Copositivity for 3rd-Order Symmetric Tensors and Applications
The strict copositivity of 4th-order symmetric tensor may apply to detect vacuum stability of general scalar potential. For finding analytical expressions of (strict) copositivity of 4th-order symmetric tensor, we may reduce its order to 3rd order to better deal with it. So, it is provided several a...
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| Veröffentlicht in: | Bulletin of the Malaysian Mathematical Sciences Society 2022, Vol.45 (1), p.133-152 |
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| creator | Liu, Jiarui Song, Yisheng |
| description | The strict copositivity of 4th-order symmetric tensor may apply to detect vacuum stability of general scalar potential. For finding analytical expressions of (strict) copositivity of 4th-order symmetric tensor, we may reduce its order to 3rd order to better deal with it. So, it is provided several analytically sufficient conditions for the copositivity of 3rd-order 2-dimensional (3-dimensional) symmetric tensors. Subsequently, applying these conclusions to 4th-order tensors, the analytically sufficient conditions of copositivity are proved for 4th-order 2-dimensional and 3-dimensional symmetric tensors. Finally, we apply these results to present analytical vacuum stability conditions for vacuum stability for
Z
3
scalar dark matter. |
| doi_str_mv | 10.1007/s40840-021-01180-1 |
| format | Article |
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Z
3
scalar dark matter.</description><identifier>ISSN: 0126-6705</identifier><identifier>EISSN: 2180-4206</identifier><identifier>DOI: 10.1007/s40840-021-01180-1</identifier><language>eng</language><publisher>Singapore: Springer Singapore</publisher><subject>Applications of Mathematics ; Dark matter ; Mathematical analysis ; Mathematics ; Mathematics and Statistics ; Stability analysis ; Tensors</subject><ispartof>Bulletin of the Malaysian Mathematical Sciences Society, 2022, Vol.45 (1), p.133-152</ispartof><rights>Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2021</rights><rights>Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2021.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c270t-a08dc256bac5b634a22b985f91cff471d89a9d49834b689f6522c4fd0b9bd5523</cites><orcidid>0000-0002-9298-8778</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s40840-021-01180-1$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s40840-021-01180-1$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,777,781,27905,27906,41469,42538,51300</link.rule.ids></links><search><creatorcontrib>Liu, Jiarui</creatorcontrib><creatorcontrib>Song, Yisheng</creatorcontrib><title>Copositivity for 3rd-Order Symmetric Tensors and Applications</title><title>Bulletin of the Malaysian Mathematical Sciences Society</title><addtitle>Bull. Malays. Math. Sci. Soc</addtitle><description>The strict copositivity of 4th-order symmetric tensor may apply to detect vacuum stability of general scalar potential. For finding analytical expressions of (strict) copositivity of 4th-order symmetric tensor, we may reduce its order to 3rd order to better deal with it. So, it is provided several analytically sufficient conditions for the copositivity of 3rd-order 2-dimensional (3-dimensional) symmetric tensors. Subsequently, applying these conclusions to 4th-order tensors, the analytically sufficient conditions of copositivity are proved for 4th-order 2-dimensional and 3-dimensional symmetric tensors. Finally, we apply these results to present analytical vacuum stability conditions for vacuum stability for
Z
3
scalar dark matter.</description><subject>Applications of Mathematics</subject><subject>Dark matter</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Stability analysis</subject><subject>Tensors</subject><issn>0126-6705</issn><issn>2180-4206</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><recordid>eNp9kE1LAzEQhoMoWLR_wNOC5-hkNsluDh5K8QsKPVjPIZtsJKXdrMlW6L936wrenMvM4XnfgYeQGwZ3DKC6zxxqDhSQUWCsBsrOyAxPB0eQ52QGDCWVFYhLMs95C-MIiRLZjDwsYx9zGMJXGI6Fj6kok6Pr5NpUvB33-3ZIwRabtssx5cJ0rlj0_S5YM4TY5Wty4c0ut_PffUXenx43yxe6Wj-_LhcrarGCgRqonUUhG2NFI0tuEBtVC6-Y9Z5XzNXKKMdVXfJG1spLgWi5d9CoxgmB5RW5nXr7FD8PbR70Nh5SN77UKEFVTIASI4UTZVPMObVe9ynsTTpqBvpkSk-m9GhK_5jSbAyVUyiPcPfRpr_qf1LfJ_tqXw</recordid><startdate>2022</startdate><enddate>2022</enddate><creator>Liu, Jiarui</creator><creator>Song, Yisheng</creator><general>Springer Singapore</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0002-9298-8778</orcidid></search><sort><creationdate>2022</creationdate><title>Copositivity for 3rd-Order Symmetric Tensors and Applications</title><author>Liu, Jiarui ; Song, Yisheng</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c270t-a08dc256bac5b634a22b985f91cff471d89a9d49834b689f6522c4fd0b9bd5523</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Applications of Mathematics</topic><topic>Dark matter</topic><topic>Mathematical analysis</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Stability analysis</topic><topic>Tensors</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Liu, Jiarui</creatorcontrib><creatorcontrib>Song, Yisheng</creatorcontrib><collection>CrossRef</collection><jtitle>Bulletin of the Malaysian Mathematical Sciences Society</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Liu, Jiarui</au><au>Song, Yisheng</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Copositivity for 3rd-Order Symmetric Tensors and Applications</atitle><jtitle>Bulletin of the Malaysian Mathematical Sciences Society</jtitle><stitle>Bull. Malays. Math. Sci. Soc</stitle><date>2022</date><risdate>2022</risdate><volume>45</volume><issue>1</issue><spage>133</spage><epage>152</epage><pages>133-152</pages><issn>0126-6705</issn><eissn>2180-4206</eissn><abstract>The strict copositivity of 4th-order symmetric tensor may apply to detect vacuum stability of general scalar potential. For finding analytical expressions of (strict) copositivity of 4th-order symmetric tensor, we may reduce its order to 3rd order to better deal with it. So, it is provided several analytically sufficient conditions for the copositivity of 3rd-order 2-dimensional (3-dimensional) symmetric tensors. Subsequently, applying these conclusions to 4th-order tensors, the analytically sufficient conditions of copositivity are proved for 4th-order 2-dimensional and 3-dimensional symmetric tensors. Finally, we apply these results to present analytical vacuum stability conditions for vacuum stability for
Z
3
scalar dark matter.</abstract><cop>Singapore</cop><pub>Springer Singapore</pub><doi>10.1007/s40840-021-01180-1</doi><tpages>20</tpages><orcidid>https://orcid.org/0000-0002-9298-8778</orcidid></addata></record> |
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| subjects | Applications of Mathematics Dark matter Mathematical analysis Mathematics Mathematics and Statistics Stability analysis Tensors |
| title | Copositivity for 3rd-Order Symmetric Tensors and Applications |
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