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NUMERICAL IMPLEMENTATION OF THE TWO-DIMENSIONAL INCOMPRESSIBLE NAVIER–STOKES EQUATION
YONGHO CHOI,DARAE JEONG,SEUNGGYU LEE,JUNSEOK KIM 한국산업응용수학회 2015 Journal of the Korean Society for Industrial and A Vol.19 No.2
In this paper, we briefly review and describe a projection algorithm for numerically computing the two-dimensional time-dependent incompressible Navier?Stokes equation. The projection method, which was originally introduced by Alexandre Chorin [A.J. Chorin, Numerical solution of the Navier?Stokes equations, Math. Comput., 22 (1968), pp. 745?762], is an effective numerical method for solving time-dependent incompressible fluid flow problems. The key advantage of the projection method is that we do not compute the momentum and the continuity equations at the same time, which is computationally difficult and costly. In the projection method, we compute an intermediate velocity vector field that is then projected onto divergence-free fields to recover the divergence-free velocity. Numerical solutions for flows inside a driven cavity are presented. We also provide the source code for the programs so that interested readers can modify the programs and adapt them for their own purposes.
Curve and Surface Smoothing Using a Modified Cahn-Hilliard Equation
Choi, Yongho,Jeong, Darea,Kim, Junseok Hindawi Limited 2017 Mathematical problems in engineering Vol.2017 No.-
<P>We present a new method using the modified Cahn-Hilliard (CH) equation for smoothing piecewise linear shapes of two- and three-dimensional objects. The CH equation has good smoothing dynamics and it is coupled with a fidelity term which keeps the original given data; that is, it does not produce significant shrinkage. The modified CH equation is discretized using a linearly stable splitting scheme in time and the resulting scheme is solved by using a Fourier spectral method. We present computational results for both curve and surface smoothing problems. The computational results demonstrate that the proposed algorithm is fast and efficient.</P>
THREE-DIMENSIONAL VOLUME RECONSTRUCTION BASED ON MODIFIED FRACTIONAL CAHN–HILLIARD EQUATION
YONGHO CHOI,이승규 한국산업응용수학회 2019 Journal of the Korean Society for Industrial and A Vol.23 No.3
We present the three-dimensional volume reconstruction model using the modified Cahn–Hilliard equation with a fractional Laplacian. From two-dimensional cross section images such as computed tomography, magnetic resonance imaging slice data, we suggest an algorithm to reconstruct three-dimensional volume surface. By using Laplacian operator with the fractional one, the dynamics is changed to the macroscopic limit of Levy process. We initialize between the two cross section with linear interpolation and then smooth and reconstruct the surface by solving modified Cahn–Hilliard equation. We perform various numerical experiments to compare with the previous research.
Differences in FDI Determinants by Sector: A Knowledge-capital Model Approach
Yongho Choi 한국무역연구원 2016 무역연구 Vol.12 No.5
This paper analyzed the differences in foreign direct investment (FDI) determinants of various sectors using the Knowledge-capital (KC) model framework. Specifically, it compared the differences in the influence of FDI determinants between the manufacturing and service sectors. In the empirical analysis of the Korean outward FDI, the study found that service FDI is likely more demand-seeking than manufacturing FDI. Moreover, service FDI does not tend to be largely affected by trade impediments, caused by the differences in idiosyncratic features between the two sectors. Although past manufacturing FDI is expected to lead current producer service FDI, which facilitates production of manufacturing goods, the Korean manufacturing FDI is not complementarily related to the Korean producer service FDI. Given the rapid growth of the global service sector, the Korean government needs to promote the overseas expansion of service companies through the reinforcement of the overseas expansion support system such as providing sufficient foreign market information, supporting R&D activities for new service development and quality upgrade, and improving the customized financial support system.
ROBUST AND ACCURATE METHOD FOR THE BLACK-SCHOLES EQUATIONS WITH PAYOFF-CONSISTENT EXTRAPOLATION
CHOI, YONGHO,JEONG, DARAE,KIM, JUNSEOK,KIM, YOUNG ROCK,LEE, SEUNGGYU,SEO, SEUNGSUK,YOO, MINHYUN Korean Mathematical Society 2015 대한수학회논문집 Vol.30 No.3
We present a robust and accurate boundary condition for pricing financial options that is a hybrid combination of the payoff-consistent extrapolation and the Dirichlet boundary conditions. The payoff-consistent extrapolation is an extrapolation which is based on the payoff profile. We apply the new hybrid boundary condition to the multi-dimensional Black-Scholes equations with a high correlation. Correlation terms in mixed derivatives make it more difficult to get stable numerical solutions. However, the proposed new boundary treatments guarantee the stability of the numerical solution with high correlation. To verify the excellence of the new boundary condition, we have several numerical tests such as higher dimensional problem and exotic option with nonlinear payoff. The numerical results demonstrate the robustness and accuracy of the proposed numerical scheme.
최용호 ( Yongho Choi ) 전북대학교 인문학연구소 2018 건지인문학 Vol.0 No.23
This paper aims to examine Kripke’s meaning scepticism, or sceptical paradox and sceptical solution about meaning in the late 20<sup>th</sup> century, and show an argument against his negative thesis about meaning. Frist, historical background of meaning scepticism will be introduced. Next, each of his negative views about meaning will be reorganized as an argument. Finally, my argument will be provided against the negative prospective of meaning. 1) There is another practical area of language that cannot be regarded as an area depending only on agreement of community. 2) It is true that the sceptic about meaning relies on his memory, which is criticized by himself. 3) Basic principles of logic can be a good candidate of low-level fact for meaning ascription. 4) How much degree of justification do we need to determine whether a candidate is a fact about meaning ascription? 5) Should we admit that the argument of the sceptic is sound? I have suggested my opinions for each of them, 1) ~ 5). And I believe that my argument implies a conclusion that we have a good starting point to go opposite way of the unpromising line about meaning.