1990 Fiscal Year Final Research Report Summary
On Applications of Global Variation Theory
Project/Area Number 
63460003

Research Category 
GrantinAid for General Scientific Research (B)

Allocation Type  Singleyear Grants 
Research Field 
代数学・幾何学

Research Institution  Nagoya University 
Principal Investigator 
SHIKATA Yoshihiro Nagoya Univ. Sci. Professor > 名古屋大学, 理学部, 教授 (50028114)

CoInvestigator(Kenkyūbuntansha) 
OZAWA Tetsuya Nagoya Univ. Sci., Lecturer, 理学部, 講師 (20169288)
OMOTO Hideo Nagoya Univ. Sci., Assistant, 理学部, 助手 (20022684)
TSUCHIYA Akihiro Nagoya Univ. Sci., Professor, 理学部, 教授 (90022673)
AOMOTO Kazuhiko Nagoya Univ. Sci., Professor, 理学部, 教授 (00011495)
MORIMOTO Akihiko Nagoya Univ. Sci., Professor, 理学部, 教授 (30022510)

Project Period (FY) 
1989 – 1990

Keywords  (invariant) superpotential / topological classification of phenomena / inverse problem of differential equation / models with necessary condition / multiplicity of phenomena for potential 
Research Abstract 
This research was started from the purely mathematical problem to reassemble the potential theory, which played the main role in the theory closed geodesics, into a fundamental technique for the mathematical inverse problems. On the way, we noticed the technique is also effective for the problems in the field of biophysics, material science, biology and physiology, as a new method to construct a model with necessity. We joined into active groups in these field to develop further the mathematical theory and tried to establish a theoretical breakthrough in the fields, because the conventional models are only those with sufficient conditions, in the other words, the existing models are taken for granted only when they yield the solution coincidie with the observed phenomena. The logical approach of this type requiring only the sufficient condition can not deny the existence of the other models which also gives the same solution, resulting too many models in some cases. Therefore it is necessary to construct a theory of models with necessity, reversing the logics above, which may distinguish the real models. We are getting some results along this line as follows ; 1) We get a partial success in the theory of alpha rhythm of EEG and a relation to ECG. 2) We solved the dendritic growth problem of snow crystal as an inverse problem of the partial differential equation. 3) We get a model with necessity for growth of the yeast and seaurchin. 4) We considered the 1/f noise problem in our line to get the necessary characteristic for the filter. 5) We treated the motion of vorteces and get a evaluation of some singularities.

Research Products
(8 results)