• 대한수학회보
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• 제52권1호
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• pp.239-246
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• 2015

If for every elements x and y of an associative algebraic structure (S, ${\cdot}$) there exists a positive integer r such that $ab=b^ra$, then S is called quasi-commutative. Evidently, every abelian group or commutative semigroup is quasi-commutative. Also every finite Hamiltonian group that may be considered as a semigroup, is quasi-commutative however, there are quasi-commutative semigroups which are non-group and non commutative. In this paper, we provide three finitely presented non-commutative semigroups which are quasi-commutative. These are the first given concrete examples of finite semigroups of this type.

• 대한수학회보
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• 제39권2호
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• pp.277-282
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• 2002

We Show that When ($M,\;\omega$) is a closed, simply connected, symplectic manifold for all $\gamma\;\in\;\pi_1(Ham(M),\;id)$ the following inequality holds: $\parallel\gamma\parallel\;{\geq}\;sup_{\={x}}\;|A(\={x})|,\;where\;\parallel\gamma\parallel$ is the coarse Hofer's norm, $\={x}$ run over all extensions to $D^2$ of an orbit $x(t)\;=\;{\varphi}_t(z)$ of a fixed point $z\;\in\;M,\;A(\={x})$ the symplectic action of $\={x}$, and the Hamiltonian diffeomorphisms {${\varphi}_t$} of M represent $\gamma$.

• 대한수학회보
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• 제53권4호
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• pp.1197-1211
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• 2016

Let R be a finite commutative ring with nonzero identity. We define ${\Gamma}(R)$ to be the graph with vertex set R in which two distinct vertices x and y are adjacent if and only if there exists a unit element u of R such that x + uy is a unit of R. This graph provides a refinement of the unit and unitary Cayley graphs. In this paper, basic properties of ${\Gamma}(R)$ are obtained and the vertex connectivity and the edge connectivity of ${\Gamma}(R)$ are given. Finally, by a constructive way, we determine when the graph ${\Gamma}(R)$ is Hamiltonian. As a consequence, we show that ${\Gamma}(R)$ has a perfect matching if and only if ${\mid}R{\mid}$ is an even number.

• 한국정보과학회논문지:시스템및이론
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• 제31권1_2호
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• pp.19-26
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• 2004

이 논문에서는 정점이나 에지 고장이 있는 이중 루프 네트워크에서 임의의 두 정점을 연결하는 고장 없는 최장 경로를 고찰하여, 고장인 요소의 수가 둘 흑은 그 이하인 경우 이분 그래프인 이중 루프 네트워크 G(mn；1, m)은 강한 해밀톤 laceable 그래프임을 보인다. G(mn；1, m)은 m이 홀수이고 n이 짝수일 경우에만 이분 그래프이다.

• Journal of Mechanical Science and Technology
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• 제17권12호
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• pp.1922-1927
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• 2003

Nonlinear normal mode (NNM) vibration, in a nonlinear dual mass Hamiltonian system, which has 6$\^$th/ order homogeneous polynomial as a nonlinear term, is studied in this paper. The existence, bifurcation, and the orbital stability of periodic motions are to be studied in the phase space. In order to find the analytic expression of the invariant curves in the Poincare Map, which is a mapping of a phase trajectory onto 2 dimensional surface in 4 dimensional phase space, Whittaker's Adelphic Integral, instead of the direct integration of the equations of motion or the Birkhoff-Gustavson (B-G) canonical transformation, is derived for small value of energy. It is revealed that the integral of motion by Adelphic Integral is essentially consistent with the one obtained from the B-G transformation method. The resulting expression of the invariant curves can be used for analyzing the behavior of NNM vibration in the Poincare Map.

