• Bulletin of the Korean Mathematical Society
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• v.52 no.2
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• pp.661-677
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• 2015

In this paper, we consider the following Kirchhoff-type Schr$\ddot{o}$dinger system $$\{-\(a_1+b_1{\int}_{\mathbb{R^3}}{\mid}{\nabla}u{\mid}^2dx\){\Delta}u+{\gamma}V(x)u=\frac{2{\alpha}}{{\alpha}+{\beta}}{\mid}u{\mid}^{\alpha-2}u{\mid}v{\mid}^{\beta}\;in\;\mathbb{R}^3,\\-\(a_2+b_2{\int}_{\mathbb{R^3}}{\mid}{\nabla}v{\mid}^2dx\){\Delta}v+{\gamma}W(x)v=\frac{2{\beta}}{{\alpha}+{\beta}}{\mid}u{\mid}^{\alpha}{\mid}v{\mid}^{\beta-2}v\;in\;\mathbb{R}^3,\\u,v{\in}H^1(\mathbb{R}^3),$$ where $a_i$ and $b_i$ are positive constants for i = 1, 2, ${\gamma}$ > 0 is a parameter, V (x) and W(x) are nonnegative continuous potential functions. By applying the Nehari manifold method and the concentration-compactness principle, we obtain the existence and concentration of ground state solutions when the parameter ${\gamma}$ is sufficiently large.

• Bulletin of the Korean Mathematical Society
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• v.49 no.6
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• pp.1311-1326
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• 2012

We are concerned with the multiplicity of semiclassical solutions of the following Schr$\ddot{o}$dinger system involving critical nonlinearity and magnetic fields $$\{-({\varepsilon}{\nabla}+iA(x))^2u+V(x)u=H_u(u,v)+K(x)|u|^{2*-2}u,\;x{\in}\mathbb{R}^N,\\-({\varepsilon}{\nabla}+iB(x))^2v+V(x)v=H_v(u,v)+K(x)|v|^{2*-2}v,\;x{\in}\mathbb{R}^N,$$ where $2^*=2N/(N-2)$ is the Sobolev critical exponent and $i$ is the imaginary unit. Under proper conditions, we prove the existence and multiplicity of the nontrivial solutions to the perturbed system.

• Journal of the Korean Mathematical Society
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• v.47 no.3
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• pp.547-572
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• 2010

We study existence of positive solutions of the classical nonlinear Schr$\ddot{o}$dinger equation $-{\Delta}u\;+\;V(x)u\;-\;f(x,\;u)\;-\;H(x)u^{2*-1}\;=\;0$, u > 0 in $\mathbb{R}^n$ $u\;{\rightarrow}\;0\;as\;|x|\;{\rightarrow}\;{\infty}$. In fact, we consider the following more general quasi-linear Schr$\ddot{o}$odinger equation $-div(|{\nabla}u|^{m-2}{\nabla}u)\;+\;V(x)u^{m-1}$ $-f(x,\;u)\;-\;H(x)u^{m^*-1}\;=\;0$, u > 0 in $\mathbb{R}^n$ $u\;{\rightarrow}\;0\;as\;|x|\;{\rightarrow}\;{\infty}$, where m $\in$ (1, n) is a positive number and $m^*\;:=\;\frac{mn}{n-m}\;>\;0$, is the corresponding critical Sobolev embedding number in $\mathbb{R}^n$. Under appropriate conditions on the functions V(x), f(x, u) and H(x), existence and non-existence results of positive solutions have been established.

• Honam Mathematical Journal
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• v.1 no.1
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• pp.21-25
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• 1979

