• Journal of the Korean Statistical Society
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• v.22 no.1
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• pp.39-54
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• 1993

In the three-factor nested variance component model with equal numbers in the cells given by $y_{ijkm} = \mu + A_i + B_{ij} + C_{ijk} + \varepsilon_{ijkm}$, the exact confidence intervals of the variance component of $\sigma^2_A, \sigma^2_B, \sigma^2_C, \sigma^2_{\varepsilon}, \sigma^2_A/\sigma^2_{\varepsilon}, \sigma^2_B/\sigma^2_{\varepsilon}, \sigma^2_C/\sigma^2_{\varepsilon}, \sigma^2_A/\sigma^2_C, \sigma^2_B/\sigma^2_C$ and $\sigma^2_A/\sigma^2_B$ are not found out yet. In this paper approximate lower and upper confidence intervals are presented.

• Journal of the Chungcheong Mathematical Society
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• v.17 no.1
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• pp.85-101
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• 2004

Let A be a Hopf algebra with a linear form ${\sigma}:k{\rightarrow}A{\otimes}A$, which is convolution invertible, such that ${\sigma}_{21}({\Delta}{\otimes}id){\tau}({\sigma}(1))={\sigma}_{32}(id{\otimes}{\Delta}){\tau}({\sigma}(1))$. We define Hopf algebras, ($A_{\sigma}$, m, u, ${\Delta}_{\sigma}$, ${\varepsilon}$, $S_{\sigma}$). If B and C are opposite skew copaired Hopf algebras and $A=B{\otimes}_kC$ then we find Hopf algebras, ($A_{[{\sigma}]}$, $m_B{\otimes}m_C$, $u_B{\otimes}u_C$, ${\Delta}_{[{\sigma}]}$, ${\varepsilon}B{\otimes}{\varepsilon}_C$, $S_{[{\sigma}]}$). Let H be a finite dimensional commutative Hopf algebra with dual basis $\{h_i\}$ and $\{h_i^*\}$, and let $A=H^{op}{\otimes}H^*$. We show that if we define ${\sigma}:k{\rightarrow}H^{op}{\otimes}H^*$ by ${\sigma}(1)={\sum}h_i{\otimes}h_i^*$ then ($A_{[{\sigma}]}$, $m_A$, $u_A$, ${\Delta}_{[{\sigma}]}$, ${\varepsilon}_A$, $S_{[{\sigma}]}$) is the dual space of Drinfeld double, $D(H)^*$, as Hopf algebra.

• Korean Journal of Microbiology
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• v.45 no.1
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• pp.10-16
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• 2009

A diverse range of stresses such as heat, cold, salt, ethanol, oxygen starvation or nutrient starvation induces same stress-responsive proteins. This general stress response enhances bacterial survival significantly. In Bacillus subtilis and closely related Gram-positive bacteria Listeria monocytogenes, the general stress response is controlled by the alternative transcription factor ${\sigma}^B$. The activity of ${\sigma}^B$ is regulated post-translationally by a signal transduction network that has been extensively studied in B. subtilis, and serve as a model for L. monocytogenes. The proposed model of L. monocytogenes signal transduction network is similar to that of B. subtilis, but the energy stress pathway is missing. More than 150 general stress proteins belong to ${\sigma}^B$ regulon of B. subtilis and L. monocytogenes. In both bacteria, ${\sigma}^B$ function is primarily important for resistance to diverse stresses. In addition, ${\sigma}^B$ function contributes to the control of important virulence genes in food-borne pathogen L. monocytogenes. Therefore, understanding of the general stress response is important not only for bacterial physiology, but also for pathogenicity.

• Korean Journal of Food Science and Technology
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• v.36 no.3
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• pp.456-460
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• 2004

Effects of sigma factor (${\sigma}^{B}$) on biofilm formation in Listeria monocytogenes 10403S and ${\sigma}^{B}-deficient$ sigB null mutant were studied under high osmotic and low temperature conditions. In brain heart infusion (BHI) medium containing 6% NaCl, wild type 10403S and ${\sigma}^{B}-deficient$sigB null mutant formed biofilms of $6.83{\pm}0.38\;and\;5.33{\pm}0.45\;log\;cfu/cm^{2}$, respectively. L. monocytogenes 10403S in BHI medium containing 6% NaCl formed 4.7 times larger biofilm than without NaCl. Culture of L. monocytogenes 10403S and sigB null mutant at $4^{\circ}C$ did not show any significant differences in biofilm formation. The results suggest biofilm formation is activated by ${\sigma}^{B}$ and NaCl, whereas not affected by low temperature stress in L. monocytogenes 10403S. More studies are necessary to determine biofilm formation mechanism in osmotolerant L. monocytogenes.

• Journal of the Korean Data and Information Science Society
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• v.9 no.2
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• pp.159-164
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• 1998

The two-factor nested variance component model with equal numbers in the cells are given by $y_{ijk}\;=\;{\mu}\;+\;A_i\;+\;B_{ij}\;+\;C_{ijk}$ and the confidence intervals for the ratio of variance components, ${\sigma}^{2}_{A}/{\sigma}^{2}_{B}$ are obtained in various forms by many authors. This article shows the probability ranges of these confidence intervals on ${\sigma}^{2}_{A}/{\sigma}^{2}_{B}$ proved by the mathematical computation.

