{"id":"https://openalex.org/W2019945347","doi":"https://doi.org/10.1016/0012-365x(88)90213-0","title":"Combinatorial resolution of systems of differential equations. IV. separation of variables","display_name":"Combinatorial resolution of systems of differential equations. IV. separation of variables","publication_year":1988,"publication_date":"1988-12-01","ids":{"openalex":"https://openalex.org/W2019945347","doi":"https://doi.org/10.1016/0012-365x(88)90213-0","mag":"2019945347"},"language":"en","primary_location":{"id":"doi:10.1016/0012-365x(88)90213-0","is_oa":false,"landing_page_url":"https://doi.org/10.1016/0012-365x(88)90213-0","pdf_url":null,"source":{"id":"https://openalex.org/S18902827","display_name":"Discrete Mathematics","issn_l":"0012-365X","issn":["0012-365X","1872-681X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete 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/A5053405840","display_name":"Pierre Leroux","orcid":null},"institutions":[{"id":"https://openalex.org/I159129438","display_name":"Universit\u00e9 du Qu\u00e9bec \u00e0 Montr\u00e9al","ror":"https://ror.org/002rjbv21","country_code":"CA","type":"education","lineage":["https://openalex.org/I159129438","https://openalex.org/I49663120"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Pierre Leroux","raw_affiliation_strings":["Universit\u00e9 du Qu\u00e9bec \u00e0 Montr\u00e9al, Canada","Universit\u00e9 du Qu\u00e9bec \u00e0 Montr\u00e9al; Canada"],"affiliations":[{"raw_affiliation_string":"Universit\u00e9 du Qu\u00e9bec \u00e0 Montr\u00e9al, Canada","institution_ids":["https://openalex.org/I159129438"]},{"raw_affiliation_string":"Universit\u00e9 du Qu\u00e9bec \u00e0 Montr\u00e9al; Canada","institution_ids":["https://openalex.org/I159129438"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5034846169","display_name":"G\u00e9rard Viennot","orcid":null},"institutions":[{"id":"https://openalex.org/I15057530","display_name":"Universit\u00e9 de Bordeaux","ror":"https://ror.org/057qpr032","country_code":"FR","type":"education","lineage":["https://openalex.org/I15057530"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"G\u00e9rard X. Viennot","raw_affiliation_strings":["Universit\u00e9 de Bordeaux I, France","Universite de Bordeaux I (France)"],"affiliations":[{"raw_affiliation_string":"Universit\u00e9 de Bordeaux I, France","institution_ids":["https://openalex.org/I15057530"]},{"raw_affiliation_string":"Universite de Bordeaux I (France)","institution_ids":["https://openalex.org/I15057530"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5053405840"],"corresponding_institution_ids":["https://openalex.org/I159129438"],"apc_list":{"value":3000,"currency":"USD","value_usd":3000},"apc_paid":null,"fwci":1.8789,"has_fulltext":false,"cited_by_count":23,"citation_normalized_percentile":{"value":0.86962514,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"72","issue":"1-3","first_page":"237","last_page":"250"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9977999925613403,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9977999925613403,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9911999702453613,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11567","display_name":"semigroups and automata theory","score":0.9908000230789185,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8628317713737488},{"id":"https://openalex.org/keywords/interpretation","display_name":"Interpretation (philosophy)","score":0.6030682921409607},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.5988864302635193},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.5424725413322449},{"id":"https://openalex.org/keywords/separation-of-variables","display_name":"Separation of variables","score":0.5312281250953674},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.5040335059165955},{"id":"https://openalex.org/keywords/forcing","display_name":"Forcing (mathematics)","score":0.5015201568603516},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4910471439361572},{"id":"https://openalex.org/keywords/examples-of-differential-equations","display_name":"Examples of differential equations","score":0.43657350540161133},{"id":"https://openalex.org/keywords/resolution","display_name":"Resolution (logic)","score":0.41593316197395325},{"id":"https://openalex.org/keywords/differential-algebraic-equation","display_name":"Differential algebraic equation","score":0.4090614914894104},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3666521906852722},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3455580472946167},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.31691014766693115},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.25248807668685913},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09332683682441711}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8628317713737488},{"id":"https://openalex.org/C527412718","wikidata":"https://www.wikidata.org/wiki/Q855395","display_name":"Interpretation (philosophy)","level":2,"score":0.6030682921409607},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.5988864302635193},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.5424725413322449},{"id":"https://openalex.org/C159722891","wikidata":"https://www.wikidata.org/wiki/Q913323","display_name":"Separation of variables","level":3,"score":0.5312281250953674},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.5040335059165955},{"id":"https://openalex.org/C197115733","wikidata":"https://www.wikidata.org/wiki/Q1003136","display_name":"Forcing (mathematics)","level":2,"score":0.5015201568603516},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4910471439361572},{"id":"https://openalex.org/C204854254","wikidata":"https://www.wikidata.org/wiki/Q303072","display_name":"Examples of differential equations","level":5,"score":0.43657350540161133},{"id":"https://openalex.org/C138268822","wikidata":"https://www.wikidata.org/wiki/Q1051925","display_name":"Resolution (logic)","level":2,"score":0.41593316197395325},{"id":"https://openalex.org/C186219872","wikidata":"https://www.wikidata.org/wiki/Q955889","display_name":"Differential algebraic equation","level":4,"score":0.4090614914894104},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3666521906852722},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3455580472946167},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.31691014766693115},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.25248807668685913},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09332683682441711},{"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/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/0012-365x(88)90213-0","is_oa":false,"landing_page_url":"https://doi.org/10.1016/0012-365x(88)90213-0","pdf_url":null,"source":{"id":"https://openalex.org/S18902827","display_name":"Discrete Mathematics","issn_l":"0012-365X","issn":["0012-365X","1872-681X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics","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":10,"referenced_works":["https://openalex.org/W93695394","https://openalex.org/W416739458","https://openalex.org/W2008257663","https://openalex.org/W2045484872","https://openalex.org/W2068757705","https://openalex.org/W2127407604","https://openalex.org/W2196559987","https://openalex.org/W2584784847","https://openalex.org/W6603837579","https://openalex.org/W6652333383"],"related_works":["https://openalex.org/W2049253768","https://openalex.org/W2502480061","https://openalex.org/W2101685990","https://openalex.org/W2480309503","https://openalex.org/W1193285027","https://openalex.org/W2889253678","https://openalex.org/W3021188244","https://openalex.org/W3121290032","https://openalex.org/W4320000798","https://openalex.org/W2321083928"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-03-10T14:07:55.174380","created_date":"2025-10-10T00:00:00"}
