• 대한수학회보
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• 제49권2호
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• pp.435-443
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• 2012

The Yamabe invariant is a topological invariant of a smooth closed manifold, which contains information about possible scalar curvature on it. It is well-known that a product manifold $T^m{\times}B$ where $T^m$ is the m-dimensional torus, and B is a closed spin manifold with nonzero $\^{A}$-genus has zero Yamabe invariant. We generalize this to various T-structured manifolds, for example $T^m$-bundles over such B whose transition functions take values in Sp(m, $\mathbb{Z}$) (or Sp(m - 1, $\mathbb{Z}$) ${\oplus}\;{{\pm}1}$ for odd m).

• 대한수학회보
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• 제32권2호
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• pp.303-308
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• 1995

We consider a torus T, that is, a compact surface with genus 1 and $\Omega = D^2 \times S^1$ topologically with $\partial\Omega = T$, where $D^2$ is the open unit disk and $S^1$ is the unit circle. Let $\omega = (x,y)$ denote the generic point on T. For a smooth immersion $u : T \to R^3$, we define the Dirichlet functional by $$ E(u) = \frac{2}{1} \int_{T} $\mid$\nabla u$\mid$^2 d\omega $$ and the volume functional by $$ V(u) = \frac{3}{1} \int_{T} u \cdot u_x \Lambda u_y d\omege $$.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 2003년도 춘계학술대회 논문집
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• pp.756-759
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• 2003

Steam Generator is one of the most important structural part of nuclear power plant. It is manufactured by welding process of various steel forgings such as shell, head, torus and tube sheet. These steel forgings have been made by open die forging process. After steel melting and ingot making, open die forging has been carried out to get a good quality which means high soundness and homogeniety of the steel forgings by using high capacity hydraulic press. This paper introduced open die forging status and investigated forging method of the ultra large steel forgings which is used for the steam generator of 1000MW nuclear power plant. For the same thing. the type of steel forgings consisting steam generator is classified by shell, head, torus and tube sheet. And corresponding forging processes of the steel forgings have been investigated.

• 대한수학회지
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• 제43권6호
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• pp.1269-1287
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• 2006

As a continuation of computing the zeta function of a regular covering graph by Mizuno and Sato in [9], we derive in this paper computational formulae for the zeta functions of a graph bundle and of any (regular or irregular) covering of a graph. If the voltages to derive them lie in an abelian or dihedral group and its fibre is a regular graph, those formulae can be simplified. As a by-product, the zeta function of the cartesian product of a graph and a regular graph is obtained. The same work is also done for a discrete torus and for a discrete Klein bottle.

• 대한수학회보
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• 제48권1호
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• pp.197-211
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• 2011

Every (1, 1)-knot is represented by a 4-tuple of integers (a, b, c, r), where a > 0, b $\geq$ 0, c $\geq$ 0, d = 2a+b+c, $r\;{\in}\;\mathbb{Z}_d$, and it is well known that all 2-bridge knots and torus knots are (1, 1)-knots. In this paper, we describe some conditions for 4-tuples which determine 2-bridge knots and determine all 4-tuples representing any given 2-bridge knot.

• Kyungpook Mathematical Journal
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• 제52권2호
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• pp.223-243
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• 2012

There is a special connection between the Alexander polynomial of (1, 1)-knot and the certain polynomial associated to the Dunwoody 3-manifold ([3], [10] and [13]). We study the polynomial(called the Dunwoody polynomial) for the (1, 1)-knot obtained by the certain cyclically presented group of the Dunwoody 3-manifold. We prove that the Dunwoody polynomial of (1, 1)-knot in $\mathbb{S}^3$ is to be the Alexander polynomial under the certain condition. Then we find an invariant for the certain class of torus knots and all 2-bridge knots by means of the Dunwoody polynomial.

• Journal of Information Processing Systems
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• 제12권4호
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• pp.681-687
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• 2016

Today's modern world requires a digital watermarking technique that takes the redundancy of an image into consideration for embedding a watermark. The novel algorithm used in this paper takes into consideration the redundancies of spatial domain and wavelet domain for embedding a watermark. Also, the cryptography-based secret key makes the algorithm difficult to hack and help protect ownership. Watermarking is blind, as it does not require the original image. Few coefficient matrices and secret keys are essential to retrieve the original watermark, which makes it redundant to various intentional attacks. The proposed technique resolves the challenge of optimizing transparency and robustness using a Canny-based edge detector technique. Improvements in the transparency of the cover image can be seen in the computed PSNR value, which is 44.20 dB.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2006년도 춘계학술대회논문집
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• pp.62-65
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• 2006

In this paper, nonlinear nonplanar vibration of a flexible rectangular cantilever beam is analyzed when one-to-one resonance occurs to the beam. The planar and nonplanar motions of the beam are analyzed in time and frequency domains. In frequency domain, FFT analyzer is used to perform autospectrum and cepstrum analyses for nonlinear response of the beam. In time domain, an oscilloscope is used to investigate the phase difference between the planar and nonplanar motions and to perform Torus analysis in the phase space. Through those analyzing process, the main frequencies of superharmonic, subharmonic, and super-subharmonic motions are investigated in the nonplanar motion due to one-to-one resonance. Analyzing the phase difference between the planar and nonplanar motions, it is observed that the phase difference varies in time.

• 한국시뮬레이션학회논문지
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• 제6권2호
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• pp.89-104
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• 1997

Performance bottleneck of parallel computer systems has mostly been I/O devices because of disparity between processor speed and I/O speed. Therefore I/O node placement strategy is required such that it can minimize the number of I/O nodes, I/O access time and I/O traffic in an interconnection network. In this paper, we propose an optimal distance-k embedding algorithm, and analyze its effect on system performance when this algorithm is applied to n x n torus architecture. We prove this algorithm is an efficient I/O node placement using software simulation. I/O node placement using the proposed algorithm shows the highest performance among other I/O node placements in all cases. It is because locations of I/O nodes are uniformly distributed in the whole network, resulting in reduced traffic in the intE'rconnection network.

• 천문학회보
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• 제39권1호
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• pp.60.2-60.2
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• 2014

The dust cloud around ${\lambda}$-Orionis is seen to be circular symmetric with the large angular extent (${\sim}8^{\circ}$). However, whether the three dimensional structure of the cloud is shell or torus ring is not yet fully resolved. We studied the structure of the dust cloud using a three-dimensional Monte-Carlo simulation code, MoCafe (Monte Carlo radiative transfer). The dust density structure of the cloud was inferred based on the star-count method. We assumed that the cloud is a spherical shell or a torus ring and calculated the radial profiles of scattered light originating from a central OB association. Comparison of the results with the S2/68 ultraviolet observations indicates that the cloud is a spherical shell. We also compared the Av map around ${\lambda}$-Orionis with the optical depth obtained based on the star-count.