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23
2025/09
非平稳多分量信号分离的时频方法
在自然界中，以信号形式呈现的现实世界现象(或以时间序列形式获取的数据)通常受到多种因素的影响，表现为时间上重叠的多分量信号(或时间序列)。为了更好地理解这类现象并便于信号处理，需要从盲源数据中提取目标多分量信号的未知成分。这是一个具有悠久历史的逆问题，可追溯到1795年，当时法国工程师Gaspard de Prony开发了一种巧妙的计算方法，称为Prony's方法，用于分离平稳信号。然而，对于非平稳信号(即分量频率为时间变量函数的信号)，直到十多年前Ingrid Daubechies及其合作者引入同步压缩变换(SST)之前，一直缺乏严谨的数学处理方法。遗憾的是，尽管许多研究人员付出了努力，SST仍仅能在非常严格的条件下应用，此外，一些不理想的限制仍然未能得到解决。在本次报告中，我们将讨论SST的两项改进。首先，在原始SST中引入时变参数，以消除部分限制条件，特别是在频率分离方面的限制，从而更稳健地分离信号分量。其次，我们将探讨我们最新开发的小调频率变换(chirplet transform)，该方法甚至能够分离具有交叉瞬时频率曲线的多分量信号。与传统的时间-频率二维空间不同，小调频率变换将信号映射到时间-频率-调频率(chirprate)的三维空间中。报告中还将展示相关的演示案例。
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16
2025/09
新型电力系统智能配电网的多模态电力智能分布式预测研究
介绍了新型电力系统负荷的发展和关键驱动因素，论述了电力预测的种类和新对象，提出了多模态电力智能分布式预测需要解决的问题，构建了多模态电力智能分布式预测数据空间，研究了多模态电力影响因素的知识挖掘过程，介绍了智能预测的理论方法，建立了多模态电力智能分布式预测模型，进行了应用案例介绍和研究总结。附录：介绍了数据空间在电力装备智能工厂建设中的设计与应用
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18
2025/09
Category Theory meets Factorization Theory: the category AtoMon
We introduce the category AtoMon of atomic monoids and atom-preserving homomorphisms as a non-full subcategory of the usual category of monoids and monoid homomorphisms. By computing all limits and colimits, we show that AtoMon is complete and cocomplete. We also explore arithmetic aspects of products and coproducts, deriving explicit formulas for key invariants related to factorization lengths. This work aims to build a bridge between category theory and factorization theory, offering a categorical framework for the study of atomic factorizations.
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16
2025/09
法政与公共管理学院人才招聘暨青年学者论坛
张媞（湖南大学）：合同订立——要约与要约邀请的区别；高淼（湖南大学）：村务监督的内涵与外延；韩秋杰（新疆大学）：刑事责任年龄降低的立法反思与实现路径。
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20
2025/09
文苑大讲堂2025年第27讲： 情动的伦理 （周末专家河北行）
情动转向（affective turn)是从德勒兹理论中发展出来的一个重要的文化理论话题。德勒兹在对斯宾诺莎《伦理学》的解读中表明，情动是一种情感的流变，情感始终是在快乐和悲苦之间不停地变化，对德勒兹来说，重要是要积极的情动，要发展出一种快乐主义伦理学。
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19
2025/09
文苑大讲堂2025年第26讲：古代文史类学术论文写作规范与馆藏资源利用
学术规范是所有从事学术研究的学者必须遵循的规范，也是学术创新的前提。本次入学教育以文史类学术论文的写作规范为主要内容，包括学术论文引用、注释与参考文献著录的具体规则，也涉及图书馆馆藏资源，特别是馆藏电子资源与数据库的使用。
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14
2025/09
Decay of correlations for dynamical systems admitting induced Weak Gibbs-Markov maps
In [2, 3], L. S. Young introduced induced Gibbs Markov maps. It was shown that the existence of induced Gibbs Markov maps with integrable return time implies the existence of amixing invariant probability measure absolutely continuous with respect to reference measure,and the rate of decay of correlations is related to the tail of the return time. In this talk, I willdiscuss how to obtain similar results under weaker assumptions, which allows the induced mapnot necessarily to be full branch.The main results presented in this talk are detailed in [1].[1] Ullah, A., Vilarinho, H. Statistical properties of dynamical systems via induced weak Gibbs Markovmaps. Nonlinearity 38 (2025), 045024.[2] Young, L.-S. Statistical properties of dynamical systems with some hyperbolicity.Ann. of Math. (2)147, 3 (1998), 585-650.[3] Young, L.-S. Recurrence times and rates of mixing. Israel J. Math. 110 (1999),153-188.
