{"id":"https://openalex.org/W1982904671","doi":"https://doi.org/10.1155/2011/804836","title":"Necessary and Sufficient Condition for Stability of Generalized Expectation Value","display_name":"Necessary and Sufficient Condition for Stability of Generalized Expectation Value","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W1982904671","doi":"https://doi.org/10.1155/2011/804836","mag":"1982904671"},"language":"en","primary_location":{"id":"doi:10.1155/2011/804836","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2011/804836","pdf_url":"https://downloads.hindawi.com/journals/jam/2011/804836.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/jam/2011/804836.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5110623423","display_name":"Aziz El Kaabouchi","orcid":null},"institutions":[{"id":"https://openalex.org/I4210086593","display_name":"Institut Sup\u00e9rieur des Mat\u00e9riaux du Mans","ror":"https://ror.org/001s4x714","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210086593"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Aziz El Kaabouchi","raw_affiliation_strings":["Institut Suprieur des Matriaux et Mcaniques Avancs, 44 F. A. Bartholdi, 72000 Le Mans, France","Institut Sup\u00e9rieur des Mat\u00e9riaux et M\u00e9caniques Avanc\u00e9s, 44 F. A. Bartholdi, 72000 Le Mans"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut Suprieur des Matriaux et Mcaniques Avancs, 44 F. A. Bartholdi, 72000 Le Mans, France","institution_ids":["https://openalex.org/I4210086593"]},{"raw_affiliation_string":"Institut Sup\u00e9rieur des Mat\u00e9riaux et M\u00e9caniques Avanc\u00e9s, 44 F. A. Bartholdi, 72000 Le Mans","institution_ids":["https://openalex.org/I4210086593"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101590021","display_name":"Sumiyoshi Abe","orcid":"https://orcid.org/0000-0002-0430-5819"},"institutions":[{"id":"https://openalex.org/I178574317","display_name":"Mie University","ror":"https://ror.org/01529vy56","country_code":"JP","type":"education","lineage":["https://openalex.org/I178574317"]},{"id":"https://openalex.org/I4210086593","display_name":"Institut Sup\u00e9rieur des Mat\u00e9riaux du Mans","ror":"https://ror.org/001s4x714","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210086593"]}],"countries":["FR","JP"],"is_corresponding":true,"raw_author_name":"Sumiyoshi Abe","raw_affiliation_strings":["Department of Physical Engineering, Mie University, Mie 514-8507, Japan","Institut Suprieur des Matriaux et Mcaniques Avancs, 44 F. A. Bartholdi, 72000 Le Mans, France","Department of Physical Engineering, Mie University, Mie 514-8507","Institut Sup\u00e9rieur des Mat\u00e9riaux et M\u00e9caniques Avanc\u00e9s, 44 F. A. Bartholdi, 72000 Le Mans"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physical Engineering, Mie University, Mie 514-8507, Japan","institution_ids":["https://openalex.org/I178574317"]},{"raw_affiliation_string":"Institut Suprieur des Matriaux et Mcaniques Avancs, 44 F. A. Bartholdi, 72000 Le Mans, France","institution_ids":["https://openalex.org/I4210086593"]},{"raw_affiliation_string":"Department of Physical Engineering, Mie University, Mie 514-8507","institution_ids":["https://openalex.org/I178574317"]},{"raw_affiliation_string":"Institut Sup\u00e9rieur des Mat\u00e9riaux et M\u00e9caniques Avanc\u00e9s, 44 F. A. Bartholdi, 72000 Le Mans","institution_ids":["https://openalex.org/I4210086593"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5101590021"],"corresponding_institution_ids":["https://openalex.org/I178574317","https://openalex.org/I4210086593"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":0.2409,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.54764537,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"2011","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12261","display_name":"Statistical Mechanics and Entropy","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12261","display_name":"Statistical Mechanics and Entropy","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11520","display_name":"Advanced Thermodynamics and Statistical Mechanics","score":0.9977999925613403,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11270","display_name":"Complex Systems and Time Series Analysis","score":0.9937000274658203,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.7199556231498718},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6230785846710205},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.607617199420929},{"id":"https://openalex.org/keywords/value","display_name":"Value (mathematics)","score":0.5174375176429749},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.48474642634391785},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.43959394097328186},{"id":"https://openalex.org/keywords/statistical-mechanics","display_name":"Statistical mechanics","score":0.41314923763275146},{"id":"https://openalex.org/keywords/probability-distribution","display_name":"Probability distribution","score":0.4122706353664398},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1981896162033081},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1625138223171234},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1372166872024536}],"concepts":[{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.7199556231498718},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6230785846710205},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.607617199420929},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.5174375176429749},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.48474642634391785},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.43959394097328186},{"id":"https://openalex.org/C99874945","wikidata":"https://www.wikidata.org/wiki/Q188715","display_name":"Statistical mechanics","level":2,"score":0.41314923763275146},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.4122706353664398},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1981896162033081},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1625138223171234},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1372166872024536},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1155/2011/804836","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2011/804836","pdf_url":"https://downloads.hindawi.com/journals/jam/2011/804836.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jam/1331818637","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jam/1331818637","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:RePEc:hin:jnljam:804836","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/JAM/2011/804836.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:653a66a6c926418c8b8eb8570b2b278d","is_oa":false,"landing_page_url":"https://doaj.org/article/653a66a6c926418c8b8eb8570b2b278d","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Applied Mathematics, Vol 2011 (2011)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2011/804836","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2011/804836","pdf_url":"https://downloads.hindawi.com/journals/jam/2011/804836.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1982904671.pdf","grobid_xml":"https://content.openalex.org/works/W1982904671.grobid-xml"},"referenced_works_count":27,"referenced_works":["https://openalex.org/W1553236419","https://openalex.org/W1564500292","https://openalex.org/W1592472301","https://openalex.org/W1672879477","https://openalex.org/W1710243769","https://openalex.org/W1969160346","https://openalex.org/W1989308357","https://openalex.org/W1996151186","https://openalex.org/W1999815076","https://openalex.org/W2008676721","https://openalex.org/W2021252433","https://openalex.org/W2039590286","https://openalex.org/W2048759097","https://openalex.org/W2049494813","https://openalex.org/W2072443785","https://openalex.org/W2088362568","https://openalex.org/W2096229390","https://openalex.org/W2110730115","https://openalex.org/W2146161374","https://openalex.org/W2319104638","https://openalex.org/W2913075478","https://openalex.org/W2951708757","https://openalex.org/W3099497943","https://openalex.org/W3102655150","https://openalex.org/W3103991570","https://openalex.org/W3104838429","https://openalex.org/W3105579589"],"related_works":["https://openalex.org/W1541882734","https://openalex.org/W4378783825","https://openalex.org/W1986220090","https://openalex.org/W2498186742","https://openalex.org/W629112805","https://openalex.org/W2368454205","https://openalex.org/W2035826341","https://openalex.org/W1624830178","https://openalex.org/W2049150502","https://openalex.org/W2278299187"],"abstract_inverted_index":{"A":[0],"class":[1,29],"of":[2,5,36],"generalized":[3],"definitions":[4],"expectation":[6],"value":[7],"is":[8,24],"often":[9],"employed":[10],"in":[11],"nonequilibrium":[12],"statistical":[13],"mechanics":[14],"for":[15,26],"complex":[16],"systems.":[17],"Here,":[18],"the":[19],"necessary":[20],"and":[21],"sufficient":[22],"condition":[23],"presented":[25],"such":[27],"a":[28,37],"to":[30],"be":[31],"stable":[32],"under":[33],"small":[34],"deformations":[35],"given":[38],"arbitrary":[39],"probability":[40],"distribution.":[41]},"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2016-06-24T00:00:00"}