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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Coupling by change of measures for dimension-free Harnack inequality
无维 哈纳克不等式 测度 耦合
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2023/5/12
简要介绍概率论中的耦合方法及其在基础数学中的应用。引入新的变测度耦合，以简单的随机微分方程为例，将其应用于建立无穷维Harnack不等式、Bisnut导数公式和分布积分公式。
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：离散型数学在信息科学中的一些应用
离散 数学 信息科学
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2023/5/12
上世纪六十年代以来，随着数字通信技术的快速发展，离散型数学（组合设计和图论，数论，代数以及有限域上代数几何）逐渐成为通信许多应用领域的重要数学工具。本报告沿着六十年来历史发展的足迹，通俗介绍在代数纠错码和信息安全方面一些重要发展和数学问题，以实际例子说明数学所起的作用。
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars： Derivation of the Vlasov equation from quantum many-body Fermionic systems with singular interaction
奇异相互作用 量子多体 费米子系统 弗拉索夫方程
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2023/5/12
We consider the combined mean-field and semiclassical limit for a system of the N fermions interacting through singular potentials. We prove the uniformly in the Planck constant h propagation of quant...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Solitons and Breathers in the modulus KdV equations
模量 KdV方程 孤子 呼吸器
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2023/5/12
Compared to the soliton solutions, the breathers, which are constructed in the mKdV or Gardner equation via integrability methods, are less studied. In our numerical study, we show the interactions be...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：中国式现代化与积极应对人口老龄化战略
中国式现代化 积极应对 人口老龄化
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2023/5/10
人口快速老龄化、超大规模老年人口是中国式现代化面临的重要国情。当下，中国正面临人口老龄化加速发展期与实现中国式现代化过程叠加的发展新阶段，创造有利于经济高质量发展的人口条件，以及形成适应人口老龄化的经济发展新模式，是中国社会主义现代化发展的必由之路。因此，要以积极的态度看待人口老龄化带来的风险和挑战，挖掘老龄社会中存在的机遇，并主动应对人口老龄化问题，从根本上解决造成人口老龄化不断加速的难点、痛点...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：含任意未知输入下的状态估计与参数辨识
任意未知输入 状态估计 参数辨识
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2023/5/10
现存的含未知输入系统的卡尔曼滤波方法假设噪声协方差矩阵已知而且要求系统强可观。针对实际中广泛存在的不精确知道噪声协方差矩阵或系统非强可观的情况，如何在工程应用如机器人定位中实现卡尔曼滤波是一个重要且亟需解决的难题。本报告中，报告人将探讨含未知输入滤波领域的研究现状，并以基于相关性的方法为典型，讨论含未知输入下噪声协方差矩阵的可辨识性问题。如果时间允许，报告人也将探讨其在机器人智能感知与决策方面的一...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Harmonic analysis meets wave equation
谐波分析 符合 波动方程
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2023/5/10
In this talk I plan to survey some progress on Hardy and BMO spaces, Riesz transforms, Bochner-Riesz means and spherical means by using the method of wave equation,and show interesting connections and...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Introduction to Allard’s regularity theorem（I）
阿拉德 正则性 定理 导论
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2023/5/10
In this short seminar, we will discuss the proof of the Allard regularity theorem, which is an $\epsilon$-regularity theorem for the mean curvature equation in the Geometric Measure Theory(GMT) settin...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Singular integral and geometry
奇异积分 几何 谐波分析
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2023/5/8
The geometric considerations enter in a decisive way in many questions of harmonic analysis. For example, the estimation of the Fourier transform of surface-carried measure, which played a key role in...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Numerical PDEs for Fluid-Structure Interaction (FSI) Problems
流固耦合 数值 偏微分方程
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2023/5/8
The interaction of a flexible structure with a flowing fluid in which it is submersed or by which it is surrounded gives rise to a rich variety of physical phenomena with applications in many fields o...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：两水平非正规因子设计的构造
两水平 非正规因子 设计 构造
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2023/5/6
因子设计可分为正规设计和非正规设计，其中正规设计结构简单，试验次数被限制在2的幂次上。非正规设计结构复杂，但具有较为灵活的试验次数，并可用于估计更多的因子效应。作为一类特殊的非正规设计，平行平面设计受到了越来越多的关注。正规设计也被称为单平面设计，由来自同一家族的几个单平面行并置得到的设计被称为平行平面设计。由三个平行平面构成的平行平面设计是最常用的非正规设计。将其推广到具有f个平面的平行平面设计...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Stability conditions and quadratic differentials
稳定性条件 二次微分 三角分类
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2023/5/6
Stability conditions on triangulated categories are introduced by Bridgeland. For 3-Calabi-Yau triangulated categories from quivers with potentials, the space of stability conditions on this triangula...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Projective measure without Projective Baire
投射贝尔 投射测量 勒贝格可测
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2023/5/6
In this talk, I will give some of the context and a sketch of the proof of the following result which I proved a while ago: It is consistent (relative to a Mahlo catrdinal) that there is a projective ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：斜坡上浅水波的研究进展
斜坡 上浅水波 泄洪渠
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2023/5/6
在倾斜的泄洪渠上，水流往往不是等高的层流，会形成周期滚动激波，简称滚波。由于滚波的水深不是常值，其激波处的水深必定比相同泄洪量层流大。为了避免洪水外溢导致的非必要经济损失，滚波强度与泄洪渠坡度、截面形状、渠宽等变量之间的关系是水利工程学研究的主要问题之一。数学上，假设流体垂直尺度远小于水平尺度，对三维自由表面无旋不可压Navier-Stokes 方程做垂直方向的积分，我们得到Saint-Venan...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars： Solution Landscapes of Nematic Liquid Crystal Systems
向列 液晶系统 解决方案
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2023/5/6
Nematic liquid crystals (NLCs) are anisotropic material intermediate that combines the fluidity of liquids with the orientational order of solids. NLCs are best known for their applications in the thr...