• 산업경영시스템학회지
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• 제23권59호
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• pp.1-10
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• 2000

The traveling salesman problem is a representative NP-Complete problem. It needs lots of time to get a solution as the number of city increase. So, we need an efficient heuristic algorithm that gets good solution in a short time. Almost edges that participate in optimal path have somewhat low value cost. This paper discusses the property of nearest neighbor and 3-opt. This paper uses nearest neighbor's property to select candidate edge. Candidate edge is a set of edge that has high probability to improve cycle path. We insert edge that is one of candidate edge into intial cycle path. As two cities are connected. It does not satisfy hamiltonian cycle's rule that every city must be visited and departed only one time. This paper uses 3-opt's method to sustain hamiltonian cycle while inserting edge into cycle path. This paper presents a highly efficient heuristic algorithm verified by numerous experiments.

• 한국통계학회:학술대회논문집
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• 한국통계학회 2003년도 춘계 학술발표회 논문집
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• pp.85-90
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• 2003

In this paper we develop a method for finding optimal ordering of K statistical models. This is based on a dependent paired comparison experimental arrangement whose results can naturally be represented by a completely oriented graph (also so called tournament graph). Introducing preference probabilities, strong transitivity conditions, and an optimal criterion to the graph, we show that a Hamiltonian path obtained from row sum ranking is the optimal ordering. Necessary theories involved in the method and computation are provided. As an application of the method, generalized variances of K multivariate normal populations are compared by a Bayesian approach.

• 제어로봇시스템학회논문지
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• 제4권6호
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• pp.707-712
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• 1998

본 논문에서는 선형 시불변 시스템에 대해 상태되먹임을 이용한 폐루프계의 지정된 영역내의 극배치법을 제안한다. 본 제안된 기법은 해밀톤 행렬의 하중행렬 Q의 설정에 의해 지정된 영역 (α중심, γ반경)내에 극배치가 가능함을 보인다. 먼저, Gershgorin의 이론을 적용하기 위해 해밀톤 행렬을 등가 변환시킨 후 행렬의 각 계수를 α와 γ의 관계를 이용하여 유도한다. 위의 관계를 만족하는 해밀톤 행렬의 각 하중행렬과 변환행렬을 이용하여 폐루프계의 상태되먹임 제어칙을 구한다. 또한 본 기법은 해밀톤 행렬과 최적제어와의 관계를 지니고 있으므로 얻어진 폐루프계는 최적제어법에서와 동일한 강인함을 가지게 된다. 끝으로 예제를 통하여 지정된 영역내의 극배치가 이루어짐을 보인다.

• Structural Engineering and Mechanics
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• 제31권5호
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• pp.621-624
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• 2009

The time delay in active and semi-active controls is an important research subject. Many researches on the time-delay control for deterministic systems have been made (Hu and Wang 2002, Yang et al. 1990, Abdel-Mooty and Roorda 1991, Pu 1998, Cai and Huang 2002), while the study on that for stochastic systems is very limited. The effects of the time delay on the control of nonlinear systems under Gaussian white noise excitations have been studied by Bilello et al. (2002). The controlled linear systems with deterministic and random time delay subjected to Gaussian white noise excitations have been treated by Grigoriu (1997). Recently, a stochastic averaging method for quasi-integrable Hamiltonian systems with time delay has been proposed (Liu and Zhu 2007). In the present paper, a stochastic optimal time-delay control method for stochastically excited nonlinear structural systems is proposed based on the stochastic averaging method for quasi Hamiltonian systems with time delay and the stochastic dynamical programming principle. An example of stochastically excited and controlled hysteretic column is given to illustrate the proposed control method.

• 정보처리학회논문지A
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• 제18A권5호
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• pp.205-214
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• 2011

본 논문은 널리 알려진 3차원 꼬인 큐브를 기반으로 하는 새로운 상호연결망 꼬인 큐브 토러스(TT) 네트워크를 제안한다. 꼬인 큐브 토러스 네트워크는 동일한 노드수를 갖는 honeycomb 토러스보다 짧은 지름을 갖고, 망 비용이 개선된 연결망이다. 본 논문에서는 꼬인 큐브 토러스의 라우팅 알고리즘을 제안하고, 지름, 망 비용, 이분할에지수, 해밀토니안 사이클을 분석한다.