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Science China Mathematics 2024年第3期67卷 627-646页

作者： Hui Xiao Ion Grama Quansheng Liu Institut fur Mathematik und Angewandte Informatik Universitat HildesheimHildesheim 31141Germany Academy of Mathematics and Systems Science Chinese Academy of SciencesBeijing 100190China LMBA Universite Bretagne SudCNRS UMR 6205Vannes F-56000France

Let(g_(n))_(n≥1) be a sequence of independent and identically distributed positive random d×d matrices and consider the matrix product G_(n)=g_(n)…g_*** suitable conditions,we establish the Berry-Esseen bounds on the rate of convergence in the central limit theorem and Cramer-type moderate deviation expansions,for any matrix norm ‖G_(n)‖ of G_(n),its entries G_(n)^(i,j) and its spectral radius ρ(G_(n)).Extended versions of their joint law with the direction of the random walk G_(n)x are also established,where x is a starting point in the unit sphere of R~d.

关键词： Berry-Esseen bound Cramér-type moderate deviation product of random matrices operator norm entry spectral radius

spectral radius of uniform hypergraphs and degree sequences

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Frontiers of Mathematics in China 2017年第6期12卷 1279-1288页

作者： Dongmei CHEN Zhibing CHEN Xiao-Dong ZHANG College of Mathematics and Statistics Shenzhen University Shenzhen 518060 China School of Mathematical Sciences MOE-LSC and SHL-MAC Shanghai Jiao Tong University Shanghai 200240 China

We present several upper bounds for the adjacency and signless Laplacian spectral radii of uniform hypergraphs in terms of degree sequences.

关键词： spectral radius uniform hypergraph degree sequence

spectral radius of r-uniform supertrees with perfect matchings

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Frontiers of Mathematics in China 2018年第6期13卷 1489-1499页

作者： Lei ZHANG An CHANG Center for Discrete Mathematics and Theoretical Computer'Science Fuzhou University Fuzhou 350116China

supertree is a connected and acyclic hypergraph. The set of r-uniform supertrees with n vertices and the set of r-uniform supertrees with perfect matchings on rk vertices are denoted by Tn and Tr,k, respectively. H. Li, J. Shao, and L. Qi [J. Comb. Optim., 2016, 32(3): 741–764] proved that the hyperstar Sn,r attains uniquely the maximum spectral radius in Tn. Focusing on the spectral radius in Tr,k, this paper will give the maximum value in Tr,k and their corresponding supertree.

关键词： Supertrees spectral radius perfect matching 15A42 05C50 05C65

spectral radius of Non-negative Matrices and Digraphs

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Acta Mathematica Sinica,English Series 2002年第2期18卷 293-300页

作者： ZHANG Xiao Dong Department of Mathematics.East China Normal University,Shanghai 200062.P.R.China E-mail:xdzhang2@hotmail.comLI Jiong Sheng Department of Mathematics.University of Science and Technology of China,Hefei 230026,P.R China Department of Mathematics East China Normal University Shanghai P. R. China Department of Mathematics University of Science and Technology of China Hefei P. R. China

We present,an upper and a lower bound for the spectral radius of non-negative matrices. Then we give the bounds for the spectral radius of digraphs.

关键词： Non-negative matrix Digraph spectral radius

Unicyclic Graphs of Minimal spectral radius

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Acta Mathematica Sinica,English Series 2013年第2期29卷 281-286页

作者： Ling Sheng SHI Department of Mathematical Sciences Tsinghua University

It was conjectured by Li and Feng in 1979 that the unicyclic graph formed by a cycle of order g linking to an endvertex of a path of length k minimizes the spectral radius of all unicyclic graphs of order g ＋ k and girth g. In 1987, Cao proved that this conjecture is true for k ≥ g（g - 2）/8 and false for k = 2 and sufficiently large g. In this note, we show that g 〉12 suffices for the counterexample and give more counterexamples with large girth for any integer k 〉 1.

