大连理工-哈工大2014数学学术交流报告会日程表

大连理工-哈工大2014数学学术交流报告会日程表

 

哈工大数学系学术交流报告团应邀于2014年11月21-23日来大连理工大学数学科学学院进行学术交流活动。报告团成员包括：付永强（教授，系副主任），郑宝东（教授），陈明浩（教授），陈胜（教授），杨国俅（副教授），雷强（副教授），张超（副教授），靳水林（副教授），康文（讲师），矫贺明（讲师），李祝春（讲师）。学术交流日程如下：

 

22日：学术报告会   报告地点：研教楼207
		主持人
8:30-8:50	开幕式（卢玉峰、付永强讲话），合影	刘西民
	报告人/报告题目
8:50-9:25	报告人：陈胜（哈工大） 报告题目： Weak connectedness of tensor product of digraphs	付永强
9:25-9:50	报告人：杨国俅（哈工大） 报告题目：The connected sum of knot and meridional knot
9:50-10:15	报告人：李风玲（大连理工） 报告题目：Invariants of 3-manifolds from intersecting kernels of Heegaard splittings
10:15-10:30	茶    歇
10:30-10:55	报告人：雷强（哈工大） 报告题目：A Quantum Logic Including Unbounded Observables	刘西民
10:55-11:20	报告人：张超（大连理工） 报告题目：Task-group Relatedness and Generalization Bounds for Regularized Multi-task Learning
11:20-1:30	午餐与午休
1:30-1:55	报告人：康文（哈工大） 报告题目：Stabilization of Vibrating Systems with disturbance:Lyapunov Approach	郑宝东
1:55-2:20	报告人：李祝春（哈工大） 报告题目：On the Synchronization of a Kuramoto type model with applications in power grids
2:20-2:45	报告人：肖现涛（大连理工） 报告题目：A Smoothing Function Approach to Joint Chance-Constrained Programs
2:45-3:00	茶    歇
3:00-3:25	报告人：靳水林（哈工大） 报告题目：算子代数的独立性	张立卫
3:25-3:50	报告人：石瑞 报告题目：A reduction theory for operators in type I von Neumann algebras
3:50-4:15	报告人：矫贺明（哈工大） 报告题目：Existence of classical solutions to the Dirichlet problem for a class of degenerate Hessian equations.
4:15-4:40	茶    歇
4:40-5:05	报告人：张超（哈工大） 报告题目：Existence and Uniqueness of Weak Solutions for 2D Low-Curvature Equation	陈明浩
5:05-5:30	报告人：段犇（大连理工） 报告题目：Smooth transonic Euler-Poisson flows
23日上午：研讨（教学、科研、人才培养、管理等）

 

 

 

学术报告题目和摘要

 

报告人：康文

报告题目：Stabilization of Vibrating Systems with disturbance:Lyapunov Approach报告摘要：In this talk, we focus on stabilizing controller design and dynamic analysis for vibrating systems described by one-dimensional partial differential equations with boundary disturbance.

 

报告人：雷强

报告题目：A Quantum Logic Including Unbounded Observables

报告摘要：In quantum mechanics, many observables for a quantum system are represented as self-adjoint linear operators (possibly unbounded) on a complex Hilbert space. We introduce a binary relation on  of all self-adjoint linear operators (including unbounded) on . We obtain that  implies that  are affiliated with some abelian von Neumann algebra at the same time. Depending on , can be constructed to be a generalized orthoalgebra.  Then we present the orthoalgebra order  and the traditional order  on  and give some properties about these two orders. We prove that for ,  if and only if the proposition  has a value in  implies the proposition  has a value in  for every Borel set  not containing . Moreover, we study the existence of the infimum  and supremum  for  with respect to. Finally, we prove that  where  and  are the significant quantum observables corresponding to the position and momentum.

 

报告人：陈胜（哈工大）

报告题目： Weak connectedness of tensor product of digraphs

报告摘要：In this talk， first we will introduce the concepts of weight and diameter for weak connected diagraphs. Then we will present a complete characterization for digraphs whose tensor product is weakly connected, which solves an open problem posed by Harary and Trauth (1966).

 

 

报告人：杨国俅（哈工大）

报告的题目：The connected sum of knot and meridional knot

报告摘要：We show that ,for any knot K and any meridional knot K', then t(K#K') is not less than t(K) or t(K').

 

报告人：矫贺明（哈工大）

报告题目：Existence of classical solutions to the Dirichlet problem for a class of degenerate Hessian equations.

报告摘要：This talk is based on one of my recent work about the degenerate Hessian equations. I will introduce some new ideas to deal with the estimates for solutions of a class of degenerate Hessian equations. As a consequence, the existence of the classical solution is proved.

