• Journal of the Korean Statistical Society
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• 제22권1호
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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.

• East Asian mathematical journal
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• 제18권2호
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• pp.271-282
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• 2002

Let R be a ring with an endomorphism $\sigma$ and a derivation $\delta$. An ideal I of R is ($\sigma,\;\delta$)-ideal of R if $\sigma(I){\subseteq}I$ and $\delta(I){\subseteq}I$. An ideal P of R is a ($\sigma,\;\delta$)-prime ideal of R if P(${\neq}R$) is a ($\sigma,\;\delta$)-ideal and for ($\sigma,\;\delta$)-ideals I and J of R, $IJ{\subseteq}P$ implies that $I{\subseteq}P$ or $J{\subseteq}P$. An ideal Q of R is ($\sigma,\;\delta$)-semiprime ideal of R if Q is a ($\sigma,\;\delta$)-ideal and for ($\sigma,\;\delta$)-ideal I of R, $I^2{\subseteq}Q$ implies that $I{\subseteq}Q$. The ($\sigma,\;\delta$)-prime radical (resp. prime radical) is defined by the intersection of all ($\sigma,\;\delta$)-prime ideals (resp. prime ideals) of R and is denoted by $P_{(\sigma,\delta)}(R)$(resp. P(R)). In this paper, the following results are obtained: (1) $P_{(\sigma,\delta)}(R)$ is the smallest ($\sigma,\;\delta$)-semiprime ideal of R; (2) For every extended endomorphism $\bar{\sigma}$ of $\sigma$, the $\bar{\sigma}$-prime radical of an Ore extension $P(R[x;\sigma,\delta])$ is equal to $P_{\sigma,\delta}(R)[x;\sigma,\delta]$.

• Journal of Advanced Marine Engineering and Technology
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• 제24권6호
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• pp.24-33
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• 2000

This paper investigates the relationship between J-integral and crack tip opening displacement, ${\delta}_t$ using Gordens results of numerical analysis. Estimation were carried out for several strength levels such as ultimate, flow, yield, ultimate-flow, flow-yield stress to determine the influence of strain hardening and the ratio of crack length to width on the $J-{\delta}_t$ relationship. It was found that for SE(B) specimens, the $J-{\delta}_t$ relationship can be applied to relate J to ${\delta}_t$ as follows $J=m_j{\times}{\sigma}_i{\times}{\delta}_t$ where $m_j=1.27773+0.8307({\alpha}/W)$, ${\sigma}_i:{\sigma}_U$, ${\sigma}_{U-F}={\frac{1}{2}} ({\sigma}_U+{\sigma}_F$), ${\sigma}_F$, ${\sigma}_F}$ $Y=({\sigma}_F+{\sigma}_Y)$, ${\sigma}_Y$

• 대한수학회지
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• 제42권1호
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• pp.53-63
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• 2005

Let R be a ring R and ${\sigma}$ be an endomorphism of R. R is called ${\sigma}$-rigid (resp. reduced) if $a{\sigma}r(a) = 0 (resp{\cdot}a^2 = 0)$ for any $a{\in}R$ implies a = 0. An ideal I of R is called a ${\sigma}$-ideal if ${\sigma}(I){\subseteq}I$. R is called ${\sigma}$-quasi-Baer (resp. right (or left) ${\sigma}$-p.q.-Baer) if the right annihilator of every ${\sigma}$-ideal (resp. right (or left) principal ${\sigma}$-ideal) of R is generated by an idempotent of R. In this paper, a skew polynomial ring A = R[$x;{\sigma}$] of a ring R is investigated as follows: For a ${\sigma}$-rigid ring R, (1) R is ${\sigma}$-quasi-Baer if and only if A is quasi-Baer if and only if A is $\={\sigma}$-quasi-Baer for every extended endomorphism $\={\sigma}$ on A of ${\sigma}$ (2) R is right ${\sigma}$-p.q.-Baer if and only if R is ${\sigma}$-p.q.-Baer if and only if A is right p.q.-Baer if and only if A is p.q.-Baer if and only if A is $\={\sigma}$-p.q.-Baer if and only if A is right $\={\sigma}$-p.q.-Baer for every extended endomorphism $\={\sigma}$ on A of ${\sigma}$.

• 한국초지조사료학회지
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• 제9권1호
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• pp.34-42
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• 1989

