• Bulletin of the Korean Mathematical Society
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• v.48 no.3
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• pp.469-474
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• 2011

The Kauffman bracket skein module $K_t$(M) of a 3-manifold M becomes an algebra for t = -1. We prove that this algebra has no non-trivial nilpotent elements for M being the exterior of the twist knot in 3-sphere and, therefore, it is isomorphic to the $SL_2(\mathbb{C})$-character ring of the fundamental group of M. Our proof is based on some properties of Chebyshev polynomials.

• Bulletin of the Korean Mathematical Society
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• v.54 no.6
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• pp.1927-1933
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• 2017

We prove that there are rational homology balls $B_p$ smoothly embedded in the 2-handlebodies associated to certain knots. Furthermore we show that, if we rationally blow up the 2-handlebody along the embedded rational homology ball $B_p$, then the resulting 4-manifold cannot be obtained just by a sequence of ordinary blow ups from the 2-handlebody under a certain mild condition.

• Bulletin of the Korean Mathematical Society
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• v.50 no.6
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• pp.1989-2000
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• 2013

We show that for any given closed orientable 3-manifold M with a Heegaard surface of genus g, any positive integers b and n, there exists a knot K in M which admits a (g, b)-bridge splitting of distance greater than n with respect to the Heegaard surface except for (g, b) = (0, 1), (0, 2).

• Journal of the Korean Mathematical Society
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• v.36 no.1
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• pp.51-71
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• 1999

We classify all conjugacy classes of 3-braids that are related by flypes on representatives. Among them we determine which classes have representatives that admit both (+) and (-) flypes as an effort to search for a potential example of a pair of transversal knots that are topologically isotopic and have the same Bennequin number but are not transversally isotopic.

• Communications of the Korean Mathematical Society
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• v.10 no.2
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• pp.483-490
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• 1995

A parametric cubic spline interpolating at fixed number of nodes is constructed by formulating a parametric cubic $g^2$ B-splines $S_3(t)$ with not equally spaced parametric knots. Since the fact that each component is in $C^2$ class is not enough to provide the geometric smoothness of parametric curves, the existence of $S_3(t)$ oriented toward the modified second-order geometric continuity is focalized in our work.

• Proceedings of the Korean Society of Marine Engineers Conference
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• 2001.05a
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• pp.163-167
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• 2001

The paper introduce the basic concept for the variable graph description of blending functions in NURBS using some control method; the control points, knot vectors and weight points in 3D space.

• Communications of the Korean Mathematical Society
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• v.38 no.3
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• pp.913-924
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• 2023

We consider the number of colors for colorings of links by the symmetric group S₃ of degree 3. For knots, such a coloring corresponds to a Fox 3-coloring, and thus the number of colors must be 1 or 3. However, for links, there are colorings by S₃ with 4 or 5 colors. In this paper, we show that if a 2-bridge link admits a coloring by S₃ with 5 colors, then the link also admits such a coloring with only 4 colors.

• Journal of the Korean Society of Marine Environment & Safety
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• v.24 no.6
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• pp.646-653
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• 2018

Marine accidents caused by dragging anchors occur constantly due to enlargement of ships' size and unusual weather conditions. Nevertheless, vessel operators rely on their experience because the calculations of actual holding power and external forces are complex and inconvenient. The purpose of this study was to propose a program for the anchor dragging risk assessment in order to provide crew and VTSO with the information to determine easily the danger of dragging and take appropriate action. The input data in this program were composed of the ship's basic particulars, anchoring condition, and external environment etc. on calculating for the wind pressure, frictional force, drift force, and holding power. Three dragging anchor accidents were applied to the program's data input at the time of the day, then the result was assessed by 'warning', which was verified with a high confidence. As a result, the risk of dragging anchors can be predicted in advance through this program. In further studies, it is necessary to simplify the input data and improve user convenience through automatic input from various equipment.

• Journal of Conservation Science
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• v.31 no.1
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• pp.65-73
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• 2015

The purposes of this study are helping the understanding on the Dae-hwe kind relics, verifying the deformation rate stability during conservation treatment and enhancing the conservation treatment work by investigating the status and analyzing the material of Taejo's portrait mounting decorative knots in the National Palace Museum of Korea collection. The result of material analysis on the decorative knots was that the outer threads are silk threads, inner threads are cotton threads, the width of the metal threads was $500{\sim}600{\mu}m$ and the major component of it was 55wt% copper. The result of verification on the deformation rate during the form correction of the bell tassel was that it has been found as stable by having the deformation rate of 1 TPCM or less. The result of glue selection test to be used on the repairing of tassel cross-section with its thread cut was that wheat starch adhesive has been found most appropriate because it has the highest tensile strength at all concentrations. The conservation and treatment procedure was established based on above results of analysis and test on the relic and the conservation treatment work including packaging has been completed in accordance with the established procedure.

• Journal of the Korean Wood Science and Technology
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• v.18 no.3
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• pp.53-68
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• 1990

This research has been executed for maximization of lumber yield and more efficient use of small diameter logs. Sample logs from thinnings carne from densed artificial stands at the Kwangnung Experimental Forests situated in the central region of Korean peninsula. Species of sample logs were obtained to execute sawing and strength test for larch, and lumber strength test in full size for pitch pine and Korean pine. A survey on sawmills consuming domestic logs was carried out to know sawmill production, costs and utilization structure of lumber as a guide to business analysis. Results showed that sawing pattern from small logs less than 15cm in diameter was necessary to cut 9cm by 9cm square per one log in order to obtain high lumber recovery and provide for wide market needs. The total lumber yield of squares plus side boards was 56 percent to 58 percent from small logs and the yield for log sweep in 30 percent decreased by 24.5 percent in sawing production, compared to yield for straight logs. In sawing efficiency, production of lumber by twin band saw could be improved 238 percent higher than lumber of the same species produced by conventional sawmilling methods, and sawing accuracy with twin band saw was much higher at the lumber production than band saw. Lumber from the small larch logs has shown 70 knots per $m^2$ on its faces and also lumber showed lots of face checkings by air drying on the yard, compared to other species. MOR in bending of lumber in full size from small logs of larch was found ranging from 380kg/$cm^2$ to 460kg/$cm^2$, resulting in 40 percent less than the strength from clear small specimens. In lumber containing knots, cross grain, etc, longitudinal stress wave speed was delayed about 48 percent by defects in lumber from both larch and pitch pine logs. The surveyed sample sawmills consumed the domestic logs at the rate of 54 percent to 84 percent in the total timber consumption, showing high consumption at mills located in the mountains.