• Korean Journal of Mathematics
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• v.17 no.3
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• pp.299-314
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• 2009

We investigate the multiple nontrivial solutions of the asymmetric beam equation $u_{tt}+u_{xxxx}=b_1[{(u + 2)}^+-2]+b_2[{(u + 3)}^+-3]$ with Dirichlet boundary condition and periodic condition on t. We reduce this problem into a two-dimensional problem by using variational reduction method and apply the Mountain Pass theorem to find the nontrivial solutions of the equation.

• Bulletin of the Korean Mathematical Society
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• v.47 no.2
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• pp.231-249
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• 2010

Asymptotic behavior of three-dimensional mixed, periodic and rotating magnetohydrodynamic system is investigated as the Rossby number goes to zero. The system presents the difficulty to be singular and mixed, that is hyperbolic in the vertical direction and parabolic in the horizontal one. The divergence free condition and the spectral properties of the penalization operator are crucial in the proofs. The main tools are the energy method, the Schochet's method and products laws in anisotropic Sobolev spaces.

• Korean Journal of Mathematics
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• v.16 no.3
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• pp.389-402
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• 2008

We show the existence of at least two solutions for a class of systems of the critical growth nonlinear suspension bridge equations with Dirichlet boundary condition and periodic condition. We first show that the system has a positive solution under suitable conditions, and next show that the system has another solution under the same conditions by the linking arguments.

• Korean Journal of Mathematics
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• v.19 no.4
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• pp.481-493
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• 2011

We prove a theorem which shows the existence of at least three ${\pi}$-periodic solutions of the wave equation with asymptotical linearity. We obtain this result by the finite dimensional reduction method which reduces the critical point results of the infinite dimensional space to those of the finite dimensional subspace. We also use the critical point theory and the variational method.

• Korean Journal of Mathematics
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• v.16 no.4
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• pp.545-551
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• 2008

We investigate the multiple solutions for a parabolic boundary value problem with jumping nonlinearity crossing no eigenvalues. We show the existence of the unique solution of the parabolic problem with Dirichlet boundary condition and periodic condition when jumping nonlinearity does not cross eigenvalues of the Laplace operator $-{\Delta}$. We prove this result by investigating the Lipschitz constant of the inverse compact operator of $D_t-{\Delta}$ and applying the contraction mapping principle.

• 제어로봇시스템학회:학술대회논문집
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• 1993.10a
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• pp.40-46
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• 1993

In this paper, we design a multirate controller for a given multirate sampled-data system which has a periodic output measurement scheme. A sufficient condition for maintaining observability in multirate sampled-data systems is given first. The design strategy for disturbance rejection is proposed. The proposed controller has IMC structure, and can be deomposed into a disturbance estimator and the inverse of fast plants.

• Honam Mathematical Journal
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• v.26 no.4
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• pp.589-608
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• 2004

We investigate the multiplicity of the periodic solutions of the nonlinear wave equation with jumping nonlinearity. By category theory we prove that the jumping problem has at least 2k+1 solutions for the positive source term.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 2003.05a
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• pp.32-33
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• 2003

Mechanism of a periodic oscillation of shock-induced combustion over a two- dimensional wedges and axi-symmetric cones were investigated through a series of numerical simulations at off-attaching condition of oblique detonation waves(ODW). A same computational domain over 40 degree half-angle was considered for two-dimensional and axi-symmetric shock-induced combustion phenomena. For two-dimensional shock-induced combustion, a 2H2+02+17N2 mixture was considered at Mach number was 5.85with initial temperature 292 K and initial pressureof 12 KPa. The Rankine-Hugoniot relation has solution of attached waves at this condition. For axi-symmetric shock-induced combustion, a H2+2O2+2Ar mixture was considered at Mach number was 5.0 with initial temperature 288 K and initial pressure of 200 mmHg. The flow conditions were based on the conditions of similar experiments and numerical studies.[1, 3]Numerical simulation was carried out with a compressible fluid dynamics code with a detailed hydrogen-oxygen combustion mechanism.[4, 5] A series of calculations were carried out by changing the fluid dynamic time scale. The length wedge is varied as a simplest way of changing the fluid dynamic time scale. Result reveals that there is a chemical kinetic limit of the detached overdriven detonation wave, in addition to the theoretical limit predicted by Rankine-Hugoniot theory with equilibrium chemistry. At the off-attaching condition of ODW the shock and reaction waves still attach at a wedge as a periodically oscillating oblique shock-induced combustion, if the Rankine-Hugoniot limit of detachment isbut the chemical kinetic limit is not.Mechanism of the periodic oscillation is considered as interactions between shock and reaction waves coupled with chemical kinetic effects. There were various regimes of the periodicmotion depending on the fluid dynamic time scales. The difference between the two-dimensional and axi-symmetric simulations were distinct because the flow path is parallel and uniform behind the oblique shock waves, but is not behind the conical shock waves. The shock-induced combustion behind the conical shockwaves showed much more violent and irregular characteristics.From the investigation of characteristic chemical time, condition of the periodic instability is identified as follows; at the detaching condition of Rankine-Hugoniot theory, (1) flow residence time is smaller than the chemical characteristic time, behind the detached shock wave with heat addition, (2) flow residence time should be greater than the chemical characteristic time, behind an oblique shock wave without heat addition.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.12 no.6
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• pp.931-939
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• 2001

The slot coupling characteristics was analysed in a radial-line slot antenna for its design. The previously proposed waveguide model with a periodic boundary condition on its narrow walls and periodically arranged slots on its wide wall was used. The magnetic field integral equation and two dyadic Green\`s functions for respective regions was derived and the method of moments was used. To maximize the efficiency of numerical analysis and to extract singularities, two different kinds of basis functions, the entire domain basis function and the sub-domain one, are used. In addition, the Ewald sum technique for the rectangular waveguide and the Shanks transform for the half space were used to accelerate the computation of the slowly convergent potential Green\`s functions. Simulation results expressed the effects of the various design parameters on the slot coupling.

• Journal of the Korean Society for Precision Engineering
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• v.22 no.12 s.177
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• pp.184-189
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• 2005

An experimental study of the femtosecond laser machining of Si materials was carried out. Direct laser machining of the materials for the feature size of a few micron scale has the advantage of low cost and simple process comparing to the semiconductor process, E-beam lithography, ECM and other machining process. Further, the femtosecond laser is the better tool to machine the micro parts due to its characteristics of minimizing the heat affected zone(HAZ). As a result of line cutting of Si, the optimal condition had the region of the effective energy of 2mJ/mm-2.5mJ/mm with the power of 0.5mW-1.5mW. The polarization effects of the incident beam existed in the machining qualities, therefore the sample motion should be perpendicular to the projection of the electric vector. We also observed the periodic ripple patterns which come out in condition of the pulse overlap with the threshold energy. Finally, we could machined the groove with the linewidth of below $2{\mu}m$ for the application of MEMS device repairing, scribing and arbitrary patterning.