• 대한수학회논문집
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• 제20권4호
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• pp.645-648
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• 2005

Let K be a Galois extension of a field F with G = Gal(K/F). Let L be an extension of F such that $K\;{\otimes}_F\;L\;=\; N_1\;{\oplus}N_2\;{\oplus}{\cdots}{\oplus}N_k$ with corresponding primitive idempotents $e_1,\;e_2,{\cdots},e_k$, where Ni's are fields. Then G acts on $\{e_1,\;e_2,{\cdots},e_k\}$ transitively and $Gal(N_1/K)\;{\cong}\;\{\sigma\;{\in}\;G\;/\;{\sigma}(e_1)\;=\;e_1\}$. And, let R be a commutative F-algebra, and let P be a prime ideal of R. Let T = $K\;{\otimes}_F\;R$, and suppose there are only finitely many prime ideals $Q_1,\;Q_2,{\cdots},Q_k$ of T with $Q_i\;{\cap}\;R\;=\;P$. Then G acts transitively on $\{Q_1,\;Q_2,{\cdots},Q_k\},\;and\;Gal(qf(T/Q_1)/qf(R/P))\;{\cong}\;\{\sigma{\in}\;G/\;{\sigma}-(Q_1)\;=\;Q_1\}$ where qf($T/Q_1$) is the quotient field of $T/Q_1$.

• 대한안전경영과학회지
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• 제16권1호
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• pp.169-176
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• 2014

This research discusses the characteristics and the implementation strategies for two types of quality metrics to analyze innovation effects in six sigma projects: fixed specification type and moving specification type. $Z_{st}$, $P_{pk}$ are quality metrics of fixed specification type that are influenced by predetermined specification. In contrast, the quality metrics of moving specification type such as Strictly Standardized Mean Difference(SSMD), Z-Score, F-Statistic and t-Statistic are independent from predetermined specification. $Z_{st}$ sigma level obtains defective rates of Parts Per Million(PPM) and Defects Per Million Opportunities(DPMO). However, the defective rates between different industrial sectors are incomparable due to their own technological inherence. In order to explore relative method to compare defective rates between different industrial sectors, the ratio of specification and natural tolerance called, $P_{pk}$, is used. The drawback of this $P_{pk}$ metric is that it is highly dependent on the specification. The metrics of F-Statistic and t-Statistic identify innovation effect by comparing before-and-after of accuracy and precision. These statistics are not affected by specification, but affected by type of statistical distribution models and sample size. Hence, statistical significance determined by above two statistics cannot give a same conclusion as practical significance. In conclusion, SSMD and Z-Score are the best quality metrics that are uninfluenced by fixed specification, theoretical distribution model and arbitrary sample size. Those metrics also identify the innovation effects for before-and-after of accuracy and precision. It is beneficial to use SSMD and Z-Score methods along with popular methods of $Z_{st}$ sigma level and $P_{pk}$ that are commonly employed in six sigma projects. The case studies from national six sigma contest from 2011 to 2012 are proposed and analyzed to provide the guidelines for the usage of quality metrics for quality practitioners.

• BMB Reports
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• 제35권6호
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• pp.547-552
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• 2002

