• Journal of the Korean Mathematical Society
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• v.55 no.5
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• pp.1031-1043
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• 2018

Let R be a commutative ring with $1{\neq}0$, I a proper ideal of R, and m and n positive integers. In this paper, we define I to be a weakly (m, n)-closed ideal if $0{\neq}x^m\;{\in}I$ for $x{\in}R$ implies $x^n{\in}I$, and R to be an (m, n)-von Neumann regular ring if for every $x{\in}R$, there is an $r{\in}R$ such that $x^mr=x^n$. A number of results concerning weakly(m, n)-closed ideals and (m, n)-von Neumann regular rings are given.

• Journal of the Korean Mathematical Society
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• v.53 no.3
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• pp.549-582
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• 2016

All rings are commutative with $1{\neq}0$ and n is a positive integer. Let ${\phi}:{\Im}(R){\rightarrow}{\Im}(R){\cup}\{{\emptyset}\}$ be a function where ${\Im}(R)$ denotes the set of all ideals of R. We say that a proper ideal I of R is ${\phi}$-n-absorbing primary if whenever $a_1,a_2,{\cdots},a_{n+1}{\in}R$ and $a_1,a_2,{\cdots},a_{n+1}{\in}I{\backslash}{\phi}(I)$, either $a_1,a_2,{\cdots},a_n{\in}I$ or the product of $a_{n+1}$ with (n-1) of $a_1,{\cdots},a_n$ is in $\sqrt{I}$. The aim of this paper is to investigate the concept of ${\phi}$-n-absorbing primary ideals.

• Journal of the Korean Mathematical Society
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• v.53 no.6
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• pp.1225-1236
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• 2016

Let R be a commutative ring with $1{\neq}0$ and n a positive integer. In this article, we introduce the n-Krull dimension of R, denoted $dim_n\;R$, which is the supremum of the lengths of chains of n-absorbing ideals of R. We study the n-Krull dimension in several classes of commutative rings. For example, the n-Krull dimension of an Artinian ring is finite for every positive integer n. In particular, if R is an Artinian ring with k maximal ideals and l(R) is the length of a composition series for R, then $dim_n\;R=l(R)-k$ for some positive integer n. It is proved that a Noetherian domain R is a Dedekind domain if and only if $dim_n\;R=n$ for every positive integer n if and only if $dim_2\;R=2$. It is shown that Krull's (Generalized) Principal Ideal Theorem does not hold in general when prime ideals are replaced by n-absorbing ideals for some n > 1.

• Communications of the Korean Mathematical Society
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• v.38 no.1
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• pp.39-46
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• 2023

Let R be a commutative ring, M be a Noetherian R-module, and N a 2-absorbing submodule of M such that r(N :_R M) = 𝖕 is a prime ideal of R. The main result of the paper states that if N = Q₁ ∩ ⋯ ∩ Q_n with r(Q_i :_R M) = 𝖕_i, for i = 1, . . . , n, is a minimal primary decomposition of N, then the following statements are true. (i) 𝖕 = 𝖕_k for some 1 ≤ k ≤ n. (ii) For each j = 1, . . . , n there exists m_j ∈ M such that 𝖕_j = (N :_R m_j). (iii) For each i, j = 1, . . . , n either 𝖕_i ⊆ 𝖕_j or 𝖕_j ⊆ 𝖕_i. Let Γ_E(M) denote the zero-divisor graph of equivalence classes of zero divisors of M. It is shown that {Q₁∩ ⋯ ∩Q_n-1, Q₁∩ ⋯ ∩Q_n-2, . . . , Q₁} is an independent subset of V (Γ_E(M)), whenever the zero submodule of M is a 2-absorbing submodule and Q₁ ∩ ⋯ ∩ Q_n = 0 is its minimal primary decomposition. Furthermore, it is proved that Γ_E(M)[(0 :_R M)], the induced subgraph of Γ_E(M) by (0 :_R M), is complete.

• Journal of the Korean Magnetics Society
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• v.14 no.5
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• pp.174-179
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• 2004

Attenuation of conduction noise through microstrip line attached with the high lossy iron flakes-rubber composites has been investigated in GHz frequencies. Microstrip line was designed with characteristic impedance of 50 $\Omega$ and a length corresponding to the center frequency of 3 GHz. Iron flakes were fabricated by mechanical forging of spherical iron powders using an attrition mill. The fabricated microstrip line shows a ideal propagation characteristics of S$\sub$11/ < -60 dB and S$\sub$21/ = 0 dB. Attaching a noise absorbing sheet on the microstrip line, S$\sub$11/ increases to about -10 dB and S$\sub$21/ decreases to -20～-60 dB depending on the length of absorbing sheet. The calculated power loss is as high as 80% in the frequency range 2～8 GHz. It is suggested that the most critical material parameter is magnetic loss for the enhancement of noise attenuation.

