We construct a class of C*-metric algebras. We prove that for a discrete group Γ with a 2-cocycle σ,the closure of the seminorm ||[Ml1,·]|| on Cc(Γ, σ) is a Leibniz Lip-norm on the twisted reduced group C*-al...We construct a class of C*-metric algebras. We prove that for a discrete group Γ with a 2-cocycle σ,the closure of the seminorm ||[Ml1,·]|| on Cc(Γ, σ) is a Leibniz Lip-norm on the twisted reduced group C*-algebra C*r(Γ, σ) for the pointwise multiplication operator Mlon l2(Γ), induced by a proper length function l on Γ with the property of bounded θ-dilation. Moreover, the compact quantum metric space structures depend only on the cohomology class of 2-cocycles in the Lipschitz isometric sense.展开更多
We establish a new partial C^(0)-estimate along a continuity path mixed with conic singularities along a simple normal crossing divisor and a positive twisted(1,1)-form on Fano manifolds.As an application,this estimat...We establish a new partial C^(0)-estimate along a continuity path mixed with conic singularities along a simple normal crossing divisor and a positive twisted(1,1)-form on Fano manifolds.As an application,this estimate enables us to show the reductivity of the automorphism group of the limit space,which leads to a new proof of the Yau-Tian-Donaldson conjecture.展开更多
提出了一种基于DI-FCM(double indices fuzzy C-means)算法框架的无监督距离学习算法——基于混合距离学习的双指数模糊C均值算法HDDI-FCM(double indices fuzzy C-m eans with hybrid distance).数据集未知距离度量被表示为若干已有距...提出了一种基于DI-FCM(double indices fuzzy C-means)算法框架的无监督距离学习算法——基于混合距离学习的双指数模糊C均值算法HDDI-FCM(double indices fuzzy C-m eans with hybrid distance).数据集未知距离度量被表示为若干已有距离的线性组合,然后执行HDDI-FCM,在对数据集进行有效聚类的同时进行距离学习.为了保证迭代算法收敛,引入了Steffensen迭代法来改进计算簇中心点的迭代公式.讨论了算法中参数的选择.基于UCI(University of California,Irvine)数据集的实验结果表明该算法是有效的.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.11171109 and 11801177)the Science and Technology Commission of Shanghai Municipality(Grant No.18dz2271000)。
文摘We construct a class of C*-metric algebras. We prove that for a discrete group Γ with a 2-cocycle σ,the closure of the seminorm ||[Ml1,·]|| on Cc(Γ, σ) is a Leibniz Lip-norm on the twisted reduced group C*-algebra C*r(Γ, σ) for the pointwise multiplication operator Mlon l2(Γ), induced by a proper length function l on Γ with the property of bounded θ-dilation. Moreover, the compact quantum metric space structures depend only on the cohomology class of 2-cocycles in the Lipschitz isometric sense.
基金supported by Le Centre de recherche en géométrie et topologie Fellowship during the visit to Institut des sciences mathématiques of Universitédu QuébecàMontréal。
文摘We establish a new partial C^(0)-estimate along a continuity path mixed with conic singularities along a simple normal crossing divisor and a positive twisted(1,1)-form on Fano manifolds.As an application,this estimate enables us to show the reductivity of the automorphism group of the limit space,which leads to a new proof of the Yau-Tian-Donaldson conjecture.
文摘提出了一种基于DI-FCM(double indices fuzzy C-means)算法框架的无监督距离学习算法——基于混合距离学习的双指数模糊C均值算法HDDI-FCM(double indices fuzzy C-m eans with hybrid distance).数据集未知距离度量被表示为若干已有距离的线性组合,然后执行HDDI-FCM,在对数据集进行有效聚类的同时进行距离学习.为了保证迭代算法收敛,引入了Steffensen迭代法来改进计算簇中心点的迭代公式.讨论了算法中参数的选择.基于UCI(University of California,Irvine)数据集的实验结果表明该算法是有效的.