The aim of our study was to investigate the protective effects of intraperitoneally-administrated vitamin E, dl-alpha lipoic acid, and linalool on the level of total lipid and fatty acid in guinea pig brains with oxidative stress that was induced by $H_2O_2$. The total brain lipid content in the $H_2O_2$ group decreased when compared to the $H_2O_2$ + vitamin E (p<0.05), $H_2O_2$ + linalool (p<0.05), ALA (p<0.05), control (p<0.01), linalool (p<0.01), and vitamin E (p<0.01) groups. While the proportion of total saturated fatty acid (${\Sigma}SFA$) in the $H_2O_2$ group significantly increased (p<0.005) when compared to the vitamin E group, it only slightly increased (p<0.01) when compared to the control and $H_2O_2$ + vitamin E groups. The ratio of the total unsaturated fatty acid (${\Sigma}USFA$) in the $H_2O_2$ groups was lower (p<0.05) than the control, vitamin E, and $H_2O_2$ + vitamin E groups. The level of the total polyunsaturated fatty acid (${\Sigma}PUEA$) in the $H_2O_2$ group decreased in when compared to the control, vitamin E, and $H_2O_2$ + vitamin E groups. While the proportion of the total w3 (omega 3), w6 (omega 6), and PUFA were found to be lowest in the $H_2O_2$ group, they were slightly increased (p<0.05) in the lipoic acid group when compared to the control and $H_2O_2$ + lipoic acid groups. However, the level of ${\Sigma}SFA$ in the $H_2O_2$ group was highest; the level of ${\Sigma}USFA$ in same group was lowest. As the proportion of ${\Sigma}USFA$ and ${\Sigma}PUFA$ were found to be highest in the linalool group, they were decreased in the $H_2O_2$ group when compared to the control group. Our results show that linalool has antioxidant properties, much the same as vitamin E and lipoic acid, to prevent lipid peroxidation. Additionally, vitamin E, lipoic acid, and linalool could lead to therapeutic approaches for limiting damage from oxidation reaction in unsaturated fatty acids, as well as for complementing existing therapy for the treatment of complications of oxidative damage.

• Journal of the Korean Data and Information Science Society
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• 제22권6호
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• pp.1251-1256
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• 2011

Consider a p-variate ($p{\geq}4$) normal distribution with mean ${\theta}$ and identity covariance matrix. Using a simple property of noncentral chi square distribution, the generalized Bayes estimators dominating the Lindley estimator under quadratic loss are given based on the methods of Brown, Brewster and Zidek for estimating a normal variance. This result can be extended the cases where covariance matrix is completely unknown or ${\Sigma}={\sigma}^2I$ for an unknown scalar ${\sigma}^2$.

• 대한수학회지
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• 제54권1호
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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.

• 대한수학회보
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• 제22권1호
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• pp.23-29
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• 1985

Let H be an arbitrary complex Hilbert space. We constructed an extension K of H by means of weakly convergent sequences in H and the Banach limit. Let .phi. be the faithful *-representation of L(H) on K. In this note, we investigated the relations between spectra of T in L(H) and .phi.(T) in L(K) and we obtained the following results: 1) If T is a compact operator on H, then .phi.(T) is also a compact operator on K (Proposition 6), 2) .sigma.$_{l}$ (.phi.(T)).contnd..sigma.$_{l}$ (T) for any operator T.mem.L(H) (Corollary 10), 3) For every operator T.mem.L(H), .sigma.$_{ap}$ (.phi.(T))=.sigma.$_{ap}$ (T))=.sigma.$_{ap}$ (T)=.sigma.$_{p}$(.phi.(T)) (Lemma 12, 13) and .sigma.$_{c}$(.phi.(T))=.sigma.(Theorem 15).15).

• 충청수학회지
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• 제20권3호
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• pp.333-342
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• 2007

Suppose that ${\mu}$ is a finite positive Borel measure on the unit ball $B{\subset}C^n$. The boundary of B is the unit sphere $S=\{z:{\mid}z{\mid}=1\}$. Let ${\sigma}$ be the rotation-invariant measure on S such that ${\sigma}(S)=1$. In this paper, we will show that if $sup_{{\zeta}{\in}S}\;{\int}_{B}\;P(z,{\zeta})d{\mu}(z)$<${\infty}$ where $P(z,{\zeta})$ is the Poission-Szeg$\ddot{o}$ kernel for B, then ${\mu}$ is a Carleson measure. We will also show that if $sup_{{\zeta}{\in}S}\;{\int}_{B}\;P(z,{\zeta})d{\mu}(z)$<${\infty}$, then the operator T such that T(f) = P[f] is compact as a mapping from $L^p(\sigma)$ into $L^p(B,d{\mu})$.

