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In this paper, we establish two upper bounds for the maximum &lt;inline-formula&gt;&lt;tex-math id=\"M2\"&gt;\\begin{document}$ M $\\end{document}&lt;\/tex-math&gt;&lt;\/inline-formula&gt;-eigenvalue of partially symmetric nonnegative tensors, which improve some existing results. Numerical examples are proposed to verify the efficiency of the obtained results.&lt;\/p&gt;<\/jats:p>","DOI":"10.3934\/mfc.2021018","type":"journal-article","created":{"date-parts":[[2021,9,30]],"date-time":"2021-09-30T10:48:47Z","timestamp":1632998927000},"page":"33","source":"Crossref","is-referenced-by-count":3,"title":["Sharp upper bounds on the maximum $M$-eigenvalue of fourth-order partially symmetric nonnegative tensors"],"prefix":"10.3934","volume":"5","author":[{"given":"Yuyan","family":"Yao","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gang","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"2321","reference":[{"key":"key-10.3934\/mfc.2021018-1","doi-asserted-by":"publisher","unstructured":"H. Che, H. Chen, Y. Wang.On the $M$-eigenvalue estimation of fourth-order partially symmetric tensors, <i>J. Ind. Manag. 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