• Journal of the Korean Mathematical Society
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• v.54 no.3
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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.

• Communications of the Korean Mathematical Society
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• v.19 no.4
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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)$.

• Honam Mathematical Journal
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• v.31 no.2
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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.

• Journal of the Korean Mathematical Society
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• v.53 no.2
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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.

• Bulletin of the Korean Mathematical Society
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• v.23 no.2
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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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• v.17 no.3
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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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• 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 $f^{\prime}(-{\infty})<{\lambda}_1,{\lambda}_n<(3{\mu}+{\nu})f^{\prime}(+{\infty})<{\lambda}_{n+1}$.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.1 no.1
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• pp.17-28
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• 1983

A preliminary determination of latitudes and longitudes of the Ilsan Station of Yonsei University Observatory and the Guancheon-Dae, an astronomical observatory in Yi Dynasty, has been made using TMIA theodolite in June, 1982. The results obtained are, respectively, $\phi=37^\circ{41}'19"(\pm{11")}N\;\lambda=126^\circ{46'36"(\pm{10")}E$ for the Ilson Station, and $\phi=37^\circ{35'03"}(\pm{09")N}$ for the Guancheon-Dae. It is, however, too early to make any conclusion on this determination, but should be awaited until repeated reinvestigations are made by those of this field of work utilizing the precise equipments.lizing the precise equipments.

• BMB Reports
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• v.40 no.5
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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.

• Journal of Korean Tunnelling and Underground Space Association
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• v.9 no.1
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• pp.49-62
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• 2007

A new earth pressure equation acting on the vertical shafts in cohesionless soils has been proposed by modifying the equations proposed by others. In order to verify the modified equation, model tests which can control uniform wall displacement with depth to radial direction were conducted. Model tests were performed with three different wall friction angles and two different relative densities. The measured values were larger than estimated values when assuming $\lambda=1$ ; smaller than those when assuming $\lambda=1-sin\phi$. The parameter, $\lambda$ is the ratio of tangential stress to vertical stress and is the most critical value in proposed equation. A method which can estimate the earth pressure on vertical shafts in layered soils is also proposed by reasonably assuming the failure surface of layered soils and using the modified equation. In order to verify the proposed method, in-situ measurement data have been collected from the three in-situ vertical shafts installed in layered soils. Most of earth pressures converted from measured data match reasonably well with estimated values using proposed method.