• Bulletin of the Korean Mathematical Society
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• v.47 no.1
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• pp.29-37
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• 2010

We establish the existence of weak solutions in an infinite subsonic channel in the self-similar plane to the two-dimensional Burgers system. We consider a boundary value problem in a fixed domain such that a part of the domain is degenerate, and the system becomes a second order elliptic equation in the channel. The problem is motivated by the study of the weak shock reflection problem and 2-D Riemann problems. The two-dimensional Burgers system is obtained through an asymptotic reduction of the 2-D full Euler equations to study weak shock reflection by a ramp.

• Proceedings of the KIEE Conference
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• 1998.07b
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• pp.598-600
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• 1998

In this paper, a robust controller is proposed to achieve the accurate tracking for uncertain robot manipulators with hydraulic actuator dynamics. The parameter uncertainty can be quantified by the linear parameterization technique. A switching controller is proposed to guarantee the global asymptotic stability of the plant. In order to eliminate the chattering caused by the switching controller, a smoothing controller is proposed using the boundary layer technique around the sliding surface. It is shown that the smoothing controller guarantees the uniform ultimate boundedness of the tracking, error. The proposed controller shows good better tracking performance.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.21 no.10
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• pp.2703-2709
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• 1996

This paper proposes an exact numerical method for analyzing a dipole antenna attached on a dielectric slab. A Green's function for an infinitesimal current filament on a dielectric slab is derived and a field integral equation is formulated using a boundary condition. The moment Method is used to solve the field integral equation to otain current distribution on the antenna. Since an asymptotic function is used to compute the impedance matrix elements, the computataion time is significantly reduced. Using the computed current distributions, the input impedances, the resonance lengths and the resonant resistances of the antennas for various values of the thichnessandthe dielectric constant of the slab are obtained. It was found that the resonant length and the resonant resistance are decrease monotonically as the dielectric constant increases, however, those are changed up-and-down as the substrate thickness increases.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.8 no.1
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• pp.72-80
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• 1996

Two analytical solutions for oscillations in a rectangular harbour are presented. In this paper, the correct solution is obtained by use of matched asymptotic expansion method, which was first derived by Mei(1989). The other solution derived from eigenfunction expansion method is also presented, in which more accurate numerical integration is employed. In order to check the solutions, amplification factors inside the harbor are calculated and plotted by both analytical methods and numerical boundary integral equation method.

• Journal of Korean Society for Quality Management
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• v.26 no.1
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• pp.74-87
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• 1998

This study considers optimal design of accelerated life tests under constant stress using that the first passage time to cross a critical boundary through amount of accumulated degradation has an inverse Gaussian distribution when the degradation process follows to a Brownian motion with positive drift of log linear function of stress. Optimum plans for Type I censoring are derived by minimizing the asymptotic variance of estimated quantiles at the use stress. Sensitivity analyses are also conducted to see how sensitive the optimality criterion is with respect to the uncertainties involved in the guessed values.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.1
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• pp.121-126
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• 1994

A mutual integral, which has the conservation property, is applied to the problem of a crack in an isotropic elastic material. The stress intensity factors $K_{I}, K_{II}, K_{III}$ and T-stress for the problem in an infinite medium are easily obtained by using the mutual integral without solving the boundary value problem. The auxiliary solutions necessary in the proposed method are taken from the known asymptotic solutions. This method is amenable to numerical evaluation of the stress intensity factors and T-stress if the crack in a finite medium is considered.

• Steel and Composite Structures
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• v.38 no.3
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• pp.293-304
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• 2021

The aim of this paper is to analyze the nonlinear bending of functionally graded (FG) curved nanobeams reinforced by carbon nanotubes (CNTs) in thermal environment. Chen-Yao's surface elastic theory and geometric nonlinearity are also considered. The nanobeams are subjected to uniform loadings and placed on three-parameter substrates. The Euler-Lagrange equations are employed to deduce the equations of equilibrium. Then, the asymptotic solutions and boundary value problems are analytically determined by utilizing the two-step perturbation technique. Finally, the effects of the surface parameters, geometric factors, foundation stiffness, volume fraction, thermal effects and layout type of CNTs on the nonlinear bending of the nanobeams are discussed.

• Smart Structures and Systems
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• v.30 no.3
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• pp.239-243
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• 2022

We investigate the influence of nonlinear viscoelastic damping on the response of a cantilever sensor covered by piezoelectric layers in a symmetric or asymmetric configuration. We formulate an initial-boundary-value problem which consistently incorporates both geometric and material nonlinearities including the effect of viscoelastic damping which cannot be ignored for micro- and nano-mechanical sensor operation in a vacuum environment. We employ an asymptotic multiple-scales methodology to yield the system nonlinear frequency response near its primary resonance and employ a model-based estimation procedure to deduce the system damping backone curve from controlled experiments in vacuum. We discuss the effect of nonlinear damping on sensor applications for scanning probe microscopy.

• Bulletin of the Korean Mathematical Society
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• v.60 no.2
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• pp.361-388
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• 2023

In this study, we deal with American lookback option prices on dividend-paying assets under a stochastic volatility (SV) model. By using the asymptotic analysis introduced by Fouque et al. [17] and the Laplace-Carson transform (LCT), we derive the explicit formula for the option prices and the free boundary values with a finite expiration whose volatility is driven by a fast mean-reverting Ornstein-Uhlenbeck process. In addition, we examine the numerical implications of the SV on the American lookback option with respect to the model parameters and verify that the obtained explicit analytical option price has been obtained accurately and efficiently in comparison with the price obtained from the Monte-Carlo simulation.

• Journal of the Korean Society for Precision Engineering
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• v.14 no.2
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• pp.152-159
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• 1997

The asymptotic convergence of a coupled dynamic system, which is motivated from infinite dimensional adaptive systems, is investigated. The convergence analysis is formulated in abstract Banch spaces and is shown to applicable to a broad class of infinite dimensional systems including adaptive identification and adaptive control. Particularly it is shown that if a uniquely existing solution is p-th power integrable, then the solution converges to zero asymptotically. The persistence of excitation(PE) of a signal which arises in an infinite dimensional adaptive system is investigated. The PE property is not completely known yet for infinite dimensional adaptive systems, however it should be investigated in relation to spatial variable, boundary conditions as well as time variable.