• Kyungpook Mathematical Journal
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• v.47 no.2
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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 $n_1$, $n_2$, ${\cdots}$, $n_r$.

• Bulletin of the Korean Mathematical Society
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• v.55 no.3
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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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• v.51 no.3
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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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• v.19 no.2
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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.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.32B no.5
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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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• v.6 no.10
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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.

• Journal of the Korean Mathematical Society
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• v.49 no.5
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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.

• Journal of KIISE:Computer Systems and Theory
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• v.33 no.9
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• pp.684-690
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• 2006

This paper proposes a message transmission model for hard real-time communications of periodic messages on a switched Ethernet and also proposes an algorithm to schedule the messages to be transmitted within their deadlines. The proposed scheduling algorithm is a distributed one and is peformed by the source and the destination nodes without the modification of the operational features of the standard Ethernet switch. When a new periodic message needs to be transmitted, it is first checked whether it can be scheduled on both the transmission and the reception links without affecting the already-scheduled messages, and a feasible schedule is made for the new message if it is schedulable. The proposed scheduling algorithm guarantees the transmission of periodic messages within their deadline and allows flexible message transmission on a hard real-time switched Ethernet through the dynamic addition of new periodic messages during run-time.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.10 no.7
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• pp.1214-1221
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• 2006

Header compression scheme is suggested as a solution to reduce the inefficient overhead of general packet stream data. Especially, it is shown that there are more overhead rate for real-time media stream links such as voice because of its short payload size, and it is possible to get higher bandwidth efficiency using the header compression scheme. There are two kinds of error recovery in header compression such as Periodic Header Refresh(PHR) and Header Request(HR) schemes. In this paper, we analyze the performance of these two compression recovery schemes, and some results such as the overhead rate, bandwidth gain and bandwidth efficiency(BE) are presented.

• Journal of the Korean Mathematical Society
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• v.46 no.5
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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.