Banach asked whether a normed space must be Hilbert if, for one fixed dimension greater than one, all subspaces of that dimension are linearly isometric. We prove the complex case. By the codimension-one reduction, the essential finite-dimensional problem is to characterize a balanced convex body in a complex $(n+1)$-s...
Xi-Nan Dai, W.-D. Deng, Yi-Dong Shi et al.· 0 citations
Bayesian filtering provides a principled framework for online state estimation under uncertainty, yet its application to systems with high-dimensional states and complicated posterior distributions remains challenging. Recent generative models, such as flow matching, have shown potential in Bayesian filtering. However,...
Rui-Qi Feng, Chong-Yi Wang, Tao Zhang et al.· 0 citations
In Question~3.1 of his 1995 paper on depth and transfer, Carlson asked whether the depth of a finite-group cohomology ring is always realized by the dimension of one of its associated primes. We give a negative answer. Let \[ G=\SG{128}{859},\qquad k=\kbar. \] An exact presentation certificate proves that $\depth H^*(G...
Xinan Dai, Wenhao Deng, Yingdong Shi et al.· 1 citation
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