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pro vyhledávání: '"YI, ZHENG"'
Let $M$ be an $n\times n$ real symmetric matrix. The spread of $M$ is defined as the difference between its largest and smallest eigenvalue. When considering the spread of graph-related matrices, this topic has attracted significant attention, result
Externí odkaz:
http://arxiv.org/abs/2412.14789
Autor:
Fan, Yi-Zheng
Hu and Ye conjectured that for a $k$-th order and $n$-dimensional tensor $\mathcal{A}$ with an eigenvalue $\lambda$ and the corresponding eigenvariety $\mathcal{V}_\lambda(\mathcal{A})$, $$\mathrm{am}(\lambda) \ge \sum_{i=1}^\kappa \mathrm{dim}(V_i)(
Externí odkaz:
http://arxiv.org/abs/2410.20830
General criteria on spectral extremal problems for hypergraphs were developed by Keevash, Lenz, and Mubayi in their seminal work (SIAM J. Discrete Math., 2014), in which extremal results on \alpha-spectral radius of hypergraphs for \alpha>1 may be de
Externí odkaz:
http://arxiv.org/abs/2409.17679
Let $K$ be a simplicial complex, and let $\Delta_i^{up}(K)$ be the $i$-th up normalized Laplacian of $K$. Horak and Jost showed that the largest eigenvalue of $\Delta_i^{up}(K)$ is at most $i+2$, and characterized the equality case by the orientable
Externí odkaz:
http://arxiv.org/abs/2407.13791
A graph $G$ is factored into graphs $H$ and $K$ via a matrix product if there exist adjacency matrices $A$, $B$, and $C$ of $G$, $H$, and $K$, respectively, such that $A = BC$. In this paper, we study the spectral aspects of the matrix product of gra
Externí odkaz:
http://arxiv.org/abs/2407.04150
Let $K$ be a simplical complex, and let $\mathcal{L}_i^{up}(K), \mathcal{Q}_i^{up}(K)$ be the $i$-th up Laplacian and signless Laplacian of $K$, respectively. In this paper we proved that the largest eigenvalue of $\mathcal{L}_i^{up}(K)$ is not great
Externí odkaz:
http://arxiv.org/abs/2405.19078
Let $F$ be a graph and let $\mathcal{B}_r(F)$ be the class of $r$-uniform Berge-$F$ hypergraphs. In this paper, by establishing a relationship between the spectral radius of the adjacency tensor of a uniform hypergraph and its local structure via wal
Externí odkaz:
http://arxiv.org/abs/2403.02064
Autor:
Zhou, Qing, Zhen, Yi-Zheng, Xu, Xin-Yu, Zhao, Shuai, Yang, Wen-Li, Fei, Shao-Ming, Li, Li, Liu, Nai-Le, Chen, Kai
Publikováno v:
Physical Review A 109, 022427 (2024)
Local unitary equivalence is an important ingredient for quantifying and classifying entanglement. Verifying whether or not two quantum states are local unitary equivalent is a crucial problem, where only the case of multipartite pure states is solve
Externí odkaz:
http://arxiv.org/abs/2402.13489
In this paper, by the representation theory of symmetric group, we give a decomposition of the Laplace operator (in matrix form) of a covering simplicial complex into the direct sum of some matrices, including the Laplace operator of the underlying s
Externí odkaz:
http://arxiv.org/abs/2312.12709
Publikováno v:
Phys. Rev. E 108, 054119 (2023)
Annealing is the process of gradually lowering the temperature of a system to guide it towards its lowest energy states. In an accompanying paper [Luo et al. Phys. Rev. E 108, L052105 (2023)], we derived a general bound on annealing performance by co
Externí odkaz:
http://arxiv.org/abs/2311.10424