{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T13:18:27Z","timestamp":1772284707860,"version":"3.50.1"},"reference-count":9,"publisher":"Elsevier BV","issue":"12","license":[{"start":{"date-parts":[[2012,12,1]],"date-time":"2012-12-01T00:00:00Z","timestamp":1354320000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2012,12,1]],"date-time":"2012-12-01T00:00:00Z","timestamp":1354320000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2016,12,15]],"date-time":"2016-12-15T00:00:00Z","timestamp":1481760000000},"content-version":"vor","delay-in-days":1475,"URL":"http:\/\/www.elsevier.com\/open-access\/userlicense\/1.0\/"}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Applied Mathematics Letters"],"published-print":{"date-parts":[[2012,12]]},"DOI":"10.1016\/j.aml.2012.06.001","type":"journal-article","created":{"date-parts":[[2012,6,15]],"date-time":"2012-06-15T13:43:46Z","timestamp":1339767826000},"page":"2193-2197","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":3,"title":["Relative entropy and discrete Poincar\u00e9 inequalities for reducible matrices"],"prefix":"10.1016","volume":"25","author":[{"given":"Jacek","family":"Banasiak","sequence":"first","affiliation":[]},{"given":"Proscovia","family":"Namayanja","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"key":"10.1016\/j.aml.2012.06.001_br000005","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1007\/s10440-011-9666-y","article-title":"Asynchronous exponential growth of a general structured population model","volume":"119","author":"Banasiak","year":"2012","journal-title":"Acta Appl. Math."},{"issue":"2","key":"10.1016\/j.aml.2012.06.001_br000010","doi-asserted-by":"crossref","first-page":"503","DOI":"10.4310\/CMS.2009.v7.n2.a12","article-title":"Exponential decay for the growth\u2013fragmentation equation\/cell-division equation","volume":"7","author":"Lauren\u00e7ot","year":"2009","journal-title":"Communications in Mathematical Science"},{"key":"10.1016\/j.aml.2012.06.001_br000015","series-title":"Transport Equations in Biology","author":"Perthame","year":"2007"},{"key":"10.1016\/j.aml.2012.06.001_br000020","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1142\/S0218339000000067","article-title":"Markov semigroups and stability of the cell maturity distribution","volume":"8","author":"Rudnicki","year":"2000","journal-title":"Journal of Biological Systems"},{"key":"10.1016\/j.aml.2012.06.001_br000025","series-title":"Functional Analysis, Sobolev Spaces and Partial Differential Equations","author":"Brezis","year":"2010"},{"key":"10.1016\/j.aml.2012.06.001_br000030","doi-asserted-by":"crossref","first-page":"353","DOI":"10.1016\/0954-349X(93)90025-F","article-title":"A limiting property for the powers of a reducible, nonnegative matrix","volume":"4","author":"Dietzenbacher","year":"1993","journal-title":"Structural Change and Economic Dynamics"},{"key":"10.1016\/j.aml.2012.06.001_br000035","unstructured":"R. Rudnicki, Modele i Metody Biologii Matematycznej, in Polish, in print."},{"key":"10.1016\/j.aml.2012.06.001_br000040","series-title":"Applications of the Theory of Matrices","author":"Gantmacher","year":"1959"},{"key":"10.1016\/j.aml.2012.06.001_br000045","series-title":"Nonnegative Matrices and Markov Chains","author":"Seneta","year":"2006"}],"container-title":["Applied Mathematics Letters"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0893965912002741?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0893965912002741?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:38:50Z","timestamp":1760240330000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0893965912002741"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,12]]},"references-count":9,"journal-issue":{"issue":"12","published-print":{"date-parts":[[2012,12]]}},"alternative-id":["S0893965912002741"],"URL":"https:\/\/doi.org\/10.1016\/j.aml.2012.06.001","relation":{},"ISSN":["0893-9659"],"issn-type":[{"value":"0893-9659","type":"print"}],"subject":[],"published":{"date-parts":[[2012,12]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Relative entropy and discrete Poincar\u00e9 inequalities for reducible matrices","name":"articletitle","label":"Article Title"},{"value":"Applied Mathematics Letters","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.aml.2012.06.001","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"Copyright \u00a9 2012 Elsevier Ltd. All rights reserved.","name":"copyright","label":"Copyright"}]}}