• 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.10 no.4
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• pp.849-854
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• 1995

The interpolation of scattered data with radial basis functions is knwon for its good fitting. But if data get large, the coefficient matrix becomes almost singular. We introduce different knots and nodes to improve condition number of coefficient matrix. The singulaity of new coefficient matrix is investigated here.

• Kyungpook Mathematical Journal
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• v.54 no.2
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• pp.271-292
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• 2014

We introduce a new method to transform a knot diagram into a diagram of an unknot using a polynomial representation of the knot. Here the unknotting sequence of a knot diagram with least number of crossing changes can be realized by a family of polynomial maps. The number of singular knots in this family is defined to be the singularity index of the diagram. We show that the singularity index of a diagram is always less than or equal to its unknotting number.

• Journal of the Korean Society of Costume
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• v.59 no.4
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• pp.1-13
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• 2009

The purpose of this study is to examine the types of and figurative characteristics of in women's embroidered handicrafts of Korea. It also aims to revive Korean traditional beauty, to examine the applicability of Korean traditional design that has both modern beauty and practicality, and to develop Korean women's embroidered handicrafts. The types of women's embroidered of Korea include Jumoni (pouches), Bojagi (wrapping cloths), and other accessories made by sewing. Jumoni consisting of 55.51% of them was the most frequently used handicraft followed by Bojagi (8.66%), and other accessories (35.83%). In terms of the patterns used, animal pattern and plant pattern were used the most frequently. In addition, complex patterns using two or three patterns together(70.49) were more frequent than singular patterns (29.53%). Pictorial type of pattern arrangement (58.24%) was used the most frequently and dense type (39.76%) and sparse type (2.00%) were followed. In terms of the materials on which embroidery was used, Dahn (85.82%) was used the most frequently followed by wool (5.67%), cotton (4.26%), silk (3.55%), and Sa (0.70%). Various techniques of stitches were used such as outline stitch (40.56%), satin and running stitch (29.32%), French nut stitch (28.11%), long and short stitch (21.28%), double leaf stitch (20.88%), and so on. Among them, satin stitch (63.05%) was the most popular type of stitch techniques. Strings (23.56%), maedeup (Korean traditional knots, 8.62%), or tassels (9.77%) were also attached for the purpose of both practicality and of decoration. There were some cases that added cloissone or red-pepper shaped decorations.