• Journal of the Chungcheong Mathematical Society
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• v.13 no.1
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• pp.139-144
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• 2000

The generalized noncommutative torus $T_{\rho}^d$ of rank m was defined in [2]. Assume that for the completely irrational noncommutative subtorus $A_{\rho}$ of rank m of $T_{\rho}^d$ there is no integer q > 1 such that $tr(K_0(A_{\rho}))=\frac{1}{q}{\cdot}tr(K_0(A_{\rho^{\prime}}))$ for $A_{\rho^{\prime}}$ a completely irrational noncommutative torus of rank m. All $C^*$-algebras ${\Gamma}({\eta})$ of sections of locally trivial $C^*$-algebra bundles ${\eta}$ over $M=\prod_{i=1}^{e}S^{2k_i}{\times}\prod_{i=1}^{s}S^{2n_i+1}$, $\prod_{i=1}^{s}\mathbb{PR}_{2n_i}$, or $\prod_{i=1}^{s}L_{k_i}(n_i)$ with fibres $T_{\rho}^d{\otimes}M_c(\mathbb{C})$ were constructed in [6, 7, 8]. We prove that ${\Gamma}({\eta}){\otimes}M_{p^{\infty}}$ is isomorphic to $C(M){\otimes}A_{\rho}{\otimes}M_{cd}(\mathbb{C}){\otimes}M_{p^{\infty}}$ if and only if the set of prime factors of cd is a subset of the set of prime factors of p, that $\mathcal{O}_{2u}{\otimes}{\Gamma}({\eta})$ is isomorphic to $\mathcal{O}_{2u}{\otimes}C(M){\otimes}A_{\rho}{\otimes}M_{cd}(\mathbb{C})$ if and only if cd and 2u - 1 are relatively prime, and that $\mathcal{O}_{\infty}{\otimes}{\Gamma}({\eta})$ is not isomorphic to $\mathcal{O}_{\infty}{\otimes}C(M){\otimes}A_{\rho}{\otimes}M_{cd}(\mathbb{C})$ if cd > 1 when no non-trivial matrix algebra can be ${\Gamma}({\eta})$.

• Journal of the Institute of Electronics Engineers of Korea CI
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• v.41 no.2
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• pp.9-22
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• 2004

This paper presents a parallel genetic algorithm for the Multi-disk data allocation problem an NP-complete problem. This problem is to find a method to distribute a Binary Cartesian Product File on disk-arrays to maximize parallel disk I/O accesses. A Sequential Genetic Algorithm(SGA), DAGA, has been proposed and showed the superiority to the other proposed methods, but it has been observed that DAGA consumes considerably lengthy simulation time. In this paper, a parallel version of DAGA(ParaDAGA) is proposed. The ParaDAGA is a 2-dimension torus-based Parallel Genetic Algorithm(PGA) and it is based on a distributed population structure. The ParaDAGA has been implemented on the parallel computer simulated on a single processor platform. Through the simulation, we study the impact of varying ParaDAGA parameters and compare the quality of solution derived by ParaDAGA and DAGA. Comparing the quality of solutions, ParaDAGA is superior to DAGA in all cases of configurations in less simulation time.

• Journal of the Korean Mathematical Society
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• v.35 no.2
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• pp.331-340
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• 1998

We define the spherical non-commutative torus $L_{\omega}$/ as the crossed product obtained by an iteration of l crossed products by actions of, the first action on C( $S^{2n＋l}$). Assume the fibres are isomorphic to the tensor product of a completely irrational non-commutative torus $A_{p}$ with a matrix algebra $M_{m}$ ( ) (m > 1). We prove that $L_{\omega}$/ $M_{p}$ (C) is not isomorphic to C(Prim( $L_{\omega}$/)) $A_{p}$ $M_{mp}$ (C), and that the tensor product of $L_{\omega}$/ with a UHF-algebra $M_{p{\infty}}$ of type $p^{\infty}$ is isomorphic to C(Prim( $L_{\omega}$/)) $A_{p}$ $M_{m}$ (C) $M_{p{\infty}}$ if and only if the set of prime factors of m is a subset of the set of prime factors of p. Furthermore, it is shown that the tensor product of $L_{\omega}$/, with the C＊-algebra K(H) of compact operators on a separable Hilbert space H is not isomorphic to C(Prim( $L_{\omega}$/)) $A_{p}$ $M_{m}$ (C) K(H) if Prim( $L_{\omega}$/) is homeomorphic to $L^{k}$ (n)$\times$ $T^{l'}$ for k and l' non-negative integers (k > 1), where $L^{k}$ (n) is the lens space.$T^{l'}$ for k and l' non-negative integers (k > 1), where $L^{k}$ (n) is the lens space.e.

