• 대한수학회지
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• 제54권3호
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• pp.1015-1030
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• 2017

This paper is concerned with the following Klein-Gordon-Maxwell system: $$\{-{\Delta}u+{\lambda}V(x)u-(2{\omega}+{\phi}){\phi}u=f(x,u),\;x{\in}\mathbb{R}^3,\\{\Delta}{\phi}=({\omega}+{\phi})u^2,\;x{\in}\mathbb{R}^3$$ where ${\omega}$ > 0 is a constant and ${\lambda}$ is the parameter. Under some suitable assumptions on V (x) and f(x, u), we establish the existence and multiplicity of nontrivial solutions of the above system via variational methods. Our conditions weaken the Ambrosetti Rabinowitz type condition.

• 대한수학회논문집
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• 제19권4호
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• pp.701-713
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• 2004

We obtain the Hyers-Ulam-Rassias stability of a betatype functional equation $f(\varphi(x),\phi(y))$ = $ \psi(x,y)f(x,y)+ \lambda(x,y)$ with a restricted domain and the stability in the sense of R. Ger of the equation $f(\varphi(x),\phi(y))$ = $ \psi(x,y)f(x,y)$ with a restricted domain in the following settings: $g(\varphi(x),\phi(y))-\psi(x,y)g(s,y)-\lambda(x,y)$\mid$\leq\varepsilon(x,y)$ and $\frac{g(\varphi(x),\phi(y))}{\psi(x,y),g(x,y)}-1 $\mid$ \leq\epsilon(x,y)$.

• 호남수학학술지
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• 제31권2호
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• pp.219-231
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• 2009

For a mapping satisfying the inequality ${\parallel}{\lambda}f(x)+2{\lambda}f(y)+2f({\lambda}z){\parallel}{\leq}{\parallel}2f({\lambda}({\frac{2}{x}}+y+z)){\parallel}+{\phi}(x,y,z)$, we will study the stability problem of this mapping.

• 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.

• 대한수학회보
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• 제23권2호
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• pp.117-121
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• 1986

Connes [2] showed that if M is an injective .sigma.-finite factor of type II $I_{1}$ and $B_{\phi}$=C1 for some normal faithful state .phi. on M then M is isomorphic to the Araki-wood factor. In [7], Haagerup has succeeded to show that if M is an injective factor of type II $I_{1}$ with separable predual, then $B_{\phi}$=C1 for every normal faithful state on M. Since injective factors of type II $I_{\lambda}$, 0.leq..lambda.<1, were classified [9], this together classifies all injective factors of type III with separable predual. It is not known for non-injective case. In this paper we consider some conditions under which the bicentralizers be trivial.ivial.

• Korean Journal of Mathematics
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• 제17권3호
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• pp.283-291
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• 2009

We investigate the existence of multiple solutions (${\xi},{\eta}$) for perturbations of the parabolic system with Dirichlet boundary condition $$(0.1)\;\begin{array}{lcr}{\xi}_t=-L{\xi}+g_1(3{\xi}+{\eta})-s{\phi}_1-h_1(x,t)\;in\;{\Omega}{\times}(0,\;2{\pi}),\\{\eta}_t=-L{\eta}+g_2(3{\xi}+{\eta})-s{\phi}_1-h_2(x,t)\;in\;{\Omega}{\times}(0,\;2{\pi}).\end{array}$$ We show the existence of multiple solutions (${\xi},{\eta}$) for perturbations of the parabolic system when the nonlinearity $g^{\prime}_1,\;g^{\prime}_2$ are bounded and $3g^{\prime}_1(-{\infty})+g^{\prime}_2(-{\infty})<{\lambda}_1,\;{\lambda}_n<3g^{\prime}_1(+{\infty})+g^{\prime}_2(+{\infty})<{\lambda}_{n+1}$.

• Korean Journal of Mathematics
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• 제16권4호
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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 $f^{\prime}(-{\infty})<{\lambda}_1,{\lambda}_n<(3{\mu}+{\nu})f^{\prime}(+{\infty})<{\lambda}_{n+1}$.

