• Communications of the Korean Mathematical Society
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• v.22 no.3
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• pp.353-357
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• 2007

Let $(g,\;\delta)$ be a Lie bialgebra. Here we give an explicit formula for the Poisson bracket on a subalgebra of $U(g)^{\circ}$ induced by the given cobracket $\delta$.

• East Asian mathematical journal
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• v.24 no.2
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• pp.201-212
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• 2008

We characterize operators between Banach spaces sending unconditionally weakly p-summable sequences into sequences that lie in the range of a vector measure of bounded variation. Further, we describe operators between Banach spaces taking unconditionally weakly p-summable sequences into sequences that lie in the range of a vector measure.

• Journal of the Chungcheong Mathematical Society
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• v.6 no.1
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• pp.105-111
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• 1993

In this paper we show that if a semi-restricted Lie algebra L has an one dimensional toral Cartan subalgebra, then L is simple and $L\simeq_-sl(2)$ or $W(1:\underline{1})$. And we study that if L is simple but not simple and H is 2-dimensional, then H is a torus.

• Bulletin of the Korean Mathematical Society
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• v.34 no.4
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• pp.519-524
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• 1997

We extent the notion of equivalent relation $\approx$ for Kac-Moody algebras to generalized Kac-Moody algebras and prove some analogues of results for Kac-Moody algebras.

• Korean Journal of Mathematics
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• v.14 no.2
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• pp.273-280
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• 2006

Lipschitzian semigroup is a semigroup of Lipschitz operators which contains $C_0$ semigroup and nonlinear semigroup. In this paper, we establish the cannonical exponential formula of Lipschitzian semigroup from its Lie generator and the approximation theorem by Laplace transform approach to Lipschitzian semigroup.

• Kyungpook Mathematical Journal
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• v.48 no.2
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• pp.223-232
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• 2008

We estimate the real rank of CCR C*-algebras under some assumptions. A applications we determine the real rank of the reduced group C*-algebras of non-compac connected, semi-simple and reductive Lie groups and that of the group C*-algebras of connected nilpotent Lie groups.

• Communications of the Korean Mathematical Society
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• v.34 no.4
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• pp.1079-1098
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• 2019

In this paper we give some branching rules for the fundamental representations of Kac-Moody Lie algebras associated to T-shaped graphs. These formulas are useful to describe generators of the generic rings for free resolutions of length three described in [7]. We also make some conjectures about the generic rings.

• Bulletin of the Korean Chemical Society
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• v.11 no.4
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• pp.332-333
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• 1990

The most general algebraic Hamiltonian for vibron model of diatomic molecules is obtained by using the theorems on the Jordan Schwinger representations of Lie groups.

• Journal of Environmental Health Sciences
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• v.17 no.2
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• pp.67-77
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• 1991

The purpose of this study was to investigate the psychosomatic health status of printers. The 77 printers and 24 control group were analysed about salary, drinking, smoking, education, sex, marriage, age and working age by the THI (Todai Health Index) questionaire. THI was modified from CMI(Cornell Medical Index) and developed by Tokyo University Research Team in Japan. The resuts obtained were summarized as follows. 1. The printers, who get more salary showed high score about mental conplaints, especially, mental irritability(j), nervusness (E), lie Scale(L), aggressiveness(F) and irregualr life(G) and lower salary showed generally high score about physical complaints, especially, mouth and anus (D), digestive symptom(C) multiple subjective symptom(I). 2. According to the printers drinking amount shows the difference, eg nondrinker scored higher on mouth and anus(D), 90mg/week drinker scored higher on multiple subjective symptom(I), digestive symptom(C), depression(K), nervousness(E), and irregular life(G), 91~179mg/week drinker scored higher on impulsiveness(H), mental irritability(J), 270~359mg/week drinker scored higher on respiratory(A), lie scale (L) and aggressiveness (F). 3. The nonsmoker scored high level on mouth and anus(D), mental irritability(J). The previous smoker scored on multiple symptom(I), eyes and skin(B), digestive(C), lie scale(L), and depression(K). The present smoker scored on respiratory(A), impulsivehess(H), aggressiveness(F), nervousness(E), and irregular life(G). 4. According to the printers working age showed almost high score about subjective symptoms on 1~3 year. 5. Men printers high scored on respiratory(A). lie scale(L), aggressiveness(F), women printers scored about mental complaints, especially, impulsiveness(H), mental irritability(J), depression (K), nervousness (E). 6. According to the printers age showed high scored about, below 20 years were lie scale(L). aggressiveness(F), irregular life(G) 21~30years were multiple subjective symptom(I) respiratory (A), eyes and skin(B), mouth and anus(D), impulsiveness(H), mental irritability(J), depression (K), nervousness(E), and over 41 years were digestive(C). 7. Married printers scored high level on eyes and skin(B), digestive(C) and impulsivehess(H), and single printers on respiratory(A), mouth and anus(D), lie scale(L), mental irritability(J). 8. According to education shows the difference, eg high school scored higher on eyes and skin (B), mental irritability(J), depression(K), nervousness(E), collage and over scored higher on multiple subjective symptom(I ), respiratory (A), mouth and anus (D), lie scale (L), aggressiveness (F), irregular life (G), and middle school scored high on digestive (C), impulsiveness (H).

• East Asian mathematical journal
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• v.22 no.2
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• pp.249-257
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• 2006

Let n be a 2-step nilpotent Lie algebra which has an inner product <,> and has an orthogonal decomposition $n=\delta{\oplus}\varsigma$ for its center $\delta$ and the orthogonal complement $\varsigma\;of\;\delta$. Then Each element Z of $\delta$ defines a skew symmetric linear map $J_Z:\varsigma{\rightarrow}\varsigma$ given by $=$ for all $X,\;Y{\in}\varsigma$. Let $\gamma$ be a unit speed geodesic in a 2-step nilpotent Lie group H(2, 1) with its Lie algebra n(2, 1) and let its initial velocity ${\gamma}$(0) be given by ${\gamma}(0)=Z_0+X_0{\in}\delta{\oplus}\varsigma=n(2,\;1)$ with its center component $Z_0$ nonzero. Then we showed that $\gamma(0)$ is conjugate to $\gamma(\frac{2n{\pi}}{\theta})$, where n is a nonzero intger and $-{\theta}^2$ is a nonzero eigenvalue of $J^2_{Z_0}$, along $\gamma$ if and only if either $X_0$ is an eigenvector of $J^2_{Z_0}$ or $adX_0:\varsigma{\rightarrow}\delta$ is not surjective.