• 한국초전도학회:학술대회논문집
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• 한국초전도학회 2009년도 Korea Superconductivity Society Meeting 2009
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• pp.12-12
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• 2009

• Bulletin of the Korean Chemical Society
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• 제29권11호
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• pp.2172-2182
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• 2008

• 정보처리학회논문지A
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• 제11A권3호
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• pp.189-198
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• 2004

본 논문에서는 m${\times}$n 메쉬 연결망의 첫 행과 마지막 행에 랩어라운드 링크를 갖는 연결망 M$_2$(m,n) (m$\geq$2, n$\geq$3)의 고장 해밀톤 성질을 고려한다. 이분 그래프인 M$_2$(m,n)에 하나의 결함 링크가 발생했을 때 임의의 두 노드가 다른(같은) 집합에 속한 경우 두 노드를 잇는 길이 mn-1(mn-2)인 경로가 존재함을 보인다. ［1］에서 보인 P$_{m}$ ${\times}$C$_{n}$ 의 연구 결과와 비교하면 P$_{m}$ ${\times}$C$_{n}$ 또한 이러한 해밀톤 성질을 지닌다. 그러나 P$_{m}$ ${\times}$C$_{n}$ 이 m개의 랩어라운드 에지를 지니는 것에 반해 M$_2$(m,n)은 단지 두 개의 링크를 추가하여 이러한 해밀톤 성질을 지닌다. 또한 M$_2$(m,n)은 다차원 메쉬, 재귀원형군, 하이퍼큐브, 이중 루프 네트워크, k-ary n-큐브와 같은 여러 상호 연결망의 스패닝 부 그래프이다. 따라서 M$_2$(m,n)의 고장 해밀톤 성질은 이들 연결망들의 고장 해밀톤들 성질을 밝히는데 활용될 수 있다. 본 논문의 결과를 3차원 메쉬, 재귀원형군, 하이퍼큐브에 적용시켜 이들 연결망의 고장 해밀톤 성질들을 보인다.

• 대한수학회보
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• 제32권1호
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• pp.1-11
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• 1995

Let $p, q \in R^2 and H : R^{2n} \to R^n$ be differentiable. An autonomous Hamiltonian system has the form $$ (0.1) \dot{p} = -\frac{\partial q}{\partial H}(p, q), \dot{q} = \frac{\partial p}{\partial H}(p, q) $$.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2001년도 추계학술대회논문집 I
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• pp.85-89
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• 2001

Hamiltonian modeling approach has been extensively adopted for rigid body dynamics whereas its usage for deforming flexible continuum dynamics has been limited. A set of Hamilton＇s equations for flexible body motion with finite deformation has been derived and applied for a nonlinear impact problem.

• Korean Journal of Mathematics
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• 제7권2호
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• pp.301-313
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• 1999

In this paper we obtain similar limit theorems of the Generalized Curie - Weiss model for a new class Hamiltonian. We expressed the saddlepoint approximation by large deviation rate and then obtain the limit theorems.

• Bulletin of the Korean Chemical Society
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• 제11권4호
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• pp.332-333
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• 1990

The most general algebraic Hamiltonian for vibron model of diatomic molecules is obtained by using the theorems on the Jordan Schwinger representations of Lie groups.

• 대한수학회보
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• 제59권1호
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• pp.119-139
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• 2022

This paper deals with the λ-labeling and L(2, 1)-coloring of simple graphs. A λ-labeling of a graph G is any labeling of the vertices of G with different labels such that any two adjacent vertices receive labels which differ at least two. Also an L(2, 1)-coloring of G is any labeling of the vertices of G such that any two adjacent vertices receive labels which differ at least two and any two vertices with distance two receive distinct labels. Assume that a partial λ-labeling f is given in a graph G. A general question is whether f can be extended to a λ-labeling of G. We show that the extension is feasible if and only if a Hamiltonian path consistent with some distance constraints exists in the complement of G. Then we consider line graph of bipartite multigraphs and determine the minimum number of labels in L(2, 1)-coloring and λ-labeling of these graphs. In fact we obtain easily computable formulas for the path covering number and the maximum path of the complement of these graphs. We obtain a polynomial time algorithm which generates all Hamiltonian paths in the related graphs. A special case is the Cartesian product graph K_n☐K_n and the generation of λ-squares.

• 대한수학회지
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• 제46권2호
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• pp.363-447
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• 2009

The author previously defined the spectral invariants, denoted by $\rho(H;\;a)$, of a Hamiltonian function H as the mini-max value of the action functional ${\cal{A}}_H$ over the Novikov Floer cycles in the Floer homology class dual to the quantum cohomology class a. The spectrality axiom of the invariant $\rho(H;\;a)$ states that the mini-max value is a critical value of the action functional ${\cal{A}}_H$. The main purpose of the present paper is to prove this axiom for nondegenerate Hamiltonian functions in irrational symplectic manifolds (M, $\omega$). We also prove that the spectral invariant function ${\rho}_a$ : $H\;{\mapsto}\;\rho(H;\;a)$ can be pushed down to a continuous function defined on the universal (${\acute{e}}tale$) covering space $\widetilde{HAM}$(M, $\omega$) of the group Ham((M, $\omega$) of Hamiltonian diffeomorphisms on general (M, $\omega$). For a certain generic homotopy, which we call a Cerf homotopy ${\cal{H}}\;=\;\{H^s\}_{0{\leq}s{\leq}1}$ of Hamiltonians, the function ${\rho}_a\;{\circ}\;{\cal{H}}$ : $s\;{\mapsto}\;{\rho}(H^s;\;a)$ is piecewise smooth away from a countable subset of [0, 1] for each non-zero quantum cohomology class a. The proof of this nondegenerate spectrality relies on several new ingredients in the chain level Floer theory, which have their own independent interest: a structure theorem on the Cerf bifurcation diagram of the critical values of the action functionals associated to a generic one-parameter family of Hamiltonian functions, a general structure theorem and the handle sliding lemma of Novikov Floer cycles over such a family and a family version of new transversality statements involving the Floer chain map, and many others. We call this chain level Floer theory as a whole the Floer mini-max theory.

• 한국멀티미디어학회논문지
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• 제18권9호
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• pp.1083-1090
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• 2015

A generalized recursive circulant network(GR) is widely used in the design and implementation of local area networks and parallel processing architectures. In this paper, we investigate the routing of a message on this network, that is a key to the performance of this network. We would like to transmit maximum number of packets from a source node to a destination node simultaneously along paths on this network, where the i^th packet traverses along the i^th path. In order for all packets to arrive at the destination node securely, the i^th path must be node-disjoint from all other paths. For construction of these paths, employing the Hamiltonian Circuit Latin Square(HCLS), a special class of (n x n) matrices, we present O(n²) parallel routing algorithm on generalized recursive circulant networks.