• 대한수학회보
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• 제50권3호
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• pp.823-832
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• 2013

We present a new algorithm for solving a system of nonlinear equations with convex constraints which combines proximal point and projection methodologies. Compared with the existing projection methods for solving the problem, we use a different system of linear equations to obtain the proximal point; and moreover, at the step of getting next iterate, our projection way and projection region are also different. Based on the Armijo-type line search procedure, a new hyperplane is introduced. Using the separate property of hyperplane, the new algorithm is proved to be globally convergent under much weaker assumptions than monotone or more generally pseudomonotone. We study the convergence rate of the iterative sequence under very mild error bound conditions.

• Nonlinear Functional Analysis and Applications
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• 제27권3호
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• pp.471-497
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• 2022

In this paper, we study a system of nonlinear wave equations associated with the helical flows of Maxwell fluid. By constructing a N-order iterative scheme, we prove the local existence and uniqueness of a weak solution. Furthermore, we show that the sequence associated with N-order iterative scheme converges to the unique weak solution at a rate of N-order.

• 대한전기학회논문지
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• 제41권9호
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• pp.1104-1109
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• 1992

A mathematical model of cancerous system based on immunological surveillance has been proposed by Lee. The model involves a system of 12 coupled nonlinear differential equations due to cellular kinetics and each of them can be modeled bilinearly. This paper discusses only the properties of solutions to the nonlinear differential equations and identification.

• 한국정밀공학회지
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• 제22권4호
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• pp.128-135
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• 2005

Overhead crane systems consist of trolley, girder, rope, objects, trolley motor, girder motor, and hoist motor. The dynamic system of these systems becomes a nonlinear state equations. These equations are obtained by the nonlinear equations of motion which are derived from transfer functions of driving motors and equations of motion for objects. From these state equations, Lyapunov functions of overhead crane systems are derived from integral method. These functions secure stability of autonomous overhead crane systems. Also constraint equations of driving motors of trolley, girder, and hoist are derived from these functions. From the results of computer simulation, it is founded that overhead crane systems is secure.

• 대한전기학회논문지:전력기술부문A
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• 제48권4호
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• pp.379-387
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• 1999

In general, solving or analyzing nonilinear dynamical equations is very difficult and requires special techniques. To avoid these difficulties, systems are generally linearized in an attempt to predict their begavior. These linearized equations, however, may not predict true system behavior. Therefore, the nonlinear dynamical analysis using bifurcation theory may become a fundamental framework in understanding nonlinear situation in power systems. In this paper, we propose a systematic procedure based on a bifurcation theory to analyze nonlinear behaviors in power systems. We show usefulness of our procedure by applying 3-bus model system. In addition, we consider nonlinear model of SMES and verify the effect of SMES in power system's nonlinear behaviors.

• 대한수학회보
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• 제51권6호
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• pp.1697-1710
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• 2014

The initial-boundary value problem for a class of nonlinear higher-order wave equations system with a damping and source terms in bounded domain is studied. We prove the existence of global solutions. Meanwhile, under the condition of the positive initial energy, it is showed that the solutions blow up in the finite time and the lifespan estimate of solutions is also given.

• Coupled systems mechanics
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• 제2권2호
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• pp.159-174
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• 2013

The present work aims at investigating the nonlinear dynamics, bifurcations, and stability of an axially accelerating beam with an intermediate spring-support. The problem of a parametrically excited system is addressed for the gyroscopic system. A geometric nonlinearity due to mid-plane stretching is considered and Hamilton's principle is employed to derive the nonlinear equation of motion. The equation is then reduced into a set of nonlinear ordinary differential equations with coupled terms via Galerkin's method. For the system in the sub-critical speed regime, the pseudo-arclength continuation technique is employed to plot the frequency-response curves. The results are presented for the system with and without a three-to-one internal resonance between the first two transverse modes. Also, the global dynamics of the system is investigated using direct time integration of the discretized equations. The mean axial speed and the amplitude of speed variations are varied as the bifurcation parameters and the bifurcation diagrams of Poincare maps are constructed.

• 대한기계학회논문집
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• 제14권6호
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• pp.1426-1435
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• 1990

본 연구에서는 확률론적 등가선형화 기법을 사용하여 비선형 랜덤 시스템을 선형화하였다.또 이 선형화된 시스템을 최근에 새로이 제안된 방법을 적용하여 비 백색잡음형태의 랜덤 가진을 받을 때 그 거동을 구하였다.

• Coupled systems mechanics
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• 제1권1호
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• pp.39-57
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• 2012

This study intends to explore dynamic interaction behaviors between actively controlled maglev vehicle and guideway girders by considering the nonlinear forms of electromagnetic force and current exactly. For this, governing equations for the maglev vehicle with ten degrees of freedom are derived by considering the nonlinear equation of electromagnetic force, surface irregularity, and the deflection of the guideway girder. Next, equations of motion of the guideway girder, based on the mode superposition method, are obtained by applying the UTM-01 control algorithm for electromagnetic suspension to make the maglev vehicle system stable. Finally, the numerical studies under various conditions are carried out to investigate the dynamic characteristics of the maglev system based on consideration of the linear and nonlinear electromagnetic forces. From numerical simulation, it is observed that the dynamic responses between nonlinear and linear analysis make little difference in the stable region. But unstable responses in nonlinear analysis under poor conditions can sometimes be obtained because the nominal air-gap is too small to control the maglev vehicle stably. However, it is demonstrated that this unstable phenomenon can be removed by making the nominal air-gap related to electromagnetic force larger. Consequently it is judged that the nonlinear analysis method considering the nonlinear equations of electromagnetic force and current can provide more realistic solutions than the linear analysis.

• Journal of applied mathematics & informatics
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• 제30권5_6호
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• pp.773-785
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• 2012

In this paper, we establish sufficient conditions for the existence and uniqueness of solutions to a general class of three-point boundary value problems for a coupled system of nonlinear fractional differential equations. The differential operator is taken in the Caputo fractional derivatives. By using Green's function, we transform the derivative systems into equivalent integral systems. The existence is based on Schauder fixed point theorem and contraction mapping principle. Finally, some examples are given to show the applicability of our results.