Study on matrix equations over a Laurent polynomial ring obtained from differential equations with a time-delay

2009 Fiscal Year Final Research Report

• Project/Area Number: 19540128
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Nara University of Education
• Principal Investigator: ITO Naoharu Nara University of Education, 教育学部, 教授 (90246661)
• Project Period (FY): 2007 – 2009
• Keywords: ローラン多項式環 / 時間遅れ / 線形微分方程式系 / 行列方程式 / 自己相反行列多項式

Research Abstract

In this research, a Laurent polynomial ring obtained from differential equations with a time-delay is investigated. Then, the existence conditions and computation methods of solutions for matrix equations over the ring are studied. We can apply these results to the investigation of qualitative properties of the differential equations with a time-delay. Moreover, the distribution of zeros of a self-reciprocal polynomial is also studied.

Research Products

• [Book]
  • Author(s): Naoharu Ito, Reinhold Kustner, Harald Wimmer
  • Publisher: A class of self-inversive matrix polynomials with characteristic roots on the unit circle(in preparation)