• Bulletin of the Korean Mathematical Society
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• v.57 no.1
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• pp.207-218
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• 2020

Some modular representations of reflection groups related to Weyl groups are considered. The rational cohomology of the classifying space of a compact connected Lie group G with a maximal torus T is expressed as the ring of invariants, H*(BG; ℚ) ≅ H*(BT; ℚ)^W(G), which is a polynomial ring. If such Lie groups are locally isomorphic, the rational representations of their Weyl groups are equivalent. However, the integral representations need not be equivalent. Under the mod p reductions, we consider the structure of the rings, particularly for the Weyl group of symplectic groups Sp(n) and for the alternating groups A_n as the subgroup of W(SU(n)). We will ask if such rings of invariants are polynomial rings, and if each of them can be realized as the mod p cohomology of a space. For n = 3, 4, the rings under a conjugate of W(Sp(n)) are shown to be polynomial, and for n = 6, 8, they are non-polynomial. The structures of H*(BT^n-1; 𝔽_p)^A_n will be also discussed for n = 3, 4.

• Kyungpook Mathematical Journal
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• v.47 no.3
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• pp.335-340
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• 2007

Let M be a hyperbolic 3-manifold such that ${\partial}M$ has at least two boundary tori ${\partial}_oM$ and ${\partial}_1M$. Suppose that M contains an essential orientable surface P of genus $g$ with one outer boundary component ${\partial}_oP$, lying in ${\partial}_oM$ and having slope ${\lambda}$ in ${\partial}_oM$, and $p$ inner boundary components ${\partial}_iP$, $i=1$, ${\cdots}$, $p$, each having slope ${\alpha}$ in ${\partial}_1M$. Let ${\beta}$ be a slope in ${\partial}_1M$ and suppose that $M({\beta})$ is toroidal. Let $\hat{T}$ be a minimal essential torus in $M({\beta})$, which means that $\hat{T}$ is pierced a minimal number of times by the core of the ${\beta}$-Dehn filling, among all essential tori in $M({\beta})$. Let $T=\hat{T}{\cap}M$ and denote by $t$ the number of components of ${\partial}T$. In this paper we prove: (i) if $t{\geq}3$, then ${\Delta}({\alpha},{\beta}){\leq}6+\frac{10g-5}{p}$, (ii) If $t=2$, then ${\Delta}({\alpha},{\beta}){\leq}13+\frac{24g-12}{p}$, (iii) If $t=1$, then ${\Delta}({\alpha},{\beta}){\leq}1$.

• Tribology and Lubricants
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• v.28 no.6
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• pp.283-288
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• 2012

In this study, a new sliding contact problem involving an elastomeric seal, a spherical particle and a hard coated steel counterface was modeled to investigate the detailed wear mechanisms related to the sealing surface. The model was also used to design the optimum coating conditions. A three-dimensional finite element contact problem was modeled and analyzed using the nonlinear finite element code, MARC. The deformed steel surface and stress distributions are presented for different coating layers and thicknesses. When the coating thickness is relatively small, the entrapped particle produces surface plastic deformations such as groove and torus. In addition, the sealing surface can be damaged by abrasive wear as well as fatigue wear. For a relatively thick and multi-layered coating, on the other hand, surface plastic deformation does not occur, and the amount of abrasive and fatigue wear is reduced. Therefore, the proposed contact model and results can be used in the design of various sealing systems, further intensive studies are required.

• The Bulletin of The Korean Astronomical Society
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• v.41 no.1
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• pp.66.2-66.2
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• 2016

Red quasars have been suspected to be an intermediate population between merger-driven star-forming galaxies and normal quasars. In this scenario, red quasars are expected to have dusty red color coming from the dust extinction by dust and gas in their host galaxy. However, several studies have proposed different explanation of the red color of red quasars, which are i) a moderate viewing angle between type 1 and 2 quasars, ii) an unusual covering factor of dust torus, and iii) an anomalous synchrotron emission with a peak at NIR wavelength. In this study, we investigate the factor leading to the red color of red quasars by using the line luminosity ratios of the hydrogen Balmer to Paschen series of 11 red quasars. We find the Pb/Hb luminosity ratios of the red quasars are significantly higher than those of normal quasars. Moreover, we compare the Pb/Hb luminosity ratios of the red quasars to the theoretically expected line luminosity ratios computed from the CLOUDY code. We find the line luminosity ratios of the red quasars cannot be explained by the theoretical line luminosity ratios with any physical conditions. We conclude that red color of red quasars comes from dust extinction by their host galaxy. This result is consistent with the picture that red quasars are an intermediate population between the merger-driven star-forming galaxies and normal quasars.

• The Bulletin of The Korean Astronomical Society
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• v.39 no.1
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• pp.69.1-69.1
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• 2014

We perform an MHD simulation combined with observed vector field data to clarify an eruptive dynamics in the solar flare. We first extrapolate a 3D coronal magnetic field under a Nonlinear Force-Free Field (NLFFF) approximation based on the vector field, and then we perform an MHD simulation where the NLFFF prior to the flare is set as an initial condition. Vector field was obtained by the Soar Dynamics Observatory (SDO) at 00:00 UT on February 15, which is about 90 minutes before the X2.2-class flare. As a result, the MHD simulation successfully shows an eruption of strongly twisted lines whose values are over one-turn twist, which are produced through the tether-cut magnetic reconnection in strongly twisted lines of the NLFFF. Eventually, we found that they exceed a critical height at which the flux tube becomes unstable to the torus instability determining the condition that whether a flux tube might escape from the overlying field lines or not. In addition to these, we found that the distribution of the observed two-ribbon flares is similar to the spatial variance of the footpoints caused by the reconnection of the twisted lines being resided above the polarity inversion line. Furthermore, because the post flare loops obtained from MHD simulation well capture that in EUV image taken by SDO, these results support the reliability of our simulation.

