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几何变分问题在临界点处的正则性与稳定性（张翼）
几何变分问题 临界点 正则性 稳定性
2023/2/22
几何不等式，特别是（包括Wullf能量下的）等周不等式和Sobolev不等式，不仅是建立分析和几何相关理论的重要基础，也是众多科研模型以及计算机算法研究中不可或缺的部分。它们所对应的变分问题的解的正则性与稳定性，也是在分析与几何交叉的相关领域中的核心问题之一。其中有大量的关键问题亟待解决。与此同时，这些问题也与数学以外的科研领域中的许多问题相关。它们的解决也将推动这些方向的理论发展与完善。
仿射Deligne-Lusztig簇首先由Rapoport引入。其几何结构蕴含了志村簇重要的算术信息。不可约分支的参数化问题是仿射Deligne-Lusztig簇研究领域的一个主要的公开问题。为了解决这一难题, 陈苗芬和朱歆文提出了一个著名猜想：不可约分支的轨道集与Weyl模的特定权空间的晶体基之间存在典则的一一对应。通过构造不可约分支上的晶体结构，我们给出了陈-朱猜想的完整证明，并得到了计算不可...
Based on the numerical method proposed in Hu et al. (2018) [22] for Kohn-Sham equation, further improvement on the efficiency is obtained in this paper by i). designing a numerical method with the str...
一致超图中路和圈扩张的反Ramsey数（李瞳、闫桂英）
一致超图中路 圈扩张 反Ramsey数
2023/2/22
For an r-graph F, the anti-Ramsey number ar(n,r,F) is the minimum number c of colors such that for any edge-coloring of the complete r-graph on n vertices with at least c colors, there is a copy of F ...
图谱方法改进GV界（马志明、闫桂英）
图谱方法 改进 GV界
2023/2/22
This paper improves Gilbert-Varshamov bound by graph spectral method. Gilbert graph Gq,n,d is a graph with all vectors in Fnq as vertices where two vertices are adjacent if their Hamming distance is l...
This paper studies the dual-role-facility location game with generalized service costs, in which every agent plays a dual role of facility and customer, and is associated with a facility opening cost ...
Inductively approaching subsets by almost finite sets, we refute Scheepers’ conjecture under CH. More precisely, we prove the following.
基于二阶锥规划的SONC优化和非负性证明（王杰）
二阶锥规划 SONC优化 非负性证明
2023/2/22
The second-order cone (SOC) is a class of simple convex cones and optimizing over them can be done more efficiently than with semidefinite programming. It is interesting both in theory and in practice...
退化双曲面的应变张量及匹配性（姚鹏飞）
退化双曲面 应变张量 匹配性
2023/2/22
We prove the regularity of solutions to the strain tensor equation on degenerated hyperbolic surfaces $S$ where the Gauss curvature is zero on a part of the boundary. Furthermore, we obtain the densit...
偏微分方程约束形状优化问题的改进的边界型离散形状梯度（龚伟）
偏微分方程 约束形状优化 边界型 离散形状梯度
2023/2/22
We propose in this paper two kinds of continuity preserving discrete shape gradients of boundary type for PDE-constrained shape optimizations. First, a modified boundary shape gradient formula for sha...
非精确两层网格法的新型收敛性分析方法（张晨松）
非精确 两层网格法 收敛性 分析方法
2023/2/22
Two-grid methods with exact solution of the Galerkin coarse-grid system have been well studied by the multigrid community: an elegant identity has been established to characterize the convergence fact...
针对缺失数据生成模型精度低和训练速度慢的问题,本文基于流模型框架提出了一种改进非线性独立成分估计(Nonlinear independent components estimation,NICE)的缺失时间序列生成方法.该方法依靠流模型框架生成模型精度高、训练过程速度快的优势,并结合粒子群优化算法(Particle swarm optimization,PSO)优化NICE生成网络采样的退火参数,...
实际工业过程中,量测数据除了在线仪表采集的快速率数据,还有离线化验等慢速率辅助量测数据.为了更好地利用离线化验数据,增加在线估计的精度,针对随机跳变系统,引入迁移学习思想,提出迁移交互多模型估计(Transfer interacting multiple model state estimator,IMM-TF)新策略.首先,将离线化验数据的边缘分布作为可以迁移的知识,迁移到贝叶斯后验分布,实现辅...
加权与近似加权势博弈及其在博弈控制论中的应用
加权 近似加权势博弈 博弈控制论
2023/1/5
With the tool of semi-tensor product of matrices, an algorithm is proposed to verify whether a finite game is a weighted potential game (WPG) without pre-knowledge on its weights. Then the algorithm i...