學(xué)術(shù)報告預(yù)告（主講人：夏永輝，時間：3月19日）
報告題目: 四元數(shù)體上微分方程的基本框架
報告人: 夏永輝教授(浙江師范大學(xué))
報告時間: 2021年3月19日(星期五), 9:30-10:30
報告地點: 騰訊會議, 會議號: 516 819 188
報告摘要: 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.
報告人簡介: 夏永輝老師現(xiàn)為浙江師范大學(xué)特聘教授、博士生導(dǎo)師。獲省部級科技獎勵3項，入選“閩江學(xué)者特聘教授”，獲“福建青年科技獎”,近年來主持國家自然科學(xué)基金3項(其中面上2項)，參與國家重點1項，與合作者一起在本學(xué)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.、《中國科學(xué)》等上發(fā)表系列學(xué)術(shù)論文，建立了線性四元數(shù)體上微分方程的基本框架；改進了非自治Hartman-Grobman線性化的主要結(jié)果。推廣了龐加萊和李雅普諾夫關(guān)于二維平面系統(tǒng)可積的充要條件的經(jīng)典理論,將此可積理論推廣到了任意有限維。
歡迎感興趣的老師和同學(xué)參加！
