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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：The Proper Basis for Zero-dimensional Polynomial Ideals
零维 多项式理想 正确基 Grobner基
2023/11/29
The Grobner basis for a zero-dimensional polynomial ideal comprises a univariate polynomial in the least variable. The elimination process in Buchberger's algorithm unnecessarily involves the least va...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：C1,1/3- very weak solutions to the two dimensional Monge–Ampère equation
二维 Monge–Ampère方程 C1,1/3极弱解
2023/11/29
For any θ<1/3 , we show that very weak solutions to the two-dimensional Monge–Ampère equation with regularity C1,θ are dense in the space of continuous functions. This result is shown by a convex inte...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Global strong solutions to the two-dimensional radially symmetric compressible MHD
二维径向对称 可压缩 磁流体动力学 全局强解
2023/12/11
In this talk, I will present our recent result the 2D radially symmetric compressible MHD with density-dependent viscosity. Under the condition of beta>1, we prove the global existence of the radially...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：A link invariant from higher-dimensional Heegaard Floer homology
高维 Heegaard-Floer同调 链接不变量
2023/11/13
We define a higher-dimensional analogue of symplectic Khovanov homology. Consider the standard Lefschetz fibration of a 2n-dimensional Milnor fiber of the A_{k-1} singularity. We represent a link by a...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Mixed volume of infinite-dimensional convex compact sets II
无限维 凸紧集 混合体积
2023/11/6
Using the results presented in the previous lecture, namely the generalization of the Tsirelson's theorem [2] to mixed volumes, we calculate the mixed volume of the closed convex hulls of the two orth...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Mixed volume of infinite-dimensional convex compact sets I
无限维 凸紧集 混合体积
2023/11/6
Let K be a convex compact subset of a separable Hilbert space H. One of the most important geometric characteristics of K is its intrinsic volumes. In the finitedimensionalcase (K ? R^d), the intrinsi...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On a two dimensional nonlocal shallow-water model
二维 非局部 浅水模型 三维欧拉系统
2023/4/14
In this talk, we first review some related progresses on one dimensional shallow water models. Then we introduce the derivation of a new nonlocal shallow water model from the 3D Euler system with free...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On the stability of multi-dimensional rarefaction waves
多维 稀薄波 稳定性
2023/4/17
In his pioneering work in 1860, Riemann proposed the Riemann problem and solved it for isentropic gas in terms of shocks and rarefaction waves. It eventually became the foundation of the theory of one...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Higher dimensional Heegaard Floer homology and Hecke algebras
高维 希加德弗洛尔同调 赫克代数
2023/4/18
Higher dimensional Heegaard Floer homology (HDHF) is a higher dimensional analogue of Heegaard Floer homology in dimension three. It's partly used to study contact topology in higher dimensions. In a ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Finding solutions to the multi-dimensional compressible Euler equations
多维 可压缩 欧拉方程 解
2023/4/24
This talk will survey some results for the two- or three-space dimensional compressible Euler equations. We shall present non-uniqueness results of weak entropy solutions using convex integration and ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Estimating Time-Varying Networks for High-Dimensional Time Series
高维 时间序列 时变网络
2023/4/25
We explore time-varying networks for high-dimensional locally stationary time series, using the large VAR model framework with both the transition and (error) precision matrices evolving smoothly over...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Backpropagation and sensitivity analysis in high-dimensional hyperbolic chaos
高维 双曲混沌 反向传播 敏感性分析
2023/4/26
We devise fast algorithms for computing the linear response, which is the parameter-gradient of long-time statistics of hyperbolic chaotic dynamical systems. The algorithm is in the form of progressiv...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Splitting Numerical Schemes for Two-dimensional Maxwell-Debye Equations
二维 麦克斯韦-德拜方程组 拆分数值方案
2023/4/27
In this talk, we are interested in designing some efficient numerical methods for Maxwell-Debye equations in metamaterials with negative refractive index. Dimensional splitting method is used to reduc...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Model-free conditional screening for ultrahigh-dimensional survival data via conditional distance correlation
条件距离 相关性 超高维 生存数据 无模型 条件筛选
2023/5/4
How to select the active variables which have significant impact on the event of interest is a very important and meaningful problem in the statistical analysis of ultrahigh-dimensional data. In many ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Fixed Effects Bayesian Testing in High-Dimensional Linear Mixed Models
高维 线性混合模型 固定效应 贝叶斯检验
2023/5/5
Hypothesis testing on high-dimensional fixed effects is indispensable for investigating the utility of the predictors on response. In this case, the conventional frequentist methods designed for cases...