• Journal of the Korean Mathematical Society
• /
• v.52 no.6
• /
• pp.1305-1321
• /
• 2015

We dene new link invariants which are called the quasitoric braid index and the cyclic length of a link and show that the quasitoric braid index of link with k components is the product of k and the cycle length of link. Also, we give bounds of Gordian distance between the (p,q)-torus knot and the closure of a braid of two specific quasitoric braids which are called an alternating quasitoric braid and a blockwise alternating quasitoric braid. We give a method of modication which makes a quasitoric presentation from its braid presentation for a knot with braid index 3. By using a quasitoric presentation of $10_{139}$ and $10_{124}$, we can prove that $u(10_{139})=4$ and $d^{\times}(10_{124},K(3,13))=8$.

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

• Kyungpook Mathematical Journal
• /
• v.55 no.1
• /
• pp.169-180
• /
• 2015

We study the braid indices of the Kanenobu knots. It is known that the Kanenobu knots have the same HOMFLYPT polynomial and the same Khovanov-Rozansky homology. The MFW inequality is known for giving a lower bound of the braid index of a link by applying the HOMFLYPT polynomial. Therefore, it is not easy to determine the braid indices of the Kanenobu knots. In our previous paper, we gave upper bounds and sharper lower bounds of the braid indices of the Kanenobu knots by applying the 2-cable version of the zeroth coefficient HOMFLYPT polynomial. In this paper, we give sharper upper bounds of the braid indices of the Kanenobu knots.

• Kyungpook Mathematical Journal
• /
• v.51 no.2
• /
• pp.205-215
• /
• 2011

Given a knot diagram D, we construct a semi-threading circle of it which can be an axis of D as a closed braid depending on knot diagrams. In particular, we consider semi-threading circles of minimal diagrams of a knot with respect to overpasses which give us some information related to the braid index. By this notion, we try to give another proof of the fact that, for every nontrivial knot K, the braid index b(K) of K is not less than the minimum number l(K) of overpasses of diagrams. Also, they are the same for a torus knot.

• Journal of the Korean Society of Fashion and Beauty
• /
• v.2 no.3 s.3
• /
• pp.11-18
• /
• 2004

The purpose of this study was to review the origin and background of well-being, the emerging well-being culture, and the phenomenon and features of the hair beauty affected by it. For this purpose, the researcher reviewed dissertations written between 199a and 2002, copies of the beauty journal Short Hair published between 2002 and 2003, beauty newspapers published between March, 2003 and June, 2004, and relevant Internet sites. When we review the well-being hair style tendency, we may be reminded of a light shaggy cut style with a thick wave volume or a natural wave highlighted, or a natural style with a natural color rendered by the braid technique. The well-being hair styles may be inspired by such natural images as the earth, sand, rock, wind, feather and flowers, while using cut, permanent wave or coloring technique for the hairs, in order to create new hair styles. The goal is to make men in contact with the nature. Meanwhile, as people are more concerned about diverse hair textures, natural and healthy hairs, they want their hairs to look comfortable and active rather than luxurious. The well-being cut styles may be categorized into cut style highlighting healthy hairs with a Bobos luxury and soft and light stroke cut reminiscent of a Bohemian freedom. The well-being permanent style may be divided into thick wave, natural wave, and the permanent style using a strong wave to make hairs look bloated. The hair colors reminding us of some natural images are used to highlight a well-being image. In addition, the concept of well-being pursuing a happy and healthy life has been being introduced into the permanent wave material liquids; such liquids made from natural materials, fruits or herbs increase, while environmental-friendly liquids or materials are used more for healthy hairs. The reason why the well-being culture influences hair styles importantly may be that people's desire of healthy body and mind and a comfortable life is reflected in hair styles. In conclusion, as the hair styles or an index for a new cultural current in our modern age are influenced by the well-being phenomenon, more and more people will put priority on healthy hairs. So, it is deemed necessary to apply the well-being hair styles appropriately to render satisfactory hair styles.