# Hakata Workshop; Summer Meeting 2017

Last-modified: 2017-06-23 (金) 10:35:32 (510d)

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## Hakata Workshop; Summer Meeting 2017 †

**～Discrete Mathematics and its Applications～**

Our purpose of this meeting is giving an opportunity to make a speech and to communicate with researchers who study various fields not only Combinatorics.

Further information is available from the organizers below.

### Organizers †

- Yoshihiro Mizoguchi (Kyushu University),
- Tetsuji Taniguchi (Hiroshima Institute of Technology),
- Makoto Tagami ( Kyushu Institute of Technology),
- Hirotake Kurihara (Kitakyushu National College of Technology),
- Shuya Chiba (Kumamoto University).

### Supported by †

- Graduate School of Mathematics, Kyushu University
- JSPS KAKENHI(Grant-in-Aid for Scientific Research (C)) Grant Number 25400217.
- JSPS KAKENHI(Grant-in-Aid for Scientific Research (C)) Grant Number 17K05346

### Date †

Saturday, June 17, 2017

### Location †

- Seminar Room I (2F) in Reference Eki Higashi Building. 1-16-14 Hakata-Eki-Higashi, Hakata-Ku, Fukuoka City, 812-0013 (see http://www.re-rental.com/ , Google maps )

### Program †

Speaker | Title | |
---|---|---|

13:43--13:45 | Opening (Tetsuji Taniguchi) | |

13:45--14:30 | Michio Seto (National Defense Academy) (this is joint work with S. Suda) | An application of de Branges-Rovnyak space theory to graph theory |

14:45--15:30 | Koji Momihara (Faculty of Education, Kumamoto University) | Three-valued Gauss periods and related strongly regular Cayley graphs |

15:45--16:30 | Shoichi Kamada (Graduate School of Science and Technology, Kumamoto University) | Fractal analysis for subset sum problems |

16:45--17:30 | Yusuke Yamauchi ( Hiroshima Institute of Technology) | On a regularity theorem for rectangular domain |

17:30--17:35 | Closing(Yoshihiro Mizoguchi) |

### Abstract †

#### Michio Seto (NDA) (this is joint work with S. Suda) †

- Title: An application of de Branges-Rovnyak space theory to graph theory
- Abstract: Let be inclusion of two finite simple graphs. In this talk, we deal with inner product spaces encoding the data of the defect of in . Our construction of those inner product spaces is based on de Branges-Rovnyak space theory in functional analysis. Further, applying the theory of quasi-orthogonal decomposition developed by de Branges and Vasyunin-Nikolskii, some inequalities concerning inclusion are derived.

#### Koji Momihara †

- Title: Three-valued Gauss periods and related strongly regular Cayley graphs
- Abstract: It is well-known that the Cayley graph on a finite field with the set of zeros of a nondegenerate elliptic quadratic form as its connection set is strongly regular. Recently, Bamberg, Lee, Xiang and the speaker found new strongly regular Cayley graphs by halving the elliptic quadric. Two-valued Gauss periods and a partition of a conic are behind this construction. In this talk, we show that the construction can be also done within the framework of three-valued Gauss periods. As a consequence, we obtain two new infinite families of strongly regular Cayley graphs.

#### Shoichi Kamada †

- Title: Fractal analysis for subset sum problems
- Abstract: The subset sum problem has several aspects such as combinatorial aspects, number theoretic aspects, and so on. In this talk, we estimate the information dimension for the subset sum problem, which gives the aspect of fractal analysis. For the equation of the subset sum problem, it can be considered that the probability distribution of their coefficients comes from that of fractional parts of real numbers. We show that this enables us to estimate the information dimension.

#### Yusuke Yamauchi †

- Title: On a regularity theorem for rectangular domain
- Abstract: There exists a large amount of literature on a regularity theorem of elliptic boundary value problem on smooth domains. In the field of elliptic partial differential equation, non-smoothness of the domain has some difficulties, and there are few results. In this talk, we show a regularity theorem on rectangular domain.