• Journal of the Korean Mathematical Society
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• v.37 no.3
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• pp.491-502
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• 2000

The disjoint union of mapping class groups g,1 gives us a braided monoidal category so that it gives rise to a double loop space structure. We show that there exists a natural twist in this category, so it gives us a ribbon category. We show that there exists a natural twist in this category, so it gives us a ribbon category. We explicitly express this structure by showing how the twist acts on the fundamental group of the surface Sg,l. We also make an explicit description of this structure in terms of the standard Dehn twists, as well as in terms of Wajnryb's Dehn twists. We show that the inverse of the twist g for the genus g equals the Dehn twist along the fixed boundary of the surface Sg,l.

• Bulletin of the Korean Mathematical Society
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• v.53 no.2
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• pp.601-614
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• 2016

Let $N_{g,s}$ denote the nonorientable surface of genus g with s boundary components. Recently Paris and Szepietowski [12] obtained an explicit finite presentation for the mapping class group $\mathcal{M}(N_{g,s})$ of the surface $N_{g,s}$, where $s{\in}\{0,1\}$ and g + s > 3. Following this work, we obtain a finite presentation for the subgroup $\mathcal{T}(N_{g,s})$ of $\mathcal{M}(N_{g,s})$ generated by Dehn twists.

• Communications of the Korean Mathematical Society
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• v.21 no.2
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• pp.337-345
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• 2006

John Harer conjectured that the canonical map from braid group to mapping class group induces zero homology homomorphism. To prove the conjecture it suffices to show that this map preserves the first Araki-Kudo-Dyer-Lashof operation. To get information on this homology operation we need to investigate the image of braiding under the Harer map. The main result of this paper is to give both algebraic and geometric interpretations of the image of braiding under the Harer map. For this we need to calculate long chains of consecutive actions of Dehn twists on the fundamental group of surface.

• Bulletin of the Korean Mathematical Society
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• v.61 no.3
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• pp.585-595
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• 2024

We show that a pseudo-Anosov map constructed as a product of the large power of Dehn twists of two filling curves always has a geodesic axis on the curve graph of the surface. We also obtain estimates of the stable translation length of a pseudo-Anosov map, when two filling curves are replaced by multicurves. Three main applications of our theorem are the following: (a) determining which word realizes the minimal translation length on the curve graph within a specific class of words, (b) giving a new class of pseudo-Anosov maps optimizing the ratio of stable translation lengths on the curve graph to that on Teichmüller space, (c) giving a partial answer of how much power is needed for Dehn twists to generate right-angled Artin subgroup of the mapping class group.

• Journal of The Korean Astronomical Society
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• v.32 no.2
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• pp.83-89
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• 1999

We have conducted a V, I, J, and H surface photometry of a barred galaxy NGC 4314 to analyze the morphology and luminosity distribution of the galaxy. By applying a semi two-dimensional profile decomposition method, we derived the luminosity fractions and the scale lengths of the three distinct components, bulge, disk, and bar: $L_b {\approx}0.35,\;L_d{\approx}0.35,\;L_{bar}{\approx}0.30,\;r_e{\approx}22",\;r_o {\approx} 50"$, and a $\approx$ 60". The bulge of NGC 4314 seems to be triaxial due to the isophotal twists but its luminosity distribution is well approximated by the $r^{1/4}$-law.

• Korean Journal of Mathematics
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• v.23 no.1
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• pp.115-128
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• 2015

Plumbing surfaces of links were introduced to study the geometry of the complement of the links. A basket surface is one of these plumbing surfaces and it can be presented by two sequential presentations, the first sequence is the flat plumbing basket code found by Furihata, Hirasawa and Kobayashi and the second sequence presents the number of the full twists for each of annuli. The minimum number of plumbings to obtain a basket surface of a knot is defined to be the basket number of the given knot. In present article, we first find a classification theorem about the basket number of knots. We use these sequential presentations and the classification theorem to find the basket number of all prime knots whose crossing number is 7 or less except two knots $7_1$ and $7_5$.

• Journal of the Korean Mathematical Society
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• v.61 no.1
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• pp.1-28
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• 2024

In this article, we associate a contact structure to the conjugacy class of a periodic surface homeomorphism, encoded by a combinatorial tuple of integers called a marked data set. In particular, we prove that infinite families of these data sets give rise to Stein fillable contact structures with associated monodromies that do not factor into products to positive Dehn twists. In addition to the above, we give explicit constructions of symplectic fillings for rational open books analogous to Mori's construction for honest open books. We also prove a sufficient condition for the Stein fillability of rational open books analogous to the positivity of monodromy for honest open books due to Giroux and Loi-Piergallini.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 2002.04a
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• pp.155-160
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• 2002

Recently, the development of aerospace and automobile industries has brought new technological challenges, rebated to the growing complexity of products and the new geometry of the models. High speed milling with a 5-Axis milling machine has been widely used fur 3D sculptured surface parts. When turbine blades are machined by a 5-axis milling, their thin and cantilever shape causes vibrations, deflections and twists. Therefore, the surface roughness and the waviness of the workpiece are not good. In this paper, the effects of cutter orientation and the lead/tilt angle used to machine turbine blades with a 5-axis high speed ball end-milling were investigated to improve geometric accuracy and surface integrity. The experiments were performed using a lead/tilt angle of 15$^{\circ}$ to the workpiece with four cutter directions such as horizontal outward, horizontal inward, vertical outward, and vortical inward directions. Workpiece deflection, surface roughness and the machined surface were all measured with various cutter orientations such as cutting directions, and lead/tilt angle. The results show that the best cutting strategy for machining turbine blades with a 5-axis milling is horizontal inward direction with a tilt angle.

• Proceedings of the Korean Society For Composite Materials Conference
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• 2001.05a
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• pp.151-154
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• 2001

Shape memory alloy (SMA) has demonstrated its potentials for various smart structure applications. SMA wires undergo a reversible phase transformation from martensite to austenite as temperature increases. This transformation leads to shape recovery and associated recovery strains. If SMA actuators are embedded off the neutral surface and are oriented in arbitrary angles with respect to a beam axis, then the beam bends and twists due to the coupling effects of recovery strains activated. In this study, the bending and twisting of a SMA/Composite beam were controlled by both electric resistive heating and passive elastic tailoring. 3-dimensional finite element formulations were derived and validated to analyze the responses of the SMA/Composite beam. Numerical results show that the shape of the SMA/Composite beam can be controlled by judicious choices of control temperatures, SMA angles, and elastic tailoring.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• v.17 no.5
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• pp.530-535
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• 2004

We have studied 90$^{\circ}$ twisted nematic mode switching by fringe electric field(F-TN mode) using a liquid crystal (LC) with negative dielectric anisotropy. In the device, two polarizers are parallel each other, electrodes exist only on bottom substrate, and one of rubbing direction is coincident with polarizer axis. Therefore, the cell shows a black state before a voltage is applied. With a bias voltage generating fringe-electric field, the LC twists perpendicular to fringe electric field such that the LCs are almost homogeneously aligned except near the bottom surface since the negative type of the LC is used. Consequently, the new device exhibits much wider viewing angle than that of the conventional TN mode due to in-plane switching and relatively high transmittance since the LC director above whole electrode area aligns parallel to the polarizer axis.