• Kyungpook Mathematical Journal
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• 제47권2호
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• pp.295-309
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• 2007

In this paper, we characterize the Seifert matrices of $p$-periodic links whose quotients are 2-bridge links $C(2,n_1,-2,n_2,{\cdots},n_r,(-2)^r)$ and give formulas for the signatures and determinants of the 3-periodic links of these kind in terms of $n_1$, $n_2$, ${\cdots}$, $n_r$.

• 대한수학회보
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• 제55권3호
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• pp.799-808
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• 2018

We generalize some of the congruences in [20] to periodic knotted trivalent graphs. As an application, a criterion derived from one of these congruences is used to obstruct periodicity of links of few crossings for the odd primes p = 3, 5, 7, and 11. Moreover, we derive a new criterion of periodic links. In particular, we give a sufficient condition for the period to divide the crossing number. This gives some progress toward solving the well-known conjecture that the period divides the crossing number in the case of alternating links.

• Kyungpook Mathematical Journal
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• 제51권3호
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• pp.261-281
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• 2011

In this paper, we will construct symmetric links by using the method adapted from the graph theory, and study a Seifert matrix of a symmetric link from the information of the Seifert matrix of the base link and the corresponding group action.

• East Asian mathematical journal
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• 제19권2호
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• pp.317-335
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• 2003

In this paper, we characterize SL(2, $\mathbb{C}$)-representations of an n-periodic link $\tilde{L}$ in terms of SL(2, $\mathbb{C}$)-representations of its quotient link L and express the SL(2, $\mathbb{C}$)-representation variety R($\tilde{L}$) of $\tilde{L}$ as the union of n affine algebraic subsets which have the same dimension. Also, we show that the dimension of R($\tilde{L}$) is bounded by the dimensions of affine algebraic subsets of the SL(2, $\mathbb{C}$)-representation variety R(L) of its quotient link L.

• 전자공학회논문지B
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• 제32B권5호
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• pp.720-729
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• 1995

We proposed a XMESH(crossed-mesh) topology as a suitable interconnection for the massively parallel computer architectures, and presented performance analysis of the proposed interconnection topology. Horizontally, the XMESH has the same links as those of the toroidal mesh(TMESH) or toroid, but vertically, it has diagonal cross links instead of the vertical links. It reveals desirable interconnection characteristics for the massively parallel computers as the number of nodes increases, while retaining the same structural advantages of the TMESH such as the symmetric structure, periodic placement of subsystems, and constant degree, which are highly recommended features for VLSI/WSI implementations. Furthermore, n*k XMESH can be easily expanded without increasing the diameter as long as n.leq.k.leq.n+4. Analytical performance evaluations show that the XMESH has a shorter diameter, a shorter mean internode distance, and a higher message completion rate than the TMESH or the diagonal mesh(DMESH). To confirm these results, an optimal self-routing algorithm for the proposed topology is developed and is used to simulate the average delay, the maximum delay, and the throughput in the presence of contention. In all cases, the XMESH is shown to outperform the TMESH and the DMESH regardless of the communication load conditions or the number of nodes of the networks, and can provide an attractive alternative to those networks in implementing massively parallel computers.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제6권10호
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• pp.2620-2631
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• 2012

In this paper, a rerouting-controlled ISL (Inter-Satellite link) handover protocol for LEO satellite networks (RCIHP) is proposed. Through topological dynamics and periodic characterization of LEO satellite constellation, the protocol firstly derives the ISL related information such as the moments of ISL handovers and the intervals during which ISLs are closed and cannot be used to forward packet. The information, combined with satellite link load status, is then been utilized during packet forwarding process. The protocol makes a forwarding decision on a per packet basis and only routes packets to living and non-congested satellite links. Thus RCIHP avoids periodic rerouting that occurs in traditional routing protocols and makes it totally unnecessary. Simulation studies show that RCIHP has a good performance in terms of packet dropped possibility and end-to-end delay.

• 대한수학회지
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• 제49권5호
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• pp.993-1015
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• 2012

In this paper, we study the quantum sl($n$) representation category using the web space. Specially, we extend sl($n$) web space for $n{\geq}4$ as generalized Temperley-Lieb algebras. As an application of our study, we find that the HOMFLY polynomial $P_n(q)$ specialized to a one variable polynomial can be computed by a linear expansion with respect to a presentation of the quantum representation category of sl($n$). Moreover, we correct the false conjecture [30] given by Chbili, which addresses the relation between some link polynomials of a periodic link and its factor link such as Alexander polynomial ($n=0$) and Jones polynomial ($n=2$) and prove the corrected conjecture not only for HOMFLY polynomial but also for the colored HOMFLY polynomial specialized to a one variable polynomial.

• 한국정보과학회논문지:시스템및이론
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• 제33권9호
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• pp.684-690
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• 2006

본 논문에서는 스위칭이더넷에서의 주기적 메시지에 대해 경성 실시간 통신을 위한 메시지 전송 모델을 제안하고, 각 메시지들을 마감시간 안에 전송하기 위한 메시지 스케쥴링 알고리즘을 제안한다. 제안하는 스케쥴링 알고리즘은 중앙노드 없이 동작하는 분산 알고리즘이고 스위치에 새로운 기능의 추가없이 송신자와 수신자 노드 사이에서 동작한다. 제안한 알고리즘은 새로운 주기적 메시지에 대한 전송요청이 오면 이미 스케쥴 되어 있는 주기적 메시지에 영향을 미치지 않고 송신 링크와 수신 링크에서 스케쥴링 가능한지 검사를 하고, 스케쥴링이 가능하면 전송 스케쥴을 생성한다. 본 논문에서 제안하는 스케쥴링 알고리즘은 스위칭이더넷에서 주기적 메시지에 대해 마감시간 내 전송을 보장하고, 새로운 메시지에 대한 동적인 추가가 용이하여 경성 실시간 시스템에서 유연한 메시지 전송 기법을 제공한다.

• 한국정보통신학회논문지
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• 제10권7호
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• pp.1214-1221
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• 2006

헤더 압축 기술은 기존의 일반적인 패킷 데이터의 비효율적인 오버 헤드를 줄이기 위한 방안으로 제안되었다. 특히 음성과 같은 실시간 미디어 스트림 경우에는 더욱 큰 오버헤드율을 보이게 되는데, 헤더 압축을 통해 보다 높은 대역폭 효율을 얻을 수 있다. 본 논문에서는 PHR(periodic Header Refresh) 방법과 HR(Header Request) 방법 의 두가지 에러 복구 기법 에 관하여 각각 성능 분석을 실시하였다. 그 결과로 Overhead Rate, Bandwidth Gain, 그리고 Bandwidth Efficiency 등의 분석 결과가 제시되었다.

• 대한수학회지
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• 제46권5호
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• pp.919-947
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• 2009

In this paper, we give a recursive formula for the Jones polynomial of a 2-bridge knot or link with Conway normal form C($-2n_1$, $2n_2$, $-2n_3$, ..., $(-1)_r2n_r$) in terms of $n_1$, $n_2$, ..., $n_r$. As applications, we also give a recursive formula for the Jones polynomial of a 3-periodic link $L^{(3)}$ with rational quotient L = C(2, $n_1$, -2, $n_2$, ..., $n_r$, $(-1)^r2$) for any nonzero integers $n_1$, $n_2$, ..., $n_r$ and give a formula for the span of the Jones polynomial of $L^{(3)}$ in terms of $n_1$, $n_2$, ..., $n_r$ with $n_i{\neq}{\pm}1$ for all i=1, 2, ..., r.