* 組合せ数学・数値解析学合同ワークショップ((&size(13){このセミナーは，[[グローバルCOEプログラム「マス・フォア・インダストリ研究教育拠点」:http://gcoe-mi.jp/]]の支援を受けて開催されます。&br; This seminar is supported by [[Global COE Program "Education and Research Hub for Mathematics-for-Industry":http://gcoe-mi.jp/]].};)) [#m322cc3e]
''～ Combinatorics and Numerical Analysis Joint Workshop ～''
**Organizers [#xb11a6e1]
-[[溝口 佳寛:http://imi.kyushu-u.ac.jp/~ym/]]（九大IMI），[[谷口 哲至:http://researchmap.jp/tetsuzit-14/]]（松江高専），三枝崎剛（大分高専）
[[Yoshihiro Mizoguchi:http://imi.kyushu-u.ac.jp/~ym/]] (Kyushu University),~
[[Tetsuji Taniguchi:http://researchmap.jp/tetsuzit-14/]] (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)
**Date [#cdeebbd2]
-2012年 2月17日(金) 10:00-18:00~
(February 17, 2012. 10:00-18:00)
**Location [#ec2c564b]
-九州大学
[[西新プラザ:http://www.kyushu-u.ac.jp/university/institution-use/nishijin/index.htm]] 中会議室(2F)~
(Meeting Room, [[Nishijin Plaza:http://www.kyushu-u.ac.jp/university/institution-use/nishijin/english.htm]], Kyushu University)
**Program [#a25b6bb0]
-10:00-11:00, [[Yaokun Wu（上海交通大学）>#wu-05]]
--Title: TBA
-11:30-12:10, [[小関 健太（国立情報学研究所）>#ozeki-05]]
--Title: On the Hamiltonicity of graphs on a surface
-13:50-14:50, [[陳 小君（香港理工大学）>#chen-05]]
--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）>#kimura-05]]
--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）>#tanaka-05]]
--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）>#hirasaka-05]]
--Title: Characterization of '''p'''-valenced association schemes
**Abstract [#c2089740]
***Yaokun Wu（上海交通大学） [#wu-05]
Yaokun Wu (Shanhai Jiao Tong University)
-Title: TBA
//~
// (English)
//-Abstract:
***小関 健太（国立情報学研究所） [#ozeki-05]
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).
***陳 小君（香港理工大学） [#chen-05]
Xiaojun Chen (The Hong Kong University of Science and Technology)
-Title: TBA
//~
// (English)
//-Abstract:
***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） [#kimura-05]
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.
***田中 守（東北大学大学院 理学研究科） [#tanaka-05]
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.
***平坂 貢（釜山国立大学） [#hirasaka-05]
Mitsugu Hirasaka (Pusan National University)
-Title: Characterization of '''p'''-valenced association schemes
-Abstract:
Let &mimetex{(X, \, \{R_i\}_{0 \leq i \leq d})}; be an assocaition scheme
and '''p''' a prime.
We say that &mimetex{(X, \, \{R_i\}_{0\leq i \leq d})}; is '''p'''-valenced if &mimetex{k_i}; is
a power of '''p'''
for each '''i''' with &mimetex{0 \leq i \leq d}; where &mimetex{k_i}; is the constant
out-degree of the digraph &mimetex{(X, \, R_i)};.
In this talk we show some conditions for a '''p'''-valenced association scheme to be
induced by a transitive permutation group.
