• Title/Summary/Keyword: torus

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PRIMITIVE/SEIFERT KNOTS WHICH ARE NOT TWISTED TORUS KNOT POSITION

  • Kang, Sungmo
    • Honam Mathematical Journal
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    • v.35 no.4
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    • pp.775-791
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    • 2013
  • The twisted torus knots and the primitive/Seifert knots both lie on a genus 2 Heegaard surface of $S^3$. In [5], J. Dean used the twisted torus knots to provide an abundance of examples of primitive/Seifert knots. Also he showed that not all twisted torus knots are primitive/Seifert knots. In this paper, we study the other inclusion. In other words, it shows that not all primitive/Seifert knots are twisted torus knot position. In fact, we give infinitely many primitive/Seifert knots that are not twisted torus knot position.

Hyper-Torus : A New Torus Network based on 3-dimensional Hypercube (하이퍼-토러스 : 3차원 하이퍼큐브 기반의 새로운 토러스 네트워크)

  • Ki, Woo-Seo;Kim, Jeong-Seop;Lee, Hyung-Ok;Oh, Jae-Chul
    • 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.

NERON SYMBOL ON ${\kappa}-HOLOMORPHIC$ TORUS

  • Sim, Kyung-Ah;Woo, Sung-Sik
    • Bulletin of the Korean Mathematical Society
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    • v.37 no.4
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    • pp.843-854
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    • 2000
  • S. Turner has shown that a Neron symbol can be calculated from the values of K-meromorphic theta functions corresponding to divisors on K-holomorphic torus of strongly diagonal type. Using an isogeny to a K-holomorphic torus of strongly diagonal type, he constructed a Neron symbol on K-holomorphic torus of diagonal type. In this work, we provide a simple formula of the Neron symbol on the Tate curve. And then we construct the Neron symbol on K-holomorphic torus of diagonal or st rongly diagonal type without using isogenies.

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NEW FAMILIES OF HYPERBOLIC TWISTED TORUS KNOTS WITH GENERALIZED TORSION

  • Keisuke, Himeno;Masakazu, Teragaito
    • Bulletin of the Korean Mathematical Society
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    • v.60 no.1
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    • pp.203-223
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    • 2023
  • A generalized torsion element is an obstruction for a group to admit a bi-ordering. Only a few classes of hyperbolic knots are known to admit such an element in their knot groups. Among twisted torus knots, the known ones have their extra twists on two adjacent strands of torus knots. In this paper, we give several new families of hyperbolic twisted torus knots whose knot groups have generalized torsion. They have extra twists on arbitrarily large numbers of adjacent strands of torus knots.

Twisted Cube Torus(TT): A New Class of Torus Interconnection Networks Based on 3-Dimensional Twisted Cube (꼬인 큐브 토러스: 3차원 꼬인 큐브에 기반한 새로운 토러스 상호연결망)

  • Kim, Jong-Seok;Lee, Hyeong-Ok;Kim, Sung-Won
    • The KIPS Transactions:PartA
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    • v.18A no.5
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    • pp.205-214
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    • 2011
  • We propose a new interconnection network, called Twisted cube torus(TT) network based on well-known 3-dimensional twisted cube. Twisted cube torus network has smaller diameter and improved network cost than honeycomb torus with the same number of nodes. In this paper, we propose routing algorithm of Twisted cube torus network and analyze its diameter, network cost, bisection width and hamiltonian cycle.

An Analysis of the Degree of Embedding between Torus Structure and Hyper-Torus One (토러스 구조와 하이퍼-토러스 구조 상호간 임베딩 정도의 분석)

  • Kim, Jong-Seok;Lee, Hyeong-Ok
    • 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.

MULTIPLICITY RESULTS AND THE M-PAIRS OF TORUS-SPHERE VARIATIONAL LINKS OF THE STRONGLY INDEFINITE FUNCTIONAL

  • Jung, Tack-Sun;Choi, Q-Heung
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.12 no.4
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    • pp.239-247
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    • 2008
  • Let $I{\in}C^{1,1}$ be a strongly indefinite functional defined on a Hilbert space H. We investigate the number of the critical points of I when I satisfies two pairs of Torus-Sphere variational linking inequalities and when I satisfies m ($m{\geq}2$) pairs of Torus-Sphere variational linking inequalities. We show that I has at least four critical points when I satisfies two pairs of Torus-Sphere variational linking inequality with $(P.S.)^*_c$ condition. Moreover we show that I has at least 2m critical points when I satisfies m ($m{\geq}2$) pairs of Torus-Sphere variational linking inequalities with $(P.S.)^*_c$ condition. We prove these results by Theorem 2.2 (Theorem 1.1 in [1]) and the critical point theory on the manifold with boundary.

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