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14
2025/09
(Non)-existence of physical measures for doubly intermittent maps
I will introduce the concept of a physical measure and discuss a new family of simple one-dimensional maps which may admit different kinds of physical measures and, in some cases, no physical measures.
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13
2025/09
N heteroclinic cycles coexist in a 3D (N+1)-zone piecewise smooth system for arbitrary positive integer N
The Shi’lnikov criterion shows that three-dimensional smooth autonomous differential equations can display chaos with the existence assumption of a heteroclinic cycle connecting saddle-focus equilibria. However, it is challenging to confirm this assumption in a given system, since common methods are to be developed. Although it has been partially extended to two-zone piecewise linear systems, there is very little work on piecewise systems with multiple discontinuous boundaries. This paper analytically investigates three types of heteroclinic cycles with a number of N in a new class of three-dimensional (N + 1)-zone non-smooth systems for arbitrary integer N ≥ 1. Moreover, the classical criterion above has been extended to the considered system with theoretical analysis as well as numerical experiments, where the developed criteria in this paper apply not only to systems exhibiting saddle-focus behavior but also to those possessing both saddle and saddle-focus equilibria. In addition, the existence conditions established for chaos induced by N heteroclinic cycles in this work, generalize the previous reported case of N = 1, 2 to the case of arbitrary N ≥ 1.
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13
2025/09
2025年微分动力系统学术研讨会
9月13日8:30-8:40 开幕式 8:40-9:00 参会人员合影9:00-9:40 田学廷 Orbit structure of chaotic dynamical systems9:40-10:20 许地生 The Zimmer program for partially hyperbolic systems10:20-10:40 休 息10:40-11:20 张金华 Nonhyperbolic ergodic measures11:20-12:00 廖 刚 Prime orbit theorem for14:40-15:20 王式柔 Folding entropy, folding-type entropy formula, and non-equilibrium statistical mechanics15:20-16:00 吴伟胜 Equilibrium states of geodesic flow16:00-16:40 历智明 Ergodic optimization for random dynamical systems16:40-17:00 休息17:00-17:30 余道骅 Derived-from-expanding endomorphism on T 217:30-18:00 吴万楼 The Lyapunov exponents of hyperbolic measures for C1 vector fields9月14日8:30-9:10 Raul Ures Measures of maximal entropy that are SRB 10:10-10:50 Maria R. Hertz How frequent is the butterfly effect?10:50-11:30 张宏坤 动力系统与神经网络14:40-15:20 杨启贵 Simple systems and chaos complexity of linearreaction-diffusion equations15:20-16:00 周云华 Dynamics near a class of nonhyperbolic fixed points16:00-16:40陈剑宇 A nonuniformly hyperbolic diffeomorphism with arbitrary number of ergodic components and close to the identity16:40-17:00 休 息17:00-17:30 罗炽逸 Ergodic measures with large entropy have uniformly large measure on Pesin setsfor surface diffeomorphisms17:30-18:00 唐艳杰 Spectral decomposition and skew-product for group actions9月15日8:30-9:10 梁超 Density and openness properties of non-uniformly hyperbolic diffeomorphisms revisited9:10-9:40 瞿聪聪 Dimension approximation and estimate for hyperbolic systems9:40-10:00 休 息10:00-10:30 袁艺 Ergodic and topological theory for systems with non-uniform structure10:30-11:00 庾辰炜 Variations of topological theory and ergodic theory under non-uniform specification
