会议名称：2018年厦门市数学会年会
会议日期：2018年12月1日
会议地点：厦门大学海韵园实验楼105
时间 | 事项 | 地点 |
9:00-9:10 | 开幕式、合影 | 厦门大学 海韵校区 实验楼105 |
9:10-9:40 | 程金发（厦门大学）：Generalizations of Rodrigues Type Formulas for Hypergeometric Dierence Equations on Nonuniform Lattices | 主持人 欧启通 |
9:40-10:10 | 叶星旸（集美大学）: 反常扩散方程最优控制问题的谱方法及其应用 |
10:10-10:30 | 茶歇 |
10:30-11:00 | 郭利涛（厦门理工学院）: Relation of extra edge connectivity and component edge connectivity for regular networks | 主持人 张文 |
11:00-11:30 | 吴丽华（华侨大学）：Algebro-geometric solutions to the extended coupled modified Korteweg-de Vries hierarchy |
学术报告题目与摘要
Generalizations of Rodrigues Type Formulas for Hypergeometric Dierence Equations on Nonuniform Lattices
程金发（厦门大学）
报告摘要：Abstract. By building a second order adjoint dierence equations on nonuni-form lattices, the generalized Rodrigues type representation for the second kind solution of a second order dierence equation of hypergeometric type on nonuniform lattices is given. The general solution of the equation in the form of a combination of a standard Rodrigues formula and a "generalized" Rodrigues formula is also established。
反常扩散方程最优控制问题的谱方法及其应用
叶星旸（集美大学）
报告摘要：研究状态变量积分受限的反常扩散方程最优控制问题的时空谱方法，其控制方程为一个时间分数阶扩散方程. 利用最优化理论中的 Kuhn-Tucker 条件分别推导了连续和离散的最优控制问题的最优性条件, 分析了谱离散解的先验误差估计, 并利用梯度投影算法求解离散最优化问题.通过数值算例验证了理论分析结果.最后，利用最优控制问题实现了一类时间分数阶扩散方程初始条件的重构。
Relation of extra edge connectivity and component edge connectivity for regular networks
郭利涛（厦门理工学院）
报告摘要：Reliability of interconnection networks is important to design multiprocessor systems. The extra edge connectivity and component edge connectivity are two parameters for the reliability evaluation. The k-extra edge connectivity is the cardinality of the minimum extra edge cut such that is not connected and each component of has at least k vertices. The t-component edge connectivity of a graph G is the minimum edge number of a set F such that G-F is not connected and G-F has at least t components. In this paper, we find the relation of extra edge connectivity and component edge connectivity for regular networks. As an application, we determine the component edge connectivity of BC networks, k-ary n-cubes, folded hypercubes, star graphs, and balanced hypercubes.
Algebro-geometric solutions to the extended coupled modified Korteweg-de Vries hierarchy
吴丽华（华侨大学）
报告摘要：Based on the compatibility condition of a matrix spectral problem and its auxiliary problem, a extended coupled modified Korteweg-de Vries hierarchy is derived. The corresponding three-sheeted Riemann surface is defined by the characteristic polynomial of Lax matrix for the extended coupled modified Korteweg-de Vries hierarchy. We introduce the vector-valued Baker-Akhiezer function and meromorphic function and then arrive at their explicit Riemann theta function representations with the aid of their zeros, singularities, as well as the theory of algebraic geometry. The asymptotic expansions of the meromorphic function and its Riemann theta function representation give rise to the algebro-geometric solutions for the entire extended coupled modified Korteweg-de Vries hierarchy.
