{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,23]],"date-time":"2025-07-23T12:13:09Z","timestamp":1753272789962,"version":"3.37.3"},"reference-count":29,"publisher":"Wiley","license":[{"start":{"date-parts":[[2020,1,8]],"date-time":"2020-01-08T00:00:00Z","timestamp":1578441600000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11671228","11801430"],"award-info":[{"award-number":["11671228","11801430"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11671228","11801430"],"award-info":[{"award-number":["11671228","11801430"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2020,1,8]]},"abstract":"<jats:p><jats:italic>M<\/jats:italic>-eigenvalues of fourth-order partially symmetric tensors play important roles in the nonlinear elastic material analysis and the entanglement problem of quantum physics. In this paper, we introduce <jats:italic>M<\/jats:italic>-identity tensor and establish two <jats:italic>M<\/jats:italic>-eigenvalue inclusion intervals with <jats:italic>n<\/jats:italic> parameters for fourth-order partially symmetric tensors, which are sharper than some existing results. Numerical examples are proposed to verify the efficiency of the obtained results. As applications, we provide some checkable sufficient conditions for the positive definiteness and establish bound estimations for the <jats:italic>M<\/jats:italic>-spectral radius of fourth-order partially symmetric nonnegative tensors.<\/jats:p>","DOI":"10.1155\/2020\/2474278","type":"journal-article","created":{"date-parts":[[2020,1,8]],"date-time":"2020-01-08T18:30:53Z","timestamp":1578508253000},"page":"1-8","source":"Crossref","is-referenced-by-count":9,"title":["<i>M<\/i>-Eigenvalues-Based Sufficient Conditions for the Positive Definiteness of Fourth-Order Partially Symmetric Tensors"],"prefix":"10.1155","volume":"2020","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6701-3373","authenticated-orcid":true,"given":"Gang","family":"Wang","sequence":"first","affiliation":[{"name":"School of Management Science, Qufu Normal University, Rizhao, Shandong 276800, China"}]},{"given":"Linxuan","family":"Sun","sequence":"additional","affiliation":[{"name":"School of Management Science, Qufu Normal University, Rizhao, Shandong 276800, China"}]},{"given":"Lixia","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Xidian University, Xi\u2019an, Shanxi 710071, China"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1007\/s10659-009-9205-5"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1016\/s0020-7462(01)00066-x"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.3934\/dcdsb.2001.1.257"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1016\/j.nahs.2015.12.002"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1016\/j.nahs.2019.06.001"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1007\/s11464-009-0016-6"},{"year":"2017","key":"7"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1002\/nla.2125"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2018.01.025"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1007\/s11464-018-0675-2"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1002\/nla.537"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1002\/nla.1996"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1016\/j.apm.2015.04.036"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2016.03.025"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1002\/nla.2134"},{"issue":"3","key":"18","first-page":"1286","volume":"20","year":"2009","journal-title":"SIAM Journal on Matrix Analysis on Optimization"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.3934\/jimo.2018153"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2019.01.013"},{"key":"21","doi-asserted-by":"publisher","DOI":"10.1016\/j.aml.2019.106137"},{"key":"22","doi-asserted-by":"publisher","DOI":"10.1002\/nla.1858"},{"key":"23","doi-asserted-by":"publisher","DOI":"10.1080\/03081087.2015.1049582"},{"issue":"2","key":"24","first-page":"227","volume":"14","year":"2018","journal-title":"Pacific Journal of Optimization"},{"key":"25","doi-asserted-by":"publisher","DOI":"10.11650\/tjm\/180905"},{"key":"26","doi-asserted-by":"publisher","DOI":"10.1080\/03081087.2018.1561823"},{"key":"27","doi-asserted-by":"publisher","DOI":"10.3934\/jimo.2019129"},{"key":"28","doi-asserted-by":"publisher","DOI":"10.1007\/s11075-018-0506-2"},{"key":"29","doi-asserted-by":"publisher","DOI":"10.3934\/dcdsb.2017009"},{"key":"30","doi-asserted-by":"publisher","DOI":"10.1186\/s13660-017-1363-6"},{"key":"31","doi-asserted-by":"publisher","DOI":"10.1515\/math-2019-0090"}],"container-title":["Complexity"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2020\/2474278.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2020\/2474278.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2020\/2474278.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,8]],"date-time":"2020-01-08T18:30:56Z","timestamp":1578508256000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/complexity\/2020\/2474278\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,1,8]]},"references-count":29,"alternative-id":["2474278","2474278"],"URL":"https:\/\/doi.org\/10.1155\/2020\/2474278","relation":{},"ISSN":["1076-2787","1099-0526"],"issn-type":[{"type":"print","value":"1076-2787"},{"type":"electronic","value":"1099-0526"}],"subject":[],"published":{"date-parts":[[2020,1,8]]}}}