• Journal of the Society of Naval Architects of Korea
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• v.29 no.4
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• pp.58-65
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• 1992

In this paper, wave resistance for a submerged body is calculated by a higher order panel method. The Neumann-Kelvin problem is solved by the source or normal dipole distribution method. The body surface is represented by a bicubic B-spline and the singularity strengths are approximated by a bilinear form. The results calculated by the higher order panel method are compared with those by the lowest order panel method developed by Hess & Smith. The convergence rate of the higher order panel method is much better than the lowest order panel method. But the wave resistance calculated by the higher order panel method still shows discrepancy with an analytic solution at low Froude number like that by the lowest order panel method.

• Journal of the Society of Naval Architects of Korea
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• v.30 no.3
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• pp.41-50
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• 1993

This paper compares various potential based panel methods for the analysis of two-dimensional hydrofoil. The strength of singularity on each panel is assumed to be constant or linear. Robin boundary condition as well as Neumann and Dirichlet boundary conditions are applied to various formulations to evaluate the accuracies of the methods. Pressures and lifts are computed for various two-dimensional hydrofoil geometries and are compared with the analytic solutions. Extensive studies are performed on the local errors near the trailing edge, known to be sensitive to the foil geometry with sharp trailing edge and high camber. Robin boundary condition with the perturbation velocity potential formulation shows the best accuracy and convergence rate.

• Communications of the Korean Mathematical Society
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• v.33 no.2
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• pp.409-421
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• 2018

Let X be a complex manifold of dimension n $n{\geqslant}2$ and let ${\Omega}{\Subset}X$ be a weakly q-convex domain with smooth boundary. Assume that E is a holomorphic line bundle over X and $E^{{\otimes}m}$ is the m-times tensor product of E for positive integer m. If there exists a strongly plurisubharmonic function on a neighborhood of $b{\Omega}$, then we solve the ${\bar{\partial}}$-problem with support condition in ${\Omega}$ for forms of type (r, s), $s{\geqslant}q$ with values in $E^{{\otimes}m}$. Moreover, the solvability of the ${\bar{\partial}}_b$-problem on boundaries of weakly q-convex domains with smooth boundary in $K{\ddot{a}}hler$ manifolds are given. Furthermore, we shall establish an extension theorem for the ${\bar{\partial}}_b$-closed forms.

• Advances in Computational Design
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• v.9 no.1
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• pp.73-80
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• 2024

The aim of this paper is to remove the rigid body motion in the interior boundary value problem (BVP) of plane elasticity by solving the interior and exterior BVPs simultaneously. First, we formulate the interior and exterior BVPs simultaneously. The tractions applied on the contour in two problems are the same. After adding and subtracting the two boundary integral equations (BIEs), we will obtain a couple of BIEs. In the coupled BIEs, the properties of relevant integral operators are modified, and those integral operators are generally invertible. Finally, a unique solution for boundary displacement of interior region can be obtained.

• Journal of the Society of Naval Architects of Korea
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• v.28 no.2
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• pp.28-39
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• 1991

A study on the optimization problems to find forebode shapes with minimum wavemaking and frictional resistance was performed. The afterbody was fixed as a given hull and only forebode offsets were treated as design variables. Design variables were divided into the offsets of given hull and small variation from them. For the wavemaking resistance calculation, Neumann-Kelvin theory was applied to the given hull and thin ship theory was applied to the small variation. ITTC 1957 model-ship correlation line was used for the calculation of frictional resistance. Hull surface was represented mathmatically using shape function. As object function, such as wavemaking and frictional rersistance, was quadratic form of offsets and constraints linear, quadratic programing problem could be constructed. The complementary pivot method was used to find the soulution of the quadratic programing problem. Calculations were perfomed for the Series 60 $C_{B}$=0.6. at Fn=0.289. A realistic hull form could be obtained by using proper constraints. From the results of calculation for the Series 60 $C_{B}$=0.6, it was concluded that present method gave optimal shape of bulbous bow showing a slight improvement in the wave resistance performance at design speed Fn=0.289 compared with the results from the ship theory only.

