• Kyungpook Mathematical Journal
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• v.60 no.3
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• pp.485-505
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• 2020

We present a complete description of all the extreme points of the unit ball of 𝓛_s(²𝑙³_∞) which leads to a complete formula for ║f║ for every f ∈ 𝓛_s(²𝑙³_∞)^∗. We also show that $extB_{{\mathcal{L}}_s(^2l^3_{\infty})}{\subset}extB_{{\mathcal{L}}_s(^2l^n_{\infty})}$ for every n ≥ 4. Using the formula for ║f║ for every f ∈ 𝓛_s(²𝑙³_∞)^∗, we show that every extreme point of the unit ball of 𝓛_s(²𝑙³_∞) is exposed. We also characterize all the smooth points of the unit ball of 𝓛_s(²𝑙³_∞).

• Kyungpook Mathematical Journal
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• v.58 no.1
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• pp.47-54
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• 2018

We classify the extreme, exposed and smooth bilinear forms of the unit ball of the space of bilinear forms on $l^2_{\infty}$.

• Communications of the Korean Mathematical Society
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• v.32 no.4
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• pp.991-997
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• 2017

We classify the extreme, exposed and smooth symmetric 3-linear forms of the unit ball of ${\mathcal{L}}_s(^3l^2_{\infty})$, respectively.

• Kyungpook Mathematical Journal
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• v.57 no.2
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• pp.223-232
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• 2017

We classify the extreme and exposed symmetric bilinear forms of the unit ball of the space of symmetric bilinear forms on ${\mathbb{R}}^2$ with hexagonal norms. We also show that every extreme symmetric bilinear forms of the unit ball of the space of symmetric bilinear forms on ${\mathbb{R}}^2$ with hexagonal norms is exposed.

• Communications of the Korean Mathematical Society
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• v.34 no.2
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• pp.487-494
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• 2019

We classify all the extreme and exposed bilinear forms of the unit ball of ${\mathcal{L}}(^2l^3_{\infty})$ which leads to a complete formula of ${\parallel}f{\parallel}$ for every $f{\in}{\mathcal{L}}(^2l^3_{\infty})^*$. It follows from this formula that every extreme bilinear form of the unit ball of ${\mathcal{L}}(^2l^3_{\infty})$ is exposed.

• Korean Journal of Agricultural Science
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• v.25 no.1
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• pp.26-32
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• 1998

Three major trails of campus forest in Chungnam National University were selected to investigate the use impacts on environmental deterioration of trail according to the different amount of use. Rook-exposed, root-exposed, deepening, widening, diverged points as the deterioration types of trail which were surveyed at total of 92 points in major trail of campus forest in Chungnam National University. Major deterioration types of trail were widening, rock-exposure, root-exposure, in order of frequency. And trail conditions (trail slope and maximum depth) of deteriorated points were significantly different from those of non-deteriorated points.

• Journal of the Korean Mathematical Society
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• v.60 no.1
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• pp.213-225
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• 2023

For every n ≥ 2, let ℝⁿ_‖·‖ be Rn with a norm ‖·‖ such that its unit ball has finitely many extreme points more than 2n. We devote to the description of the sets of extreme and exposed points of the closed unit balls of 𝓛(²ℝⁿ_‖·‖) and 𝓛_𝒮(²ℝⁿ_‖·‖), where 𝓛(²ℝⁿ_‖·‖) is the space of bilinear forms on ℝⁿ_‖·‖, and 𝓛_𝒮(²ℝⁿ_‖·‖) is the subspace of 𝓛(²ℝⁿ_‖·‖) consisting of symmetric bilinear forms. Let 𝓕 = 𝓛(²ℝⁿ_‖·‖) or 𝓛_𝒮(²ℝⁿ_‖·‖). First we classify the extreme and exposed points of the closed unit ball of 𝓕. We also show that every extreme point of the closed unit ball of 𝓕 is exposed. It is shown that ext B_{𝓛𝒮(²ℝⁿ‖·‖)} = ext B_{𝓛(²ℝⁿ‖·‖)} ∩ 𝓛_𝒮(²ℝⁿ_‖·‖) and exp B_{𝓛𝒮(²ℝⁿ‖·‖)} = exp B_{𝓛(²ℝⁿ‖·‖)} ∩ 𝓛_𝒮(²ℝⁿ_‖·‖), which expand some results of [18, 23, 28, 29, 35, 38, 40, 41, 43].

• Proceedings of the Korean Institute of Building Construction Conference
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• 2016.05a
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• pp.164-165
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• 2016

To express the original texture of the concrete, exposed concrete finishing technique has been applied in many buildings. However, it is likely to cause quality problems after construction is completed. In addition, because of costs and time issues, reconstruction and maintenance works are difficult and ineffective. Therefore, step-by-step proactive quality management based on sufficient consensus among participants(client, designer, contractor) is very importatnt. This study analyzed factors causing low quality exposed concrete and quality contol points applied to 'A' headquarter construction project.

• Journal of Korean Society of Forest Science
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• v.95 no.2
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• pp.216-219
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• 2006

After long exposure to low-density $SO_2$ the five tree species showed different changes in their visible damage: Ailanthus altissima showed no visible damage; Acanthopanax sessiliflorus, Populus alba ${\times}$ Populus glandulosa, and Platanus orientalis showed typical damage of yellow spots on their leaves; and Liriodendron tulipifera showed serious damage on the end of leaf tip. The photosynthesis rate of Liriodendron tulipifera and Acanthopanax sessiliflorus was usually lower than the control group: Ailanthus altissima, Populus alba ${\times}$ Populus glandulosa, and Platanus orientalis showed no difference from the control group, while Acanthopanax sessiliflorus and Liriodendron tulipifera showed large changes. In regard to the light compensation points, Ailanthus altissima showed similar values, Populus alba ${\times}$ Populus glandulosa and Platanus orientalis exposed to $SO_2$, showed 3 to $5{\mu}mol{\cdot}m^{-2}{\cdot}s^{-1}$ higher values than the control group, and Acanthopanax sessiliflorus and Liriodendron tulipifera exposed to $SO_2$ showed approximately twice higher light compensation points.

• The Journal of the Society of Korean Medicine Diagnostics
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• v.16 no.3
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• pp.41-48
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• 2012

Objectives: The aims of this study are to design a optimized mechanical structure of digital tongue imaging system (DTIS) equipped with LEDs in aspects of object distance and camera angle of coverage. Methods and Results: We tried to find optimized object distance while recording a rectangular object of common tongue size. In case object distance is 22 cm or less, edge of the rectangle was not taken beyond the shooting range. In contrast, if object distance is 40 cm or more, the rectangle image was too small. Therefore when considering the variation of subjects, we selected distance of 35-40 cm as appropriate object distance for the DTIS. We also tried to find optimized angle between camera view axis and horizontal line. We photographed from the side of the face of 7 adults with exposed tongue. We drew an exposed tongue lines to connect the tongue tip points and the tongue root points by using the photos acquired from the side faces. And then we calculated the tongue exposure angles between the vertical line and the exposed tongue lines. Mean tongue exposure angle was $28.3^{\circ}$ when tongue was lightly exposed and $13.3^{\circ}$ when maximally. So we determined $73^{\circ}$ as appropriate slope angle of part in contact with face of the DTIS and by considering that the standard variation was great, we designed control gears to adjust the slope of the camera view axis and to regulate the object distance. Conclusions: We designed a optimized mechanical structure in object distance and slope angle of part in contact with face of the DTIS.