兰州大学萃英学院学术报告

应兰州大学萃英学院和数学与统计学院邀请，英国肯特大学Markus Rosenkranz教授来我校访问并作学术报告。

报告题目：Boundary Problems via Integro-Differential Algebra

报告时间：7月28日（星期二）15：00

报告地点：观云楼802

报告人：Markus Rosenkranz

报告题目：Operator Rings for Integro-Differential Algebras

报告时间：7月29日（星期三）15：00

报告地点：观云楼802

报告人：Markus Rosenkranz

报告内容：

Title:Boundary Problems via Integro-Differential Algebra

Abstract:The setting of differential algebra extends naturally to certain structures with a notion of integration that interacts nicely with the derivation. Such structures are called integro-differential algebras.

They allow us to formulate and solve boundary problems in an algebraic setting using certain operator rings. Based on a simple example, we show how the algebaic formulation comes about. We will see that the boundary conditions are encoded in a certain projector acting on the function space. Given a fundamental system of the differential operator, the underlying initial value problem can be solved by variation of constants. Putting together the solution operator of the initial value problem and the projector, we obtain the Green's operator of the boundary problem. If desired, one can extract the classical Green's function from the Green's operator of a two-point boundary value problem. We give a short outlook on how this can be generalized to the wider class of Stieltjes boundary problems with distributional Green's functions.

Title:Operator Rings for Integro-Differential Algebras

Abstract:We take a detailed look at the ring of integro-differential operators, analyzing its computational efficiency in the light of the Groebner-Shirshov bases theory. We discuss the normal forms of the operator ring and how its components fit into the description of boundary problems. We conclude with an outlook at extended Mikusinski calculus that allows to incorporate Stieltjes boundary conditions in addition to the usual setting with initial conditions.

报告人简介:

Rosenkranz教授毕业于奥地利Johannes Kepler University。师从Grobner基的发起人Bruno Burchbergr和Heinz W. Engl。Rosenkranz教授研究微分方程边值问题和积分算子的代数方法和符号计算，是这些领域的后起之秀。他引进的积分微分代数概念成为微分方程边值问题的崭新方法，给予微积分中微分和积分算子的相互作用以代数刻画。他与合作者一起建立积分微分多项式的概念，算法和模型，并与微分积分算子环联系起来。他在这一开创性领域发表多篇论文，专著和程序包。他与多国数学家合作，并指导国际团队对这一方向进行研究。他还组织计算代数和微分代数等方面的多次国际会议。

萃英学院

2015年7月24日