{"id":"https://openalex.org/W2914649761","doi":"https://doi.org/10.1007/s11424-019-8356-0","title":"Characteristic Decomposition: From Regular Sets to Normal Sets","display_name":"Characteristic Decomposition: From Regular Sets to Normal Sets","publication_year":2019,"publication_date":"2019-02-01","ids":{"openalex":"https://openalex.org/W2914649761","doi":"https://doi.org/10.1007/s11424-019-8356-0","mag":"2914649761"},"language":"en","primary_location":{"id":"doi:10.1007/s11424-019-8356-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11424-019-8356-0","pdf_url":null,"source":{"id":"https://openalex.org/S45848134","display_name":"Journal of Systems Science and Complexity","issn_l":"1009-6124","issn":["1009-6124","1559-7067"],"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":"Journal of Systems Science and Complexity","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/A5026125145","display_name":"Chenqi Mou","orcid":"https://orcid.org/0000-0002-5070-5928"},"institutions":[{"id":"https://openalex.org/I82880672","display_name":"Beihang University","ror":"https://ror.org/00wk2mp56","country_code":"CN","type":"education","lineage":["https://openalex.org/I82880672"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Chenqi Mou","raw_affiliation_strings":["LMIB \u2013 School of Mathematics and Systems Science/Beijing Advanced Innovation Center for Big Data and Brain Computing, Beihang University, Beijing, 100191, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LMIB \u2013 School of Mathematics and Systems Science/Beijing Advanced Innovation Center for Big Data and Brain Computing, Beihang University, Beijing, 100191, China","institution_ids":["https://openalex.org/I82880672"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100737019","display_name":"Dongming Wang","orcid":"https://orcid.org/0000-0003-2762-6567"},"institutions":[{"id":"https://openalex.org/I82880672","display_name":"Beihang University","ror":"https://ror.org/00wk2mp56","country_code":"CN","type":"education","lineage":["https://openalex.org/I82880672"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Dongming Wang","raw_affiliation_strings":["Centre National de la Recherche Scientifique, 75794, Paris cedex 16, France","LMIB \u2013 SKLSDE \u2013 School of Mathematics and Systems Science/Beijing Advanced Innovation Center for Big Data and Brain Computing, Beihang University, Beijing, 100191, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Centre National de la Recherche Scientifique, 75794, Paris cedex 16, France","institution_ids":[]},{"raw_affiliation_string":"LMIB \u2013 SKLSDE \u2013 School of Mathematics and Systems Science/Beijing Advanced Innovation Center for Big Data and Brain Computing, Beihang University, Beijing, 100191, China","institution_ids":["https://openalex.org/I82880672"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5026125145"],"corresponding_institution_ids":["https://openalex.org/I82880672"],"apc_list":{"value":3090,"currency":"USD","value_usd":3090},"apc_paid":null,"fwci":0.5392,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.67327413,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"32","issue":"1","first_page":"37","last_page":"46"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9997000098228455,"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/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9939000010490417,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9818999767303467,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/lexicographical-order","display_name":"Lexicographical order","score":0.8238967657089233},{"id":"https://openalex.org/keywords/ideal","display_name":"Ideal (ethics)","score":0.7589353322982788},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.6923907995223999},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6571558713912964},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.6061840653419495},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.5042344331741333},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4143030643463135},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.39167630672454834},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3676351308822632},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.33305248618125916},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1921217441558838},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.17001476883888245},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.11160469055175781}],"concepts":[{"id":"https://openalex.org/C159254197","wikidata":"https://www.wikidata.org/wiki/Q1144915","display_name":"Lexicographical order","level":2,"score":0.8238967657089233},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.7589353322982788},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.6923907995223999},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6571558713912964},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.6061840653419495},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.5042344331741333},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4143030643463135},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39167630672454834},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3676351308822632},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.33305248618125916},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1921217441558838},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.17001476883888245},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11160469055175781},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s11424-019-8356-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11424-019-8356-0","pdf_url":null,"source":{"id":"https://openalex.org/S45848134","display_name":"Journal of Systems Science and Complexity","issn_l":"1009-6124","issn":["1009-6124","1559-7067"],"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":"Journal of Systems Science and Complexity","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":39,"referenced_works":["https://openalex.org/W22319829","https://openalex.org/W52950217","https://openalex.org/W145236249","https://openalex.org/W1493847008","https://openalex.org/W1542519396","https://openalex.org/W1563257127","https://openalex.org/W1577951736","https://openalex.org/W1594760108","https://openalex.org/W1975442862","https://openalex.org/W1976541507","https://openalex.org/W1990451653","https://openalex.org/W1992805538","https://openalex.org/W2027044504","https://openalex.org/W2031245794","https://openalex.org/W2031399497","https://openalex.org/W2036549578","https://openalex.org/W2038345254","https://openalex.org/W2039228526","https://openalex.org/W2053029682","https://openalex.org/W2056521839","https://openalex.org/W2059522106","https://openalex.org/W2065989671","https://openalex.org/W2077725083","https://openalex.org/W2103185909","https://openalex.org/W2120467997","https://openalex.org/W2123254909","https://openalex.org/W2128687423","https://openalex.org/W2136020592","https://openalex.org/W2221569317","https://openalex.org/W2476587762","https://openalex.org/W2592998205","https://openalex.org/W2752581437","https://openalex.org/W2963086861","https://openalex.org/W2995200218","https://openalex.org/W4205227699","https://openalex.org/W4238858352","https://openalex.org/W4248084437","https://openalex.org/W4285719527","https://openalex.org/W6602452458"],"related_works":["https://openalex.org/W1993634787","https://openalex.org/W3125614403","https://openalex.org/W2476923378","https://openalex.org/W2803221307","https://openalex.org/W2951826204","https://openalex.org/W4211001408","https://openalex.org/W2903963821","https://openalex.org/W2366147410","https://openalex.org/W62366039","https://openalex.org/W239928435"],"abstract_inverted_index":null,"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}