• Journal of the Korean Mathematical Society
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• v.51 no.3
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• pp.443-462
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• 2014

Using a simple recurrence relation, we give a new method to compute the Jones polynomials of closed braids: we find a general expansion formula and a rational generating function for the Jones polynomials. The method is used to estimate the degree of the Jones polynomials for some families of braids and to obtain general qualitative results.

• Journal of applied mathematics & informatics
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• v.40 no.1_2
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• pp.117-132
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• 2022

Reverse edge magic(REM) labeling of the graph G = (V, E) is a bijection of vertices and edges to a set of numbers from the set, defined by λ : V ∪ E → {1, 2, 3, …, |V| + |E|} with the property that for every xy ∈ E, constant k is the weight of equals to a xy, that is λ(xy) - [λ(x) + λ(x)] = k for some integer k. We given the construction of REM labeling for the Cartesian Product, Unions of Braids and Unions of Triangular Belts. The Kotzig array used in this paper is the 3 × (2r + 1) kotzig array. we test the konow results about REM labelling that are related to the new results we found.

• 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.

• Kyungpook Mathematical Journal
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• v.57 no.2
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• pp.331-360
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• 2017

Unknotting numbers for torus knots and links are well known. In this paper, we present a new approach to determine the position of unknotting number crossing changes in a toric braid such that the closure of the resultant braid is equivalent to the trivial knot or link. Further we give unknotting numbers of more than 600 knots.

• Kyungpook Mathematical Journal
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• v.32 no.3_spc
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• pp.435-443
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• 1992

• Journal of the Korea Fashion and Costume Design Association
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• v.10 no.1
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• pp.45-53
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• 2008

Different method of textile fabrication had existed since the ancient times, but the most dominant form was the 'weaving' method which embodies the cross fabrication of vertical and horizontal threads using special weaving machines (looms). In addition, fabrication methods like knitting, felt, and lace were commonly practiced while intertwinement methods like twisting, braiding, and knotting techniques were frequently used for weaving strings and braid type textiles. In the past, people did not pay attention to strings and braids because they were classified as non-textiles, but, in this paper, we have expanded the scope of definition of textile to include strings and braids, and seek to conduct in-depth research on various different intertwinement of textiles. The adaptation of intertwinement method in arts and crafts enables limitless creative works reflecting the ever-changing taste and style of the creator. This creativity is further broadened by the fact that intertwinement methods encompass no set patterns and the subject and shape of its creation is as broad as its artistic pursuits. We can infer the knowledge of our ancestors, their aesthetic taste, and the pattern of life from these creations. In addition, these creations can provide comfort and improve the quality of life of modem people who are deeply deprived of sentimental and emotional solitude in the technological civilization of the 21stcentury. The main purpose of this paper is to examine traditional Korean arts and crafts made using the intertwinement methodology through the context of strings, braids, straw crafts and knotting method. Then it will conduct through research on the different materials, forms, characteristics, usage and other key notions based on the currently preserved records and relics to contribute to the research on traditional textiles and provide the foundations to the development of the Korean culture and cultural products, reflecting the true sole and aesthetics of traditional Korean textile crafts.

• Kyungpook Mathematical Journal
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• v.55 no.4
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• pp.779-806
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• 2015

We construct a state model for the two-variable Kauman polynomial using planar trivalent graphs. We also use this model to obtain a polynomial invariant for a certain type of trivalent graphs embedded in $\mathbb{R}^3$.

• Journal of the Korean Mathematical Society
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• v.40 no.2
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• pp.179-193
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• 2003

The braid-permutation group is a group of welded braids which is the extension of Artin's braid groups by the symmetric groups. It is also described as a subgroup of the automorphism group of a free group. We also show that the plus-construction of the classifying space of the infinite braid-permutation group has the following two types of splittings BBP(equation omitted) B∑(equation omitted) $\times$ X, BBP(equation omitted) B $^{＋}$$\times$ Y＝S$^1$$\times$Y, where X, Y are some spaces.

• Kyungpook Mathematical Journal
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• v.55 no.1
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• pp.191-203
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• 2015

We introduce a quasitoric virtual braid and show that every virtual link can be obtained by the closure of a quasitoric virtual braid. Also, we show that the set of quasitoric virtual braids with n strands forms a group which is a subgroup of the n-virtual braid group.

• Journal of the Korea Fashion and Costume Design Association
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• v.21 no.4
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• pp.127-137
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• 2019

Nail art, which has been popularized recently, has increased convenience in the direction of nail art design harmonized with clothing and the increased interest and usage of nail art decoration. This study set out to propose practical planar and three-dimensional nail art designs in harmony with modern clothes by applying trimmings common in 18th century women's clothing, which used a variety of attachable decorations. As for the methodology, the investigator examined theories in previous studies, literature, and analyzed the types of trimming in female portraits from the 18th century at the museum at the Palace of Versailles in France. Planar and three-dimensional nail art designs were created for each of the top three trimming types- braids, laces, and ribbons, which were identified through analysis. The study applied the trimmings of the 18th century women's clothes to nail art design and had the following results: First, the top three trimming types were identified based on the analysis of the 18th century portraits. They were then used as motifs in the production of planar and three-dimensional nail art designs. The results show that the motifs of the clothes trimmings were fit for and had practical possibilities for expression in nail art designs. Secondly, diversity and the expansion of ideas in the study of nail art design were promoted. In addition, elements were increased to have mutually complementary effects with clothes. Finally, the study made various attempts at nail design methods by adopting a range of nail art expression techniques including hand painting, 2D & 3D art techniques, and using planar and three-dimensional nail decorations, thus proposing a positive direction for the organization of a curriculum to make use of 18th century women's clothing motifs in nail art education.