• Korean Journal of Mathematics
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• v.13 no.2
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• pp.161-176
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• 2005

We consider a model of population dynamics whose mortality function is unbounded. We note that the regularity of the solution depends on the growth rate of the mortality near the maximum age. We propose Gauss-Legendre methods along the characteristics to approximate the solution when the solution is smooth enough. It is proven that the scheme is convergent at fourth-order rate in the maximum norm. We also propose discontinuous Galerkin finite element methods to approximate the solution which is not smooth enough. The stability of the method is discussed. Several numerical examples are presented.

• Proceedings of the Korea Institute of Applied Superconductivity and Cryogenics Conference
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• 2003.02a
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• pp.193-195
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• 2003

In superconductor power systems, a quench detector can misrecognize oscillation about current or voltage control as a quench. So, for the correct detection of a quench, it seems need to guarantee a smooth control of current or voltage. In this paper, we have studied a control function and control parameter for smooth control of current or voltage.

• Journal of the Korean Statistical Society
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• v.31 no.3
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• pp.343-357
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• 2002

This paper proposes a method for producing smooth and positive estimates of the intensity function of an inhomogeneous Poisson process based on the shrinkage of wavelet coefficients of the observed counts. The information projection is used in conjunction with the level-dependent thresholds to yield smooth and positive estimates. This work is motivated by and demonstrated within the context of a problem involving gamma-ray burst data in astronomy. Simulation results are also presented in order to show the performance of the information projection estimators.

• Journal of computational fluids engineering
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• v.9 no.3
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• pp.73-80
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• 2004

A LS(Level Set) formulation is developed for computing two-phase flows on non- orthogonal meshes. Compared with the VOF(Volume-of-Fluid) method based on a non-smooth volume-fraction function, the LS method can calculate an interfacial curvature more accurately by using a smooth distance function. Also, it is quite straightforward to implement for 3-D irregular meshes compared with the VOF method requiring much more complicated geometric calculations. The LS formulation is implemented into a general purpose program for 3-D flows and verified through several test problems.

• Structural Engineering and Mechanics
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• v.8 no.4
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• pp.325-341
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• 1999

A procedure for the computation of the load carrying capacity of perfectly plastic plates in bending is presented. The approach, based on the kinematic theorem of limit analysis, requires the evaluation of the minimum of a convex, but non-smooth, function under linear equality constraints. A systematic solution procedure is devised, which detects and eliminates the finite elements which are predicted as rigid in the collapse mechanism, thus reducing the problem to the search for the minimum of a smooth and essentially unconstrained function of nodal velocities. Both Kirchhoff and Mindlin plate models are considered. The effectiveness of the approach is illustrated by means of some examples.

• Communications of the Korean Mathematical Society
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• v.33 no.3
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• pp.935-942
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• 2018

In this paper, we prove that any stable f-harmonic map from sphere ${\mathbb{S}}^n$ to Riemannian manifold (N, h) is constant, where f is a smooth positive function on ${\mathbb{S}}^n{\times}N$ satisfying one condition with n > 2. We also prove that any stable f-harmonic map ${\varphi}$ from a compact Riemannian manifold (M, g) to ${\mathbb{S}}^n$ (n > 2) is constant where, in this case, f is a smooth positive function on $M{\times}{\mathbb{S}}^n$ satisfying ${\Delta}^{{\mathbb{S}}^n}(f){\circ}{\varphi}{\leq}0$.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.6 no.2
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• pp.127-137
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• 2006

This paper presents an $H_{\infty}$ controller synthesis method for discrete time fuzzy dynamic systems based on a piecewise smooth Lyapunov function. The basic idea of the proposed approach is to construct controllers for the fuzzy dynamic systems in such a way that a Piecewise smooth Lyapunov function can be used to establish the global stability with $H_{\infty}$ performance of the resulting closed loop fuzzy control systems. It is shown that the control laws can be obtained by solving a set of Bilinear Matrix Inequalities (BMIs). An example is given to illustrate the application of the proposed method.

• 한국전산유체공학회:학술대회논문집
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• 2008.03a
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• pp.340-346
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• 2008

A level-set method is developed for computation of drop motions in various engineering applications. Compared with the volume-of-fluid method based on a non-smooth volume-fraction function, the LS method can calculate an interface curvature more accurately by using a smooth distance function. Also, it is straightforward to implement for two-phase flows in complex geometries unlike the VOF method requiring much more complicated geometric calculations. The LS method is applied to simulation of inkjet process, thin film pattering and droplet collisions.

• 한국전산유체공학회:학술대회논문집
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• 2008.10a
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• pp.340-346
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• 2008

A level-set method is developed for computation of drop motions in various engineering applications. Compared with the volume-of-fluid method based on a non-smooth volume-fraction function, the LS method can calculate an interface curvature more accurately by using a smooth distance function. Also, it is straightforward to implement for two-phase flows in complex geometries unlike the VOF method requiring much more complicated geometric calculations. The LS method is applied to simulation of inkjet process, thin film pattering and droplet collisions.

• Proceedings of the Korean Society of Marine Engineers Conference
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• 2006.06a
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• pp.85-86
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• 2006

In this paper, a nonlinear controller based on adaptive sliding-mode method which has a sliding surface vector including new boundary function is proposed and applied to a two-wheeled voiding mobile robot (WMR). This controller makes the welding point of WMR achieve tracking a reference point which is moving on a smooth curved welding path with a desired constant velocity. The mobile robot is considered in view of a kinematic model and a dynamic model in Cartesian coordinates. The proposed controller can overcome uncertainties and external disturbances by adaptive sliding-mode technique. To design the controller, the tracking error vector is defined, and then the new sliding is proposed to guarantee that the error vector converges to zero asymptotically. The stability of the dynamic system will be shown through the Lyapunov method. The simulations is shown to prove the effectiveness of the proposed controller.