Abelian군(群)의 presheaf에 관한 직적(直積)과 직화(直和)를 Category 입장에서 정의(定義)하고 presheaf $F_{\lambda}\;({\lambda}{\epsilon}{\Lambda})$들의 두 직적(直積)(또는 直和)은 서로 동형적(同型的) 관계(關係)에 있으며, 특히 ${\phi}:X{\rightarrow}Y$가 homeomorphism이라 하고 ${\phi}_*F$를 X상(上)의 presheaf F의 direct image이라 하면 (1) $({\phi}_*F, \;{\phi}_*(f_{\lambda})_{{\lambda}{\epsilon}{\Lambda}})$가 $({\phi}_*F_{\lambda})_{{\lambda}{\epsilon}{\Lambda}}$의 직적(直積)일 때 오직 그때 한하여 $(F,\;(f_{\lambda})_{{\lambda}{\epsilon}{\Lambda}})$는 $(F_{\lambda})_{{\lambda}{\epsilon}{\Lambda}})$의 직적(直積)이다. (2) $({\phi}_*F,\;{\phi}_*(l_{\lambda})_{{\lambda}{\epsilon}{\Lambda}})$가 $({\phi}_*F_{\lambda})_{{\lambda}{\epsilon}{\Lambda}}$의 직화(直和)일 때 오직 그때 한하여 $(F,\;(l_{\lambda})_{{\lambda}{\epsilon}{\Lambda}})$는 $(F_{\lambda})_{{\lambda}{\epsilon}{\Lambda}})$의 직화(直和)이다. Let $(F_{\lambda})_{{\lambda}{\epsilon}{\Lambda}})$ be an indexed set of presheaves of abelian group on topological space X. We can define the cartesian product $$\prod_{{\lambda}{\epsilon}{\Lambda}}\;F_{\lambda}$$ of $(F_{\lambda})_{{\lambda}{\epsilon}{\Lambda}})$ by $$(\prod_{{\lambda}{\epsilon}{\Lambda}}\;F_{\lambda})(U)=\prod_{{\lambda}{\epsilon}{\Lambda}}(F_{\lambda}(U))$$ for U open in X $${\rho}_v^u:\;(\prod_{{\lambda}{\epsilon}{\Lambda}}\;F_{\lambda})(U){\rightarrow}(\prod_{{\lambda}{\epsilon}{\Lambda}}\;F_{\lambda})(V)((s_{\lambda})_{{\lambda}{\epsilon}{\Lambda}}{\rightarrow}(_{\lambda}{\rho}_v^u(s_{\lambda}))_{{\lambda}{\epsilon}{\Lambda}})$$ for $V{\subseteq}U$ open in X where $_{\lambda}{\rho}^U_V$ is a restriction of $F_{\lambda}$, And we have natural presheaf morphisms ${\pi}_{\lambda}$ and ${\iota}_{\lambda}$ such that ${\pi}_{\lambda}(U):\;({\prod}_\;F_{\lambda})(U){\rightarrow}F_{\lambda}(U)((s_{\lambda})_{{\lambda}{\epsilon}{\Lambda}}{\rightarrow}s_{\lambda})$ ${\iota}_{\lambda}(U):\;F_{\lambda}(U){\rightarrow}({\prod}\;F_{\lambda})(U)(s_{\lambda}{\rightarrow}(o,o,{\cdots}\;{\cdots}o,s_{\lambda},o,{\cdots}\;{\cdots}o)$ for $(s_{\lambda}){\epsilon}{\prod}_{\lambda}\;F_{\lambda}(U)$ and $(s_{\lambda}){\epsilon}F_{\lambda}(U)$.

• Phonetics and Speech Sciences
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• v.2 no.3
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• pp.23-27
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• 2010

The purpose of this study was to find how English vowels /a, e, i, o, u/ affect the production of English labials /p, b, f, v/ by Korean learners of English. Sixty syllables were composed by five vowels and four labials in the syllable types CV, VC, and VCV. The nonsense syllables were produced three times by nine subjects. The major results show that (1) in inter-vocalic position, the subjects had higher scores in producing /v/ composed with /a, e, o/ and /u/, while subjects had lower scores in producing /p/ with /i/ and /o/, (2) in post-vocalic position, the subjects had higher scores in producing /v/ and /f/ with /a, e/, and /o/, while subjects had lower scores in producing /b/ with /e/ and /i/, and (3) in pre-vocalic position, the subjects had higher scores in producing /v/ with /e, o, u/ and /f/ with /u/, while subjects had lower scores in producing /b/ with /e/, /i/ and /u/. The results suggest that on the whole, Korean learners of English have much difficulty in producing /p/ with /i/ in inter-vocalic condition and /b/ with /i, /e/ in pre-vocalic position.

• Journal of Plant Biology
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• v.29 no.1
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• pp.53-65
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• 1986

The montane forests of Ulreung Island, Korea, were investigated by the ZM school method. By comparing the montane forests of this island with those of Korean Peninsula and of Japan, a new order, F a g e t a l i a m u l t i n e r v i s, a new alliance, F a l g i o n m u l t i n e r v i s, a new association, H e p a t i c o-F a g e t u m m u l t i n e r v i s and Rhododendron brachycarpum-Pinus parviflora community were recognized. The H e p a t i c o - F a g e t u m m u l t i n e r v i s was further subdivided into four subassociations; Subass. of Sasa kurilensis, Subass. of Rumohra standishii, Subass. of Rhododendron brachycarpum and Subass. of typicum. Each community was described in terms of floristic, structural and environmental features.

• Bulletin of the Korean Mathematical Society
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• v.53 no.6
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• pp.1753-1769
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• 2016

This paper is concerned with the quasilinear $Schr{\ddot{o}}dinger$ system $$(0.1)\;\{-{\Delta}u+a(x)u-{\Delta}(u^2)u=Fu(u,v)+h(x)\;x{\in}{\mathbb{R}}^N,\\-{\Delta}v+b(x)v-{\Delta}(v^2)v=Fv(u,v)+g(x)\;x{\in}{\mathbb{R}}^N,$$ where $N{\geq}3$. The potential functions $a(x),b(x){\in}L^{\infty}({\mathbb{R}}^N)$ are bounded in ${\mathbb{R}}^N$. By using mountain pass theorem and the Ekeland variational principle, we prove that there are at least two solutions to system (0.1).

