• Korean Journal of Mathematics
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• v.16 no.4
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• pp.553-564
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• 2008

We have a concern with the existence of solutions (${\xi},{\eta}$) for perturbations of the parabolic system with Dirichlet boundary condition $$(0.1)\;\begin{array}{lcr}{\xi}_t=-L{\xi}+{\mu}g(3{\xi}+{\eta})-s{\phi}_1-h_1(x,t)\;in\;{\Omega}{\times}(0,2{\pi}),\\{\eta}_t=-L{\eta}+{\nu}g(3{\xi}+{\eta})-s{\phi}_1-h_2(x,t)\;in\;{\Omega}{\times}(0,2{\pi})\end{array}.$$ We prove the uniqueness theorem when the nonlinearity does not cross eigenvalues. We also investigate multiple solutions (${\xi}(x,t),\;{\eta}(x,t)$) for perturbations of the parabolic system with Dirichlet boundary condition when the nonlinearity f' is bounded and $f^{\prime}(-{\infty})<{\lambda}_1,{\lambda}_n<(3{\mu}+{\nu})f^{\prime}(+{\infty})<{\lambda}_{n+1}$.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.15 no.10 s.89
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• pp.938-943
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• 2004

In this paper, we propose a T-shaped DGS for CPW and provide the closed-form solutions for power loss rate, and bandwidth of the DGS. The proposed T-shaped DGS structure has a range of capacitance(C) 5.5 times wider than the dumbbell-shaped DGS structure. In addition we also analyze relations between R, L, C values of the DGS equivalent circuit and total loss rate, BW, $\omega_0$ of the DGS.

• Korean Journal of Microbiology
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• v.51 no.2
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• pp.141-147
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• 2015

Four halophilic bacteria were isolated from a salt water tank of more than 25% above salinity used for production of salt. HJS1 and HJS6 strains were identified as having ${\beta}$-glucosidase producing capabilities at high salinity. ${\beta}$-Glucosidase produced from these bacterial strains showed the best activity at 56-79 U/ml in NaCl (0-5%), showing the highest ${\beta}$-glucosidase activity at NaCl 3%. A salt tolerant ${\beta}$-glucosidase can maintain at least 75% activity of the enzyme in 0-20% NaCl concentration. The 16S rRNA gene sequences of strains HJS1 and HJS6 shows 99.8% similarity with Roseivivax roseus $BH87090^T$. Those sequences were registered as AB971835 and AB971836 in the NCBI GenBank. DNA-DNA hybridization test revealed that both strains showed 90.1 to 90.3% hybridization values with R. roseus $BH87090^T$, which was the closest phylogenetic neighbor. Major Cellular fatty acids of strains HJS1 and HJS6 were $C_{16:0}$, $C_{18:1}$ ${\omega}7c$, $C_{19:0}$ cyclo ${\omega}8c$ and 11-methyl $C_{18:1}$ and the major quinone was Q-10. Their fatty acid composition and quinone were very similar to Roseivivax roseus $BH87090^T$. Meanwhile, Roseivivax roseus $BH87090^T$ did not produce any ${\beta}$-glucosidase. Based on the molecular and chemotaxonomic properties, strains HJS1 and HJS6 were identified as members of Roseivivax roseus.

• Honam Mathematical Journal
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• v.26 no.4
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• pp.455-462
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• 2004

We prove that if ${\mathbb{K}}^*$ is adjoint operator on $W_2{^2}({\Omega})$, then ${\mathbb{K}}^*v(t,\;{\tau})=,\;v(x,\;y){\in}W_2{^2}({\Omega})$ ; it is also related to the decomposition of solution of Fredholm equations.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.4
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• pp.635-641
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• 2014

The existence and the regularity of the particle trajectory flow X(x, t) along a velocity field u on $\mathbb{R}^n$ are discussed under the BMO-blow-up condition: $${\int}_{0}^{T}{\parallel}{\omega}({\tau}){\parallel}_{BMO}d{\tau}&lt;{\infty}$$ of the vorticity ${\omega}{\equiv}{\nabla}{\times}u$. A comment on our result related with the mystery of turbulence is presented.

