• Korean Journal of Mathematics
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• 제17권1호
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• pp.103-112
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• 2009

We show the existence of the solutions for the following nonlinear elliptic problem under the Dirichlet boundary condition. To show the existence of the solutions we use the variational formulation.

• 한국산업정보학회논문지
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• 제11권5호
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• pp.62-66
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• 2006

We investigate various $\Phi(t)-stability$ of comparison differential equations and we abtain necessary and/or sufficient conditions for the uniform asymptotic and exponential asymptotic stability of the nonlinear differential equation x'=f(t, x).

• 대한산업공학회지
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• 제38권4호
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• pp.249-253
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• 2012

This paper suggests a numerical method for valuation of American options under the Kou model (double exponential jump diffusion model). The method is based on approximation of underlying asset price using a finite-state, time-homogeneous Markov chain. We examine the effectiveness of the proposed method with simulation results, which are compared with those from the conventional numerical method, the finite difference method for PIDE (partial integro-differential equation).

• 대한수학회논문집
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• 제31권3호
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• pp.603-611
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• 2016

In this paper, we show that if $\mathcal{A}$ is a differential subalgebra of Banach algebras $\mathcal{B}({\ell}^r)$, $1{\leq}r{\leq}{\infty}$, then solutions of the infinite dimensional linear system associated with a matrix in $\mathcal{A}$ have its p-exponential stability being equivalent to each other for different $1{\leq}p{\leq}{\infty}$.

• International Journal of Control, Automation, and Systems
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• 제3권4호
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• pp.601-611
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• 2005

In this paper, an active vibration control of a tensioned, elastic, axially moving string is investigated. The dynamics of the translating string are described with a non-linear partial differential equation coupled with an ordinary differential equation. A right boundary control to suppress the transverse vibrations of the translating continuum is proposed. The control law is derived via the Lyapunov second method. The exponential stability of the closed-loop system is verified. The effectiveness of the proposed control law is simulated.

• 대한수학회논문집
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• 제26권4호
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• pp.709-720
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• 2011

We obtain special type of differential equations which their solution are random variable with known continuous density function. Stochastic differential equations (SDE) of continuous distributions are determined by the Fokker-Planck theorem. We approximate solution of differential equation with numerical methods such as: the Euler-Maruyama and ten stages explicit Runge-Kutta method, and analysis error prediction statistically. Numerical results, show the performance of the Rung-Kutta method with respect to the Euler-Maruyama. The exponential two parameters, exponential, normal, uniform, beta, gamma and Parreto distributions are considered in this paper.

• East Asian mathematical journal
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• 제27권1호
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• pp.91-100
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• 2011

It is important to find an optimal strategy which maximize the surplus of the insurance company at the maturity time T. The purpose of this paper is to give an explicit expression for the optimal reinsurance and investment strategy, under the CEV model, which maximizes the expected exponential utility of the final value of the surplus at T. To do this optimization problem, the corresponding Hamilton-Jacobi-Bellman equation will be transformed a linear partial differential equation by applying a Legendre transform.

• 대한기계학회논문집A
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• 제28권1호
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• pp.11-21
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• 2004

In this paper, an active vibration control of a tensioned elastic axially moving string is investigated. The dynamics of the translating string ale described by a non-linear partial differential equation coupled with an ordinary differential equation. The time varying control in the form of the right boundary transverse motions is suggested to stabilize the transverse vibration of the translating continuum. A control law based on Lyapunov's second method is derived. Exponential stability of the translating string under boundary control is verified. The effectiveness of the proposed controller is shown through the simulations.

• 대한수학회보
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• 제51권1호
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• pp.221-227
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• 2014

Our goal is to relax a sufficient condition for the exponential almost sure stability of a certain class of stochastic differential equations. Compared to the existing theory, we prove the almost sure stability, replacing Lipschitz continuity and linear growth conditions by the existence of a strong solution of the underlying stochastic differential equation. This result is extendable for the regime-switching system. An explicit example is provided for the illustration purpose.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2005년도 ICCAS
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• pp.2260-2265
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• 2005

In this paper, an active vibration control of a tensioned elastic axially moving string is investigated. The dynamics of the translating string are described by a non-linear partial differential equation coupled with an ordinary differential equation. A time varying control in the form of right boundary transverse motions is proposed in stabilizing the transverse vibrations of the translating continuum. A control law based on Lyapunov's second method is derived. Exponential stability of the closed-loop system is verified. The effectiveness of the proposed controller is shown through simulations.