• 대한수학회지
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• 제55권3호
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• pp.735-747
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• 2018

Let M be a real hypersurface of a complex space form with constant curvature c. In this paper, we study the hypersurface M admitting Miao-Tam critical metric, i.e., the induced metric g on M satisfies the equation: $-({\Delta}_g{\lambda})g+{\nabla}^2_g{\lambda}-{\lambda}Ric=g$, where ${\lambda}$ is a smooth function on M. At first, for the case where M is Hopf, c = 0 and $c{\neq}0$ are considered respectively. For the non-Hopf case, we prove that the ruled real hypersurfaces of non-flat complex space forms do not admit Miao-Tam critical metrics. Finally, it is proved that a compact hypersurface of a complex Euclidean space admitting Miao-Tam critical metric with ${\lambda}$ > 0 or ${\lambda}$ < 0 is a sphere and a compact hypersurface of a non-flat complex space form does not exist such a critical metric.

• 대한수학회보
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• 제46권6호
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• pp.1159-1173
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• 2009

This paper deals with the critical blow-up and extinction exponents for the non-Newton polytropic filtration equation. We reveals a fact that the equation admits two critical exponents $q_1,\;q_2\;{\in}\;(0,+{\infty})$) with $q_1\;{<}\;q_2$. In other words, when q belongs to different intervals (0, $q_1),\;(q_1,\;q_2),\;(q_2,+{\infty}$), the solution possesses complete different properties. More precisely speaking, as far as the blow-up exponent is concerned, the global existence case consists of the interval (0, $q_2$]. However, when q ${\in}\;(q_2,+{\infty}$), there exist both global solutions and blow-up solutions. As for the extinction exponent, the extinction case happens to the interval ($q_1,+{\infty}$), while for q ${\in}\;(0,\;q_1$), there exists a non-extinction bounded solution for any nonnegative initial datum. Moreover, when the critical case q = $q_1$ is concerned, the other parameter ${\lambda}$ will play an important role. In other words, when $\lambda$ belongs to different interval (0, ${\lambda}_1$) or (${\lambda}_1$,+${\infty}$), where ${\lambda}_1$ is the first eigenvalue of p-Laplacian equation with zero boundary value condition, the solution has completely different properties.

• Korean Journal of Mathematics
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• 제14권2호
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• pp.259-271
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• 2006

We consider a semilinear elliptic boundary value problem with Dirichlet boundary condition $Au+bu^+-au^-=t_{1{\phi}1}+t_{2{\phi}2}$ in ${\Omega}$ and ${\phi}_n$ is the eigenfuction corresponding to ${\lambda}_n(n=1,2,{\cdots})$. We have a concern with the multiplicity of solutions of the equation when ${\lambda}_1$ < a < ${\lambda}_2$ < b < ${\lambda}_3$.

• 대한수학회보
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• 제47권1호
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• pp.167-178
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• 2010

We discuss the critical points of the functional $F_{\lambda,\mu}(J,g)=\int_M(\lambda\tau+\mu\tau^*)d\upsilon_g$ on the spaces of all almost Hermitian structures AH(M) with $(\lambda,\mu){\in}R^2-(0,0)$, where $\tau$ and $\tau^*$ being the scalar curvature and the *-scalar curvature of (J, g), respectively. We shall give several characterizations of Kahler structure for some special classes of almost Hermitian manifolds, in terms of the critical points of the functionals $F_{\lambda,\mu}(J,g)$ on AH(M). Further, we provide the almost Hermitian analogy of the Hilbert's result.

• Journal of Advanced Marine Engineering and Technology
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• 제34권8호
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• pp.1057-1067
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• 2010

다단 기어연쇄, 베어링, 축, 로터로 구성되는 함포용 synchro system의 구동장치를 개발하기 위하여, AGMA규격에 의한 기어 굽힘강도, 면압강도해석, 기어치형설계를 포함한 정적설계를 수행하였다. 또한 전달행렬법을 효과적으로 적용시킬 수 있는 Hibner's branch법과 자유도가 큰 경우에도 계산 오차 없이 고유특성치를 빠뜨리지 않고 산출할 수 있는 ${\lambda}$-matrix법을 도입하여 함포용 Synchro system의 좌우 선회용과 상하 고각형의 위험속도 해석 및 평가를 하였고, 운전속도 범위 내에 위험속도가 존재하지 않았다.

