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

• Journal of the Korean Mathematical Society
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• v.47 no.3
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• pp.445-454
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• 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
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• v.11 no.3
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• pp.13-22
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• 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.

• Composites Research
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• v.31 no.6
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• pp.293-298
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• 2018

In this paper, we have studied the physical properties of braided composites for use as aircraft stringers. Process variables such as drum winder speed, braid velocity, and mandrel diameter for $30^{\circ}$, $45^{\circ}$ and $60^{\circ}$ braid preforms were quantified and different epoxy resin types were applied to the braided preform using TGDDM, YD-128. Physical properties such as tensile strength and flexural strength of braided composites were investigated. Thermal properties and decomposition temperature of epoxy resin were investigated by TGA analysis. As a result, the lower the angle of the braid composites, the higher the tensile strength and the Flexural strength. The physical properties of braided composites fabricated using TGDDM epoxy resin were superior to the physical properties of braided composites fabricated using YD-128 epoxy resin. This is because the molecular weight of TGDDM epoxy resin was higher than that of YD-128 epoxy resin.

• Journal of Power System Engineering
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• v.9 no.3
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• pp.71-78
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• 2005

A high-pressure hose includes rebar layers of the synthetic fiber such as nylon or a steel wire to control internal pressure. The hose assembly is manufactured through the swaging process to clamp the hose into the metal fittings. Usually, the hose behavior is affected by the resultant of the longitudinal and circumferential forces produced by the internal pressure. The rebar layers can appear the most ideal rebar effect when they are arranged to the same direction as the resultant force. The braid angle applied in the rebar layers is an important factor in determining ultimate burst pressure and overall hose life. Failure can occur on the contacted parts of a hose with the metal fittings under severe operating conditions such as high pressure and temperature of the inner fluid. In this paper, the mechanical behavior between the hose and the metal fittings during the swaging process and the stress variation characteristics of a high-pressure hose under a constant applied pressure are analyzed with respect to the braid angle of steel wire using the finite element method.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.66 no.1
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• pp.243-248
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• 2017

This study used general carbon fibers(CF), which can be utilized for a low voltage cable screen, as well as metal-coated carbon fibers(MCF) to make cables and analyzed the properties of electromagnetic effectiveness. Both braid CF and MCF cables with 3,000 strands, 16 spindles, and braid density of 90% or over were adopted. The tape-type MCF specimens were spread into a tape(width: 15mm) using a hot melt to make a cable. The shield effectiveness was measured up to the 1GHz range in accordance with IEC 62153-4-6; braid shielded cables featured a superior shielding effect at 63dB than tape-type shielded cables. That was because the tape-type shielded cable has relatively more gaps and holes between carbon fibers than the braid type, resulting in a more inflow or emission of electromagnetic waves. In the case of braid cables, the characteristics of their electromagnetic waves were enhanced, with higher spindles and higher conductivity of carbon fibers. The shield effectiveness of the MCF shielded cable, however, was lower than that of tin-coated one.

• Proceedings of the Korean Society For Composite Materials Conference
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• 2005.04a
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• pp.21-24
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• 2005

Three dimensional circular braided Glass/Aramid hybrid fabric/epoxy resin composite was fabricated. FBG sensor was embedded along the braid yam in order to monitor the internal dimensional changes of the 3-D braid composite. The amount of cure and thermal shrinkage of epoxy resin was also determined using FBG sensor system. FBG sensors with different grating length were embedded and their response were compared. The thermo-optic coefficient of FBG sensor was measured by several preliminary experiments. The internal strain that measured by FBG sensor and electric strain gauge was compared during compressive test. The released residual strain of the fabricated tubular composite was estimated using cutting method. The internal strain of the composite was estimated using FBG sensor system, and the result was compared with the value from electric strain gauge. It was found that FBG sensor system is a very useful technique to investigate inside region of complicated structure.

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

• Journal of the Korean Mathematical Society
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• v.50 no.4
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• pp.865-877
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• 2013

The disjoint union of mapping class groups of surfaces forms a braided monoidal category $\mathcal{M}$, as the disjoint union of the braid groups $\mathcal{B}$ does. We give a concrete and geometric meaning of the braidings ${\beta}_{r,s}$ in $\mathcal{M}$. Moreover, we find a set of elements in the mapping class groups which correspond to the standard generators of the braid groups. Using this, we can define an obvious map ${\phi}\;:\;B_g{\rightarrow}{\Gamma}_{g,1}$. We show that this map ${\phi}$ is injective and nongeometric in the sense of Wajnryb. Since this map extends to a braided monoidal functor ${\Phi}\;:\;\mathcal{B}{\rightarrow}\mathcal{M}$, the integral homology homomorphism induced by ${\phi}$ is trivial in the stable range.

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