• 한국측량학회지
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• 제1권1호
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• pp.17-28
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• 1983

연세대학교천문대의 일산관측소와 조선시대의 천문대인 관천대의 경위도를 1982년 6월에 TMIA theodolite로 예비 관측하였다. 그 결과는 먼저, 일산관측소에 대해서는 $\phi=37^\circ{41}'19"(\pm{11")}N\;\lambda=126^\circ{46'36"(\pm{10")}E$ 이고, 관천대에 대해서는 $\phi=37^\circ{35'03"}(\pm{09")N}$이다. 이와같이 얻은 결과는 절대로 확정적인 것이라고 할 수 없고, 앞으로 이 방면의 일에 종사하는 전문가에 의한 수차의 재측정이 정밀한 기기를 사용하여 이루어질 때까지 기다려야 한다.정밀한 기기를 사용하여 이루어질 때까지 기다려야 한다.

• BMB Reports
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• 제40권5호
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• pp.740-748
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• 2007

To gain insight into the structure and function of repressor proteins of bacteriophages of gram-positive bacteria, repressor of temperate Staphylococcus aureus phage ${\phi}11$ was undertaken as a model system here and purified as an N-terminal histidine-tagged variant (His-CI) by affinity chromatography. A ~19 kDa protein copurified with intact His-CI (~ 30 kDa) at low level was resulted most possibly due to partial cleavage at its Ala-Gly site. At ~10 nM and higher concentrations, His-CI forms significant amount of dimers in solution. There are two repressor binding sites in ${\phi}11$ cI-cro intergenic region and binding to two sites occurs possibly by a cooperative manner. Two sites dissected by HincII digestion were designated operators $O_L$ and $O_R$, respectively. Equilibrium binding studies indicate that His-CI binds to $O_R$ with a little more strongly than $O_L$ and binding species is probably dimeric in nature. Interestingly His-CI binding affinity reduces drastically at elevated temperatures ($32-42^{\circ}C$). Both $O_L$ and $O_R$ harbor a nearly identical inverted repeat and studies show that ${\phi}11$ repressor binds to each repeat efficiently. Additional analyses indicate that ${\phi}11$ repressor, like $\lambda$ repressor, harbors an N-terminal domain and a C-terminal domain which are separated by a hinge region. Secondary structure of ${\phi}11$ CI even nearly resembles to that of $\lambda$ phage repressor though they differ at sequence level. The putative N-terminal HTH (helix-turn-helix) motif of ${\phi}11$ repressor belongs to the HTH -XRE-family of proteins and shows significant identity to the HTH motifs of some proteins of evolutionary distant organisms but not to HTH motifs of most S. aureus phage repressors.

• 한국터널지하공간학회 논문집
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• 제9권1호
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• pp.49-62
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• 2007

본 연구에서는 사질토 지반에 설치된 수직갱에 작용하는 토압에 대한 기존 제안식을 수정하였다. 이를 검증하기 위하여 깊이에 관계없이 동일한 반경방향 변위를 일으킬 수 있는 실내 모형시험장치를 개발하였으며, 벽면마찰각과 상대 밀도를 변수로 시험하였다. 실내 모형시험 결과는 수정식에서 접선방향 토압계수(수직응력에 대한 접선방향 응력 비)인 $\lambda$값을 $\lambda=1-sin\phi$와$\lambda=1$을 사용하였을 경우의 토압 사이에 분포하였다. 다층지반에 설치된 원형수직갱 배면지반의 파괴면을 가정하고 수정식을 적용하여 다층지반에 설치된 원형수직갱에 작용하는 토압 산정방법을 제안하였다. 시공현장의 3개의 수직갱으로부터 계측 데이터를 획득하였으며 이를 토압으로 환산하여 제안된 방법을 검증하였다. 계측 데이터로부터 환산된 대부분의 환산 토압은 제안된 방법의 토압과 잘 일치하였다.