Mathematical structure of discrete integrable systems for ultra-discrete limit, and that on finite field

2017 Fiscal Year Final Research Report

• Project/Area Number: 26800075
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Mathematical analysis
• Research Institution: Nihon University
• Principal Investigator: MADA Jun 日本大学, 生産工学部, 准教授 (80396853)
• Project Period (FY): 2014-04-01 – 2018-03-31
• Keywords: 応用数学 / 可積分系 / 離散系 / セルオートマトン / 数理医学 / 血管新生

Outline of Final Research Achievements

I proved that the discrete KdV equation (the bilinear form, the nonlinear form) and the discrete Toda equations (semi-infinite boundary conditions, molecular boundary conditions, periodic boundary conditions) have the Laurent property, the irreducibility and co-primeness.
The other hand, from recent time-lapse imaging experiments on the dynamics of endothelial cells (ECs) in angiogenesis, I proposed a mathematical model of ECs by methods of a discrete system and a ultra-discrete discrete system. Furthermore, I proposed a continuous model and an extended model incorporating the influence of vascular endothelial growth factor (VEGF).

Free Research Field

数物系科学