报告题目1：Stability Analysis for Semi-Markovian Switched Singular Stochastic Systems

报告人：胡增辉（郑州大学）

报告时间：2020年12月19日(周六)上午8:30-9：30

腾讯会议ID：318 146 210

报告摘要：In this talk, we study the stability problem for switched singular stochastic systems with semi-Markovian signals. A refined description for state jumps of the switched singular stochastic system is presented, which indicates that the original system is equivalent to an impulsive switched system. Based on the equivalent dynamics decomposition, sufficient conditions of stochastic stability and almost surely exponential stability are established by using the stochastic Lyapunov function method and multiple Lyapunov functions method, respectively.

个人简介：胡增辉，郑州大学运筹学与控制论专业在读博士生，研究生国家奖学金获得者，现为Automatica，IEEE Transactions on Cybernetics和IEEE Transactions on Circuits and Systems II: Express Briefs等期刊审稿人。目前主要研究随机混杂系统、网络化控制系统、奇异系统、事件触发控制，发表相关学术论文10篇。

报告题目2：A Vector General Nonlinear Schrödinger Equationwith (m + n) Components

报告人：李若梦（郑州大学）

报告时间：2020年12月19日(周六)上午9:30-10：30

腾讯会议ID：318 146 210

报告摘要：A vector general nonlinear Schrödinger equation with (m + n) components is proposed, which is a new integrable generalization of the vector nonlinear Schrödinger equation and the vector derivative nonlinear Schrödinger equation. Resorting to the Riccati equations associated with the Lax pair and the gauge transformations between the Lax pairs, a general N-fold Darboux transformation of the vector general nonlinear Schrödinger equation with (m + n) components is constructed, which can be reduced directly to the classical N-fold Darboux transformation and the generalized Darboux transformation without taking limits. As an illustrative example, some exact solutions of the two-component general nonlinear Schrödinger equation are obtained by using the general Darboux transformation, including a first-order rogue-wave solution, a fourth-order rogue-wave solution, a breather solution, a breather–rogue-wave interaction, two solitons and the fission of a breather into two solitons. It is a very interesting phenomenon that, for all M > 0, there exists a rogue-wave solution for the two-component general nonlinear Schrödinger equation such that the amplitude of the rogue wave is M times higher than its background wave.

个人简介：李若梦，郑州大学讲师。2018年7月博士毕业于郑州大学数学与统计学院。2018年7月-2020年5月郑州大学物理系博士后。研究方向为孤立子与可积系统。主持国家自然科学基金青年基金一项，发表相关学术论文6篇。

报告题目3：Domination number and Laplacian eigenvalues of graphs

报告人：薛杰（郑州大学）

报告时间：2020年12月19日(周六)上午10:30-11：30

腾讯会议ID：318 146 210

报告摘要：In this talk, we discuss the relations between the domination number and Laplacian eigenvalue distribution of graphs. For a graph with diameter d, a lower bound of the domination number is (d+1)/3. We show that the domination number of a tree is (d+1)/3 if and only if it contains (d+1)/3 Laplacian eigenvalues less than 1.

个人简介：薛杰，郑州大学博士后。2019年6月博士毕业于华东师范大学，2019年6月-至今，在郑州大学数学与统计学院从事博士后研究工作，研究方向为图谱理论，主持国家自然科学基金青年基金一项，发表相关学术论文20篇。

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