• 대한수학회지
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• 제52권6호
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• pp.1305-1321
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• 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
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• 제55권1호
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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.

• 대한수학회지
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• 제54권3호
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• pp.749-762
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• 2017

The surface singular braid monoid corresponds to marked graph diagrams of knotted surfaces in braid form. In a quest to resolve linearity problem for this monoid, we will show that if it is defined on at least two or at least three strands, then its two or respectively three dimensional representations are not faithful. We will also derive new presentations for the surface singular braid monoid, one with reduced the number of defining relations, and the other with reduced the number of its singular generators. We include surface singular braid formulations of all knotted surfaces in Yoshikawa's table.

• Kyungpook Mathematical Journal
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• 제55권1호
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• pp.169-180
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• 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.

• 대한수학회지
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• 제34권3호
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• pp.673-693
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• 1997

In this work, the irreducible complex representations of degree 4 of $B_4$, the braid group on 4 strings, are classified. There are 4 families of representations: A two-parameter family of representations for which the image of $P_4$, the pure braid group on 4 strings, is abelian; two families of representations which are the composition of an irreducible representation of $B_3$, the braid group on 3 strings, with a certain special homomorphism $\pi : B_4 \longrightarrow B_3$; a family of representations which are the tensor product of 2 irreducible two-dimensional representations of $B_4$.

• 대한수학회지
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• 제40권2호
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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.

• 호남수학학술지
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• 제33권3호
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• pp.407-418
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• 2011

There are two kinds of closing method for a given braid ${\beta}{\in}B_{2n}$, a braid closure $\hat{\beta}$ and a plat closure $\bar{\beta}$. In the article, we find a relation between the Conway potential function ${\nabla}_{\hat{\beta}}$ of braid closure $\hat{\beta}$ and ${\nabla}_{\hat{\beta}}$ of plat closure $\bar{\beta}$.

• 충청수학회지
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• 제23권3호
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• pp.555-561
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• 2010

For the pure braid groups, this paper gives a positive finite presentation whose generators are the standard Artin generators, and determines whether the submonoid generated by the Artin generators is a Garside monoid or not.

• Fibers and Polymers
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• 제5권3호
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• pp.182-186
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• 2004

The effect of braid construction parameters on yarn cross-sectional shape is presented in this paper. The location of the yam within the braid unit cell is quantified by a compaction factor. A range of braided fabrics were produced and optically measured for actual yarn cross-sectional shape. A comparison of the theoretical and experimental values shows good correlation. Design curves can be produced with the developed model to allow selection of appropriate braid process parameter to create yarns with desired cross-sectional geometries.

• 접착 및 계면
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• 제8권4호
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• pp.14-22
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• 2007

본 연구에서는 페놀수지의 열안정성 그리고 glass braid/페놀수지 복합재료의 동역학적 열특성에 미치는 유리분말 및 액상 니트릴고무(NBR)의 영향을 열중량분석기와 동역학적 열분석기를 이용하여 조사하였다. 수용성 페놀수지에 충진된 유리분말과 NBR은 페놀수지의 열안정성과 복합재료의 저장탄성률 그리고 tan ${\delta}$ 변화에 중요한 영향을 미쳤다. 유리분말의 충진은 페놀수지의 열안정성을 향상시키는 반면, NBR의 존재는 특정 온도영역에서 페놀수지의 중량감소를 초래하였다. 충진제의 유 무에 따른 페놀수지의 열안정성은 경화온도뿐만 아니라 경화시간에도 의존하였다. 스트립형태의 glass braid/페놀수지 복합재료의 저장탄성률과 tan ${\delta}$의 변화는 유리분말과 NBR이 혼합된 매트릭스의 도입과 경화조건에 의해 크게 영향을 받았다.