学术报告预告（主讲人：夏永辉，时间：3月19日）

报告题目: 四元数体上微分方程的基本框架

报告人: 夏永辉教授(浙江师范大学)

报告时间:  2021年3月19日(星期五), 9:30-10:30

报告地点: 腾讯会议, 会议号: 516 819 188

报告摘要: This talk is to give a frame work for the theory of linear QDEs, which can be applied to quantum mechanics, fluid mechanics, Frenet frame in differential geometry, kinematic modeling, attitude dynamics, Kalman filter design, spatial rigid body dynamics, etc. We prove that the set of all the solutions to the linear homogenous QDEs is actually a right-free module, not a linear vector space. On the noncommutativity of the quaternion algebra, many concepts and properties for the ODEs cannot be used. They should be redefined accordingly. A definition of Wronskian is introduced under the framework of quaternions which is different from standard one in the ODEs. Liouville formula for QDEs is given. Also, it is necessary to treat the eigenvalue problems with left and right sides, accordingly. Upon these, we studied the solutions to the linear QDEs. Furthermore, we present two algorithms to evaluate the fundamental matrix. Some concrete examples are given to show the feasibility of the obtained algorithms. Finally, a conclusion and discussion end the paper.

报告人简介: 夏永辉老师现为浙江师范大学特聘教授、博士生导师。获省部级科技奖励3项，入选“闽江学者特聘教授”，获“福建青年科技奖”,近年来主持国家自然科学基金3项(其中面上2项)，参与国家重点1项，与合作者一起在本学科方向的SCI期刊Proc. Amer. Math. Soc.、J. Differential Equations、SIAM J. Appl. Math.、Studies. Appl. Math.、Proc. Edinburgh Math. Soc.、Phys. Rew. E.、《中国科学》等上发表系列学术论文，建立了线性四元数体上微分方程的基本框架；改进了非自治Hartman-Grobman线性化的主要结果。推广了庞加莱和李雅普诺夫关于二维平面系统可积的充要条件的经典理论,将此可积理论推广到了任意有限维。

欢迎感兴趣的老师和同学参加！