• 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 $d^{\times}(10_{124},K(3,13))=8$.

• Journal of the Korean Mathematical Society
• /
• v.34 no.3
• /
• pp.673-693
• /
• 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 $B_4$.

• Journal of the Chungcheong Mathematical Society
• /
• v.23 no.3
• /
• pp.555-561
• /
• 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.

• Journal of the Korean Mathematical Society
• /
• v.54 no.3
• /
• pp.749-762
• /
• 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.

• Honam Mathematical Journal
• /
• v.33 no.3
• /
• pp.407-418
• /
• 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 $\bar{\beta}$.

• Fibers and Polymers
• /
• v.5 no.3
• /
• pp.182-186
• /
• 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.

• Journal of the Korean Mathematical Society
• /
• v.47 no.3
• /
• pp.445-454
• /
• 2010

The braid group $B_n$ maps homomorphically into the Temperley-Lieb algebra $TL_n$. It was shown by Zinno that the homomorphic images of simple elements arising from the dual presentation of the braid group $B_n$ form a basis for the vector space underlying the Temperley-Lieb algebra $TL_n$. In this paper, we establish that there is a dual presentation of Temperley-Lieb algebras that corresponds to the dual presentation of braid groups, and then give a simple geometric proof for Zinno's theorem, using the interpretation of simple elements as non-crossing partitions.

• Journal of the Korea Institute of Information Security & Cryptology
• /
• v.11 no.3
• /
• pp.13-22
• /
• 2001

The notion of pseudorandomness plays an important role in modem cryptography as well as computer science. We show a simple and practical construction of a pseudorandom generator based on the intractability of the problem in braid groups. The generator is proved as secure as a hard instance of a variant of the conjugacy problem.

• Kyungpook Mathematical Journal
• /
• v.49 no.1
• /
• pp.7-14
• /
• 2009

In this short note, we consider a family of linear representations of the braid group and the fundamental group of a punctured torus bundle over the circle. We construct an irreducible (special) unitary representation of the fundamental group of a closed 3-manifold obtained by the Dehn filling.

• Proceedings of the Korean Society For Composite Materials Conference
• /
• 2004.10a
• /
• pp.163-166
• /
• 2004

Epoxy composite reinforced with 3-D braided Glass/Aramid hybrid fabric was fabricated. FBG sensor was embedded along the braid yam in order to monitor the changes of the complicated inner region of the 3-D braid structure. The good linearity between Bragg wavelength and temperature was verified by several preliminary experiments. The strain inside 3-D braided beam was estimated using FBG sensor system, and the result was compared with the calculated value. It was found that FBG sensor system is very useful technique to investigate inside region of complicated structure.