• 한국항행학회논문지
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• 제18권5호
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• pp.501-507
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• 2014

음이 아닌 입력에 대하여 음이 아닌 초기상태에서 출발한 모든 상태변수 값들이 시간에 대하여 항상 음이 아닌 값을 유지하는 시스템은 양의 시스템으로 정의된다. 본 논문에서는 상태변수에 시변 지연시간이 있는 양의 시변 선형 이산 구간 시스템의 안정조건을 새롭게 제안한다. 시변 지연시간은 최소와 최대 지연시간 범위에서 변하는 것으로 고려된다. 제안된 안정조건은 리아프노프 방정식의 상한 해 한계를 이용하여 유도되며, 매우 간단한 부등식의 형태로 표현된다. 수치예제를 통하여 새로운 안정조건들이 안정성 판단에 간단하고 효과적으로 적용될 수 있음을 확인한다.

• 물과 미래
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• 제21권4호
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• pp.407-414
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• 1988

본 논문의 목적은 하천 수질모형 시스템이 안정성 및 해감도이론에 의해 이론적으로 어떻게 분석되며, 그 결과 모형화를 위한 수치분석의 신뢰성과 수질 매개변수의 변화에 따른 모형의 민감성을 입증하는 것이다. 무한 Fourier 급수를 이용하여 전개한 안정성이론은 유한차분법을 사용한 모형의 수치해법을 분석하는데 있고, 1부 선형상태벡터식으로 표현되는 민감도이론은 BOD 부하, 유량, 온도와 같은 수질배개변수의 변동효과를 이론적으로 분석하는데 사용되었고, 그 연구 결과는 하천 수질모형시스템의 신뢰성을 파악할 수 있음이 입증되었다.

• Structural Engineering and Mechanics
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• 제81권6호
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• pp.769-780
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• 2022

This paper studies the dynamic behavior of laminated composite circular cylindrical shells interacting with a fluid. The mathematical formulation of the dynamic problem for an elastic body is developed based on the variational principle of virtual displacements and the relations of linear elasticity theory. The behavior of an ideal compressible fluid is described by the potential theory, the equations of which together with boundary conditions are transformed to a weak form. The hydrodynamic pressure exerted by the fluid on the internal surface of the shell is calculated according to the linearized Bernoulli equation. The numerical implementation of the mathematical formulation has been done using the semi-analytical finite element method. The influence of the ply angle and lay-up configurations of laminated composites on the natural vibration frequencies and the hydroelastic stability boundary have been analyzed for shells with different geometrical dimensions and under different kinematic boundary conditions set at their edges. It has been found that the optimal value of the ply angle depends on the level of filling of the shell with a fluid. The obtained results support the view that by choosing the optimal configuration of the layered composite material it is possible to change upwards or downwards the frequency and mode shape, as well as the critical velocity for stability loss over a wide range.

• 호남수학학술지
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• 제33권1호
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• pp.73-84
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• 2011

Let f, g, h, k : $\mathbb{R}^n{\rightarrow}\mathbb{C}$ be locally integrable functions. We deal with the $L^{\infty}$-version of the Hyers-Ulam stability of the quadratic functional inequality and the Pexiderized quadratic functional inequality $${\parallel}f(x + y) + f(x - y) -2f(x) - 2f(y){\parallel}_{L^{\infty}(\mathbb{R}^n)}\leq\varepsilon$$ $${\parallel}f(x + y) + g(x - y) -2h(x) - 2f(y){\parallel}_{L^{\infty}(\mathbb{R}^n)}\leq\varepsilon$$ based on the concept of linear functionals on the space of smooth functions with compact support.

• 대한수학회보
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• 제48권3호
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• pp.555-574
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• 2011

It is well known that the mathematical models provide very important information for the research of human immunodeciency virus type. However, the infection rate of almost all mathematical models is linear. The linearity shows the simple interaction between the T-cells and the viral particles. In this paper, a differential equation model of HIV infection of $CD4^+$ T-cells with Crowley-Martin function response is studied. We prove that if the basic reproduction number $R_0$ < 1, the HIV infection is cleared from the T-cell population and the disease dies out; if $R_0$ > 1, the HIV infection persists in the host. We find that the chronic disease steady state is globally asymptotically stable if $R_0$ > 1. Numerical simulations are presented to illustrate the results.

