时间：2017年11月08（星期三）14：00-16：30

地点：学院南路校区，学术会堂602

报告一题目：Theoretical and numerical analysis of a time-fractional diffusion equation

报告人：Martin Stynes, Beijing Computational Science Research Center, China

Martin Stynes was a Lecturer at Waterford Regional Technical College, Ireland from 1979 to 1984. He then moved to University College Cork, where he was successively Lecturer, Statutory Lecturer, Professor (Scale 2) — these are the equivalents of assistant/associate/full professor. He was a Fulbright Research Professor at Kent State University (USA) in 1990, Royal Society Visiting Fellow at Oxford University (U.K.) in 1991, Visiting Professor at University of Colorado at Denver (USA) in 1997, DFG Visiting Professor at Otto von Guericke University Magdeburg (Germany) in 1998, Visiting Professor at the University of South Carolina (USA) in 2004, and DFG Mercator Guest Professor at the Technical University of Dresden (Germany) in 2008. He was the elected President of the UK and Republic of Ireland Section of SIAM 2003-5. He serves on the editorial boards of the journals “Advances in Computational Mathematics”, “Computational Methods in Applied Mathematics” and “Mathematical Proceedings of the Royal Irish Academy". He took early retirement from University College Cork in 2012 in order to concentrate on research. He has been at CSRC since 2014.  

摘要：A reaction-diffusion initial-boundary problem with a Caputo time derivative of order αin (0,1) is considered. The solution of such a problem is discussed; it is shown that in general the solution has a weak singularity near the initial time t=0, and sharp pointwise bounds on the derivatives of this solution are derived. These bounds are then used in a new analysis of a standard finite difference method for the problem. This numerical analysis reveals how to choose a suitably-graded mesh that will yield an accurate approximate solution of the problem. The talk does not assume that the listener is familiar with fractional-order derivatives. It concentrates more on the properties of the solution of the differential equation than on the analysis of the numerical method. The second (shorter) part of the talk assumes that the listener has a little knowledge of finite difference methods for solving differential equations.

Reference:

M.Stynes, E.O'Riordan and J.L.Gracia, Error analysis of a finite difference method on graded meshes for a time-fractional diffusion equation, SIAM J. Numer. Anal. 55 (2017), 1057--1079. DOI: 10.1137/16M1082329

 

报告二题目：Monotonic iteration positive symmetric solutions to a boundary value problem with p-Laplacian and Stieltjes integral boundary conditions

报告人：中央财经大学统计与数学学院、孙博副教授

摘要：This paper investigates the existence of monotonic iteration positive symmetric

solutions to a boundary value problem with p-Laplacian and Stieltjes integral boundary conditions. The main tool is a monotone iterative technique. Meanwhile, an example is worked out to demonstrate the main results.

 

报告三题目：基于网络新闻文本情感分析的消费情感指数构建与比较

报告人：中央财经大学统计与数学学院、刘苗副教授

摘要：消费者信心指数主要反映消费者对于经济发展、就业状况、物价水平、生活状况、购房和投资六方面的信心情况。本文从以上六个维度出发，基于百度搜索采集2011年至2017年消费者信心相关新闻文本174606条，利用情感分析、深度神经网络学习等方法得到新闻文本的情感倾向，并以此为基础提出并构建了消费者情感指数，用于反映我国消费者的信心的情况，并将结果与传统问卷调查得到的消费者信心指数进行了对比，研究发现消费情感指数与传统消费者信心指数走势具有较强相似性，相关性约为0.7，在消费短期趋势判断更灵敏，对传统指数及经济景气指数具有一定的先导作用，体现了消费情感指数的可靠性、时效性，从侧面反映了舆论对消费者信心的影响作用。