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

• 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
• Project Status: Completed (Fiscal Year 2017)
• Budget Amount: ¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000); Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
• 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 / クラスター代数 / 有限体

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).

Research Products

• [Journal Article] A DISCRETE MATHEMATICAL MODEL FOR ANGIOGENESIS (2016)
  • Author(s): K. MATSUYA, F. YURA, J. Mada, H. KURIHARA, T. TOKIHIRO
  • Journal Title: SIAM J. APPL. MATH. Volume: 76 Issue: 6 Pages: 2243-2259
  • DOI: 10.1137/15m1038773
  • Peer Reviewed / Open Access
• [Journal Article] Integrability criterion in terms of cop rime property for the discrete Toda equation (2015)
  • Author(s): M. Kanki, J. Mada, T. Tokihiro
  • Journal Title: Journal of Mathematical Physics Volume: 56 Issue: 2 Pages: 022706-022706
  • DOI: 10.1063/1.4908109
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Irreducibility and co-primeness as an integrability criterion for discrete equations (2014)
  • Author(s): 間瀬崇史
  • Journal Title: Journal of Physics A : Mathematical and Theoretical Volume: 47 Issue: 46 Pages: 465204-465204
  • DOI: 10.1088/1751-8113/47/46/465204
  • Peer Reviewed
• [Presentation] エレベーター内の乗降者配置による稼働効率化 (2018)
  • Author(s): 塩田佳明，豊谷純，間田潤
  • Organizer: 情報処理学会
• [Presentation] 血管新生の数理モデル (2017)
  • Author(s): 間田潤
  • Organizer: 研究集会「数理科学の拡がり：可積分系・数理医学」
• [Presentation] クラスター代数とQRT系 (2016)
  • Author(s): 野邊 厚, 間田 潤
  • Organizer: 日本応用数理学会
  • Place of Presentation: 神戸学院大学（兵庫県神戸市）
  • Year and Date: 2016-03-05
• [Presentation] クラスター代数とセルオートマトン (2016)
  • Author(s): 野邊 厚, 間田 潤
  • Organizer: 日本応用数理学会
  • Place of Presentation: 北九州国際会議場（福岡県北九州市小倉）
• [Presentation] 血管新生の数理モデルについて (2015)
  • Author(s): 間田 潤, 松家 敬介, 由良 文孝, 時弘 哲治, 栗原 裕基
  • Organizer: 日本応用数理学会
  • Place of Presentation: 金沢大学（石川県金沢市）
  • Year and Date: 2015-09-10
• [Presentation] 周期離散戸田方程式における互いに素条件 (2015)
  • Author(s): 神吉 雅崇，時弘 哲治，間田 潤
  • Organizer: 日本数学会
  • Place of Presentation: 明治大学
  • Year and Date: 2015-03-24
• [Presentation] 互いに素条件による離散方程式の可積分性判定 (2014)
  • Author(s): 神吉 雅崇，時弘 哲治，間瀬 崇史，間田 潤
  • Organizer: 日本数学会
  • Place of Presentation: 広島大学
  • Year and Date: 2014-09-26