• 대한기계학회논문집
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• 제15권2호
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• pp.630-643
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• 1991

The hydrodynamic stability equations are formulated for buoyancy-induced flows adjacent to a vertical, planar, isothermal surface in cold pure water. The resulting stability equations, when reduced to ordinary differential equation by a similarity transformation, constitute a two-point boundary-value(eigenvalue) problem, which was numerically solved for various values of the density extremum parameter R=( $T_{m}$ - $T_.inf./) / ( $T_{o}$ - $T_.inf./). These stability equations have been solved using a computer code designed to accurately solve two-point boundary-value problems. The present numerical study includes neutral stability results for the region of the flows corresponding to 0.0.leq. R. leq.0.15, where the outside buoyancy force reversals arise. The results show that a small amount of outside buoyancy force reversal causes the critical Grashof number $G^*/ to increase significantly. A further increase of the outside buoyancy force reversal causes the critical Grashof number to decrease. But the dimensionless frequency parameter $B^*/ at $G^*/ is systematically decreased. When the stability results of the present work are compared to the experimental data, the numerical results agree in a qualitative way with the experimental data.erimental data.

• Journal of applied mathematics & informatics
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• 제36권1_2호
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• pp.1-14
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• 2018

In this paper, we prove the existence, uniqueness and stability of solution for some nonlinear functional-integral equations by using generalized coupled Lipschitz condition. We prove a fixed point theorem to obtain the mentioned aim in Banach space $X=C([a,b],{\mathbb{R}})$. As application we study some volterra integral equations with linear, nonlinear and single kernel.

• 대한수학회논문집
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• 제26권2호
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• pp.321-338
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• 2011

In this paper, a class of delayed epidemic model with diffusion is investigated. By analyzing the associated characteristic transcendental equation, its linear stability is investigated and Hopf bifurcation is demonstrated. Some explicit formulae determining the stability and the direction of the Hopf bifurcation periodic solutions bifurcating from Hopf bifurcations are obtained by using the normal form theory and center manifold theory. Some numerical simulation are also carried out to support our analytical findings. Finally, biological explanations and main conclusions are given.

• 대한수학회보
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• 제46권5호
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• pp.1031-1040
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• 2009

It is shown that every almost positive linear mapping h : $\mathcal{A}\rightarrow\mathcal{B}$ of a Banach *-algebra $\mathcal{A}$ to a Banach *-algebra $\mathcal{B}$ is a positive linear operator when h(rx) = rh(x) (r > 1) holds for all $x\in\mathcal{A}$, and that every almost linear mapping h : $\mathcal{A}\rightarrow\mathcal{B}$ of a unital C*-algebra $\mathcal{A}$ to a unital C*-algebra $\mathcal{B}$ is a positive linear operator when h($2^nu*y$) = h($2^nu$)*h(y) holds for all unitaries $u\in \mathcal{A}$, all $y \in \mathcal{A}$, and all n = 0, 1, 2, ..., by using the Hyers-Ulam-Rassias stability of functional equations. Under a more weak condition than the condition as given above, we prove that every almost linear mapping h : $\mathcal{A}\rightarrow\mathcal{B}$ of a unital C*-algebra $\mathcal{A}$ A to a unital C*-algebra $\mathcal{B}$ is a positive linear operator. It is applied to investigate states, center states and center-valued traces.

• 한국항행학회논문지
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• 제27권6호
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• pp.871-876
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• 2023

본 논문에서는 시변 지연 시간이 있는 선형 이산 시변 구간 시스템에 두 가지의 불확실성이 동시에 존재하는 경우에 대하여 안정조건을 다룬다. 구간 시스템은 시스템 행렬들이 구간행렬의 형태로 주어지는 시스템으로 본 논문에서는 이러한 구간 시스템 행렬과 상태변수의 지연 시간이 시변인 특성을 갖는 시스템을 대상으로 한다. 비선형성을 포함하며 그 크기만을 알 수 있는 비구조화된 불확실성과 지연상태변수의 시스템 행렬 불확실성이 동시에 존재하는 경우의 시스템 안정조건을 제안한다. 두가지 종류의 불확실성에 대하여 안정 유지 가능한 크기를 해석적인 수식으로 유도한다. 제안된 안정조건과 안정 보장 크기는 기존의 다양한 선형 이산 시스템에 대한 안정 조건들을 포함할 수 있으며, 시변 지연시간 변동 크기, 불확실성의 크기들과 구간행렬의 범위 등의 값을 모두 조건식에 포함하게 된다. 새로운 안정범위는 수치예제를 통하여 이전의 결과와 비교하며 효용성과 우수성을 검증한다.

• 제어로봇시스템학회논문지
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• 제17권9호
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• pp.897-901
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• 2011

This paper presents a TS (Takagi-Sugeno) type FLC (Fuzzy Logic Controller) with only 3 rules. The choice of parameters of FLC is very difficult job on design FLC controller. Therefore, the choice of appropriate linguistic variable is an important part of the design of fuzzy controller. However, since fuzzy controller is nonlinear, it is difficult to analyze mathematically the affection of the linguistic variable. So this choice is depend on the expert's experience and trial and error method. In the design of the system, we use a variety of response characteristics like stability, rising time, overshoot, settling time, steady-state error. In particular, it is important for a stable system design to predict the steady-state error because the system's steady-state response of the system is related to the overall quality. In this paper, we propose the method to choose the consequence linear equation's parameter of T-S type FLC in the view of steady-state error. The parameters of consequence linear equations of FLC are tuned according to the system error that is the input of FLC. The full equation of T-S type FLC is presented and using this equation, the relation between output and parameters can represented. As well as the FLC parameters of consequence linear equations affect the stability of the system, it also affects the steady-state error. In this study, The system according to the parameter of consequence linear equations of FLC predict the steady-state error and the method to remove the system's steady-state error is proposed using the prediction error value. The simulation is carried out to determine the usefulness of the proposed method.

• 한국추진공학회지
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• 제22권3호
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• pp.46-52
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• 2018

액체산소 및 탄화수소를 사용하는 연소기의 고주파 연소불안정을 해석하기 위해 단순모델로서 Crocco의 $n-{\tau}$ 시간지연 연소모델을 적용하고, 음향과 커플된 연소기 내 유동에 대해 선형해석을 수행하였다. 변수분리를 통해 편미분 포텐셜함수 식을 원통좌표계 미분방정식으로 만들고, 연소기의 접선방향 공진모드에 대한 고유 값을 계산하였다. 분사면 및 노즐입구를 경계조건으로 적용하여 미분식의 해를 구했다. 시스템의 안정성 판정을 위해 전달함수를 주파수 해석 하였으며, 관심 영역 주파수인 1T 모드 주변 주파수에서 시스템 게인 및 위상각으로 안정성 여유를 평가하였다. 또한 1T 모드 안정성 향상을 위해 배플 길이 및 형상에 대한 영향을 평가하였다.

• 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.

• 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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• 제47권6호
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• pp.1225-1234
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• 2010

Numerical solutions for the fractional differential dispersion equations with nonlinear forcing terms are considered. The backward Euler finite difference scheme is applied in order to obtain numerical solutions for the equation. Existence and stability of the approximate solutions are carried out by using the right shifted Grunwald formula for the fractional derivative term in the spatial direction. Error estimate of order $O({\Delta}x+{\Delta}t)$ is obtained in the discrete $L_2$ norm. The method is applied to a linear fractional dispersion equations in order to see the theoretical order of convergence. Numerical results for a nonlinear problem show that the numerical solution approach the solution of classical diffusion equation as fractional order approaches 2.