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pro vyhledávání: '"SHEN, WEN"'
The paper is concerned with a scalar conservation law with discontinuous gradient-dependent flux. Namely, the flux is described by two different functions $f(u)$ or $g(u)$, when the gradient $u_x$ of the solution is positive or negative, respectively
Externí odkaz:
http://arxiv.org/abs/2411.13444
The paper is concerned with a scalar conservation law with discontinuous gradient-dependent flux. Namely, the flux is described by two different functions $f(u)$ or $g(u)$, when the gradient $u_x$ of the solution is positive or negative, respectively
Externí odkaz:
http://arxiv.org/abs/2411.10443
Autor:
Shen, Wen
In this paper, we present more conclusions for $C^\ast(\mathrm{PL})$ and oriented PL cobordism, and compute the string PL bordism groups of certain dimensions. Then, we apply these results to classify certain PL manifolds of dimensions $10$ and $13$.
Externí odkaz:
http://arxiv.org/abs/2407.14028
Autor:
Shen, Wen
This paper presents any spherical fibration over certain CW complexes is stably fibre homotopy equivalent to a $\mathrm{TOP}$-linear spherical bundle. Moreover, if the CW complex is a Poincar$\mathrm{\acute{e}}$ complex, then it is of the homotopy ty
Externí odkaz:
http://arxiv.org/abs/2406.16019
Autor:
Shen, Wen
This paper gives the classifications of certain manifolds $\mathcal{M}$ of dimension $13$ up to diffeomorphism, homeomorphism, and homotopy equivalence, whose cohomology rings are isomorphic to $H^\ast(\mathrm{CP}^3\times S^7;\mathbb{Z})$. Moreover,
Externí odkaz:
http://arxiv.org/abs/2406.15697
Autor:
Fang, Fuquan, Shen, Wen
Geometry of manifolds with positive sectional curvature has been a central object dates back to the beginning of Riemannian geometry. Up to homeomorphism, there are only finitely many examples of simply connected positively curved manifolds in all di
Externí odkaz:
http://arxiv.org/abs/2307.13303
Autor:
Wang, Lei, Xu, Wei, Li, Li-Hong, Zhang, Peng-Fei, Ning, An, Xu, Rui, Cheng, Peng, Shen, Zi-Yu, Shen, Wen-Bin
According to the general relativity theory, the geopotential difference can be determined by gravity frequency shift between two clocks. Here we report on the experiments to determine the geopotential difference between two remote sites by hydrogen m
Externí odkaz:
http://arxiv.org/abs/2306.15184
This study aims to prove the emergence of symbolic concepts (or more precisely, sparse primitive inference patterns) in well-trained deep neural networks (DNNs). Specifically, we prove the following three conditions for the emergence. (i) The high-or
Externí odkaz:
http://arxiv.org/abs/2305.01939
In this paper, we explain the inference logic of large language models (LLMs) as a set of symbolic concepts. Many recent studies have discovered that traditional DNNs usually encode sparse symbolic concepts. However, because an LLM has much more para
Externí odkaz:
http://arxiv.org/abs/2304.01083
Autor:
Zhou, Huilin, Zhang, Hao, Deng, Huiqi, Liu, Dongrui, Shen, Wen, Chan, Shih-Han, Zhang, Quanshi
This paper explains the generalization power of a deep neural network (DNN) from the perspective of interactions. Although there is no universally accepted definition of the concepts encoded by a DNN, the sparsity of interactions in a DNN has been pr
Externí odkaz:
http://arxiv.org/abs/2302.13091