• Korean Journal of Optics and Photonics
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• v.20 no.1
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• pp.6-15
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• 2009

A mobile phone camera consisting of two aspheric lenses is designed, and stray light distribution on the image plane is analyzed. We assume that most of the incident light is absorbed on the inner surfaces of the lens barrel and spacers, only a small fraction of the light is scattered uniformly. Assuming that 10% of the incident light is scattered on the barrel and spacers, the maximum value of stray light is 7.1% of the ideal image intensity. The result of analysis shows that stray light originated mostly from internal reflection on the ribs. The contributions of scattering by the barrel and spacers are relatively small. To reduce the internal reflection, thin absorbing plates are inserted between lenses, and the shapes of spacers are modified. After the redesigning of the lens barrel, the maximum value of stray light is reduced to 1.1% of the ideal image intensity.

• Journal of the Korean Institute of Landscape Architecture
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• v.34 no.6 s.119
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• pp.39-53
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• 2007

Unlike conventional roof landscaping, where various kinds of plants and structures are employed, a grass roof is a roof on which herbaceous plants are grown in planting medium and which is not accessed or maintained, mainly because it doesn't have sufficient load capacity to support a regular roof garden. They are mostly built on existing roofs, whether flat slab or gabled. Planting on roofs has numerous advantages, such as creating a biotope, purifying urban air, adding moisture to the atmosphere, storing rain water, preventing flash floods, reducing energy use for heating and air conditioning, enhancing the urban landscape and providing relaxation to the city dwellers, not to mention the alleviation of global warming by absorbing $CO_2$. In addition to the general merits of roof planting, the grass roof has its own unique qualities. Only herbaceous species are planted on the roof, resulting in light weight which allows roofs of existing buildings to be planted without structural reinforcement. The species chosen are mostly short, tough perennials that don't need to be maintained. These conditions provide an ideal situation where massive planting can be done in urban areas where roofs are often the only and definitely the largest space available to be planted. If roofs are planted on a massive scale they can play a significant role in alleviating global warming, heat island effects and energy shortages. Despite the advantages of grass roofs, there are some problems. The most significant problem is the invasion of neighboring plants. They may be brought in with the planting medium, by birds or by wind. These plants have little aesthetic value comparing to the chosen species and are usually taller. Eventually they dominate and prevail over the original species. The intended planting design disappears and the roof comes to look wild. Since the primary value of a grass roof is ecological, a change in attitude towards what constitutes beauty on the roofscape is necessary. Instead of keeping the roof neat through constant maintenance, people must learn that the wild grass with bird's nests on their roof is more beautiful as it is.

• Journal of Sericultural and Entomological Science
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• v.47 no.2
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• pp.68-77
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• 2005

A characteristic of subtropical zones region MK-T2 compares with an gaeryangppong, and the 9-10 schedule the times when a leaf blooms to are fast, and ratio that a branch edge by the colds becomes lean showed 5.7%, and a growth of the new branch which went out delivers 67.2 cm, mulberry loaves of the new branch which went out, and 18.6, a form of a leaf is the 1.10 that length of a leaf grew more a bit than width of a leaf up. Thickness of a leaf is $228.2{\mu}m$, and an area is more similar than gaeryangppong as $225.6cm^2$. in plant taxonomy, the hair whom the style exists short with 0.7 mm, and go to the pistil head inside so as to be rare is distributed, and belong to Dolichostylae Pubescentes. The new branch cutting which executed without remedy processes was independent of a thickness of a case branch, and the form and 100% root was said, and an gaeryangppong compared with the fact that 10% root went out of 15 mm ideal, and was excellent very, and looked, a root went out a root the soil and water, all showed a characteristic to go out at central of a branch bases at 45% ratio. Length was 24.6 mm, and were water rate 78.8%, and mulberry of MK-T2 was carrying together sweetness and acidity to pH 4.7 while, besides, arrival was 19.21 Brix%. A larva period and pupa ratio, cocoon thickness ratio are almost similar to gaeryangppong, or weight of one cocoon, cocoon thickness, 20,002 cocoon quantity shows some results to drop, and be soft of a leaf, and feed value certifications are comparatively top-ranking. As a result of having analyzed amino acid of the 3rd day of 5th silkworm larva which bred to MK-T2, a collation absorbing an gaeryangppong went, and looked, but compared with a collation in case of tests to eat MK-T2, and looked, and the lie collations were not detected a difference at Leu, but MK-T2 tests were detected mutual almost similar amino acid creation. medical efficacy of the 3rd day of 5th silkworm larva ethanol extract which bred to MK-T2 and black results, histologic a case did not appear at HE dyeing about the kidney organization which extracted form the rats which ate a silkworm ethanol extract and dyeing all chemical organization immunity, and one step protein revelation became lower with almost unidentified levels.