• Phonetics and Speech Sciences
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• v.5 no.2
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• pp.33-41
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• 2013

This is a follow-up study on Han and Kang (2013) which argued that the Euclidean distances between /o/ and /u/ in Seoul Korean decreased in the first syllable position as speakers were among younger female speakers but not for male speakers, whereas in the second syllable position both gender groups showed a cross-generational decreasing effect of the Euclidean distance between /o/ and /u/. This study normalized the same data in Han and Kang (2013) which measured 12 speakers (six males and six females) for each Age group and investigated the spectral changes vowels /o/ and /u/ between age and gender, using the log-mean normalized statistical results. This study also examined overlap fraction values generated in SOAM 2D ($F1{\times}F2$) (cf. Wassink, 2006), which may also indicate the proximity of two vowels in question. The results showed that /o/ and /u/ vowels were making closer with /o/ raising for female speakers in $V_1$ and $V_2$ positions but only in the $V_2$ position for male speakers. That is, females led the upward movement of peripheral /o/ vowel, just like the raising of 'e' and 'o' in New York City (Labov, 1991). The results also showed that younger speakers used a rather narrow vowel space for the vowels. This also contributed to the proximity of the vowels /o/ and /u/, resulting in rather large overlap fraction values for younger speakers between these two vowels.

• Koreanishche Zeitschrift fur Deutsche Sprachwissenschaft
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• v.1
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• pp.69-90
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• 1999

Die vorliegende Arbeit setzte sich zum Ziel, deutsche verbale Phraseolexeme(vPL) auf der Grundlage einer Mehrebenenbeschreibung syntaktisch sowie semantisch zu untersuchen. Dabei $st\"{u}tzten$ wir uns vor allem auf die Valenz- und Kasustheorie sowie das 6-Stufen-Modell von G. Helbig(1983) und das Mehrebenenmodell $f\"{u}r$ vPL von B. Wotjak(1992), das seinerseits vom methodischen Ansatz her in engem Zusammenhang zu dem Beschreibungsansatz steht. Aber Wir modifizierten teilweise das Modell yon B. Wotjak(1992) und stellten einige vPL exemplarisch dar. Dieser Untersuchung lag eine verbozentrische Auffassung des Satzes zugrunde: Das Verb bildet das organisierende Zentrum des Satzes und ist fur die Grundstruktur des Satzes verantwortlich. Das Verb als $Valenztr\"{a}ger\;er\"{o}ffnet$ um sich herum bestimmte Leerstellen, deren Zahl und Art letztlich von der Verbbedeutung her determiniert sind. Auch vPL kann als $Valenztr\"{a}ger$ - wie das Verb - das strukturelle Zentrum des Satzes darstellen, d.h. vPL bildet als Ganzes das $Pr\"{a}dikat$, das wendungsextern eine bestimmte Zahl von Leerstellen $er\"{o}ffnet$ und determiniert im Satz mit seinen $inh\"{a}renten$ semantischen Merkmalen seine semantische und syntaktische Umgebung. Bei der Analyse von vPL gingen wir von der Auffassung von B. Wotjak aus, $da\ss$ Modelle zur Beschreibung von Verben prinzipiell auch auf die Beschreibung von verbalen PL anwendbar sind. In dieser Untersuchung verwendeten wir - in Anlehnung an B. Wotjak(1996:4f.) - den Terminus 'Phraseologismus' als Oberbegriff, der a) Kollokationen, $b)\;Funktionsverbgef\"{u}ge\;(FVG)$, c) Wortidiome (wortwertige idiomatische Redewendungen oder Phraseolexeme), d) Satzidiome(satzwertige idiomatische Redewendungen bzw. kommunikative Formeln/ Routineformeln), e) $Sprichw\"{o}rter\;umfa{\ss}t$. Wir $beschr\"{a}nkten$ uns den Gegenstand unserer Untersuchung auf verbale Phraseolexeme(vPL), d.h. wie oben genannte Wortidiome. VPL lassen sich $prim\"{a}r$ in bezug auf das wendungsexterne ($\"{a}u{\ss}ere$) Aktantenpotential(PLe) und $sekund\"{a}r$ in bezug auf die interne Kom­ponentenstruktur des PL(PLi) klassifizieren. Unsere Studie soil nicht nur Hintergrundwissen $f\"{u}r$ Lexikonein­tragungen vertiefen helfen, sondern auch $f\"{u}r$ den Fremdsprachen­unterricht von Nutzen sein.

• Proceedings of the Korean Ceranic Society Conference
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• 2000.10a
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• pp.80.2-80
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• 2000