Guozhen Shen

Jul 14, 2024 | arxiv.org | Guozhen Shen

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Jun 6, 2024 | pericles.pericles-prod.literatumonline.com | Wenhao Yang |Guozhen Shen

Yang Li Shandong Provincial Key Laboratory of Network Based Intelligent Computing, School of Information Science and Engineering, University of Jinan, Jinan, 250022 China School of Integrated Circuits, Shandong University, Jinan, 250101 ChinaSearch for more papers by this author

Jan 4, 2024 | onlinelibrary.wiley.com | Wenhao Yang |Guozhen Shen

Conflict of Interest The authors declare no conflict of interest. Supporting Information Filename Description adfm202312885-sup-0001-SuppMat.pdf1.5 MB Supporting Information References 1, , , , , , , , , , , , , , , , , , , , , , , , Nature 2019, 572, 106. 2, , , , , , , , , , Science 2019, 366, 210. 3, , , , Nat. Nanotechnol. 2020, 15, 529. 4, , , , , , Nano Lett. 2020, 20, 8059. 5, , Nanotechnology 2019, 31, 092001. 6, , , , , , , , , , , , , , , , Sci. Rep.

Jan 3, 2024 | pericles.pericles-prod.literatumonline.com | Wenhao Yang |Guozhen Shen

Conflict of Interest The authors declare no conflict of interest. Supporting Information Filename Description adfm202312885-sup-0001-SuppMat.pdf1.5 MB Supporting Information References 1, , , , , , , , , , , , , , , , , , , , , , , , Nature 2019, 572, 106. 2, , , , , , , , , , Science 2019, 366, 210. 3, , , , Nat. Nanotechnol. 2020, 15, 529. 4, , , , , , Nano Lett. 2020, 20, 8059. 5, , Nanotechnology 2019, 31, 092001. 6, , , , , , , , , , , , , , , , Sci. Rep.

Aug 4, 2023 | onlinelibrary.wiley.com | Guozhen Shen

Abstract It is proved in ZF $\mathsf {ZF}$ (without the axiom of choice) that a n ⩽ S n + 1 ( a ) $\mathfrak {a}^n\leqslant \mathcal {S}_{n+1}(\mathfrak {a})$ for all infinite cardinals a $\mathfrak {a}$ and all natural numbers n ≠ 0 $n\ne 0$ , where S n + 1 ( a ) $\mathcal {S}_{n+1}(\mathfrak {a})$ is the cardinality of the set of permutations with exactly n + 1 $n+1$ non-fixed points of a set which is of cardinality a $\mathfrak {a}$ .