• Kyungpook Mathematical Journal
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• v.57 no.2
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• pp.193-198
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• 2017

In this paper we investigate 2-absorbing ${\delta}$-primary ideals which unify 2-absorbing ideals and 2-absorbing primary ideals. A number of results about 2-absorbing ideals and 2-absorbing primary ideals are extended into this general framework.

• Communications of the Korean Mathematical Society
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• v.39 no.3
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• pp.575-583
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• 2024

Let R be a commutative ring with 1 ≠ 0. Let Id(R) be the set of all ideals of R and let δ : Id(R) → Id(R) be a function. Then δ is called an expansion function of the ideals of R if whenever L, I, J are ideals of R with J ⊆ I, then L ⊆ δ (L) and δ (J) ⊆ δ (I). Let δ be an expansion function of the ideals of R and m ≥ n > 0 be positive integers. Then a proper ideal I of R is called an (m, n)-closed δ-primary ideal (resp., weakly (m, n)-closed δ-primary ideal ) if a^m ∈ I for some a ∈ R implies aⁿ ∈ δ(I) (resp., if 0 ≠ a^m ∈ I for some a ∈ R implies aⁿ ∈ δ(I)). Let f : A → B be a ring homomorphism and let J be an ideal of B. This paper investigates the concept of (m, n)-closed δ-primary ideals in the amalgamation of A with B along J with respect to f denoted by A ⋈^f J.

• Kyungpook Mathematical Journal
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• v.61 no.4
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• pp.711-725
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• 2021

Let R be a commutative ring with nonzero identity, 𝓘(𝓡) the set of all ideals of R and δ : 𝓘(𝓡) → 𝓘(𝓡) an expansion of ideals of R. In this paper, we introduce the concept of 2-absorbing δ-semiprimary ideals in commutative rings which is an extension of 2-absorbing ideals. A proper ideal I of R is called 2-absorbing δ-semiprimary ideal if whenever a, b, c ∈ R and abc ∈ I, then either ab ∈ δ(I) or bc ∈ δ(I) or ac ∈ δ(I). Many properties and characterizations of 2-absorbing δ-semiprimary ideals are obtained. Furthermore, 2-absorbing δ₁-semiprimary avoidance theorem is proved.

• Proceedings of the KIEE Conference
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• 2008.04c
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• pp.9-12
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• 2008

Mathematical singularities of circuit equations with three-phase ideal transformer connections are studied. Three-wired wye-wye connections, delta-delta connections, and primary four-wired wye-delta connections are singular. The matrices of their circuit equations have zeros in their eigenvalues. Three-wired wye-delta connections, wye-wye-delta connections, and primary four-wired wye-wye connections are not singular. The physical meaning of their singularities is that they are sensitive and prone to be ill-conditioned. Equivalent shunt admittances representing ion losses and magnetizing inductances make the singular matrices non-singular in wye-connected circuits. And, equivalent series impedances representing copper losses and leakage inductances make the singular matrices non-singular in delta-connected circuits. The tableau analysis is used for the study.

• Journal of Preventive Medicine and Public Health
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• v.16 no.1
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• pp.59-65
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• 1983

Screening data from preplacement and periodic examination in Gu Mi Industrial Estate from May, 1983 to June, 1983 provide an opportunity to evaluate the accuracy of self-reported height and weight. The data for men and women were analyzed separated for effects of age, marrital status, educational level, employment status, measured height, measured weight and relative weight (percent of ideal body weight). The mean percent discrepancy from self-reported and measured height was analysed by cross-tubulation, P. value for analysis of variance and multiple correlation analysis in men and women. It is clear from the data that self-reported height and weigt differ from the quantities in systemic ways. But the magnitude of misreporting is very small on average except for weight in women. Whereas height tend to be over-reported, weight is under-reported in women but over-reported in men. Weight was accuracte for age group 20-29 years in men and age group over 40 year in women and over-reporting of weight increased with age in men and under-reporting of weight decreased with age in women. Weight was accurate in 60-64kg group in men and under 50kg group in women and under-stating of weight increased with weight in men and women. Weight was the most accurate in 100-109 percent relative weight group in men and in 90-99 percent relative weight group in women and under-stating of weight increased with relative weight and over-stating decreased with relative weight and over-stating decreased with relative weight in men and women. Height was the most accurate for group of primary school and except group of primary school, accuracy of height increased with educational level in men and women. In height, the highest measured height groups (over than 175cm measured height in men and over than 165cm measured height in women) were the most accurate and of over-reporting of height decreased with measured height. Single variable regression analysis and ANOVAs showed age(P<0.003), measured weight(P<0.0001) relative weight(P<0.0001), educational level(P<0.0005) and employment status(P<0.0007) to be significantly related to ${\Delta}WT$ in women and measured height(P<0.0001), educational level(P<0.03) and marrital status (P<0.03) to be significantly related to ${\Delta}WT$ in men. The women were more sensitive about her body weight than height.