• Journal of the Korean Mathematical Society
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• v.58 no.4
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• pp.967-976
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• 2021

We obtain the list of prime knots with arc index 12 up to 16 crossings and their minimal grid diagrams. This is a continuation of the works [5] and [8] in which Cromwell matrices were generated to obtain minimal grid diagrams of all prime knots up to arc index 11. We provide minimal grid diagrams of the prime alternating knots with arc index 12. They are the 10 crossing prime alternating knots. The full list of 19,513 prime knots of arc index 12 up to 16 crossings and their minimal grid diagrams can be found in the arXiv [6].

• The Bulletin of The Korean Astronomical Society
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• v.35 no.2
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• pp.68.1-68.1
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• 2010

Cassiopeia A supernova remnant is a young (~330 yr) remnant of Type IIb SN explosion with a massive progenitor. It shows two distinct optical knots; fast moving ejecta knots (FMKs) and quasi stationary circumstellar knots (QSFs). These knots offer an unique opportunity to explore the details of the explosion and also the end state evolution of the Type IIb SN progenitor. We have obtained NIR long-slit (30") spectra of 7 positions around the bright rim of Cas A in [Fe II] 1.644 micron using Triplespec which is a cross-dispersed near-infrared spectrograph that provides continuous wavelength coverage from 0.95-2.46um at intermediate resolution of 2700. Most of the FMKs show strong sulfur, silicon, and iron forbidden lines but no hydrogen or helium lines. The QSFs, on the other hand, show a much richer spectrum with strong hydrogen, helium, and iron lines, but no sulfur and silicon lines. We measure their fluxes and radial velocities, and derive their physical parameters such as electron density and temperature. We also measure the proper motion of these knots from two [Fe II] 1.644 micron images obtained at 3-year interval. We analyze the physical properties of these knots and discuss the evolution and explosion of the progenitor of Cas A.

• Bulletin of the Korean Mathematical Society
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• v.55 no.3
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• pp.937-956
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• 2018

This article gives the foundations of the colored Jones polynomial for singular knots. We extend Masbum and Vogel's algorithm [26] to compute the colored Jones polynomial for any singular knot. We also introduce the tail of the colored Jones polynomial of singular knots and use its stability properties to prove a false theta function identity that goes back to Ramanujan.

• Communications of the Korean Mathematical Society
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• v.33 no.2
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• pp.591-604
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• 2018

We consider a family of ribbon 2-knots with trivial Alexander polynomial. We give nonabelian SL(2, C)-representations from the groups of these knots, and then calculate the twisted Alexander polynomials associated to these representations, which allows us to classify this family of knots.

• Journal of the Korean Mathematical Society
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• v.51 no.6
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• pp.1221-1250
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• 2014

In this paper, we construct infinite families of knots in $S^3$ which admit Dehn surgery producing a graph manifold which consists of two Seifert-fibered spaces over the disk with two exceptional fibers, glued together along their boundaries. In particular, we show that for any natural numbers a, b, c, and d with $a{\geq}3$ and $b,c,d{\geq}2$, there are knots in $S^3$ admitting a graph manifold Dehn surgery consisting of two Seifert-fibered spaces over the disk with two exceptional fibers of indexes a, b, and c, d, respectively.

• Korean Journal of Human Ecology
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• v.10 no.2
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• pp.189-203
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• 2001

The pulpous of this study is to investigated the kind and feature of the knots used in four categories, "living, clothing, ceremony, and decoration", after analysing and examining 42 knot remains of the folklore museum of On yang. The method were by old books and various kind's related books, history of knots and kind of knots investigated and analyze relics were actual proof investigation of real things and supplementary materials were photos, drawings, and museum's explanation used. The results are as is following ; First, a knot is twisted by two threads, formed in the process of twisting, become in equal shape, and made in symmetry. Second, In knot's names, there are sangkang, karakge, ankyongchip, jamjary, kukhwa, bol, byongary, memi, kkondiki, kong, yonbong which are easily seen in nature. Third, a knot was used in as living things in the era of the three Kingdoms, as a decoration such as Buddhism goods in Koryo. In the era of Cho sun, Because of the development of knot's kind and the variety of service, it was the target of restriction as a luxury. Fourth, as a result of investigating museum's relics, a knot was smaller than the chief object because that is a decoration. Fifth, there are 8 kinds for living and clothing which are simple knots "doramaetup, karakgemaetup, and sangtchokmaetup". Sixth, the complex knots such as kukhwamaetup, byongarymaetup, and 3bolkamkae emaetup are used on pangchang, chokja, nambawi, and chobawi. Seventh, there are 10 kinds for ceremony, the simple knots are twisted and the complex knots such as kukhwamaetp, maehwamaetup, nabimaetup, and sasaekgupoki are used. Eighth, there are 14 kinds for decoration, the simple knots such as doraemaetup, kakagemaetup, santchokmaetup, and ankyongchipmaetup and the applied knots such as kukhwamaetup, byongarymaemaetup, changkumaetup, nabimaetup, and seokssima etup are used. There are 42 knot remains in the folklore museum of On yang. Of them, there are 33 kinds in the present, 17 used. that is because only several knots have been used. Finally, to forget the knot's way, we will set up a plan to keep with it.

• Communications of the Korean Mathematical Society
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• v.19 no.3
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• pp.531-544
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• 2004

We study a family of 2-bridge knots with 2-tangles in the 3-sphere admitting a genus two 1-bridge splitting. We also observe a geometric relation between (g - 1, 1)-splitting and (g,0)- splitting for g = 2,3. Moreover we construct a family of closed orientable 3-manifolds which are n-fold cyclic coverings of the 3-sphere branched over those 2-bridge knots.

• Bulletin of the Korean Mathematical Society
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• v.40 no.1
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• pp.101-108
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• 2003

In this paper we study the connections between cyclic presentations of groups and cyclic branched coverings of (1, 1)- knots. In particular, we prove that every π-fold strongly-cyclic branched covering of a (1, 1)-knot admits a cyclic presentation for the fundamental group encoded by a Heegaard diagram of genus π.

• Bulletin of the Korean Mathematical Society
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• v.61 no.3
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• pp.779-784
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• 2024

Baker proved that any strongly quasi-positive fibered knot is minimal with respect to the ribbon concordance among fibered knots in the three-sphere. By applying Rapaport's conjecture, which has been solved by Kochloukova, we can check that any strongly quasi-positive fibered knot is minimal with respect to the ribbon concordance among all knots in the three-sphere. In this short note, we give an alternative proof for the fact by utilizing the knot Floer homology.

• Journal of the Korean Wood Science and Technology
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• v.31 no.6
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• pp.22-30
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• 2003

This study was performed to obtain the basic data for high quality timber production and efficient utilization by investigating the effect of pruning on timber quality of domestic plantation-grown Korean pine (Pinus koraiensis Sieb. et Zucc.). The results were summarized as follows:Dead knots (unsound knots) in the pruned logs occurred more at upper parts when compared with in non-pruned ones. The numbers of knots on surface in heavily pruned trees were less than those in non-pruned trees, but there was no significant difference in moderately pruned trees. The required period to reveal clear timber surface without defects after pruning increased proportionally with the increase of knot diameter. The yield of clear lumber production increased by about 10% after 14 years from moderate pruning. The quality grade of log improved with more pruning practices. Knots appeared the most important factor in lowering the log grades.