{"id":"https://openalex.org/W1483228049","doi":"https://doi.org/10.1155/2011/762762","title":"Sufficient and Necessary Center Conditions for the Poincar\u00e9 Systems <i>P</i>(2, \u20092<i>n</i>)(<i>n</i> \u2264 5)","display_name":"Sufficient and Necessary Center Conditions for the Poincar\u00e9 Systems <i>P</i>(2, \u20092<i>n</i>)(<i>n</i> \u2264 5)","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W1483228049","doi":"https://doi.org/10.1155/2011/762762","mag":"1483228049"},"language":"en","primary_location":{"id":"doi:10.1155/2011/762762","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2011/762762","pdf_url":"https://downloads.hindawi.com/journals/jam/2011/762762.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/2011/762762.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5030080020","display_name":"Jinya Xu","orcid":null},"institutions":[{"id":"https://openalex.org/I84653119","display_name":"Academia Sinica","ror":"https://ror.org/05bxb3784","country_code":"TW","type":"facility","lineage":["https://openalex.org/I84653119"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Jinya Xu","raw_affiliation_strings":["Institute of Computer Applications, Academia Sinica, Chengdu 610041, China","Institute of Computer Applications, Academia Sinica, Chengdu 610041"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Computer Applications, Academia Sinica, Chengdu 610041, China","institution_ids":[]},{"raw_affiliation_string":"Institute of Computer Applications, Academia Sinica, Chengdu 610041","institution_ids":["https://openalex.org/I84653119"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110162244","display_name":"Zhengyi Lu","orcid":"https://orcid.org/0009-0003-4723-7187"},"institutions":[{"id":"https://openalex.org/I63354593","display_name":"Sichuan Normal University","ror":"https://ror.org/043dxc061","country_code":"CN","type":"education","lineage":["https://openalex.org/I63354593"]},{"id":"https://openalex.org/I84653119","display_name":"Academia Sinica","ror":"https://ror.org/05bxb3784","country_code":"TW","type":"facility","lineage":["https://openalex.org/I84653119"]}],"countries":["CN","TW"],"is_corresponding":true,"raw_author_name":"Zhengyi Lu","raw_affiliation_strings":["Department of Mathematics, Sichuan Normal University, Chengdu 610068, China","Institute of Computer Applications, Academia Sinica, Chengdu 610041, China","Department of Mathematics, Sichuan Normal University, Chengdu 610068","Institute of Computer Applications, Academia Sinica, Chengdu 610041"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Sichuan Normal University, Chengdu 610068, China","institution_ids":["https://openalex.org/I63354593"]},{"raw_affiliation_string":"Institute of Computer Applications, Academia Sinica, Chengdu 610041, China","institution_ids":[]},{"raw_affiliation_string":"Department of Mathematics, Sichuan Normal University, Chengdu 610068","institution_ids":["https://openalex.org/I63354593"]},{"raw_affiliation_string":"Institute of Computer Applications, Academia Sinica, Chengdu 610041","institution_ids":["https://openalex.org/I84653119"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5110162244"],"corresponding_institution_ids":["https://openalex.org/I63354593","https://openalex.org/I84653119"],"apc_list":{"value":1025,"currency":"USD","value_usd":1050},"apc_paid":{"value":1025,"currency":"USD","value_usd":1050},"fwci":0.3521,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.51883471,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":1.0,"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":1.0,"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/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9542999863624573,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9473999738693237,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/center","display_name":"Center (category theory)","score":0.869135856628418},{"id":"https://openalex.org/keywords/maple","display_name":"Maple","score":0.747868001461029},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6169450283050537},{"id":"https://openalex.org/keywords/poincar\u00e9-conjecture","display_name":"Poincar\u00e9 conjecture","score":0.5564485192298889},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5209599733352661},{"id":"https://openalex.org/keywords/symbolic-computation","display_name":"Symbolic