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    學術預告-The eigenvectors of nonnegative tensors and hypergraphs associated with spectral radius

    發布時間: 2019-08-05 10:55:02   作者:本站編輯   來源: 本站原創   瀏覽次數:

    講座主題:The eigenvectors of nonnegative tensors and hypergraphs associated with spectral radius

    主講人: 范益政 

    工作單位:安徽大學

    講座時間:2019年8月6日9:00

    講座地點:數學院大會議室

    主辦單位:煙臺大學數學與信息科學學院

    內容摘要:

        In this talk we showed that such projective eigenvariety admits a module structure, which is determined by the support of the tensor and can be characterized explicitly by the Smith normal form of the incidence matrix of the tensor. We introduced two parameters: the stabilizing index and the stabilizing dimension of the tensor, where the former is exactly the cardinality of the projective eigenvariety and the latter is the composition length of the projective eigenvariety as a module. We give some upper bounds for the two parameters, and characterize the case that there is only one eigenvector of the tensor corresponding to the spectral radius, i.e. the Perron vector. By applying the above results to the adjacency tensor of a connected uniform hypergraph, we give some upper bounds for the two parameters in terms of the structural parameters of the hypergraph such as path cover number, matching number and the maximum length of paths.

    主講人介紹:

        范益政,男,教授,博士,博士生導師,教育部新世紀優秀人才,安徽省學術和技術帶頭人,中國工業與應用數學學會圖論組合及應用專業委員會副主任委員,中國運籌學會圖論組合學分會常務理事,中國數學會圖論與組合專業委員會委員,安徽省數學會常務理事,安徽大學數學科學學院院長。主要研究方向:代數組合與譜圖理論。主持國家自然科學基金項目4項,發表論文100余篇。

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