Title: Regularity in the local CR embedding problemSpeaker: Prof. Xianghong GongUniversity of WisconsinTime: 2010-7-28, 4:00--5:00Address: 致远楼 107

Let S(A) denote a spectrum inclusion set of a matrix or operator A. We study maps T on matrices or operators such that S(T(A) * T(B)) = S(A * B) for all (A, B) pairs. Here X * Y denotes a binary operation such as X - Y, X + Y, XY, XY+YX, XY-YX.

报告人简介：G. A. Elliott教授是加拿大科学院院士、丹麦科学与通讯院院士、多伦多大学Senior Canadian Researcher 席位教授、Wales大学荣誉教授。G. A. Elliott教授是国际著名数学家，算子代数K理论和C*代数分类理论的创始人与领袖，曾获得CRM-Fields Institute Prize.和John L. Synge Award两项大奖。时间：2010年7月16号 15：00-16：002010年7月18号 15：00-16：002010年7月20号 15：00-16：00地点：致远楼102欢迎广大师生参加

在报告中，我们考虑GMRES方法，一类广泛熟知和使用并具有代表性的非对称的Krylov子空间方法。这种方法在每一迭代步由通过Arnoldi方法构造对应的Krylov子空间的一组基和随后求解变换的海森伯格最小二乘问题两部分组分。在精确的运算中，Arnoldi向量是正交的。然而，在有限精度运算中，正交性将会丢失，这可能潜在的影响收敛率和计算近似解的最终实现精度……

我们考虑线性系统序列的求解，其中 是一般的非奇异稀疏矩阵，而 是对应的右边项。这种序列在许多应用中出现，比如计算流体动力学，结构力学，数值优化，以及求解非对称正定方程问题，例如，非线性方程 对于 ，由牛顿或Broyden型方法求解导出序列

We survey the results about exact multiplicity of positive solutions of a semilinear elliptic equation with zero Dirichlet boundary condition, and the domain is the unit ball or the whole space of n-dimensional space. It is well known that if the nonlinearity is smooth, then any positive solution to the equation is radially symmetric, and the solution set consists of curves. There are numerous work on the positive radially symmetric solutions of the equation in the last two decades. I will describe a unified approach by Tiancheng Ouyang and myself (and also Philip Korman and Yi Li) which determines the exact multiplicity of solutions and classifies the global bifurcation diagrams of the equation according to the convexity conditions on the nonlinearities. Related recent results will also be discussed.

The International Workshop on Nonlinear Elliptic and Parabolic Partial Differential Equations is scheduled to be held on 24-25 July, 2010, at Tongji University, Shanghai, China. The workshop aims to discuss research results and trends in elliptic and parabolic partial differential equations and related topics. All teachers and students are welcome.Scientific Committee:Zihua Chen, Tongji Univers...

Predator-prey interaction is a basic interspecies relation for ecological and social models. We review some recent results on global bifurcation of limit cycles, steady states in general predator-prey models, some with spatial structure. These results help to explain the rich spatial- temporal patterns which the system possesses.