• Journal of the Korean Mathematical Society
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• v.54 no.1
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• pp.281-302
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• 2017

For a Banach space operator $A{\in}B(\mathcal{X})$, let ${\sigma}(A)$, ${\sigma}_a(A)$, ${\sigma}_w(A)$ and ${\sigma}_{aw}(A)$ denote, respectively, its spectrum, approximate point spectrum, Weyl spectrum and approximate Weyl spectrum. The operator A is polaroid (resp., left polaroid), if the points $iso{\sigma}(A)$ (resp., $iso{\sigma}_a(A)$) are poles (resp., left poles) of the resolvent of A. Perturbation by compact operators preserves neither SVEP, the single-valued extension property, nor the polaroid or left polaroid properties. Given an $A{\in}B(\mathcal{X})$, we prove that a sufficient condition for: (i) A+K to have SVEP on the complement of ${\sigma}_w(A)$ (resp., ${\sigma}_{aw}(A)$) for every compact operator $K{\in}B(\mathcal{X})$ is that ${\sigma}_w(A)$ (resp., ${\sigma}_{aw}(A)$) has no holes; (ii) A + K to be polaroid (resp., left polaroid) for every compact operator $K{\in}B(\mathcal{X})$ is that iso${\sigma}_w(A)$ = ∅ (resp., $iso{\sigma}_{aw}(A)$ = ∅). It is seen that these conditions are also necessary in the case in which the Banach space $\mathcal{X}$ is a Hilbert space.

• Journal of the Korean Mathematical Society
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• v.45 no.3
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• pp.771-780
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• 2008

Let $M_C=\(\array{A&C\\0&B}\)$ be a $2{\times}2$ upper triangular operator matrix acting on the Hilbert space $H{\bigoplus}K\;and\;let\;{\sigma}_w(\cdot)$ denote the Weyl spectrum. We give the necessary and sufficient conditions for operators A and B which ${\sigma}_w\(\array{A&C\\0&B}\)={\sigma}_w\(\array{A&C\\0&B}\)\;or\;{\sigma}_w\(\array{A&C\\0&B}\)={\sigma}_w(A){\cup}{\sigma}_w(B)$ holds for every $C{\in}B(K,\;H)$. We also study the Weyl's theorem for operator matrices.

• Journal of Microbiology
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• v.42 no.2
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• pp.147-151
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• 2004

$\sigma^{B}$ plays an important role in both osmoprotection and proper differentiation in Streptomyces coelicolor A3(2). We searched for candidate members of the $\sigma^{B}$ regulon from the genome database, using the consensus promoter sequence (GNNTN$_{14-16}$GGGTAC/T). The list consists of l15 genes, and includes all the known $\sigma^{B}$ target genes and many other genes whose functions are related to stress protection and dif-ferentiation.

• Korean Journal of Microbiology
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• v.47 no.2
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• pp.167-169
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• 2011

The Saccharomyces cerevisiae S288c strain does not show haploid and diploid filamentous growth, and biofilm formation, because it has a flo8 nonsense mutation unlike ${\Sigma}1278b$ strain which has a FLO8 gene. During the heat stress experiments to investigate the role of ScKns1, LAMMER kinase in S. cerevisiae, we found that ${\Sigma}1278b$ strain revealed heat sensitivity at $37^{\circ}C$, a mild heat stress in contrast to S288c strain. We also found that the disruption of ScKns1 and the addition of sorbitol suppress heat sensitivity of ${\Sigma}1278b$ strain. These results suggest the possibility that Flo8 and ScKns1 may interact to transducer a signal for regulating heat stress through a novel signaling pathway.

• Journal of the Korean Mathematical Society
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• v.46 no.5
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• pp.895-905
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• 2009

Let $B^{n+1}$ be the unit ball in the complex vector space $\mathbb{C}^{n+1}$ with the standard Hermitian metric. Let ${\Sigma}^n={\partial}B^{n+1}=S^{2n+1}$ be the boundary sphere with the induced CR structure. Let f : ${\Sigma}^n{\hookrightarrow}{\Sigma}^N$ be a local CR immersion. If N < 3n - 1, the asymptotic vectors of the CR second fundamental form of f at each point form a subspace of the CR(horizontal) tangent space of ${\Sigma}^n$ of codimension at most 1. We study the higher order derivatives of this relation, and we show that a linearly full local CR immersion f : ${\Sigma}^n{\hookrightarrow}{\Sigma}^N$, N $\leq$ 3n-2, can only occur when N = n, 2n, or 2n + 1. As a consequence, it gives an extension of the classification of the rational proper holomorphic maps from $B^{n+1}$ to $B^{2n+2}$ by Hamada to the classification of the rational proper holomorphic maps from $B^{n+1}$ to $B^{3n+1}$.