• 식물병연구
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• 제30권2호
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• pp.148-156
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• 2024

Ralstonia pseudosolanacearum은 토양과 물에서 오랫동안 생존하고, 가지과 작물에 심각한 풋마름병을 일으키는 식물병원세균이다. Simga S는 세균의 스트레스 환경에서 반응 또는 정지기 동안 유전자 발현을 조절하는 RNA 중합효소 복합체의 일부인 단백질이다. 본 연구는 스트레스 조건에서 R.pseudosolanacearum의 sigma S의 역할을 조사하기 위해서, R.pseudosolanacearum의 GMI1000 균주의 sigma S를 암호화하는 rpoS 유전자 변이체를 준비하여 야생형 균주와 세균의 특징을 비교하였다. 아울러 rpoS 유전자 역할은 원래 유전자를 변이체에 도입하여 rpoS 유전자 표현형 회복을 확인하였다. 야생형 균주와 rpoS 결여 변이체는 생장 속도, 외피다당류 생산, 식물체에서 병원성, 식물 세포벽 분해 효소 활성에서 차이를 보이지 않았다. 그러나 야생형 균주는 영양분결핍 조건에서 변이체보다 더 민감하게 반응하였고 과산화수소가 첨가된 조건에서 변이체보다 덜 민감하게 반응하였다. 흥미롭게도 영양분결핍 조건에서 rpoS 결여 변이체에서는 장기간 생균수를 유지하지만, 같은 조건에서 야생형 균주 생균수는 빠르게 감소하였다. 그리고 두 균주 배양액 pH를 측정한 결과, 야생형 균주와 변이체 간에 상당한 차이가 나타났다. 야생형 균주는 생장하면서 빠르게 배지의 pH가 감소하여 산성화되었다. 그러므로 야생형 균주의 빠른 사멸은 배지가 산성화되면서 정지기 상태 세균의 산성 pH에 대한 민감도 때문일 것이다. Biolog 분석으로 rpoS 변이체는 acetic acid, D-alanine, D-trehalose, L-histidine을 이용하지 못함을 확인하였다. 본 연구 결과는 R. pseudosolanacearum 세균의 sigma S가 영양분결핍 조건에서 정지기 동안 유기산 생산 또는 이용을 조절하며 정지기 세포사멸도 조절하는 것을 보여준다.

• 충청수학회지
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• 제24권3호
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• pp.417-426
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• 2011

Let ${\mu}$ be a finite positive Borel measure on the unit ball $B{\subset}{\mathbb{C}}^n$ and ${\nu}$ be the Euclidean volume measure such that ${\nu}(B)=1$. For the unit sphere $S=\{z:{\mid}z{\mid}=1\}$, ${\sigma}$ is the rotation-invariant measure on S such that ${\sigma}(S) =1$. Let ${\mathcal{P}}[f]$ be the Poisson-$Szeg{\ddot{o}}$ integral of f and $\tilde{\mu}$ be the Berezin transform of ${\mu}$. In this paper, we show that if there is a constant M > 0 such that ${\int_B}{\mid}{\mathcal{P}}[f](z){\mid}^pd{\mu}(z){\leq}M{\int_B}{\mid}{\mathcal{P}}[f](z){\mid}^pd{\nu}(z)$ for all $f{\in}L^p(\sigma)$, then ${\parallel}{\tilde{\mu}}{\parallel}_{\infty}{\equiv}{\sup}_{z{\in}B}{\mid}{\tilde{\mu}}(z){\mid}<{\infty}$, and we show that if ${\parallel}{\tilde{\mu}{\parallel}_{\infty}<{\infty}$, then ${\int_B}{\mid}{\mathcal{P}}[f](z){\mid}^pd{\mu}(z){\leq}C{\mid}{\mid}{\tilde{\mu}}{\mid}{\mid}_{\infty}{\int_S}{\mid}f(\zeta){\mid}^pd{\sigma}(\zeta)$ for some constant C.

• 대한수학회보
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• 제43권2호
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• pp.389-393
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• 2006

In this paper it is shown that the spectrum ${\sigma}$ is continuous at every p-hyponormal operator when restricted to the set of essentially p-hyponormal operators and moreover ${\sigma}$ is continuous when restricted to the set of compact perturbations of p-hyponormal operators whose spectral pictures have no holes associated with the index zero.