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I will give a brief introduction of delayed differential equations, and show that the question of stability of an equilibrium solution is equivalent to an algebraic equation with transcendental terms. Then I will show the new method of solving the purely imaginary eigenvalues of a transcendental characteristic equation with two transcendental terms. The results are applied to the stability and associated Hopf bifurcation of a constant equilibrium of a generalreaction-diffusion system or ordinary differential equation with delay effects. Examples from chemical reaction and predator-prey models are analyzed using the new techniques. In particular the stability and associate Hopf bifurcation of a Gierer-Meinhardt system with the gene expression time delays is analyzed by using our method. This is a joint work with Shanshan Chen, and Junjie Wei.

报告人：张根凯教授张根凯教授报告题目一：Determinant of Toeplitiz operators on bounded symmetric domains and their Dixmier trace报告一时间：2013年7月3号上午9：00-10:15地点：致远楼107报告题目二：Estimates of normal differentiation of spherical harmonics along subsphere and complementary series of SO(n, 1).报告二时间：2013年7月3号上午10:30-11:45地点：致远楼107张根凯教授简介：张根凯教授，瑞典 Chalm...

In many situations, Business processes are often constrained by scarce resources. The lack of resources can cause contention among tasks and slow down the accomplishment of larger goals. This presentation discusses a Petri net based approach for recourse requirements analysis, which can be used for more general purposes. The concept of resource- oriented workflow nets (ROWN) is introduced and the transition firing rules of ROWN are presented. Resource requirements for general workflow can be done through reachability analysis. For a class of well-structured workflows, an efficient resource analysis algorithm is developed. Task falures are also considered in resource requirement analysis.

报告人：王维克教授(上海交通大学)报告题目： 数学的抽象时间：2013年7月4日（周四）下午4：00—5：00地点：数学系致远楼10

In a recent paper by Chen (2013) the limit law of the iterated logarithm for the partial sums of i.i.d. real-valued random variables has been established. In this note we look at the corresponding problem in the Banach space setting. Letbe a real separable Banach space with topological dual . Let be a sequence of i.i.d. -valued random variables and set and ，. We show that provided that其中and is the unit ball of .

In multiple therapeutic areas of drug development, such as oncology and infectious diseases (HIV, influenza vaccines), the combined use of multiple drugs is an important strategy to achieve greater therapeutic success. We present a novel design methodology for efficient design and analysis of preclinical drug combination studies. We then focus on the design and analysis of two new anti-cancer drug development experiments. We will highlight the contributions of the novel statistical methodology brought to the therapeutic development of the two drug combination therapies. In fact, the highly effective therapies might have been missed without the facilitation of the optimal experimental design.

This talk presents a sampled-data approach for the robust control of a single qubit (quantum bit). The required robustness is defined using a sliding mode domain and the control law is designed offline and then utilized online with a single qubit having bounded uncertainties. Two classes of uncertainties are considered including uncertainties in the system Hamiltonian and uncertainties in the coupling strength of the system-environment interaction. Four cases including the case without decoherence, and cases with amplitude damping decoherence, phase damping decoherence and depolarizing decoherence are analyzed in detail. Sampling periods are specifically designed for these cases to guarantee the required robustness.

A class of generalized additive partial linear models is investigated. We propose the use of polynomial spline smoothing for estimation of nonparametric functions, and derive quasi-likelihood based estimators for the linear parameters. We establish asymptotic normality for the estimators of the parametric components. The procedure avoids solving big system of equations as in kernel-based procedures and thus results in gains in computational simplicity. We further develop a class of variable selection procedures for the linear parameters by employing a nonconcave penalized likelihood, which is shown to have an oracle property. Monte Carlo simulations and an analysis of a dataset from Pima Indian diabetes study are presented for illustration