• Proceedings of the Korean Society of Precision Engineering Conference
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• 2003.10a
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• pp.220-220
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• 2003

• 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.

• The Pure and Applied Mathematics
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• v.9 no.1
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• pp.9-17
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• 2002

In this Paper, we will show that every basically disconnected space is a projective object in the category $Tych_{\sigma}$ of Tychonoff spaces and $_{\sigma}Z^{#}$ -irreducible maps and that if X is a space such that ${\Beta} {\Lambda} X={\Lambda} {\Beta} X$, then X has a projective cover in $Tych_{\sigma}$. Moreover, observing that for any weakly Linde1of space, ${\Lambda} X : {\Lambda} X\;{\longrightarrow}\;X$ is $_{\sigma}Z^{#}$-irreducible, we will show that the projective objects in $wLind_{\sigma}$/ of weakly Lindelof spaces and $_{\sigma}Z^{#}$-irreducible maps are precisely the basically disconnected spaces.

• Journal of the Korean Mathematical Society
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• v.57 no.5
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• pp.1119-1133
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• 2020

In this paper, we derive an upper bound for the distance from a point in the immediate basin of a root of a complex polynomial to the root itself. We establish that if z is a point in the immediate basin of a root α of a polynomial p of degree d ≥ 12, then ${\mid}z-{\alpha}{\mid}{\leq}{\frac{3}{\sqrt{d}}\(6{\sqrt{310}}/35\)^d{\mid}N_p(z)-z{\mid}$, where N_p is the Newton map induced by p. This bound leads to a new bound of the expected total number of iterations of Newton's method required to reach all roots of every polynomial p within a given precision, where p is normalized so that its roots are in the unit disk.

• Korean Journal of Microbiology
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• v.29 no.4
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• pp.215-220
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• 1991

MudJ(Km.lac) operon fusions were used in the identification of osmotic-inducible genetic(osi) loci in Salmonella typhimurium. Expression of osi::lacZ(osi5001, 5027) genes were dramatically induced 39-189 fold when the osmolarity was increased. Seven osm::lacZ genes were constituvely expressed under both low and high osmotic strength. The osi5001::lacZ fusion strains showed the enhanced osmotolerance and the reduced expression of the osi5001::lacZ in the presence of 1mM proline or betaine as osmoprotectants. Four osmotic inducible genetic loci were mapped into 36 (YK531), 44 (YK504), 57 (YK501) and 84 (YK528) map unit by testing the cotransduction frequency.

• Korean Journal of Mathematics
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• v.10 no.1
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• pp.45-51
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• 2002

Observing that a realcompactification Y of a space X is Wallman if and only if for any non-empty zero-set Z in Y, $Z{\cap}Y{\neq}{\emptyset}$, we will show that for any pseudo-Lindel$\ddot{o}$f space X, the minimal quasi-F $QF({\upsilon}X)$ of ${\upsilon}X$ is Wallman and that if X is weakly Lindel$\ddot{o}$, then $QF({\upsilon}X)={\upsilon}QF(X)$.

• Journal for History of Mathematics
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• v.15 no.2
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• pp.161-168
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• 2002

We show that if the Stone-Cech compactification of $\textit{AX}$ and the minimal basically disconnected cove. of $\beta$Χ we homeomorphic and every real $\sigma$$Z(X)^#$-ultrafilter on X has the countable intersection property, then there is a covering map from $\nu$(ΛΧ) to $\nu$Χ and every real $\sigma$$Z(X)^#$-ultrafilter on Χ has the countable intersection property if and only if there is a homeomorphism from the Hewitt realcompactification of ΛΧ to the minimal basically disconnected space of $\nu$Χ.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.3
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• pp.609-616
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• 2011

Observing that $vX{\times}vY$ is a Wallman realcompactification of $X{\times}Y$ if $v(X{\times}vY)=vX{\times}vY$, we show that $v(X{\times}Y)=vX{\times}vY$ if and only if $X{\times}Y$ is z-embedded in $vX{\times}vY$ and $vX{\times}vY$ is a Wallman compactification of $X{\times}Y$.

• Bulletin of the Korean Mathematical Society
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• v.42 no.1
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• pp.157-164
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• 2005

Let $RRat_k$ ($CP^n$) denote the space of basepoint-preserving conjugation-equivariant holomorphic maps of degree k from $S^2$ to $CP^n$. A map f ; $S^2 {\to}CP^n$ is said to be full if its image does not lie in any proper projective subspace of $CP^n$. Let $RF_k(CP^n)$ denote the subspace of $RRat_k(CP^n)$ consisting offull maps. In this paper we determine $H{\ast}(RF_k(CP^2); Z/p)$ for all primes p.

• Communications of the Korean Mathematical Society
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• v.34 no.3
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• pp.967-979
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• 2019

Chaotic dynamical systems, preferably on a Cantor-like space with some arithmetic operations are considered as good pseudo-random number generators. There are many definitions of chaos, of which Devaney-chaos and pos itive topological entropy seem to be the strongest. Let $A=\{0,1,{\dots},p-1\}$. We define a continuous map on $A^{\mathbb{Z}}$ using addition with a carry, in combination with the shift map. We show that this map gives rise to a dynamical system with positive entropy, which is also Devaney-chaotic: i.e., it is transitive, sensitive and has a dense set of periodic points.