• Journal of the Korean Institute of Intelligent Systems
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• v.14 no.3
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• pp.253-261
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• 2004

Game theory is mathematical analysis developed to study involved in making decisions. In 1928, Von Neumann proved that every two-person, zero-sum game with finitely many pure strategies for each player is deterministic. As well, in the early 50's, Nash presented another concept as the basis for a generalization of Von Neumann's theorem. Another central achievement of game theory is the introduction of evolutionary game theory, by which agents can play optimal strategies in the absence of rationality. Not the rationality but through the process of Darwinian selection, a population of agents can evolve to an Evolutionary Stable Strategy (ESS) introduced by Maynard Smith. Keeping pace with these game theoretical studies, the first computer simulation of co-evolution was tried out by Hillis in 1991. Moreover, Kauffman proposed NK model to analyze co-evolutionary dynamics between different species. He showed how co-evolutionary phenomenon reaches static states and that these states are Nash equilibrium or ESS introduced in game theory. Since the studies about co-evolutionary phenomenon were started, however many other researchers have developed co-evolutionary algorithms, in this paper we propose Game theory based Co-Evolutionary Algorithm (GCEA) and confirm that this algorithm can be a solution of evolutionary problems by searching the ESS.To evaluate newly designed GCEA approach, we solve several test Multi-objective Optimization Problems (MOPs). From the results of these evaluations, we confirm that evolutionary game can be embodied by co-evolutionary algorithm and analyze optimization performance of GCEA by comparing experimental results using GCEA with the results using other evolutionary optimization algorithms.

• Journal of the Korean Mathematical Society
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• v.34 no.3
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• pp.695-706
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• 1997

We investigate the bahivor of the gradient of solutions to the refraction equation $div(( 1+ (k - 1)_\chi D)\nabla u) = 0$ under perturbation of domain D. If $u_h$ are solutions to the refraction equation corresponding to subdomains D and $D_h$ of a domain $\Omega$ in 2 dimensional plane with the same Neumann data on $\partial\Omega$, respectively, we prove that $\left\$\mid$ \nabla(u - u_h) \right\$\mid$_{L^2(\Omega)} \leq C\sqrt{dist(D, D_h)}$ where $dist(D, D_h)$ is the Hausdorff distance between D and $D_h$. We also show that this is the best possible result.

• Management Science and Financial Engineering
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• v.20 no.2
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• pp.13-25
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• 2014

We investigate an optimal retirement time and consumption/investment policy of a wage earner who expects to find a better investment opportunity after retirement by being freed from other work and participating fully in the financial market. We obtain a closed form solution to the optimization problem by using a dynamic programming method under general time-separable von Neumann-Morgenstern utility. It is optimal for the wage earner to retire from work if and only if his wealth exceeds a certain critical level which is obtained from a free boundary value problem. The wage earner consumes less and takes more risk than he would without anticipation of a better investment opportunity.

• Proceedings of the Acoustical Society of Korea Conference
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• 1996.06a
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• pp.64-68
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• 1996

수중음파전달 모델은 benchmark 시험을 통해 정확도, 적용범위, 계산시간 등의 성능을 평가받는다. 본 논문에서는 analytic 모델, 정상 모드 모델(normal mode model), 포물선 방정식 모델(parabolic equation model), 가우시안 빔 모델(Gaussian beam model), 스펙트럼 모델(spectral model) 등 거리의존 모델에 대해 benchmark 시험을 수행하였으며, benchmark 시험은 다음과 같은 세 가지 거리의존 해양환경으로 나누어 실시했다 : 1) 해수면과 해저면이 Dirichlet 경계조건인 이상 쐐기 문제(ideal wedge problem), 2) 해수면은 앞서 말한 Dirichlet 경계조건이나 해저면은 전달 손실이 있는 손실 통과 해저면 쐐기 문제(penetrable lossy bottom wedge problem), 3) 해수면은 앞서 말한 Dirichlet 경계조건이고 해저면은 Neumann 경계조건으로 서로 평행이면 음파전달 속도가 거리방향 의존인 경우, 경우 1은 anaytic 모델을 사용하고 경우 2는 정상 모드 모델, 포물선 방정식 모델, 스펙트럼 모델을 사용하였으며, 경우 3에 대해서는 가우시안 빔 모델과 포물선 방정식 모델을 사용하였다.

• Honam Mathematical Journal
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• v.31 no.4
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• pp.579-590
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• 2009

The precise form of singular functions, singular function representation and the extraction form for the stress intensity factor play an important role in the singular function methods to deal with the domain singularities for the Poisson problems with most common boundary conditions, e.q. Dirichlet or Mixed boundary condition [2, 4]. In this paper we give an elementary step to get the singular functions of the solution for Poisson problem with Neumann boundary condition or Robin boundary condition. We also give singular function representation and the extraction form for the stress intensity with a result showing the number of singular functions depending on the boundary conditions.