 

报告人：张超（哈工大）

报告题目：Existence and Uniqueness of Weak Solutions for 2D Low-Curvature Equation

报告摘要: In this talk we establish the existence and uniqueness of weak solutions for the initial-boundary value problem of a two-dimensional low-curvature equation, which is related to image analysis.

 

报告人：李祝春（哈工大）

报告题目：On the Synchronization of a Kuramoto type model with applications in power grids

 

报告人：靳水林（哈工大）

报告题目：算子代数的独立性

报告摘要：算子代数源于量子力学。量子测量问题是量子力学中核心问题，测量结果与顺序无关对应算子代数的独立。在本报告中，简要介绍算子代数独立性的一些进展工作。

 

报告人：段犇（大连理工）

报告题目：Smooth transonic Euler-Poisson flows

报告摘要：In this talk, the unique existence of smooth transonic Euler-Poisson flow in a finitely long nozzle will be discussed. Moreover, under physically acceptable boundary conditions, we prove that the flow is stable in sense of small perturbation of data at the entrance and exit. Also, we prove the unique existence of sonic curve.

 

报告人：张超（大连理工）

报告题目：Task-group Relatedness and Generalization Bounds for Regularized Multi-task Learning

报告摘要：In this paper, we study the generalization performance of regularized multi-task learning (RMTL) in a vector-valued framework, where MTL is considered as a learning process for vector-valued functions. We are mainly concerned with two theoretical questions: 1) under what conditions does RMTL perform better with a smaller task sample size than STL? 2) under what conditions is RMTL generalizable and can guarantee the consistency of each task during simultaneous learning? In particular, we investigate two types of task-group relatedness: the observed discrepancy-dependence measure (ODDM) and the empirical discrepancy-dependence measure (EDDM), both of which detect the dependence between two groups of multiple related tasks (MRTs). We then introduce the Cartesian product-based uniform entropy number (CPUEN) to measure the complexities of vector-valued function classes. By applying the specific deviation and the symmetrization inequalities to the vector-valued framework, we obtain the generalization bound for RMTL, which is the upper bound of the joint probability of the event that there is at least one task with a large empirical discrepancy between the expected and empirical risks. Finally, we present a sufficient condition to guarantee the consistency of each task in the simultaneous learning process, and we discuss how task relatedness affects the generalization performance of RMTL. Our theoretical findings answer the aforementioned two questions.

 

报告人：肖现涛（大连理工）

报告题目：A Smoothing Function Approach to Joint Chance-Constrained Programs

报告摘要：We consider a DC (difference of two convex functions) function approach for solving joint chance-constrained programs (JCCP), which was first established by Hong et al. (Oper Res 59:617–630, 2011). They used a DC function to approximate the probability function and constructed a sequential convex approximation method to solve the approximation problem. However, the DC function they used was nondifferentiable. To alleviate this difficulty, we propose a class of smoothing functions to approximate the joint chance-constraint function, based on which smooth optimization problems are constructed to approximate JCCP. We show that the solutions of a sequence of smoothing approximations converge to a Karush–Kuhn–Tucker point of JCCP under a certain asymptotic regime. To implement the proposed method, four examples in the class of smoothing functions are explored.

 

报告人：李风玲（大连理工）

报告题目：Invariants of 3-manifolds from intersecting kernels of Heegaard splittings

报告摘要：The intersecting kernel of a Heegaard splitting $H\cup_S H'$ for a closed orientable 3-manifold $M$ is the subgroup $K=\text{Ker} i_*\cap \text{Ker} {i'}_*$ of $\pi_1 (S)$, where $i:S\hookrightarrow H$ and $i':S\hookrightarrow H'$ are the inclusion maps, and $i_*$ and $i_*'$ are the induced homomorphisms between the corresponding fundamental groups. In the talk, I will explain how to derive some invariants of 3-manifolds from intersecting kernels of their Heegaard splittings. This is a joint work with Fengchun Lei and Jie Wu.

 

报告人：石瑞（大连理工）

报告题目：A reduction theory for operators in type I von Neumann algebras

报告摘要：In this paper, we study the structures of operators in a type I von Neumann algebra A . As an analogue of the Jordan canonical form theorem, for an operator a in A , we prove that if the commutant {a}' relative to A contains a bounded maximal Boolean algebra of idempotents, then the bounded maxi-mal Boolean algebras of idempotents in the commutant {a}' relative to A are the same up to similarity. Meanwhile we characterize the structures for operators in A whose relative commutants contain bounded maximal Boolean algebras of idempotents. We also classify this class of operators by K-theory for Banach algebras. We use techniques of von Neumann's reduction theory in our proofs.” In another way, we also prove a generalization of the Jordan canonical form theorem in B(H).