• Bulletin of the Korean Mathematical Society
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• v.57 no.1
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• pp.1-30
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• 2020

In this paper, we classify all twisted torus knots which are middle/hyper doubly Seifert. By the definition of middle/hyper doubly Seifert knots, these knots admit Dehn surgery yielding either Seifert-fibered spaces or graph manifolds at a surface slope. We show that middle/hyper doubly Seifert twisted torus knots admit the latter, that is, non-Seifert-fibered graph manifolds whose decomposing pieces consist of two Seifert-fibered spaces over the disk with two exceptional fibers.

• Journal of KIISE:Computer Systems and Theory
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• v.36 no.3
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• pp.158-170
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• 2009

In this paper, we propose the new torus network which has the hypercube Q3 as the basic module. The proposed Hyper-torus has the degree 4, and is the network which has the scalability, and the fine diameter. If we compare the class of the torus in the viewpoint of network cost, the hyper-torus with $1.4{\sqrt{N}}$+ 16 is proved to be approximately 65% than the torus with $4{\sqrt{N}}$ and 50% than the honeycomb with $2.45{\sqrt{N}}$. This result means that hyper-torus is better for the class of the existing mesh in the viewpoint of network cost.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.18 no.5
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• pp.1116-1121
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• 2014

Mesh structure is one of typical interconnection networks, and it is used in the part of VLSI circuit design. Torus and Hyper-Torus are advanced interconnection networks in the part of diameter and fault-tolerance of mesh structure. In this paper, we will analyze embedding between Torus and Hyper-Torus networks. We will show T(4k,2l) can be embedded into QT(m,n) with dilation 5, congestion 4, expansion 1. And QT(m,n) can be embedded into T(4k,2l) with dilation 3, congestion 3, expansion 1.

• Proceedings of the Korean Information Science Society Conference
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• 2006.06c
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• pp.211-213
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• 2006

현재 개발되어 사용되고 있는 원격의료시스템은 3계층기반의 구조를 이루고 있는데 환자들이 집중적으로 몰리는 지역에서 심각한 bottleneck현상이 발생할 수 있다. 본 논문에서는 3계층기반 원격의료시스템의 성능을 분석하고 bottleneck 현상을 해결하기 위한 방안으로 hyper-torus 구조의 4계층 아키텍처를 제안하고 Architecture Description Language인 Acme를 이용하여 성능을 비교분석 한다.

• Journal of the Korean Mathematical Society
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• v.46 no.3
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• pp.609-620
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• 2009

We establish some estimates on the hyper bilinear Hilbert transform on both Euclidean space and torus. We also use a transference method to obtain a Kenig-Stein's estimate on bilinear fractional integrals on the n-torus.

• Journal of Korea Multimedia Society
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• v.11 no.9
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• pp.1227-1237
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• 2008

In this paper, we analyze topological properties and embedding of Folded Hyper-Star network to further improve the network cost of Hypercube, a major interconnection network. Folded Hyper-Star network has a recursive expansion and maximal fault tolerance. The result of embedding is that Folded Hypercube $FQ_n$ and $n{\times}n$ Torus can be embedded into Folded Hyper-Star FHS(2n,n) with dilation 2. Also, we show Folded Hyper-Star FHS(2n,n) can be embedded into Folded Hypercube $FQ_{2n-1}$ with dilation 1.

• Honam Mathematical Journal
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• v.40 no.3
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• pp.591-600
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• 2018

In [4] Miyazaki and Motegi constructed one family of knots in $S^3$ which admits Dehn surgery producing a Seifert-fibered space over $S^2$ with four exceptional fibers. On the other hand, in [3] using doubly hyper Seifert twisted torus knots, the author constructed six families of knots in $S^3$ which admit Dehn surgery yielding a Seifert-fibered space over $S^2$ with four exceptional fibers. It is questioned in [3] whether or not the family of the knots constructed in [4] belongs to one of the six families of the knots in [3]. In this paper, we give the positive answer for this question.

• Proceedings of the Korea Information Processing Society Conference
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• 2008.05a
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• pp.581-584
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• 2008

본 논문은 피터슨 그래프를 기반으로 설계된 노드수가 증가함에 따라 분지수가 증가하는 하이퍼 피터슨을 분지수가 고정인 피터슨-토러스(PT) 네트워크에 임베딩 가능함을 보인다. 하이퍼 피터슨 $HP_{log_2n^2+3}$을 PT(n,n)에 확장율 1, 연장율 1.5n+2 그리고 밀집율 5n에 임베딩 하였다.

• The KIPS Transactions:PartA
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• v.16A no.6
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• pp.501-508
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• 2009

In this paper, we prove that folded hyper-star network FHS(2n,n) is node-symmetric and a bipartite network. We show that FHS(2n,n) can be embedded into odd network On+1 with dilation 2, congestion 1 and Od can be embedded into FHS(2n,n) with dilation 2 and congestion 1. Also, we show that $2n{\time}n$ torus can be embedded into FHS(2n,n) with dilation 2 and congestion 2.