• Journal of the Korean Society of Marine Environment & Safety
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• v.24 no.3
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• pp.325-331
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• 2018

This paper deals with the dynamical analysis of a vessel that leads to capsize in regular beam seas. The complete investigation of nonlinear behaviors includes sub-harmonic motion, bifurcation, and chaos under variations of control parameters. The vessel rolling motions can exhibit various undesirable nonlinear phenomena. We have employed a linear-plus-cubic type damping term (LPCD) in a nonlinear rolling equation. Using the fourth order Runge-Kutta algorithm with the phase portraits, various dynamical behaviors (limit cycles, bifurcations, and chaos) are presented in beam seas. On increasing the value of control parameter ${\Omega}$, chaotic behavior interspersed with intermittent periodic windows are clearly observed in the numerical simulations. The chaotic region is widely spread according to system parameter ${\Omega}$ in the range of 0.1 to 0.9. When the value of the control parameter is increased beyond the chaotic region, periodic solutions are dominant in the range of frequency ratio ${\Omega}=1.01{\sim}1.6$. In addition, one more important feature is that different types of stable harmonic motions such as periodicity of 2T, 3T, 4T and 5T exist in the range of ${\Omega}=0.34{\sim}0.83$.

• The Pure and Applied Mathematics
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• v.10 no.4
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• pp.273-277
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• 2003

The Fuglede-Putnam Theorem is that if A and B are normal operators and X is an operator such that AX = XB, then $A^{\ast}= X. In this paper, we show that if A is $\omega$-hyponormal and $B^{\ast}$ is invertible $\omega$-hyponormal such that AX = XB for a Hilbert-Schmidt operator X, then $A^{\ast}X = XB^{\ast}$.

• Journal of the Chungcheong Mathematical Society
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• v.19 no.3
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• pp.213-218
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• 2006

The 2D g-Navier-Stokes equations are a certain modified Navier-Stokes equations and have the following form, $$\frac{{\partial}u}{{\partial}t}-{\nu}{\Delta}u+(u{\cdot}{\nabla})u+{\nabla}p=f$$, in ${\Omega}$ with the continuity equation ${\nabla}{\cdot}(gu)=0$, in ${\Omega}$, where g is a suitable smooth real valued function. In this paper, we will derive 2D g-Navier-Stokes equations from 3D Navier-Stokes equations. In addition, we will see the relationship between two equations.

• Bulletin of the Korean Mathematical Society
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• v.34 no.4
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• pp.583-593
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• 1997

We have derived a simple ODE system for the mush by assuming that the temperature T, the solid fraction $\phi$ and the vertical component $\omega$ of the velocity, depend on z only. Analytical solutions of the system have presentd in case of $\omega << 1 and \phi << 1$.

• Bulletin of the Korean Mathematical Society
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• v.51 no.1
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• pp.189-206
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• 2014

In this paper, we prove the global existence and uniqueness of the dissipative Kirchhoff equation $$u_{tt}-M({\parallel}{\nabla}u{\parallel}^2){\triangle}u+{\alpha}u_t+f(u)=0\;in\;{\Omega}{\times}[0,{\infty}),\\u(x,t)=0\;on\;{\Gamma}_1{\times}[0,{\infty}),\\{\frac{{\partial}u}{\partial{\nu}}}+g(u_t)=0\;on\;{\Gamma}_0{\times}[0,{\infty}),\\u(x,0)=u_0,u_t(x,0)=u_1\;in\;{\Omega}$$ with nonlinear boundary damping by Galerkin approximation benefited from the ideas of Zhang et al. [33]. Furthermore,we overcome some difficulties due to the presence of nonlinear terms $M({\parallel}{\nabla}u{\parallel}^2)$ and $g(u_t)$ by introducing a new variables and we can transform the boundary value problem into an equivalent one with zero initial data by argument of compacity and monotonicity.