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

时滞微分方程洛朗多项式环上矩阵方程的研究

• 批准号: 19540128
• 负责人: ITO Naoharu
• 金额: $ 1.16万
• 依托单位: Nara University of Education
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2007
• 资助国家: 日本
• 起止时间: 2007 至 2009
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-19540128/
• 关键词: 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; 線形微分方程式; ローラン多項式; 微分差分作用素

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.

在这项研究中，Laurent多项式环得到的微分方程的时间延迟进行了研究。然后，研究了环上矩阵方程解的存在条件和计算方法。这些结果可用于研究时滞微分方程的定性性质。此外，还研究了自反多项式零点的分布。