• Journal of applied mathematics & informatics
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• 제17권1_2_3호
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• pp.269-282
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• 2005

We study the global asymptotic stability, global attractivity, boundedness character, and periodic nature of all positive solutions and all negative solutions of the difference equation $$x_{n+1}\;=\;{\alpha}-{\frac{x_{n-1}}{x_{n}},\;n=0,1,\;{\cdots}$$, where ${\alpha}\;\in\; R$ is a real number, and the initial conditions $x_{-1},\;x_0$ are arbitrary real numbers.

• 한국지반공학회논문집
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• 제24권9호
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• pp.23-32
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• 2008

본 논문에서는 계단식 형태로 시공되는 블록식 보강토 옹벽의 전체 안정성이 고려된 설계에 관한 내용을 다루었다. 다양한 계원과 이격거리로 설계된 네 가지 설계사례에 대해 현재 통용되고 있는 FHWA 및 NCMA 설계기준에 근거하여 내 외적 안정해석을 수행하고 그 결과를 토대로 두 설계기준의 차이점을 검토하였다. 아울러 대상옹벽에 대해 한계평형해석에 근거한 사면안정해석과 연속체역학 기반의 강도감소기법 해석을 수행하여 계단식 옹벽의 설계를 지배하는 파괴 메카니즘을 고찰하였다. 그 결과 내 외적 안정성 공히 FHWA에서 채택하고 있는 설계기준이 NCMA 보다 보수적인 결과(낮은 안전율)를 주는 것으로 나타났다. 또한 계단식 옹벽의 보강재의 소요 포설 길이는 전반적으로 전체 안정성에 좌우되는 것으로 검토되었으며 상부 옹벽의 보강재의 길이는 현 설계기준 보다 현저히 증가시켜야 하는 것으로 검토되었다.

• Advances in Computational Design
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• 제9권2호
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• pp.97-113
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• 2024

In this paper, we proposed a new class of stochastic neutral neural networks with uncertain and deterministic coefficients. Made the Sigmund activation and Lipschitz activation functions less conditional. The Lyapnov-Krasovskii functional is constructed. The linear matrix inequality (LMI) is constructed using Schur's lemma, and new criteria for the global asymptotic stability and global asymptotic robust stability of neural networks are obtained. Furthermore, we have verified that the method is effective and feasible through numerical examples.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2003년도 ICCAS
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• pp.1901-1904
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• 2003

MPC or model predictive control is representative of control methods which are able to handle physical constraints. Closed-loop stability can therefore be ensured only locally in the presence of constraints of this type. However, if the system is neutrally stable, and if the constraints are imposed only on the input, global aymptotic stability can be obtained; until recently, use of infinite horizons was thought to be inevitable in this case. A globally stabilizing finite-horizon MPC has lately been suggested for neutrally stable continuous-time systems using a non-quadratic terminal cost which consists of cubic as well as quadratic functions of the state. The idea originates from the so-called small gain control, where the global stability is proven using a non-quadratic Lyapunov function. The newly developed finite-horizon MPC employs the same form of Lyapunov function as the terminal cost, thereby leading to global asymptotic stability. A discrete-time version of this finite-horizon MPC is presented here. The proposed MPC algorithm is also coded using an SQP (Sequential Quadratic Programming) algorithm, and simulation results are given to show the effectiveness of the method.

• Journal of applied mathematics & informatics
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• 제28권3_4호
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• pp.797-804
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• 2010

The aim of this paper is to investigate the global stability, periodic nature, oscillation and the boundedness of solutions of the difference equation $x_{n+1}\;=\;\frac{A+Bx_{n-1}}{C+Dx_n^2}$, n = 0, 1, 2, ... where A, B are nonnegative real numbers and C, D > 0.

• 대한수학회논문집
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• 제29권4호
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• pp.505-518
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• 2014

Considered here is the first initial boundary value problem for the two-dimensional g-Navier-Stokes equations in bounded domains. We first study the long-time behavior of strong solutions to the problem in term of the existence of a global attractor and global stability of a unique stationary solution. Then we study the long-time finite dimensional approximation of the strong solutions.

• 대한수학회논문집
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• 제32권3호
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• pp.579-600
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• 2017

In this paper we consider a semilinear pseudoparabolic equation with polynomial nonlinearity and infinite delay. We first prove the existence and uniqueness of weak solutions by using the Galerkin method. Then, we prove the existence of a compact global attractor for the continuous semigroup associated to the equation. The existence and exponential stability of weak stationary solutions are also investigated.

• 대한수학회지
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• 제49권4호
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• pp.779-794
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• 2012

In this paper, we study the global stability of two mathematical models for human immunodeficiency virus (HIV) infection with intra-cellular delays. The first model is a 5-dimensional nonlinear delay ODEs that describes the interaction of the HIV with two classes of target cells, $CD4^+$ T cells and macrophages taking into account the saturation infection rate. The second model generalizes the first one by assuming that the infection rate is given by Beddington-DeAngelis functional response. Two time delays are used to describe the time periods between viral entry the two classes of target cells and the production of new virus particles. Lyapunov functionals are constructed and LaSalle-type theorem for delay differential equation is used to establish the global asymptotic stability of the uninfected and infected steady states of the HIV infection models. We have proven that if the basic reproduction number $R_0$ is less than unity, then the uninfected steady state is globally asymptotically stable, and if the infected steady state exists, then it is globally asymptotically stable for all time delays.

• Journal of applied mathematics & informatics
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• 제29권5_6호
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• pp.1327-1335
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• 2011

This paper demonstrates that there is a unique exponentially stable equilibrium state of a class of impulsive cellular neural network with delays. The analysis exploits M-matrix theory and generalized comparison principle to derive some easily verifiable sufficient conditions for the global exponential stability of the equilibrium state. The results extend and improve earlier publications. An example with its simulation is given for illustration of theoretical results.

• 대한수학회보
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• 제49권6호
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• pp.1255-1262
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• 2012

A type of delayed Lotka-Volterra competition reaction-diffusion system is considered. By constructing a new Lyapunov function, we prove that the unique positive steady-state solution is globally asymptotically stable when interspecies competition is weaker than intraspecies competition. Moreover, we show that the stability property does not depend on the diffusion coefficients and time delays.