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数学学科学术会议(“微分方程理论与方法”中俄研讨会)

发布者:吴瑛   发布时间:2019-04-01  浏览次数:352

一、会议概况

1.会议时间:2019年04月07日-04月09日

2.会议用餐浙师大国际交流中心(所住宾馆),早餐:07:00-7:30

3.会议地点:浙江师范大学20幢四楼第一会议室(404室)(从学校南大门进来左手边第一幢大楼)

4.主办单位:浙江师范大学数学与计算机科学学院

5.会议组织人:李继彬、陈杰诚、韩茂安

6.会议目的:

面对面交流微分方程基本理论与方法,探讨微分方程的经典理论、分支理论和发展方程的新方法和新进展;为国内外微分方程的专家之间提供一个交流与合作的学术平台,为学校青年骨干教师及研究生提供一个良好的学习平台。

7.主要参会人员:

莫斯科大学Alexander V. ILIN院士;

莫斯科大学Vasily V. FOMICHEV教授;

莫斯科大学Andrei S. FURSOV教授;

莫斯科大学Victor Yu. KOROLEV教授;

莫斯科大学Irina G. SHEVTSOVA教授;

华东师范大学倪明康教授(俄罗斯院士);

杭州师范大学申建华教授;

杭州师范大学宋永利教授;

华南理工大学李用声教授;

浙江师范大学数学系部分教师和研究生。


 二、会议日程

20190407日(星期日)

12:00-20:00

浙江师范大学国际交流中心

报到

18:00-19:00

浙江师范大学国际交流中心餐厅

晚餐


20190408日(星期一)

时间

报告人

报告题目

主持人



08:00-08:40

Alexander V. ILIN

Robust algorithms for solving inverse problems of control theory

倪明康教授

08:40-09:20

Vasily V. FOMICHEV

Multiagent Systems. Consensus.

09:20-10:00

Andrei S. FURSOV

Switchable systems stabilization methods

10:00-10:10

10:10-10:50

Victor Yu. KOROLEV

From asymptotic normality to heavy-tailedness via limit theorems for random sums and statistics with random sample sizes

夏永辉教授

10:50-11:30

Irina G. SHEVTSOVA

Convergence rate estimates in the central limit theorem for sums of independent random variables

12:00-14:00

午餐(浙师大国际交流中心餐厅)

14:00-14:40

倪明康

浅谈苏俄的数学

赵晓华教授

14:40-15:20

李用声

Global large solutions to the 3D compressible Navier-Stokes equations

15:20-15:30

15:30-16:10

申建华

Lagrange stability of impulsive Duffing equations

翼教授

16:10-16:50

宋永利

Effect of spatial average on the spatial-temporal pattern formation of reaction-diffusion systems

17:30-19:00

晚餐(浙师大国际交流中心餐厅)


20190409日(星期二)

08:30-10:30

全体人员

微分方程研究前沿展望(会议座谈)

韩茂安教授


    三、报告摘要与报告人简介

Robust algorithms for solving inverse problems of control theory

Alexander V. ILIN

Moscow State University, Faculty of Computational Mathematics and Cybernetics, Department of Nonlinear Dynamical Systems and Control Process

Abstract:

        An important class of problems in the theory of automatic control is the problem of estimating an unknown input signal.

        Some of the results on the treatment of systems will be reviewed: sufficient and necessary conditions of circulation, algorithms for the synthesis of inverters are given, some special cases are considered that reveal the structure of the task of circulation.

        The question of the robustness of the obtained algorithms is still poorly understood, and the presence of the robustness property is desirable and even necessary for the possibility of implementing the algorithms in practice.

        The use of task management in real technical systems contributes to the quality of the system as a whole. This provides a basis for research in the field of system inversion (linear and nonlinear)


Multiagent Systems. Consensus.