computation","score":0.465249627828598},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.35630056262016296},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.34893497824668884},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3150103688240051},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.13465315103530884}],"concepts":[{"id":"https://openalex.org/C2779463800","wikidata":"https://www.wikidata.org/wiki/Q5062222","display_name":"Center (category theory)","level":2,"score":0.869135856628418},{"id":"https://openalex.org/C2780414537","wikidata":"https://www.wikidata.org/wiki/Q42292","display_name":"Maple","level":2,"score":0.747868001461029},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6169450283050537},{"id":"https://openalex.org/C88221313","wikidata":"https://www.wikidata.org/wiki/Q203586","display_name":"Poincar\u00e9 conjecture","level":2,"score":0.5564485192298889},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5209599733352661},{"id":"https://openalex.org/C110812573","wikidata":"https://www.wikidata.org/wiki/Q175515","display_name":"Symbolic computation","level":2,"score":0.465249627828598},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.35630056262016296},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.34893497824668884},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3150103688240051},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.13465315103530884},{"id":"https://openalex.org/C59822182","wikidata":"https://www.wikidata.org/wiki/Q441","display_name":"Botany","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C8010536","wikidata":"https://www.wikidata.org/wiki/Q160398","display_name":"Crystallography","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":2,"locations":[{"id":"doi:10.1155/2011/762762","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2011/762762","pdf_url":"https://downloads.hindawi.com/journals/jam/2011/762762.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:doaj.org/article:ef9cfa0c91f14a55aa170736a1a7fea1","is_oa":true,"landing_page_url":"https://doaj.org/article/ef9cfa0c91f14a55aa170736a1a7fea1","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","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:10.1155/2011/762762","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2011/762762","pdf_url":"https://downloads.hindawi.com/journals/jam/2011/762762.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":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1483228049.pdf","grobid_xml":"https://content.openalex.org/works/W1483228049.grobid-xml"},"referenced_works_count":27,"referenced_works":["https://openalex.org/W1546156674","https://openalex.org/W1930532881","https://openalex.org/W1964896081","https://openalex.org/W1967000321","https://openalex.org/W1967533836","https://openalex.org/W1977467910","https://openalex.org/W1978707469","https://openalex.org/W1983273546","https://openalex.org/W1984549182","https://openalex.org/W1998630324","https://openalex.org/W2001626398","https://openalex.org/W2019340699","https://openalex.org/W2039228526","https://openalex.org/W2041764074","https://openalex.org/W2049815318","https://openalex.org/W2051825792","https://openalex.org/W2074798569","https://openalex.org/W2094763747","https://openalex.org/W2104856235","https://openalex.org/W2167303330","https://openalex.org/W2247487868","https://openalex.org/W2492155120","https://openalex.org/W2566680048","https://openalex.org/W4230659860","https://openalex.org/W4246627060","https://openalex.org/W6640255246","https://openalex.org/W6684716431"],"related_works":["https://openalex.org/W3008027610","https://openalex.org/W2187413387","https://openalex.org/W2363922099","https://openalex.org/W851952888","https://openalex.org/W2140907685","https://openalex.org/W908473976","https://openalex.org/W4210971937","https://openalex.org/W4386225212","https://openalex.org/W2384965142","https://openalex.org/W4251421746"],"abstract_inverted_index":{"We":[0],"obtain":[1],"sufficient":[2],"and":[3,38],"necessary":[4],"center":[5],"conditions":[6],"for":[7],"the":[8,22,27,39],"Poincar\u00e9":[9],"system":[10],"P":[11],"(2,":[12],"2":[13,29],"n":[14,16,30],")(":[15],"\u2264":[17],"5).":[18],"The":[19],"necessity":[20],"of":[21],"condition":[23],"is":[24,41],"derived":[25],"from":[26],"first":[28],"focal":[31],"values":[32],"by":[33,43],"symbolic":[34],"computation":[35],"with":[36],"Maple,":[37],"sufficiency":[40],"proved":[42],"Volokitin\u2032s":[44],"method.":[45]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2013,"cited_by_count":1}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2016-06-24T00:00:00"}