In this talk, I will report our recent research on time-delayed compartmental population models in a periodic environment. We first establish the theory of basic reproduction ratio R0 for such systems. It is proved that R0 serves as a threshold value for the stability of the zero solution of the associated periodic linear systems. As an illustrative example, we also apply the developed theory to a periodic SEIR model with an incubation period and obtain a threshold result on its global dynamics in terms of R0.

Malaria is an infectious disease caused by Plasmodium parasites and is transmitted among humans by female Anopheles mosquitoes. Climate factors have significant impact on both mosquito life cycle and parasite development. To consider the temperature sensitivity of the extrinsic incubation period (EIP) of malaria parasites, we formulate a delay differential equations model with a periodic time delay. We derive the basic reproduction ratio R0 and establish a threshold type result on the global dynamics in terms of R0. More precisely, we show that the unique disease-free periodic solution is globally asymptotically stable if R0<1, and the model system admits a unique positive periodic solution which is globally asymptotically stable if R0>1

in this introductory talk, I will give an overview of the network sciences, and in particular, some basic metrics and models to analyze and model social networks.

For bootstrap sample sums resulting from a sequences of random variables , a very general central limit theorem is established. The random variables do not need to be independent or identically distributed or to be of any particular dependence structure. Furthermore, no conditions, including moment conditions, are imposed in general on the marginal distributions of the . As a special case of the main result, a result of Liu (1988) concerning independent but not identically distributed is extended to a larger class of parent sequences.

We generalize the P(N)-graded Lie super algebras of Martinez-Zelmanov. This generalization is not so restrictive but sufficient enough so that we are able to have a classification for this generalized P(N)-graded Lie super-algebras. The upshot is that the generalized P(N)-graded Lie super-algebra L is centrally isogenous to a matrix Lie super-algebra coordinated by an associative super-algebra with a super- involution. Moreover, L is P(N)-graded if and only if the coordinate algebra R is commutative and the super-involution is trivial. This recovers Martinez-Zelmanov’s theorem for type P(N). The motivation of this generalization comes from the fermionic-bosonic module construction.

题目：PDE Free Boundary Problems from Biology报告人：Prof Bei Hu (Notre Dame University, USA)时间：2017年6月16日 （周五） 下午2：00-- 3：00地点：宁静楼104室欢迎各位参加

In this talk，a new model which describes the vegetation pattern formation in ecological evolution system will be discussed. The mathematical model consists of a degenerate reaction-diffusion system with a cross diffusion. It shows that the system has a global solution. Some other properties of weak solutions will be also discussed.

The presentation includes two parts. The first part is a brief introduction of adaptive designs in clinical trials. The second part presents a specific adaptive design, namely Bayesian optimal randomized design, summarized as follows. Consider a clinical trial with two or more treatments. Assignment of n patients to the treatments is sequential.