Vasily V. FOMICHEV

Moscow State University, Faculty of Computational Mathematics and Cybernetics, Department of Nonlinear Dynamical Systems and Control Process

 Abstract:

        Multiagentn systems one of the popular directions in the modern control theory. In the control theory, we are understanding group of the same controllable objects as a multiagentn system. It can be group of mobile robots, quadcopters. The task of synthesis of identical laws of control for each object (agent) is set. At the same time all group in general has to perform some general task. Special case of such tasks is the problem about consensus. In this case it is required that some parameters of agents began to coincide over time (came to consensus).


Switchable systems stabilization methods

Andrei S. FURSOV

Moscow State University, Faculty of Computational Mathematics and Cybernetics, Department of Nonlinear Dynamical Systems and Control Process

Abstract:

        Switchable systems represent an important class of dynamic systems. Many physical and technological processes cannot be described by a single mathematical model, since their behavior can change qualitatively over time. To describe such processes, mathematical models are used in the form of switchable systems. The report is devoted to the problem of stabilization of switchable linear systems. The developed constructive stabilization methods for various classes of switchable linear systems are presented.


From asymptotic normality to heavy-tailedness via limit theorems for random sums and statistics with random sample sizes

Victor Yu. KOROLEV

Department of Mathematical Statistics, Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University

Abstract:

        The communication contains a possible explanation of the emergence of heavy-tailed distributions observed in practice instead of the expected normal laws. The base for this explanation are limit theorems for random sums and statistics constructed from samples with random sizes in which the limit distributions are scale-location mixtures of normal laws. As examples of the application of a general theorem, conditions are presented for the convergence of the distributions of asymptotically normal (in the traditional sense) statistics to multivariate normal variance-mean mixtures, in particular, to the multivariate Student distributions. Some special cases are discussed. The joint asymptotic behavior of sample quantiles is considered.


Convergence rate estimates in the central limit theorem for sums of independent random variables

Irina G. SHEVTSOVA

Department of Mathematical Statistics, Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University

Abstract:

        Starting from Esseen's asymptotic expansion, we present moment-type estimates for the accuracy of the normal approximation to distributions of sums of independent random variables possessing finite moments of order between 2 and 3. The estimates are presented for the Kolmogorov (uniform) metric as well as for smooth zeta-metrics up to the third order. In the fat-tailed case, where the random summands have only second-order moments, we present new estimates for the Kolmogorov distance  involving the truncated third-order moments and second-order tails which improve the earlier results of Katz (1963), Petrov (1965), Esseen (1969), Rozovskii (1974), Wang&Ahmad (2016). 


浅谈苏俄的数学

倪明康  华东师范大学数学系教授

报告摘要

  作者将介绍自己在俄罗斯留学工作期间对高校数学教育的一些所见所闻,简单回顾近百年来苏联数学蓬勃发展的历史,介绍苏联学派的形成和发展,探索从俄罗斯叶卡捷琳娜二世到70年代的苏联数学蓬勃发展的原因,同时向大家介绍一些隐藏在著名数学家背后的故事。以上这些都是报告者个人的思考和分析,请各位同行批评指正。

个人简介:

  倪明康,华东师大数学系教授,博导,俄罗斯自然科学院外籍院士。上海市浦江学者,曾任中国数学会理事,现任中国数学会奇摄动专业委员会副理事长, 上海市数量经济学会副理事长,上海市系统工程学会理事。 2006年获俄罗斯科学院数理学博士,师从 Tikhonov 学派。20048月被俄罗斯友谊大学聘为客座教授。主要从事奇摄动动力系统理论和方法的研究,已发表论文60余篇,主要在俄罗斯科学院杂志上。曾五次参与俄罗斯国家自然科学基金研究,四次主持中国国家自然科学基金和两次主持上海市自然科学基金。出版了2本个人专著《奇异摄动问题中的渐近理论》(高等教育出版社,2009),《奇异摄动问题中的空间对照结构理论》(科学出版社,2014)。20157月荣获第六届秦元勋数学奖。


Global large solutions to the 3D compressible Navier-Stokes equations

李用声  华南理工大学教授

报告摘要:

        In this talk we discuss the 3-D compressible Navier-Stokes equations. We show the existence of the global large solutions in the critical Besov spaces with initial data satisfying a nonlinear smallness condition. Here the ``large solutions mean that the any component of the initial velocity  could be arbitrarily large. Moreover, we give an example of initial data satisfying the nonlinear smallness condition, while the norms of each component are arbitrarily large.

