20120217 の履歴(No.9)

組合せ数学・数値解析学合同ワークショップ*1 †

～ Combinatorics and Numerical Analysis Joint Workshop ～

Organizers†

溝口佳寛（九大IMI），谷口哲至（松江高専），三枝崎剛（大分高専）

Yoshihiro Mizoguchi (Kyushu University),
Tetsuji Taniguchi (Matsue College of Technology),
Tsuyoshi Miezaki (Oita National College of Technology)

Advisary: 坂内英一（上海交通大学／九州大学）

Eiichi Bannai (Shanhai Jiao Tong University / Kyushu University)

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Date†

2012年 2月17日(金) 10:00-18:00
(February 17, 2012. 10:00-18:00)

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Location†

九州大学西新プラザ中会議室(2F)
(Meeting Room, Nishijin Plaza, Kyushu University)

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Program†

10:00-11:00, Yaokun Wu（上海交通大学）
- Title: TBA
11:30-12:10, 小関健太（国立情報学研究所）
- Title: On the Hamiltonicity of graphs on a surface
13:50-14:50, 陳小君（香港理工大学）
- Title: TBA
15:20-16:00, 木村拓馬（佐世保高専），木下武彦（RIMS），中尾充宏（佐世保高専）
- Title: A numerical method to prove the existence of solutions for nonlinear parabolic problems
16:20-17:00, 田中守（東北大理）
- Title: Higher eigenvalues of the Laplacian on a graph and partitions of the graph
17:20-18:00, 平坂貢（釜山国立大学）
- Title: Characterization of p-valenced association schemes

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Abstract†

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Yaokun Wu（上海交通大学）†

Yaokun Wu (Shanhai Jiao Tong University)

Title: TBA

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小関健太（国立情報学研究所）†

Kenta Ozeki (National Institute of Informatics, Japan)

Title: On the Hamiltonicity of graphs on a surface
Abstract:

A cycle in a graph G is called Hamiltonian if it passes through all vertices in G. In this talk, we will concentrate on a Hamiltonian cycle in graphs on a Topological surface, for example, the sphere (the plane), the projective plane, the torus, and so on. One of the most classical result of this area is the one due to Tutte that stats that “every 4-connected plane graph has a Hamiltonian cycle”. I would like to introduce some other results, some of which are obtained very recently. I also mention the connection between “the toughness” and the Hamiltonicity of graphs on a surface.

This is a joint work with K. Kawarabayashi (National Institute of Informatics, Japan).

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陳小君（香港理工大学）†

Xiaojun Chen (The Hong Kong University of Science and Technology)

Title: TBA

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木村拓馬（佐世保工業高等専門学校），木下武彦（京都大学数理解析研究所），中尾充宏（佐世保工業高等専門学校）†

Takuma Kimura (Sasebo National College of Technology), Takehiko Kinoshita (RIMS, Kyoto University) and Mitsuhiro T. Nakao (Sasebo National College of Technology)

Title: A numerical method to prove the existence of solutions for nonlinear parabolic problems
Abstract:

We present numerical verification methods for parabolic problems. Our main result is a constructive a posteriori estimates of inverse operators for initial-boundary value problems in linear parabolic PDEs on a bounded domain.

The proposed a posteriori estimates is based on error analysis of the Galerkin approximation for boundary value problems in space direction and the piecewise linear interpolation for initial value problems in time. Applying the result, we can numerically prove the existence of solutions for nonlinear parabolic initial-boundary value problems. Some numerical results will be shown in the talk.

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田中守（東北大学大学院理学研究科）†

Mamoru Tanaka (Tohoku University)

Title: Higher eigenvalues of the Laplacian on a graph and partitions of the graph
Abstract:

We can regard the 2-nd eigenvalue of the Laplacian on a connected finite graph as strength of connection between two disjoint subgraphs in the graph. In this talk, I will give a relation between the k-th eigenvalue of the Laplacian on a connected finite graph and the minimum among the 2-nd eigenvalues of the Laplacians on the subgraphs in a partition of the graph.

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平坂貢（釜山国立大学）†

Mitsugu Hirasaka (Pusan National University)

Title: Characterization of p-valenced association schemes
Abstract:

Let $(X, \, \{R_i\}_{0 \leq i \leq d})$ be an assocaition scheme and p a prime. We say that $(X, \, \{R_i\}_{0\leq i \leq d})$ is p-valenced if $k_i$ is a power of p for each i with $0 \leq i \leq d$ where $k_i$ is the constant out-degree of the digraph $(X, \, R_i)$ . In this talk we show some conditions for a p-valenced association scheme to be induced by a transitive permutation group.