• 한국진공학회지
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• 제21권3호
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• pp.130-135
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• 2012

드리프트-확산 근사식을 이용한 1차원 유체 방정식으로부터 선형적 안정성 이론을 전개하여 Tosend 방전에서 전자 확산이 불안정성에 미치는 영향을 관찰하였다. 본 연구에서 관찰된 바에 따르면 Townsend 불안정성은 전자 확산과 공간 전하에 의해 형성된 전기장의 효과가 결합되어 발생하며, 공간전하에 의한 효과가 작은 영역, 즉 방전 전류가 낮은 영역에서는 전자 확산 효과가 커질수록 불안정이 더 빨리 진행된다는 것이 발견되었다.

• 대한수학회지
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• 제57권6호
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• pp.1347-1372
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• 2020

We study bifurcation for the following fractional Schrödinger equation $$\{\left.\begin{eqnarray}(-{\Delta})^su+V(x)u&=&{\lambda}f(u)&&{\text{in}}\;{\Omega}\\u&>&0&&{\text{in}}\;{\Omega}\\u&=&0&&{\hspace{32}}{\text{in}}\;{\mathbb{R}}^n{\backslash}{\Omega}\end{eqnarray}\right$$ where 0 < s < 1, n > 2s, Ω is a bounded smooth domain of ℝⁿ, (-∆)^s is the fractional Laplacian of order s, V is the potential energy satisfying suitable assumptions and λ is a positive real parameter. The nonlinear term f is a positive nondecreasing convex function, asymptotically linear that is $\lim_{t{\rightarrow}+{\infty}}\;{\frac{f(t)}{t}}=a{\in}(0,+{\infty})$. We discuss the existence, uniqueness and stability of a positive solution and we also prove the existence of critical value and the uniqueness of extremal solutions. We take into account the types of Bifurcation problem for a class of quasilinear fractional Schrödinger equations, we also establish the asymptotic behavior of the solution around the bifurcation point.

• 제어로봇시스템학회논문지
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• 제9권1호
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• pp.1-9
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• 2003

An active control of the lateral vibration of a translating tensioned Euler-Bemoulli beam is investigated. The dynamics of the translating tensioned beam is represented by a non-linear hyperbolic partial differential equation. A right boundary control law based upon the Lyapunov's second method is derived. The transverse motion of the translating tensioned beam is controlled by a time-varying external force besides a passive damping applied at the right boundary. Exponential stability of the closed loop system is proved. Simulation results demonstrate the effectiveness of the proposed controller.

• Journal of Hydrospace Technology
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• 제1권1호
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• pp.57-65
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• 1995

For the mechanism of ship capsizing, we can generally consider that it\`s caused due to pure loss of stability, parametric oscillation(low cycle resonance) of ship in waves and the broaching phenomena. Among them, low cycle resonance occurs due to the dynamic change of righting arm with respect to the relative position of ship to waves. The dynamic change depends on the encounter period of a ship in following waves. This paper discusses the following items : (1) An analytical expression of GZ curve varying with respect to the relative position of ship to waves, (2) Non-linear equation of motion describing low cycle resonance, (3) The effects of righting arm, stability range and encounter period on low cycle resonance.

• 제어로봇시스템학회논문지
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• 제10권2호
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• pp.145-152
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• 2004

In this paper, an S(stochastic)-eigenvalue and its corresponding S-eigenvector concept for linear continuous-time systems with probabilistic uncertainties are proposed. The proposed concept is concerned with the perturbation of eigenvalues due to the stochastic variable parameters in the dynamic model of a plant. An S-eigenstructure assignment scheme via the Sylvester equation approach based on the S-eigenvalue/-eigenvector concept is also proposed. The proposed control design scheme based on the proposed concept is applied to a longitudinal dynamics of an open-loop-unstable aircraft with possible uncertainties in aerodynamic and thrust effects as well as separate dynamic pressure effects. These results explicitly characterize how S-eigenvalues in the complex plane may impose stability on the system.