关键词： Extremal graph Li-Feng's conjecture spectral radius unicyclic

Additive Maps Preserving Nilpotent Operators or spectral radius

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Acta Mathematica Sinica,English Series 2005年第5期21卷 1167-1182页

作者： Zhao Fang BAI Jin Chuan HOU School of Science Xi'an Jiaotong University Xi'an 710049 P. R. China Department of Mathematics Shanxi Teachers University Linfen 041004 P. R. China

Let X be a （real or complex） Banach space with dimension greater than 2 and let B0（X） be the subspace of B（X） spanned by all nilpotent operators on X. We get a complete classification of surjective additive maps Ф on B0（X） which preserve nilpotent operators in both directions. In particular, if X is infinite-dimensional, we prove that Ф has the form either Ф（T） = cATA^-1 or Ф（T） = cAT＇A^-1, where A is an invertible bounded linear or conjugate linear operator, c is a scalar, T＇ denotes the adjoint of T. As an application of these results, we show that every additive surjective map on B（X） preserving spectral radius has a similar form to the above with ｜c｜ = 1.

关键词： Additive preservers Nilpotent operators spectral radius

Lower Bounds on the(Laplacian) spectral radius of Weighted Graphs

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Chinese Annals of Mathematics,Series B 2014年第4期35卷 669-678页

作者： Aimei YU Mei LU Department of Mathematics Beijing Jiaotong University Department of Mathematical Sciences Tsinghua University

The weighted graphs, where the edge weights are positive numbers, are considered. The authors obtain some lower bounds on the spectral radius and the Laplacian spectral radius of weighted graphs, and characterize the graphs for which the bounds are attained. Moreover, some known lower bounds on the spectral radius and the Laplacian spectral radius of unweighted graphs can be deduced from the bounds.

关键词： Weighted graphs Adjacency matrix Laplacian matrix spectral radius Lower bounds

The Linear Unicyclic Hypergraph with the Second or Third Largest spectral radius

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Acta Mathematica Sinica,English Series 2020年第10期36卷 1140-1150页

作者： Chao DING Yi Zheng FAN Jiang Chao WAN School of Mathematics and Physics Anqing Normal UniversityAnqing 246133P.R.China School of Mathematical Sciences Anhui UniversityHefei 230601P.R.China

The spectral radius of a uniform hypergraph is defined to be that of the adjacency tensor of the *** is known that the unique unicyclic hypergraph with the largest spectral radius is a nonlinear hypergraph,and the unique linear unicyclic hypergraph with the largest spectral radius is a power *** this paper we determine the unique linear unicyclic hypergraph with the second or third largest spectral radius,where the former hypergraph is a power hypergraph and the latter hypergraph is a non-power hypergraph.

关键词： Linear unicyclic hypergraph adjacency tensor spectral radius weighted incident matrix

Sharp Upper and Lower Bounds for the Laplacian spectral radius and the spectral radius of Graphs

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Acta Mathematicae Applicatae Sinica 2008年第2期24卷 289-296页

作者： Ji-ming Guo Department of Applied Mathematics China University of Petroleum Dongying 257061 China

In this paper, sharp upper bounds for the Laplacian spectral radius and the spectral radius of graphs are given, respectively. We show that some known bounds can be obtained from our bounds. For a bipartite graph G, w... 详细信息

关键词： Graph Laplacian spectral radius spectral radius upper (lower) bound bipartite graph eigen-vector

lk,s-Singular values and spectral radius of partially symmetric rectangular tensors

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Frontiers of Mathematics in China 2016年第3期11卷 605-622页

作者： Hongmei YAO Bingsong LONG Changjiang BU Jiang ZHOU College of Science Harbin Engineering University Harbin 150001 China

The real rectangular tensors arise from the strong ellipticity condition problem in solid mechanics and the entanglement problem in quantum physics. In this paper, we first study properties oflk,singular values of real rectangular tensors. Then, a necessary and sufficient condition for the positive definiteness of partially symmetric rectangular tensors is given. Furthermore, we show that the weak Perron-Frobenius theorem for nonnegative partially symmetric rectangular tensor keeps valid under some new conditions and we prove a maximum property for the largest lk,S-singular values of nonnegative partially symmetric rectangular tensor. Finally, we prove that the largest lk,s- singular value of nonnegative weakly irreducible partially symmetric rectangular tensor is still geometrically simple.

关键词： lk,s-Singular values spectral radius positive definiteness partiallysymmetric rectangular tensor weakly irreducible