• 대한수학회지
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• 제53권2호
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• pp.247-262
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• 2016

In this paper, we consider the following $Schr{\ddot{o}}dinger$-Poisson system: $$\{\begin{array}{lll}-{\Delta}u+u+{\lambda}{\phi}u={\mu}f(u)+{\mid}u{\mid}^{p-2}u,\;\text{ in }{\Omega},\\-{\Delta}{\phi}=u^2,\;\text{ in }{\Omega},\\{\phi}=u=0,\;\text{ on }{\partial}{\Omega},\end{array}$$ where ${\Omega}$ is a smooth and bounded domain in $\mathbb{R}^3$, $p{\in}(1,6]$, ${\lambda}$, ${\mu}$ are two parameters and $f:\mathbb{R}{\rightarrow}\mathbb{R}$ is a continuous function. Using some critical point theorems and truncation technique, we obtain three multiplicity results for such a problem with subcritical or critical growth.

• Progress in Superconductivity
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• 제8권2호
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• pp.132-137
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• 2007

We have studied superconducting parameters of $MgB_2$ single crystals from reversible magnetization measurements with the magnetic field both parallel and perpendicular to the c-axis of the crystals. The temperature dependence of the London penetration depth, ${\lambda}_{ab}{^{-2}}(T)$, obtained from the Hao-Clem analysis on reversible magnetization, shows a clear discrepancy from single-band theories. It is also found that the anisotropies of the London penetration depth, ${\gamma}_{\lambda}$, slowly increases with temperature while the anisotropy of the upper critical field, ${\gamma}_H$, decreases with temperature. These behaviors are in sharp contrast with the behavior of superconductors with a single band. The temperature dependence of ${\lambda}_{ab}{^{-2}}$, and the opposite temperature dependences of ${\gamma}_{\lambda}\;and\;{\gamma}_H$ can be well explained with the theory of the two-band superconductivity.

• 한국초전도ㆍ저온공학회논문지
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• 제16권4호
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• pp.26-30
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• 2014

We investigate the upper critical field anisotropy ${\Gamma}_H$ and the magnetic penetration depth anisotropy ${\Gamma}_{\lambda}$ of a high-quality $FeSe_{1-x}$ single crystal using angular dependent resistivity and torque magnetometry up to 14 T. High quality single crystals of $FeSe_{1-x}$ were successfully grown using $KCl-AlCl_3$ flux method, which shows a sharp superconducting transition at $T_C{\sim}9K$ and a high residual resistivity ratio of ~ 25. We found that the anisotropy ${\Gamma}_H$ near $T_C$ is a factor of two larger than found in the poor-quality crystals, indicating anisotropic 3D superconductivity of $FeSe_{1-x}$. Similar to the 1111-type Fe pnictides, the anisotropies ${\Gamma}_{\lambda}$ and ${\Gamma}_H$ show distinct temperature dependence; ${\Gamma}_H$ decreases but ${\Gamma}_{\lambda}$ increases with lowering temperature. These behaviors can be attributed to multi-band superconductivity, but different from the case of $MgB_2$. Our findings suggest that the opposite temperature dependence of ${\Gamma}_{\lambda}$ and ${\Gamma}_H$ is the common properties of Fe-based superconductors.

• 대한수학회지
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• 제61권1호
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• pp.133-147
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• 2024

Let G = (V, E) be a connected finite graph. We study the existence of solutions for the following generalized Chern-Simons equation on G $${\Delta}u={\lambda}e^u(e^u-1)^5+4{\pi}\sum_{s=1}^{N}\delta_{ps}$$, where λ > 0, δ_ps is the Dirac mass at the vertex p_s, and p₁, p₂, . . . , p_N are arbitrarily chosen distinct vertices on the graph. We show that there exists a critical value $\hat{\lambda}$ such that when λ > $\hat{\lambda}$, the generalized Chern-Simons equation has at least two solutions, when λ = $\hat{\lambda}$, the generalized Chern-Simons equation has a solution, and when λ < $\hat{\lambda}$, the generalized Chern-Simons equation has no solution.

• 대한수학회보
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• 제53권6호
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• pp.1805-1821
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• 2016

In this paper, we are concerned with the nonlinear elliptic equations of the p(x)-Laplace type $$\{\begin{array}{lll}-div(a(x,{\nabla}u))+{\mid}u{\mid}^{p(x)-2}u={\lambda}f(x,u) && in\;{\Omega}\\(a(x,{\nabla}u)\frac{{\partial}u}{{\partial}n}={\lambda}{\theta}g(x,u) && on\;{\partial}{\Omega},\end{array}$$ which is subject to nonlinear Neumann boundary condition. Here the function a(x, v) is of type${\mid}v{\mid}^{p(x)-2}v$ with continuous function $p:{\bar{\Omega}}{\rightarrow}(1,{\infty})$ and the functions f, g satisfy a $Carath{\acute{e}}odory$ condition. The main purpose of this paper is to establish the existence of at least three solutions for the above problem by applying three critical points theory due to Ricceri. Furthermore, we localize three critical points interval for the given problem as applications of the theorem introduced by Arcoya and Carmona.