• Journal of The Institute of Information and Telecommunication Facilities Engineering
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• v.10 no.1
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• pp.7-13
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• 2011

Matrix multiplication is a fundamental operation of linear algebra and arises in many areas of science and engineering. This paper introduces an efficient parallel matrix multiplication scheme on N ${\times}$ N mesh-connected SIMD array processor, called multiple hierarchical SIMD architecture (HMSA). The architectural characteristic of HMSA is the hierarchically structured control units which consist of a global control unit, N local control units configured diagonally, and $N^2$ processing elements (PEs) arranged in an N ${\times}$ N array. PEs are communicating through local buses connecting four adjacent neighbor PEs in mesh-torus networks and global buses running across the rows and columns called horizontal buses and vertical buses, respectively. This architecture enables HMSA to have the features of diagonally indexed concurrent broadcast and the accessibility to either rows (row control mode) or columns (column control mode) of 2D array PEs alternately. An algorithmic mapping method is used for performance evaluation by mapping matrix multiplication on the proposed architecture. The asymptotic time complexities of them are evaluated and the result shows that paralle matrix multiplication on HMSA can provide significant performance improvement.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.32B no.11
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• pp.1527-1535
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• 1995

This paper introduces an isolated word recognition system realized on a neurocomputer called E-MIND II, which is a 2-D torus wavefront array processor consisting of 256 DNP IIs. The DNP II is an all digital VLSI unit processor for the EMIND II featuring the emulation capability of more than thousands of neurons, the 40 MHz clock speed, and the on-chip learning. Built by these PEs in 2-D toroidal mesh architecture, the E- MIND II can be accelerated over 2 Gcps computation speed. In this light, the advantages of the E-MIND II in its capability of computing speed, scalability, computer interface, and learning are especially suitable for real time application such as speech recognition. We show how to map a TDNN structure on this array and how to code the learning and recognition algorithms for a user independent isolated word recognition. Through hardware simulation, we show that recognition rate of this system is about 97% for 30 command words for a robot control.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2005.11a
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• pp.690-695
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• 2005

Flexible circular cantilever beams when excited externally introduce a lot of dynamic characteristics. The non-linear elements that these flexible beams develop include non-linearity due to inertia terms, spring, and damping. They show different characteristics of motion from each other. In the modes of lower order, the non-linearity due to spring is prevalent, while the non-linearity due to inertia Is prevalent in the modes of higher order. To analyze these effects the non-linear phenomena are analyzed experimentally. When the response characteristics of non-linear vibration are analyzed using autospectrum, it is possible to analyze the subharmonic and superharmonic mot ion by comparison. The phase change is analyzed using the method of phase portrait and the non-linear characteristics of response characteristics that are developed in flexible structures can be predicted and applied to the stage of design.

• Journal of KIISE:Computer Systems and Theory
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• v.36 no.1
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• pp.40-51
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• 2009

A paired many-to-many k-disjoint path cover (paired k-DPC) of a graph G is a set of k disjoint paths joining k distinct source-sink pairs in which each vertex of G is covered by a path. In this paper, we investigate disjoint path covers in recursive circulants G($cd^m$,d) with $d{\geq}3$ and tori, and show that provided the number of faulty elements (vertices and/or edges) is f or less, every nonbipartite recursive circulant and torus of degree $\delta$ has a paired k-DPC for any f and $k{\geq}1$ with $f+2k{\leq}{\delta}-1$.

• The Bulletin of The Korean Astronomical Society
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• v.46 no.2
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• pp.66.1-66.1
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• 2021

Extinction curves observed toward individual Active Galactic Nuclei (AGN) usually show a steep rise toward Far-Ultraviolet (FUV) wavelengths and can be described by the Small Magellanic Cloud (SMC)-like dust model. This feature suggests the dominance of small dust grains of size a < 0.1 ㎛ in the local environment of AGN, but the origin of such small grains is unclear. In this paper, we aim to explain this observed feature by applying the RAdiative Torque Disruption (RATD) to model the extinction of AGN radiation from FUV to Mid-Infrared (MIR) wavelengths. We find that in the intense radiation field of AGN, large composite grains of size a > 0.1 ㎛ are significantly disrupted to smaller sizes by RATD up to dRATD > 100 pc in the polar direction and dRATD ~ 10 pc in the torus region. Consequently, optical-MIR extinction decreases, whereas FUV-near-Ultraviolet extinction increases, producing a steep far-UV rise extinction curve. The resulting total-to selective visual extinction ratio thus significantly drops to RV < 3.1 with decreasing distances to AGN center due to the enhancement of small grains. The dependence of RV with the efficiency of RATD will help us to study the dust properties in the AGN environment via photometric observations. In addition, we suggest that the combination of the strength between RATD and other dust destruction mechanisms that are responsible for destroying very small grains of a <0.05 ㎛ is the key for explaining the dichotomy observed "SMC" and "gray" extinction curve toward many AGN.