• Title/Summary/Keyword: SIGMA

### Confidence Intervals in Three-Factor-Nested Variance Component Model

• Kang, Kwan-Joong
• 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.

### PRIME RADICALS IN ORE EXTENSIONS

• Han, Jun-Cheol
• East Asian mathematical journal
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• v.18 no.2
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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 $P_{\sigma,\delta}(R)[x;\sigma,\delta]$.

### An Estimation of Constraint Factor on the ${\delta}_t$ Relationship (J-적분과 균열선단개구변위에 관한 구속계수 m의 평가)

• 장석기
• Journal of Advanced Marine Engineering and Technology
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• v.24 no.6
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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 $m_j=1.27773+0.8307({\alpha}/W)$, ${\sigma}_i:{\sigma}_U$, ${\sigma}_{U-F}={\frac{1}{2}} ({\sigma}_U+{\sigma}_F$), ${\sigma}_F$, ${\sigma}_F}$ $Y=({\sigma}_F+{\sigma}_Y)$, ${\sigma}_Y$

### SKEW POLYNOMIAL RINGS OVER σ-QUASI-BAER AND σ-PRINCIPALLY QUASI-BAER RINGS

• HAN JUNCHEOL
• Journal of the Korean Mathematical Society
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• v.42 no.1
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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 ${\sigma}$.

### The Optimal Combination and Amount of Major Nutrients Computed by the Homes Systematic Variation Technique for the Hilly Pasture Development II. Determination of the optimal combination of $\sum$anion:$\sum$ cation and the optimal appoication rate of total ions (산지초지개발을 위한 다량요소의 적정 시비비율 및 시비량결정에 관한 연구 II. 혼파초지에서 $\sum$음이온:$\sum$양이온 적정시비비율 및 적정총량분시비량)

• 정연규;김성채
• Journal of The Korean Society of Grassland and Forage Science
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• v.9 no.1
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• pp.34-42
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• 1989
• This pot experiments were conducted to find out the optimal fertilization ratios of ${\Sigma}anion$ : ${\Sigma}cation$, ${\Sigma}A$/${\Sigma}C$, and the optimal application rates of total major nutrients in an orchardgrass/ladino clover mixed sward. The optimum ratios and concentrations in equivalent basis were computed by the Homes systematic variations technique. The results were summarized as follows; 1. The optimum fertilization ratios of ${\Sigma}A$ : ${\Sigma}C$ and the optimum application rates of total nutrients for the high yields by forage species in a mixed sward were obtained (Table 6 in detail); ${\Sigma}A$ : ${\Sigma}C$ = 2 : 1 at 80 and 320 meq/pot, and 3 : 2 at 560 and 800 meq for grass and grass plus legume, and ${\Sigma}A$ : ${\Sigma}C$ = 1 : 2 for legume in general. 2. The optimum application rates of total nutrients for the high yields of grass and grass plus kgum were increased by decreasing the ${\Sigma}A$/ ${\Sigma}C$: ratio, whereas these for legume showed a valible. range without significance. 3. The yields 01 grass and grass plus legume were generally increasing by increasing both the ${\Sigma}A$/ ${\Sigma}C$ ratio and total concentration, but they were significantly higher at the ${\Sigma}A$/ ${\Sigma}C$ = 1.273 than at the 2.125 under the high total ion concentration. The legume yields were proportional to ${\Sigma}C$ ratio and increased by increasing the total ion concentration under the condition of high ${\Sigma}C$ ratio. 4. The efficiencies of ${\Sigma}A$ and ${\Sigma}C$ in relation to the grass and grass plus legume yields were highest with the low ratios of each other and the low rates of total nutrients ${\Sigma}A$ efficiency m the legume yield tended to be similar to that of ${\Sigma}A$ in the grass yield noted above. The ${\Sigma}C$ efficiency in the legume yield, however, was generally proportional to the ${\Sigma}C$ ratio except at the low rate of 80 meqlpot. 5. The yields of grass plus legume, yield components and botanical compositions in a mixed sward were greatly influenced by the ${\Sigma}A$/${\Sigma}C$ ratios, the fertilization rates of total nutrients, and the interaction of ratio and rate noted above. These effects were generally different and opposite accading to grass and legume. In addition, the soil chemical properties and mineral contents of forages were partially influenced by these systematic variations.

### PRIME RADICALS OF SKEW LAURENT POLYNOMIAL RINGS

• Han, Jun-Cheol
• Bulletin of the Korean Mathematical Society
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• v.42 no.3
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• pp.477-484
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• 2005