{"id":"https://openalex.org/W2024579677","doi":"https://doi.org/10.1007/s11424-012-0280-5","title":"On the nonexistence of nontrivial small cycles of the \u00b5 function in 3x+1 conjecture","display_name":"On the nonexistence of nontrivial small cycles of the \u00b5 function in 3x+1 conjecture","publication_year":2012,"publication_date":"2012-12-01","ids":{"openalex":"https://openalex.org/W2024579677","doi":"https://doi.org/10.1007/s11424-012-0280-5","mag":"2024579677"},"language":"en","primary_location":{"id":"doi:10.1007/s11424-012-0280-5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11424-012-0280-5","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/A5101790997","display_name":"Dengguo Feng","orcid":"https://orcid.org/0000-0002-8515-7124"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210128818","display_name":"Institute of Software","ror":"https://ror.org/033dfsn42","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210128818"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Dengguo Feng","raw_affiliation_strings":["State Key Laboratory of Information Security, Institute of Software, Chinese Academy of Sciences, Beijing, 100190, China","Chinese Academy of Sciences"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"State Key Laboratory of Information Security, Institute of Software, Chinese Academy of Sciences, Beijing, 100190, China","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210128818"]},{"raw_affiliation_string":"Chinese Academy of Sciences","institution_ids":["https://openalex.org/I19820366"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100531920","display_name":"Xiubin Fan","orcid":null},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210128818","display_name":"Institute of Software","ror":"https://ror.org/033dfsn42","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210128818"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiubin Fan","raw_affiliation_strings":["State Key Laboratory of Information Security, Institute of Software, Chinese Academy of Sciences, Beijing, 100190, China","Chinese Academy of Sciences"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"State Key Laboratory of Information Security, Institute of Software, Chinese Academy of Sciences, Beijing, 100190, China","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210128818"]},{"raw_affiliation_string":"Chinese Academy of Sciences","institution_ids":["https://openalex.org/I19820366"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072918787","display_name":"Liping Ding","orcid":"https://orcid.org/0000-0002-3793-9519"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210128818","display_name":"Institute of Software","ror":"https://ror.org/033dfsn42","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210128818"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Liping Ding","raw_affiliation_strings":["Institute of Software, Chinese Academy of Sciences, Beijing, 100190, China","Chinese Academy of Sciences"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Software, Chinese Academy of Sciences, Beijing, 100190, China","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210128818"]},{"raw_affiliation_string":"Chinese Academy of Sciences","institution_ids":["https://openalex.org/I19820366"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5041420293","display_name":"Zhangyi Wang","orcid":"https://orcid.org/0000-0001-6370-8848"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210128818","display_name":"Institute of Software","ror":"https://ror.org/033dfsn42","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210128818"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhangyi Wang","raw_affiliation_strings":["Institute of Software, Chinese Academy of Sciences, Beijing, 100190, China","Chinese Academy of Sciences"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Software, Chinese Academy of Sciences, Beijing, 100190, China","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210128818"]},{"raw_affiliation_string":"Chinese Academy of Sciences","institution_ids":["https://openalex.org/I19820366"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5101790997"],"corresponding_institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210128818"],"apc_list":{"value":3090,"currency":"USD","value_usd":3090},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.09555717,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"25","issue":"6","first_page":"1215","last_page":"1222"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13720","display_name":"Benford\u2019s Law and Fraud Detection","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T13720","display_name":"Benford\u2019s Law and Fraud Detection","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T11130","display_name":"Coding theory and cryptography","score":0.98580002784729,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11166","display_name":"Analytic Number Theory Research","score":0.9853000044822693,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.9349037408828735},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6521284580230713},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.6333520412445068},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5678181648254395},{"id":"https://openalex.org/keywords/collatz-conjecture","display_name":"Collatz conjecture","score":0.46817606687545776},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3562473952770233}],"concepts":[{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.9349037408828735},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6521284580230713},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.6333520412445068},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5678181648254395},{"id":"https://openalex.org/C128814272","wikidata":"https://www.wikidata.org/wiki/Q837314","display_name":"Collatz conjecture","level":3,"score":0.46817606687545776},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3562473952770233},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s11424-012-0280-5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11424-012-0280-5","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W43767022","https://openalex.org/W344029587","https://openalex.org/W790580293","https://openalex.org/W837172158","https://openalex.org/W995303445","https://openalex.org/W1044799907","https://openalex.org/W1555475515","https://openalex.org/W2075095499","https://openalex.org/W2076882011","https://openalex.org/W2083700790","https://openalex.org/W2117023484","https://openalex.org/W2162335506","https://openalex.org/W4246319563","https://openalex.org/W4302383489"],"related_works":["https://openalex.org/W2950288113","https://openalex.org/W1782528665","https://openalex.org/W4291209671","https://openalex.org/W2100234888","https://openalex.org/W1973978937","https://openalex.org/W2097887535","https://openalex.org/W2163633449","https://openalex.org/W4213178788","https://openalex.org/W4283323077","https://openalex.org/W3039346985"],"abstract_inverted_index":null,"counts_by_year":[{"year":2022,"cited_by_count":1}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}