In this talk, we will show the existence and stability of the spatially inhomogeneous periodic solutions for some diffusive population models subject to Dirichlet or Neumann boundary conditions. For the Dirichlet boundary condition problem, we demonstrate that the spatially inhomogeneous periodic solutions can be bifurcated from the positive steady state for both Logistic and weak Allee type population models. For a special Logistic type model, such bifurcated periodic solutions are shown to be persistent when the parameter is far away from the bifurcation values. For the Neumann boundary condition problem, we establish the existence of various spatially inhomogeneous periodic solutions for the diffusive Nicholson’s blowflies population model. Such periodic solutions are numerically observable in a relatively long time period although they are not stable. This talk is mainly based on some joint works with Junping Shi, Junjie Wei and Xingfu Zou

Center manifold method has been a very powerful approach in studying stability of nonlinear ordinary differential equation (ODE) systems and it has also proved to be useful in studying the stability of partial differential equation (PDE) systems. Through the center manifold method, we conduct stability analysis on an initial-boundary-value problem of a nonlinear Korteweg-de Vries equation posed on a finite interval (0, $2/pi /sqrt{7/3}$).

The main contribution of this paper is to propose a new convex optimization model for multiplicative noise and blur removal. The main idea is to rewrite a blur and multiplicative noise equation such that both image variable and noise variable are decoupled. The resulting objective function involves the total variation regularization term, the term of variance of the inverse of noise, the ℓ1-norm of the data fitting term among the observed image

In this talk, I will present some necessary and sufficient conditions are established for a two-agent flock model with processing delay to admit a time-asymptotic flocking. The results provide a relation based on which proper initial positions and velocities can be selected to form a flocking with predetermined position displacement distance. It is shown that the processing delay can terminate a flocking, can induce a flocking and can lead to a flocking bifurcation resulting a periodic flocking. It is also shown that the processing delay can induce flocking switches in the sense that as the processing delay varies, the flocking may follow a switching pattern as no flocking-flocking-periodic flocking-flocking-divergence. The talk is based on an ongoing project with Xiao Wang and Jianhong Wu (York University)

学 术 报 告报 告 人：穆默（教授）香港科技大学数学系报告题目：Decoupling Techniques for Coupled PDEs in Multi-Physics Applications: Algorithm, Numerical Analysis, and Software时间：2015年12月10日上午10：00地点：数学系107室欢迎参

The study of completely positive maps is motivated by applications of the theory of completely positive maps to quantum information theory, where operator valued completely positive maps on C*-algebras are used as a model for quantum operation, and quantum probability. Stinespring theorem is a very famous representation theorem in C*-algebras. In this talk, we give an analogue of stinespring theorem in Hilbert A-module. And we also consider the covariant representation on Hilbert C*-module.

报告人：香港理工大学数学系祁力群教授.报告题目：A Necessary and Sufficient Condition for Existence of a Positive Perron Vector时间: 2015年12月8日(周二)下午16:00.地点: 数学系107室.欢迎大家前往听讲

We give a brief overview on the current investigations in this area. We concentrate on the three themes: 1.Integral representations of nonlinear orthogonally additive operators; 2.Narrow orthogonally additive operators; 3.Extensions of orthogonally additive operators.