a漫

Thesis title: Stability of a point charge for the repulsive Vlasov–Poisson systemAuthors：Benoît Pausader，Klaus Widmayer，Jiaqi YangPublication：Journal of the European Mathematical SocietyAbstract: We consider solutions of the repulsive Vlasov–Poisson system which are a combination of a point charge and a small gas, i.e., measures of the form $\delta_{(X(t),V(t))}+\mu^2d{\bf x}d{\bf v}$ fo...

论文题目：On high-dimensional Poisson models with measurement error: hypothesis testing for nonlinear nonconvex optimization论文作者：Fei Jiang, Yeqing Zhou, Jianxuan Liu and Yanyuan Ma发表刊物：Annals of Statistics成果介绍：在本论文中，我们研究了含有噪声协变量的高维泊松回归模型的估计与检验问题。研究该模型对分析噪声大数据具有理论及应用上的意义。我们修正了由协变量噪声带来的估计偏差，通过极小化惩...

论文题目：Testing the effects of high-dimensional covariates via aggregating cumulative covariances论文作者：Runze Li, Kai Xu, Yeqing Zhou and Liping Zhu发表刊物：Journal of the American Statistical Association成果介绍：在本论文中，我们研究了高维协变量的显著性检验问题。在许多应用领域中，高维数据的每一分量会呈现出明显的异质性。为了能够有效处理数据的高维度和异质性，我们提出了一种基于累积协方差聚...

论文题目：On the shape of Meissner solutions to the 2-dimensional Ginzburg-Landau system论文作者：Xing-Bin Pan; Xingfei Xiang发表刊物：Math. Ann.成果介绍：外磁场强度从弱变强，超导材料从局部稳定的Meissner态变得不稳定、然后产生涡旋，相变到混合态。对于二维的超导体，我们给出了使得Meissner解局部稳定的外磁场强度估计；对局部稳定的Meissner解的形状作了精细的刻画，特别地，我们证明感应磁位势模和序参数模（...

论文题目：Cube sums of the forms and 论文作者：Shu Jie and Yin Hongbo发表刊物：Mathematische Annalen成果介绍：判断什么样的非零自然数是两个非零有理数立方的和是一个历史悠久的丢番图方程问题，我们称之为立方和问题，该问题可以追溯到费马时代。立方和问题与一类特殊的椭圆曲线的Mordell-Weil群有密切的联系。我们通过椭圆曲线的算术理论证明：对于模9余2或5的素数，和均是立方和。这给出了新的精确立方和的无穷族群...

论文题目：Representation type of cyclotomic quiver Hecke algebras of type $A_\ell^{(1)}$论文作者：Susumu Ariki，Linliang Song，Qi Wang发表刊物：Advances in Mathematics成果介绍：We first investigate a connected quiver consisting of all dominant maximal weights for an integrable highest weight module in affine type A. This quiver provides an efficient method to obtain all dominant maximal weights...

论文题目：Learning equilibrium mean-variance strategy论文作者：Min Dai, Yuchao Dong and Yanwei Jia发表刊物：Mathematical Finance成果介绍：利用强化学习理论解决金融投资问题是当前金融数学发展的一个热点之一。我们在强化学习框架下研究了一个动态均值方差投资组合优化问题，在此过程中引入了熵正则化项以促进探索。由于均值方差准则涉及到时间上的不一致性，我们的目标是学习一个均衡策略。在不完全市场条件下，我们...

论文题目：A basis theorem for the affine Kauffman category and its cyclotomic quotients论文作者：Mengmeng Gao, Hebing Rui, Linliang Song发表刊物：Journal of Algebra成果介绍：The affine Kauffman category is a strict monoidal category and can be considered as a $q$-analogue of the affine Brauer category in (Rui and Song in Math.Zeit.293,503-550,2019).In this paper,we prove a basis theorem for the...

成果介绍：We develop the theory of fundamental classes in the setting of motivic homotopy theory. Using this we construct, for any motivic spectrum, an associated twisted bivariant theory, extending the formalism of Fulton and MacPherson. We import the tools of Fulton’s intersection theory into this setting: (refined) Gysin maps, specialization maps, and formulas for excess of intersection, self-intersections, and blow-ups. We also develop a theory of Euler classes of vector bundles in this setting. For the Milnor–Witt spectrum recently constructed by Déglise–Fasel, we get a bivariant theory extending the Chow–Witt groups of Barge–Morel, in the same way the higher Chow groups extend the classical Chow groups. As another application we prove a motivic Gauss–Bonnet formula, computing Euler characteristics in the motivic homotopy category.

成果介绍：在这篇文章中，我们有一个基本的发现：利用代数学中线性无关(linear independence)的概念和数学中维数(dimension)的概念，把n维空间中多面体的体积(volume)这个基本的几何量分解成了n个n次齐次多项式。其中第n个齐次多项式恰好是纽约大学的Erwin Lutwak, Deane Yang 和 Gaoyong Zhang三位教授于2001年引入的仿射不变量（Transactions of AMS，353 (2001), 1767-1779），而前（n-1）个齐次多项式是首次发现的。这n个n次齐次多项式叫做多面体的体积分解泛函。 本文利用锥体积测度的子空间集中条件(subspace concentration condition)和变分的办法，完全解决了3维空间中体积分解泛函的极值问题，建立了严格的仿射反向等周不等式。