{"id":"https://openalex.org/W831281291","doi":"https://doi.org/10.1007/s10208-015-9268-6","title":"A Necessary and Sufficient Proximity Condition for Smoothness Equivalence of Nonlinear Subdivision Schemes","display_name":"A Necessary and Sufficient Proximity Condition for Smoothness Equivalence of Nonlinear Subdivision Schemes","publication_year":2015,"publication_date":"2015-06-29","ids":{"openalex":"https://openalex.org/W831281291","doi":"https://doi.org/10.1007/s10208-015-9268-6","mag":"831281291"},"language":"en","primary_location":{"id":"doi:10.1007/s10208-015-9268-6","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10208-015-9268-6","pdf_url":null,"source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Foundations of Computational Mathematics","raw_type":"journal-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/A5111543594","display_name":"Tom Duchamp","orcid":null},"institutions":[{"id":"https://openalex.org/I201448701","display_name":"University of Washington","ror":"https://ror.org/00cvxb145","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Tom Duchamp","raw_affiliation_strings":["Department of Mathematics, University of Washington, Box 354350, Seattle, WA, 98195-4350, USA","Department of Mathematics, University of Washington, Seattle, USA 98195-4350#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Washington, Box 354350, Seattle, WA, 98195-4350, USA","institution_ids":["https://openalex.org/I201448701"]},{"raw_affiliation_string":"Department of Mathematics, University of Washington, Seattle, USA 98195-4350#TAB#","institution_ids":["https://openalex.org/I201448701"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026650985","display_name":"Gang Xie","orcid":"https://orcid.org/0000-0002-8712-8888"},"institutions":[{"id":"https://openalex.org/I143593769","display_name":"East China University of Science and Technology","ror":"https://ror.org/01vyrm377","country_code":"CN","type":"education","lineage":["https://openalex.org/I143593769"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Gang Xie","raw_affiliation_strings":["Department of Mathematics, East China University of Science and Technology, Shanghai, 200237, China","Department of Mathematics, East China University of Science and Technology, Shanghai, China 200237"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, East China University of Science and Technology, Shanghai, 200237, China","institution_ids":["https://openalex.org/I143593769"]},{"raw_affiliation_string":"Department of Mathematics, East China University of Science and Technology, Shanghai, China 200237","institution_ids":["https://openalex.org/I143593769"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5006903519","display_name":"Thomas Yu","orcid":"https://orcid.org/0000-0002-4800-0822"},"institutions":[{"id":"https://openalex.org/I72816309","display_name":"Drexel University","ror":"https://ror.org/04bdffz58","country_code":"US","type":"education","lineage":["https://openalex.org/I72816309"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Thomas Yu","raw_affiliation_strings":["Department of Mathematics, Drexel University, 3141 Chestnut Street, 206 Korman Center, Philadelphia, PA, 19104, USA","Department of Mathematics, Drexel University, Philadelphia, USA 19104"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Drexel University, 3141 Chestnut Street, 206 Korman Center, Philadelphia, PA, 19104, USA","institution_ids":["https://openalex.org/I72816309"]},{"raw_affiliation_string":"Department of Mathematics, Drexel University, Philadelphia, USA 19104","institution_ids":["https://openalex.org/I72816309"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5006903519"],"corresponding_institution_ids":["https://openalex.org/I72816309"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":0.335,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.59251198,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"16","issue":"5","first_page":"1069","last_page":"1114"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T11138","display_name":"Tribology and Lubrication Engineering","score":0.991100013256073,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical 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/T10188","display_name":"Advanced machining processes and optimization","score":0.9865000247955322,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/subdivision","display_name":"Subdivision","score":0.8671512603759766},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7770023941993713},{"id":"https://openalex.org/keywords/smoothness","display_name":"Smoothness","score":0.6788779497146606},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.672623872756958},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.48274677991867065},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4749056100845337},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4140978157520294},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1298891007900238}],"concepts":[{"id":"https://openalex.org/C143392562","wikidata":"https://www.wikidata.org/wiki/Q449111","display_name":"Subdivision","level":2,"score":0.8671512603759766},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7770023941993713},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.6788779497146606},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.672623872756958},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.48274677991867065},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4749056100845337},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4140978157520294},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1298891007900238},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C166957645","wikidata":"https://www.wikidata.org/wiki/Q23498","display_name":"Archaeology","level":1,"score":0.0},{"id":"https://openalex.org/C95457728","wikidata":"https://www.wikidata.org/wiki/Q309","display_name":"History","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10208-015-9268-6","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10208-015-9268-6","pdf_url":null,"source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Foundations of Computational Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W124773106","https://openalex.org/W230256009","https://openalex.org/W574370508","https://openalex.org/W1488435683","https://openalex.org/W1972363811","https://openalex.org/W1981425820","https://openalex.org/W1985026044","https://openalex.org/W1998376654","https://openalex.org/W2001669569","https://openalex.org/W2003989039","https://openalex.org/W2017499683","https://openalex.org/W2030136249","https://openalex.org/W2030362796","https://openalex.org/W2034940548","https://openalex.org/W2036881824","https://openalex.org/W2048918262","https://openalex.org/W2057217736","https://openalex.org/W2064445894","https://openalex.org/W2072595795","https://openalex.org/W2090761804","https://openalex.org/W2096610373","https://openalex.org/W2104896514","https://openalex.org/W2118578342","https://openalex.org/W2144808524","https://openalex.org/W2169458238","https://openalex.org/W2170663107","https://openalex.org/W2334493726","https://openalex.org/W2341241031","https://openalex.org/W4205354563","https://openalex.org/W4239981491","https://openalex.org/W4242860699","https://openalex.org/W4297562995","https://openalex.org/W4388250268"],"related_works":["https://openalex.org/W2384806462","https://openalex.org/W4389950792","https://openalex.org/W2375549870","https://openalex.org/W4376632515","https://openalex.org/W2140072033","https://openalex.org/W2163269603","https://openalex.org/W4205312897","https://openalex.org/W1106115901","https://openalex.org/W1994442929","https://openalex.org/W2791987989"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-06-19T15:47:20.252518","created_date":"2025-10-10T00:00:00"}