• Journal of the Chungcheong Mathematical Society
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• v.19 no.2
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• pp.207-211
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• 2006

We prove the Riesz theorem in linear n-normed spaces.

• Bulletin of the Korean Mathematical Society
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• v.54 no.6
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• pp.2001-2011
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• 2017

In 1997, H. Li [12] proposed a conjecture: if $M^n(n{\geqslant}3)$ is a complete spacelike hypersurface in de Sitter space $S^{n+1}_1(1)$ with constant normalized scalar curvature R satisfying $\frac{n-2}{n}{\leqslant}R{\leqslant}1$, then is $M^n$ totally umbilical? Recently, F. E. C. Camargo et al. ([5]) partially proved the conjecture. In this paper, from a different viewpoint, we study closed convex spacelike hypersurface $M^n$ in locally symmetric Lorentz space $L^{n+1}_1$ and also prove that $M^n$ is totally umbilical if the square of length of second fundamental form of the closed convex spacelike hypersurface $M^n$ is constant, i.e., Theorem 1. On the other hand, we obtain that if the sectional curvature of the closed convex spacelike hypersurface $M^n$ in locally symmetric Lorentz space $L^{n+1}_1$ satisfies $K(M^n)$ > 0, then $M^n$ is totally umbilical, i.e., Theorem 2.

• Journal of the Korean Mathematical Society
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• v.43 no.1
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• pp.99-109
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• 2006

Approximate fibrations form a useful class of maps. By definition fibrators provide instant detection of maps in this class, and PL fibrators do the same in the PL category. We show that every closed s-hopfian t-aspherical manifold N with sparsely Abelian, hopfian fundamental group and X(N) $\neq$ 0 is a codimension-(t + 1) PL fibrator.

• Proceedings of the Korean Institute of Surface Engineering Conference
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• 2012.05a
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• pp.167-168
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• 2012

Films of CrN, $Cr_{40}Zr_9N$, and $Cr_{31}Zr_{16}N$ were deposited on a steel substrate by closed field unbalanced magnetron sputtering, and their oxidation behaviors at $700^{\circ}C$ and $800^{\circ}C$ for up to 60h in air were investigated. All the deposited films were composed of the CrN phase. Zirconium atoms in $Cr_{40}Zr_9N$ and $Cr_{31}Zr_{16}N$ films partially dissolved in the CrN phase. They advantageously refined the columnar structure, reduced the surface roughness, and increased the microhardness. The CrN film displayed relatively good oxidation resistance, owing to the formation of the highly protective $Cr_2O_3$ on its surface. The $Cr_{40}Zr_9N$ and $Cr_{31}Zr_{16}N$ films oxidized to $Cr_2O_3$ as the major phase and ${\alpha}-ZrO_2$ as the minor one. They oxidized primarily by the inward transport of oxygen. The addition of Zr could not increase the oxidation resistance of the CrN film, because the formed $ZrO_2$ that was intermixed in the $Cr_2O_3$-rich oxide layer was oxygen permeable, and developed the compressive stress in the oxide scale owing to the volume expansion during its formation.

• Journal of Korean Society of Forest Science
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• v.102 no.3
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• pp.315-322
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• 2013

This study was carried out to establish a management program and soil restoration plan through analysis of soil properties and visitor questionnaires in Songrim in Hadong, Korea. Soil bulk density in Songrim was slightly higher in the closed-woodlands ($1.31g/cm^3$) than in the open-woodlands ($1.39g/cm^3$). Soil bulk density in the closed-woodlands was higher in walking trails ($1.74g/cm^3$) than in forest areas ($1.39g/cm^3$), while the rates of pore space were lower in walking trails (42.6%) than in forest areas (50.5%). The soil porosity were lower in the closed-woodlands (34.6%) than in the open-woodlands (42.6%). Soil strength in surface soil was slightly lower in the open-woodlands ($8.5kgf/cm^2$) than in the closed-woodlands ($10.5kgf/cm^2$). The content of organic matter, total nitrogen and exchangeable cations of the woodlands was low compared with the optimum nutrient content for tree growth in Korea forest soil. According to the survey, the objective of visiting in Songrim was to enjoy recreation and landscape views. To conserve pine forest ecosystems in Songrim, the respondents said that it needs to the implement of closed-woodland periods, the establishment of smoking free zone, and the prohibition of garbage throwing and alcohol including disciplinary rules and education. Also the respondents said that pine forest ecosystem in Songrim is relatively sound, but the woodlands require the intensive management to the ecosystem and the introduction of native understory vegetation, such as grasses under pine forest ecosystem. It is recommended to designate the rest-year forest for a proper period in all woodlands to restore the Songrim soil rather than the alternation application between the rest-year for three years or non-rest-year trails, and to open partially the walking trails across the woodlands after the period. In addition, the forest within the woodland is need to designate a long-term rest-year.