• Communications of the Korean Mathematical Society
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• v.20 no.3
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• pp.443-456
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• 2005

Let G be a Lie group, let L(G) be its Lie algebra, and let exp : $L(G){\rightarrow}G$ denote the exponential mapping. For $S{\subseteq}G$, we define the tangent set of S by $L(S)\;=\;\{X\;{\in}\;L(G)\;:\;exp(tX)\;\in\;S\;for\;all\;t\;{\geq}\;0\}$. We say that a semigroup S is strictly infinitesimally generated if S is the same as the semigroup generated by exp(L(S)). We find a tangent set of the semigroup of all non-singular totally positive matrices and show that the semigroup is strictly infinitesimally generated by the tangent set of the semigroup. This generalizes the familiar relationships between connected Lie subgroups of G and their Lie algebras

• Communications of the Korean Mathematical Society
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• v.12 no.2
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• pp.269-273
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• 1997

We show that each element in the semigroup $S_n$ of all $n \times n$ non-singular stochastic totally positive matrices is generated by the infinitesimal elements of $S_n$, which form a cone consisting of all $n \times n$ Jacobi intensity matrices.

• Journal of Life Science
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• v.9 no.5
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• pp.581-589
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• 1999

This study was carried out to compare ozonation with photocatalysis degradation for removal Geosmin of algae byproduct. The change of pH was decresed from 7.02 to 2.8 after contact time 480 minute for ozonation. In case of UV-germicidal lamp, pH was very quickly increased from 7.02 to 7.5, but Halogen lamp did very slowly change pH. Geosmin degradation ratio was as following, UV-germicidal lamp/TiO2(100mg/L) O3>UV-germicidal lamp/TiO2(50mg/L)>UV-germicidal lamp(10W)>halogen lamp(50W). Instead of TiO2 suspension solution, Geosmin degradation ratio was very low using hollow bead and pellet as coated TiO2. As a result of identifing byproducts, ozonation generated three species of aldehyde such as 3-Heptanone and three species of alcohol such as Heptanal, but photocatalysis formed 1, 14-Tetradecanediol infinitesimally.