• Journal of KIISE:Computer Systems and Theory
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• v.35 no.8
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• pp.361-371
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• 2008

In this paper, the hypercube, hyperpetersen networks, whose degree is increasing in accordance with expansion of number of node and complete binary tree are one-to-one embedded into peterson-torus(PT) network which has fixed degree. The one-to-one embedding has less risk of overload or idle for the processor comparative to one-to-many and many-to-one embedding. For the algorithms which were developed on hypercube or hyperpetersen are used for PT network, it is one-to one embedded at expansion ${\doteqdot}1$, dilation 1.5n+2 and link congestion O(n) not to generate large numbers of idle processor. The complete binary tree is embedded into PT network with link congestion =1, expansion ${\doteqdot}5$ and dilation O(n) to avoid the bottleneck at the wormhole routing system which is not affected by the path length.

• Journal of KIISE:Computer Systems and Theory
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• v.34 no.5_6
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• pp.176-186
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• 2007

An interconnection network can be represented as a graph where a vertex corresponds to a node and an edge corresponds to a link. The diameter of an interconnection network is the maximum length of the shortest paths between all pairs of vertices. The fault diameter of an interconnection network G is the maximum length of the shortest paths between all two fault-free vertices when there are $_k(G)-1$ or less faulty vertices, where $_k(G)$ is the connectivity of G. The fault diameter of an R-regular graph G with diameter of 3 or more and connectivity ${\tau}$ is at least diam(G)+1 where diam(G) is the diameter of G. We show that the fault diameter of a 2-dimensional $m{\times}n$ torus with $m,n{\geq}3$ is max(m,n) if m=3 or n=3; otherwise, the fault diameter is equal to its diameter plus 1. We also show that in $d({\geq}3)$-dimensional $k_1{\times}k_2{\times}{\cdots}{\times}k_d$ torus with each $k_i{\geq}3$, there are 2d mutually disjoint paths joining any two vertices such that the lengths of all these paths are at most diameter+1. The paths joining two vertices u and v are called to be mutually disjoint if the common vertices on these paths are u and v. Using these mutually disjoint paths, we show that the fault diameter of $d({\geq}3)$-dimensional $k_1{\times}k_2{\times}{\cdots}{\times}k_d$ totus with each $k_i{\geq}3$ is equal to its diameter plus 1.

• Journal of the Korean Society of Fisheries and Ocean Technology
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• v.22 no.4
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• pp.90-97
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• 1986

• Proceedings of the Korean Information Science Society Conference
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• 2008.06a
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• pp.351-352
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• 2008

• Bulletin of the Korean Mathematical Society
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• v.36 no.3
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• pp.621-627
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• 1999

In this paper we compute Gottlieb groups for generalized lens spaces. Then we apply this result to compute Gottlieb groups for total spaces of a principal torus bundle over a lens space.

• Korean Journal of Mathematics
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• v.7 no.1
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• pp.79-84
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• 1999

• Journal of the Chungcheong Mathematical Society
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• v.6 no.1
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• pp.105-111
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• 1993

In this paper we show that if a semi-restricted Lie algebra L has an one dimensional toral Cartan subalgebra, then L is simple and $L\simeq_-sl(2)$ or $W(1:\underline{1})$. And we study that if L is simple but not simple and H is 2-dimensional, then H is a torus.