• 대한수학회논문집
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• 제30권4호
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• pp.481-491
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• 2015

We calculate volume ratio of a hypersurface orthogonal to a timelike geodesic relative to that of a hypersurface in the FLRW space-time.

• 한국경영과학회지
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• 제19권3호
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• pp.203-217
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• 1994

In this paper we develop an exponentialization procedure for the modelling of open FMS networks with general processing time at each station and limited buffer size. By imposing a reasonable assumption on the solution set, the nonlinear equation system for the exponentialization procedure is formulated as a variational inequality problem and the solution existence is examined. The efficient algorithm for the nonlinear equation system is developed using linearized Jacobi approximation method.

• Korean Journal of Mathematics
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• 제16권2호
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• pp.145-156
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• 2008

When we consider a life insurance company that sells a large number of continuous T-year term life insurance policies, it is important to find an optimal strategy which maximizes the surplus of the insurance company at time T. The purpose of this paper is to give an explicit expression for the optimal reinsurance and investment strategy which maximizes the expected exponential utility of the final value of the surplus at the end of T-th year. To do this we solve the corresponding Hamilton-Jacobi-Bellman equation.

• 제어로봇시스템학회논문지
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• 제4권6호
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• pp.703-706
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• 1998

본 논문에서는 확률 최적 제어문제에서 발생되는 Elliptic type H-J-B(Hamilton-Jacobi-Bellman) 방정식에 대한 수치해를 구하였다. 수치해를 구하기 위하여 Contraction 사상 및 유한차분법을 이용하였으며, 시스템은 It/sub ∧/ 형태의 Stochastic 방정식으로 취하였다. 수치해는 수학적인 테스트 케이스를 설정하여 검증하였으며, 최적제어 Map을 방정식의 해를 구하면서 동시에 구하였다.

• Journal of applied mathematics & informatics
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• 제7권3호
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• pp.895-904
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• 2000

The contact problem of two elastic bodies of arbitrary shape with a general kernel form, investigated from Hertz problem, is reduced to an integral equation of the second kind with Cauchy kernel. A numerical method is adapted to determine the unknown potential function between the two surfaces under certain conditions. Many cases are derived and discussed from the work.

• 대한수학회지
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• 제53권4호
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• pp.795-834
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• 2016

The main purpose of this paper is to propose a scheme of a proof of the nonsimpleness of the group $Homeo^{\Omega}$ ($D^2$, ${\partial}D^2$) of area preserving homeomorphisms of the 2-disc $D^2$. We first establish the existence of Alexander isotopy in the category of Hamiltonian homeomorphisms. This reduces the question of extendability of the well-known Calabi homomorphism Cal : $Diff^{\Omega}$ ($D^1$, ${\partial}D^2$)${\rightarrow}{\mathbb{R}}$ to a homomorphism ${\bar{Cal}}$ : Hameo($D^2$, ${\partial}D^2$)${\rightarrow}{\mathbb{R}}$ to that of the vanishing of the basic phase function $f_{\underline{F}}$, a Floer theoretic graph selector constructed in [9], that is associated to the graph of the topological Hamiltonian loop and its normalized Hamiltonian ${\underline{F}}$ on $S^2$ that is obtained via the natural embedding $D^2{\hookrightarrow}S^2$. Here Hameo($D^2$, ${\partial}D^2$) is the group of Hamiltonian homeomorphisms introduced by $M{\ddot{u}}ller$ and the author [18]. We then provide an evidence of this vanishing conjecture by proving the conjecture for the special class of weakly graphical topological Hamiltonian loops on $D^2$ via a study of the associated Hamiton-Jacobi equation.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1996년도 Proceedings of the Korea Automatic Control Conference, 11th (KACC); Pohang, Korea; 24-26 Oct. 1996
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• pp.60-63
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• 1996

This study deals with the nonlinear H$_{\infty}$ control problem of linear system using nonlinear weight. Generally the solvable condition of nonlinear H$_{\infty}$ control problem is given by the Hamilton Jacobi equality or inequality, but it is very difficult to solve. In this study, some constraints of nonlinear weight reduce the solvable condition to linear Riccati equation. Some examples of the control system design using nonlinear weight are shown.n.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1995년도 Proceedings of the Korea Automation Control Conference, 10th (KACC); Seoul, Korea; 23-25 Oct. 1995
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• pp.412-415
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• 1995

Previously obtained results of L$_{2}$-gain and H$_{\infty}$ control via state feedback of nonlinear systems are extended to a class of nonlinear system with uncertainties. The required information about the uncertainties is that the uncertainties are bounded in Euclidian norm by known functions of the system state. The conditions are characterized in terms of the corresponding Hamilton-Jacobi equations or inequalities (HJEI). An algorithm for finding an approximate local solution of Hamilton-Jacobi equation is given. This results and algorithm are illustrated on a numerical example..

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1995년도 Proceedings of the Korea Automation Control Conference, 10th (KACC); Seoul, Korea; 23-25 Oct. 1995
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• pp.10-13
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• 1995

This paper considers the linear-quadratic optimal regulator problem for nonstandard singularly perturbed systems making use of the recursive technique. We first derive a generalized Riccati differential equation by the Hamilton-Jacobi equation. In order to obtain the feedback gain, we must solve the generalized algebraic Riccati equation. Using the recursive technique, we show that the solution of the generalized algebraic Riccati equation converges with the rate of convergence of O(.epsilon.). The existence of a bounded solution of error term can be proved by the implicit function theorem. It is enough to show that the corresponding Jacobian matrix is nonsingular at .epsilon. = 0. As a result, the solution of optimal regulator problem for nonstandard singularly perturbed systems can be obtained with an accuracy of O(.epsilon.$^{k}$ ). The proposed technique represents a significant improvement since the existing method for the standard singularly perturbed systems can not be applied to the nonstandard singularly perturbed systems.

• 공학논문집
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• 제1권1호
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• pp.5-14
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• 1997

이 논문에서는 위성 탑재용 안테나를 설계하기 위해서 옵셑 그레고리언 안테나의 복사특성을 해석하였다. 거리 복사패턴을 계산하기 위해서 부반사판에 GO를 이용해서 반사파를 구하고 여기에 UTD를 이용하여 구한 회절파를 더하여 얻은 결과를 가지고 PO를 이용하여 주반사면에 유기되는 전류밀도를 구하여 복사적분식을 유도하였다. 그레고리언 안테나의 복사특성해석을 위해서 주반사판의 초점거리가 62.4$\lambda$, 반경이 100$\lambda$, 옵셑 높이가 75$\lambda$, 부반사판의 이심율 0.501. 초점간의 거리 32.82$\lambda$, 경사각이 $9^{\circ}$, 반개구각이 $15.89^{\circ}$ 인 경우를 해석하였다. 이 때 급전혼에서 복사되는 파를 x편파와 y편파로 하였을 경우, 옵셑 그레고리언 안테나의 교차편파 준위와 부엽준위가 옵셑 포물면 안테나의 경우에 비해서 각각 30dB, 10dB씩 줄어드는 특성을 보였다.