates a history of Fourier Series for the heat equation and how deeply it is related to modern famous three equations, Navier-Stokes equations in fluid dynamics, drift-diffusion equations in semiconductor, and Black-Scholes equation in finance. We also propose improved models for the heat equation with finite propagation speeds.

• Publications of The Korean Astronomical Society
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• v.19 no.1
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• pp.11-16
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• 2004

In this review article the famous 'jet equation' in a Minkowski magnetosphere around the compact objects will be fully derived for the pedagogical purposes.