会议报告题目与摘要

1. 李佳 University of Alabama at Huntsville

题目：Application of Paratransgenesis in Control of Malaria

摘要：We formulate homogeneous and stage-structured models for the interactive wild mosquitoes and paratransgenic mosquitoes carrying genetically modified bacteria that are resistant to malaria transmissions. We establish conditions for the existence and stability of equilibria for the model systems and provide numerical examples to demonstrate our findings. We then investigate how the bacteria uptake rate of wild mosquitoes and the bacteria loads of paratransgenic mosquitoes carry affect their interactive dynamics.

2. 魏木生 上海师范大学

题目：On Commuting Solutions of the Yang-Baxter-like Matrix Equation

摘要：In this talk we study the commuting solutions of the Yang-Baxter-like matrix equation $AQXA=XAX$, where $A$ is an arbitrary square matrix. From the Jordan canonical decomposition of $A$, we provide a way to derive all possible commuting solutions of the Yang-Baxter-like matrix equation.

3. 郑伟英 中科院数学与系统科学研究院

题目：三维磁流体方程组的守恒性有限元方法

摘要：三维磁流体力学方程组是计算数学和计算流体研究的热点之一，其守恒型数值方法以及离散问题的快速求解算法吸引了国内外许多著名学者的研究兴趣。我们提出了一种三维磁流体方程组的守恒性有限元方法，能够保证质量和磁通量严格守恒。此外，本报告还将从微分算子预处理的角度，重点讨论离散磁流体方程的高效求解算法。

4. 何炳生 南方科技大学、南京大学

题目：交替方向法研究的新进展

摘要：数据科学中的许多问题可以归结为（或松弛成）一个凸优化问题. 最优化方法提供给数据科学的有效工具,首推交替方向法 (ADMM), 已经得到普遍的认可.在变分不等式的框架下研究 ADMM 类方法,常常会带来很大的方便.报告介绍我们近 10 年来在变分不等式框架下研究 ADMM 的取得的主要进展，特别是近年为进一步提高 ADMM类算法效率的最优线性化交替方向法和求解多个算子问题的不定正则化方法. 报告同时也介绍这些算法被他人应用的一些案例。

5. 耿建生 南京大学

题目：KAM Tori for Reversible Derivative Beam Equations on $\mathbb{T}^2$

摘要：In the present paper, we prove an infinite dimensional reversible KAM theorem. As an application, we study the existence of KAM tori (i.e. quasi-periodic solutions) for a class of two dimensional completely resonant beam equations with derivative nonlinearities. We also use Birkhoff normal form techniques due to the lack of external parameters in equation. This is a joint work with Ge and Lou.

6. 谢和虎 中科院数学与系统科学研究院

题目：An Augmented Subspace Method for Eigenvalue Problems

摘要：First, this talk will introduce a new energy error estimate for the subspace projection method for eigenvalue problems. Furthermore, a relation between the L2 and the energy error estimates is deduced. Based on these results, we design an augmented subspace method for eigenvalue problems which has a good convergence rate. Finally, we will give two ways to construct the subspaces from geometric and algebraic multigrid method.

7. 梁振国 复旦大学

题目：薛定谔方程及其相关的扰动结果

摘要：薛定谔方程特别是量子调和振子方程是量子力学中最为基本的方程，对该方程在非自治拟周期扰动之下的解的增长性的研究有很长的历史。但是对于指数等于2的情形（一维量子调和振子方程）的研究进展非常缓慢，直到最近几年才有本质的突破。而关于位势函数指数小于2的情形，几乎没有结果。我们报告主要讨论最近量子调和振子方程的进展，包含一维和高维，有界和无界扰动的情形。报告中有一部分涉及我们最近在位势函数指数小于2的情形的一些进展结果。

8. 赵卫东 山东大学

题目：High-Order Numerical Schemes for Stochastic Optimal Control via FBSDEs

摘要：In this talk, based on the theories of optimization, stochastic optimal control and forward backward differential equations (FBSDEs), we will introduce some numerical schemes for solving stochastic optima control. In these schemes, the simplest Euler scheme is used to numerically solve the solutions of the forward SDE, and multistep schemes is used to solve the backward stochastic differential equation (BSDE) with high accuracy. Some stochastic optimal control models, coming from finance and economy, are solved by the schemes. Our numerical results show that our schemes are stable, high accurate, and effective for solving stochastic optimal control problems.

9. 谢之福 University of Southern Mississippi

题目：Variational Method with SPBC and Broucke-Henon Orbit and Schubart Orbit

摘要：N-body problem concerns the motion of celestial bodies under universal gravitational attraction. Although it has been a long history to apply variational method to N-body problem, it is relatively new to make some important progress in the study of periodic solutions. We develop the Variational Method with Structural Prescribed Boundary Conditions (SPBC) and we apply it to study periodic solutions in the 3-body problem with equal masses. We show that under an appropriate topological constraint, the action minimizer must be either the Schubart orbit (1956) or the Broucke-Henon orbit (1975). One of the main challenges is to prove that the Schubart orbit coincides with the action minimizer connecting a collinear configuration with a binary collision and an isosceles configuration which must be collinear. A geometric property of the action minimizer is introduced to overcome this challenge. The action minimizer without collisions can be extended to the Broucke-Henon orbit.

10. 曹军 Ryerson Polytechnic University

题目：An Adaptive Finite Difference Method Powered by a Posteriori Error Estimator

摘要：This talk introduces a hybrid adaptive finite difference method oriented by the a posteriori error estimation, which was originally derived within the finite element analysis context. The time-dependent heat conduction problem is chosen as benchmark case, followed by a series of more complex Euler flow simulations in which a customized a posteriori error estimator is employed to guide the finite difference mesh adaptation. While the effectiveness and usefulness of the present hybrid adaptive finite difference solver have been demonstrated in the conducted numerical experiments, the issues remaining to uncover on the theoretical front of this hybrid numerical strategy will be indicated at the end of the talk.

11. 贾志刚 江苏师范大学

题目：A Structured Condition Number for Self-adjoint Polynomial Matrix Equations with Applications in Linear Control

摘要： Based on the classic definition of condition number, a structured condition number is proposed for a class of self-adjoint polynomial matrix equations. The explicit formula of the structured condition number is derived with applying newly defined linear operators. The structured condition number can be applied to some important polynomial matrix equations, including the continuous-time algebraic Riccati equation (CARE), the discretetime algebraic Lyapunov equation (DALE), etc. Compared with the state-of-the-art condition numbers for CARE and DALE, the newly proposed structured condition number can measure the sensitivity of the solution better, which is validated by numerical examples.

12. 沙春林 南京航空航天大学

题目：Synthesization of Multi-valued Sssociative High-capacity Memory Based on Continuous Networks with a Class of Non-smooth Linear Non-decreasing Activation Functions

摘要：This paper presents a novel design method for multi-valued auto-associative and hetero-associative memories based on a continuous neural network (CNN) with a class of non-smooth linear nondecreasing activation functions. The proposed CNN is robust in terms of design parameter selection, which is dependent on a set of inequalities rather than the learning procedure. Some globally exponentially stable criteria are obtained to ensure multi-valued associative patterns to be retrieved accurately. The methodology, by generating CNN where the input data are fed via external inputs, avoids spurious memory patterns and achieves $(2r)^n$ storage capacity. These analytic results are applied to the associative memory of images. The fault-tolerant capability and the effectiveness are validated by illustrative experiments.

时间：5月26-27日上午9:00

地点：玉蜻蜓酒店三楼第四会议室

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