山地草地開發파 聯關된 草地士爆改良 및 施R巴法 改善올 薦하여 Homes의 Systematic variations 方法으로 多量要素 ${\Sigma}$Anion : ${\Sigma}$Cation 適正施服比率 및 適正總養分(${\Sigma}$A+ ${\Sigma}$C) 施肥量을 決定코자 Grass-clover 混播我培條件에서 山地土壞을 供試한 Pot 試驗으로 遂行한 結果는 1. 混播條件에서 各構成草種別 收量提高를 위한 ${\Sigma}$A/${\Sigma}$C 適正施服比率 및 適正總養分濃度를 換算 하였다(Table 6 ). 未本科 및 混合救草의 適正 ${\Sigma}$A:${\Sigma}$C=2 : 1 (80, 320meq/pot 時) 와 3 : 2 (560, 800 meq時)를 보였고, 荳科목초는 未本科收草의 경우와는 相反되게 供히 約 1 : 2比率을 보였다. 2.. 適正總養分灌度는 混合收草 및 未本科收草에서는 ${\Sigma}$A/${\Sigma}$C比率이 낮아질수록 -.般的으로 높은 濃度를 보였으나, 荳科목초는 일관성 높은 없이 多少 變異福이 컸다. 3. 未本科 및 혼합목초에서는 ${\Sigma}$A/${\Sigma}C$C 比率이 커 질수록, 總養分禮度가 增加할수록 乾物收量이 增加하였으나, 높은 農度 (560, 800meq/pot) 에서는 ${\Sigma}$A/${\Sigma}$C=2.125 보다 1. 273 처리에서 有意性 있게 높은 收量을 보였다. 反面에 두과목초의 收量은 ${\Sigma}$C 比率이 높아질수록 收量增加를 보였고, ${\Sigma}$C 比率이 높은 條件에서만 總濃度 증가에 따르는 收量增加를 보였다. 4. 두과목초에서는 ${\Sigma}$C>${\Sigma}C$A比率에서 乾物收量에 對단 ${\Sigma}$C 효율이 높은것을(80meq 例外) 除外 하고는 各구성초중 供히 ${\Sigma}$A 및 ${\Sigma}$C比率이 낮을 때, 總養分濃度가 낮을때 各 ${\Sigma}$A 및 ${\Sigma}C$C 효율이 높았다. 5. 各구성草種의 收量 및 植生밟成比率이 ${\Sigma}$A/${\Sigma}$C比率 및 總、養分濃度와 이들의 相互作用에 크게 影響을 받았고, 未本科와 두과목초間은 大體로 相反된 特性을 보였다. 또한 士壞의 化學的 特性 및 건초중 無機養分의 含量이 處理에 따라 부분적으로 變化 되었다.

• 대한수학회보
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• 제42권3호
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• pp.477-484
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• 2005

Let R be a ring with an automorphism 17. An ideal [ of R is ($\sigma$-ideal of R if $\sigma$(I).= I. A proper ideal P of R is ($\sigma$-prime ideal of R if P is a $\sigma$-ideal of R and for $\sigma$-ideals I and J of R, IJ $\subseteq$ P implies that I $\subseteq$ P or J $\subseteq$ P. A proper ideal Q of R is $\sigma$-semiprime ideal of Q if Q is a $\sigma$-ideal and for a $\sigma$-ideal I of R, I$^{2}$ $\subseteq$ Q implies that I $\subseteq$ Q. The $\sigma$-prime radical is defined by the intersection of all $\sigma$-prime ideals of R and is denoted by P$_{(R). In this paper, the following results are obtained: (1) For a principal ideal domain R, P$_{(R) is the smallest $\sigma$-semiprime ideal of R; (2) For any ring R with an automorphism $\sigma$ and for a skew Laurent polynomial ring R[x, x$^{-1}$; $\sigma$], the prime radical of R[x, x$^{-1}$; $\sigma$] is equal to P$_{(R)[x, x$^{-1}$; $\sigma$ ].

• 대한수학회보
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• 제47권2호
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• pp.385-399
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• 2010

Let $\sigma$ be an endomorphism and I a $\sigma$-ideal of a ring R. Pearson and Stephenson called I a $\sigma$-semiprime ideal if whenever A is an ideal of R and m is an integer such that $A{\sigma}^t(A)\;{\subseteq}\;I$ for all $t\;{\geq}\;m$, then $A\;{\subseteq}\;I$, where $\sigma$ is an automorphism, and Hong et al. called I a $\sigma$-rigid ideal if $a{\sigma}(a)\;{\in}\;I$ implies a $a\;{\in}\;I$ for $a\;{\in}\;R$. Notice that R is called a $\sigma$-semiprime ring (resp., a $\sigma$-rigid ring) if the zero ideal of R is a $\sigma$-semiprime ideal (resp., a $\sigma$-rigid ideal). Every $\sigma$-rigid ideal is a $\sigma$-semiprime ideal for an automorphism $\sigma$, but the converse does not hold, in general. We, in this paper, introduce the quasi $\sigma$-rigidness of ideals and rings for an automorphism $\sigma$ which is in between the $\sigma$-rigidness and the $\sigma$-semiprimeness, and study their related properties. A number of connections between the quasi $\sigma$-rigidness of a ring R and one of the Ore extension $R[x;\;{\sigma},\;{\delta}]$ of R are also investigated. In particular, R is a (principally) quasi-Baer ring if and only if $R[x;\;{\sigma},\;{\delta}]$ is a (principally) quasi-Baer ring, when R is a quasi $\sigma$-rigid ring.

• 품질경영학회지
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• 제31권2호
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• pp.194-204
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• 2003

It is very important to understand and interpret the meaning of the sigma level correctly through the Six Sigma project. Especially, the confusion over the relation between sigma level from the short-term point of view and defective proportion or DPMO from the long-term point of view may make a big gap between expected results of the Six Sigma project and real results in the field. The one-tail approximation is commonly used to calculate the sigma level both in most literatures introducing Six Sigma and actual cases of the Six Sigma project. Since the one-tail approximation undervalues the sigma level of the fields such as business and service of which the sigma level is generally low, however. there can be misleading results of the explanation of the sigma level and inappropriate project evaluation. This paper describes the relation between sigma level and defective proportion in detail and clears the difference between the one-tail and two-tail approximation.

• 충청수학회지
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• 제14권1호
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• pp.61-71
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• 2001

We introduce a new class of ${\sigma}$-coherent frames and show that HA is a ${\sigma}$-coherent frame if A is a ${\sigma}$-frame. Based on this, it is shown that a frame is ${\sigma}$-coherent iff it is isomorphic to the frame of ${\sigma}$-ideals of a ${\sigma}$-frame. Finally we show that ${\sigma}$-COhFrm and ${\sigma}$Frm are equivalent.

• 충청수학회지
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• 제17권1호
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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.