个人简介:

  李用声,华南理工大学数学学院教授,博士生导师。主要从事非线性发展程与无穷维动力系统的研究工作,涉及的方程有非线性色散方程和方程组(如Schrödinger方程及其方程组)、浅水波方程、流体力学方程组等等,研究内容包括这些方程和方程组的解的存在性、唯一性、爆破性、衰减性、整体吸引子的存在性及其分形维数估计等。在国内外重要学术刊物上发表论文约90篇, SCI收录约70篇。先后主持5项国家自然科学基金项目,曾被评为湖北省跨世纪学术骨干,作为主要完成人获得过国防科工委科技进步一等奖,曾获得全国优秀博士学位论文提名奖指导老师称号。


Lagrange stability of impulsive Duffing equations

申建华  杭州师范大学教授

报告摘要:

        By KAM theorem, we prove that all solutions of the Duffing equation with low regularity in time undergoing suitable impulses are bounded for all time and that there are many (positive Lebesgue measure) quasi-periodic solutions clustering at infinity.

个人简介:

  申建华,杭州师范大学教授、博士生导师。曾在湖南师范大学数学系任教授、博士生导师。2008年至今在杭州师范大学工作。 2001年入选教育部优秀青年教师资助计划,2002年入选湖南省高校跨世纪学科带头人。2011年至2017年任杭州师范大学数学系系主任和浙江省优势专业数学与应用数学负责人。已主持国家自然科学基金面上项目5项,主持省部级科研和人才项目7项,2000年获湖南省教委科技进步奖一等奖(第一承担人),2010年获杭州师范大学第二届我最喜爱的老师荣誉称号,2013年获杭州师范大学教学十佳。已指导培养硕士生50多名、博士生7名。


Effect of spatial average on the spatial-temporal pattern formation of reaction-diffusion systems

宋永利  杭州师范大学教授

报告摘要:

        Some quantities in the reaction-diffusion models from cellular biology or ecology depend on the spatial average of density functions instead of local density functions. We show that such nonlocal spatial average can induce instability of constant steady state, which is different from classical Turing instability. For a general scalar equation with spatial average, the occurrence of the steady state bifurcation is rigorously proved, and the formula to determine the bifurcation direction and the stability of the bifurcating steady state is given. For the two-species model, spatially non-homogeneous time-periodic orbits could arise due to spatially non-homogeneous Hopf bifurcation from the constant equilibrium. Examples from a nonlocal predator-prey model and a nonlocal cooperative Lotka-Volterra model are used to demonstrate the bifurcation scenarios. This is a joint work with J.P. Shi and Q.Y. Shi.

个人简介:

  宋永利,杭州师范大学教授、同济大学博士生导师、浙江省高等学校钱江学者特聘教授。曾出访西班牙、澳大利亚、加拿大、美国做博士后或合作研究。已在SIAM J. Applied Dynamical Systems, Journal of Differential Equations,  Journal of Nonlinear ScienceNonlinearity IEEE Transactions on Neural Networks and Learning SystemsPhysica D等国际学术期刊发表学术论文70余篇。2014年起连续5年入选中国高被引学者榜单(数学类)。曾主持、或作为项目组主要成员参与国家自然科学基金重点项目、面上项目、上海市自然科学基金、浙江省自然科学基金等项目十余项。2011年入选教育部新世纪优秀人才计划。2017年获威海市科学技术一等奖(3/3)。2018年入选浙江省151人才工程第一层次培养人选。