{"id":"https://openalex.org/W1999470997","doi":"https://doi.org/10.1109/cdc.2011.6160488","title":"Hybrid switching diffusions: Continuity and differentiability","display_name":"Hybrid switching diffusions: Continuity and differentiability","publication_year":2011,"publication_date":"2011-12-01","ids":{"openalex":"https://openalex.org/W1999470997","doi":"https://doi.org/10.1109/cdc.2011.6160488","mag":"1999470997"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2011.6160488","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2011.6160488","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Conference on Decision and Control and European Control Conference","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5008853967","display_name":"George Yin","orcid":"https://orcid.org/0000-0002-2951-0704"},"institutions":[{"id":"https://openalex.org/I185443292","display_name":"Wayne State University","ror":"https://ror.org/01070mq45","country_code":"US","type":"education","lineage":["https://openalex.org/I185443292"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"G. Yin","raw_affiliation_strings":["Department of Mathematics, Wayne State University, Detroit, MI, USA","Department of Mathematics, Wayne State University Detroit, MI 48202, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Wayne State University, Detroit, MI, USA","institution_ids":["https://openalex.org/I185443292"]},{"raw_affiliation_string":"Department of Mathematics, Wayne State University Detroit, MI 48202, USA","institution_ids":["https://openalex.org/I185443292"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5051604373","display_name":"Chao Zhu","orcid":"https://orcid.org/0000-0002-6764-6979"},"institutions":[{"id":"https://openalex.org/I43579087","display_name":"University of Wisconsin\u2013Milwaukee","ror":"https://ror.org/031q21x57","country_code":"US","type":"education","lineage":["https://openalex.org/I43579087"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"C. Zhu","raw_affiliation_strings":["Department of Mathematical Sciences, University of Wisconsin, Milwaukee, Milwaukee, WI, USA","Department of Mathematical Sciences, University of Wisconsin, Milwaukee, 53201, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, University of Wisconsin, Milwaukee, Milwaukee, WI, USA","institution_ids":["https://openalex.org/I43579087"]},{"raw_affiliation_string":"Department of Mathematical Sciences, University of Wisconsin, Milwaukee, 53201, USA","institution_ids":["https://openalex.org/I43579087"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5008853967"],"corresponding_institution_ids":["https://openalex.org/I185443292"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.06740512,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"46","issue":null,"first_page":"5017","last_page":"5022"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9965999722480774,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.9962999820709229,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.7963996529579163},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.743961751461029},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.61421799659729},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.520648181438446},{"id":"https://openalex.org/keywords/work","display_name":"Work (physics)","score":0.500727653503418},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3843649923801422},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.37576016783714294},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.35228055715560913},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2362428903579712},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1098661720752716},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.0975131094455719},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06460234522819519},{"id":"https://openalex.org/keywords/mechanical-engineering","display_name":"Mechanical engineering","score":0.06350100040435791}],"concepts":[{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.7963996529579163},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.743961751461029},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.61421799659729},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.520648181438446},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.500727653503418},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3843649923801422},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.37576016783714294},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.35228055715560913},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2362428903579712},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1098661720752716},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0975131094455719},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06460234522819519},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.06350100040435791},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cdc.2011.6160488","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2011.6160488","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Conference on Decision and Control and European Control Conference","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":50,"referenced_works":["https://openalex.org/W97620058","https://openalex.org/W241008065","https://openalex.org/W587814406","https://openalex.org/W1483382787","https://openalex.org/W1495604384","https://openalex.org/W1513091520","https://openalex.org/W1525883337","https://openalex.org/W1526071765","https://openalex.org/W1535151767","https://openalex.org/W1542958135","https://openalex.org/W1567262822","https://openalex.org/W1583915406","https://openalex.org/W1827189078","https://openalex.org/W1967779692","https://openalex.org/W1969848360","https://openalex.org/W1971776804","https://openalex.org/W1972145423","https://openalex.org/W1975083310","https://openalex.org/W1976081240","https://openalex.org/W1977544211","https://openalex.org/W1988916339","https://openalex.org/W1990784704","https://openalex.org/W2011961136","https://openalex.org/W2017032949","https://openalex.org/W2018477253","https://openalex.org/W2021266086","https://openalex.org/W2029946328","https://openalex.org/W2030161410","https://openalex.org/W2039776803","https://openalex.org/W2047188539","https://openalex.org/W2049234737","https://openalex.org/W2058823784","https://openalex.org/W2061412229","https://openalex.org/W2070056413","https://openalex.org/W2076837481","https://openalex.org/W2081877251","https://openalex.org/W2085096176","https://openalex.org/W2085725212","https://openalex.org/W2103262285","https://openalex.org/W2113203091","https://openalex.org/W2115484823","https://openalex.org/W2484199605","https://openalex.org/W2507750056","https://openalex.org/W2593901252","https://openalex.org/W2596330628","https://openalex.org/W2900812847","https://openalex.org/W4243828860","https://openalex.org/W4250550220","https://openalex.org/W4302609762","https://openalex.org/W6734276549"],"related_works":["https://openalex.org/W4285277090","https://openalex.org/W4394650907","https://openalex.org/W154364797","https://openalex.org/W4254119641","https://openalex.org/W3196207352","https://openalex.org/W2951724202","https://openalex.org/W3084261076","https://openalex.org/W4327738859","https://openalex.org/W2576399385","https://openalex.org/W2963408011"],"abstract_inverted_index":{"This":[0],"work":[1],"focuses":[2],"on":[3,29],"hybrid":[4],"switching":[5],"diffusion":[6],"systems.":[7],"After":[8],"presenting":[9],"the":[10,40],"basic":[11],"models,":[12],"a":[13],"difficult":[14],"and":[15,26],"fundamental":[16],"problem,":[17],"namely,":[18],"well":[19],"posedness":[20],"is":[21,32],"addressed.":[22],"In":[23],"particular,":[24],"continuous":[25],"smooth":[27],"dependence":[28],"initial":[30],"data":[31],"treated.":[33],"The":[34],"main":[35],"ideas":[36],"are":[37],"presented,":[38],"whereas":[39],"verbatim":[41],"proofs":[42],"can":[43],"be":[44],"found":[45],"in":[46],"[35].":[47]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
