{"id":"https://openalex.org/W2043715507","doi":"https://doi.org/10.1142/s0218127409023007","title":"HERMAN RINGS OF BLASCHKE PRODUCTS OF DEGREE 3","display_name":"HERMAN RINGS OF BLASCHKE PRODUCTS OF DEGREE 3","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W2043715507","doi":"https://doi.org/10.1142/s0218127409023007","mag":"2043715507"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127409023007","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127409023007","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","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/A5037615096","display_name":"Yoshihisa Fujimoto","orcid":null},"institutions":[{"id":"https://openalex.org/I16656306","display_name":"Meiji University","ror":"https://ror.org/02rqvrp93","country_code":"JP","type":"education","lineage":["https://openalex.org/I16656306"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"YOSHIHISA FUJIMOTO","raw_affiliation_strings":["School of Business and Administration, Meiji University, 1-9-1 Eifuku, Suginamiku, Tokyo, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Business and Administration, Meiji University, 1-9-1 Eifuku, Suginamiku, Tokyo, Japan","institution_ids":["https://openalex.org/I16656306"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5037615096"],"corresponding_institution_ids":["https://openalex.org/I16656306"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.1289123,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"19","issue":"01","first_page":"445","last_page":"451"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9952999949455261,"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"}},"topics":[{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9952999949455261,"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/T11703","display_name":"Rings, Modules, and Algebras","score":0.9764000177383423,"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/T11567","display_name":"semigroups and automata theory","score":0.9714000225067139,"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":0.7613362073898315},{"id":"https://openalex.org/keywords/irrational-number","display_name":"Irrational number","score":0.7113116383552551},{"id":"https://openalex.org/keywords/blaschke-product","display_name":"Blaschke product","score":0.6900292038917542},{"id":"https://openalex.org/keywords/ring","display_name":"Ring (chemistry)","score":0.6485065817832947},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.46272388100624084},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.45632317662239075},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.4501854181289673},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.44004905223846436},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4144347608089447},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.40253615379333496},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3884725868701935},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08206212520599365},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07951554656028748},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07855191826820374}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7613362073898315},{"id":"https://openalex.org/C94931360","wikidata":"https://www.wikidata.org/wiki/Q607728","display_name":"Irrational number","level":2,"score":0.7113116383552551},{"id":"https://openalex.org/C61518182","wikidata":"https://www.wikidata.org/wiki/Q4380191","display_name":"Blaschke product","level":2,"score":0.6900292038917542},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.6485065817832947},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.46272388100624084},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.45632317662239075},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.4501854181289673},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.44004905223846436},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4144347608089447},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.40253615379333496},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3884725868701935},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08206212520599365},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07951554656028748},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07855191826820374},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","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/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127409023007","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127409023007","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","score":0.46000000834465027,"display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W41873585","https://openalex.org/W172293542","https://openalex.org/W2059697367","https://openalex.org/W2067710345","https://openalex.org/W2600224051","https://openalex.org/W4210689425","https://openalex.org/W4232709242","https://openalex.org/W4251981560"],"related_works":["https://openalex.org/W3088646517","https://openalex.org/W2973552040","https://openalex.org/W2185277279","https://openalex.org/W4220768180","https://openalex.org/W2377639682","https://openalex.org/W2792087242","https://openalex.org/W2387799803","https://openalex.org/W3100817393","https://openalex.org/W3120892761","https://openalex.org/W2797611542"],"abstract_inverted_index":{"Let":[0],"F":[1,10,52],"a,\u03bb":[2,11],"be":[3],"the":[4,8,27,64,79,93],"Blaschke":[5],"product":[6],"of":[7,63,95,108],"form":[9],"=":[12,84],"\u03bbz":[13],"2":[14],"((z":[15],"-":[16,18],"a)/(1":[17],"\u0101z))":[19],"and":[20,45,58,97],"\u03b1":[21,36],"denote":[22],"an":[23,55],"irrational":[24,109],"number":[25],"satisfying":[26],"Brjuno":[28],"condition.":[29],"Henriksen":[30],"[1997]":[31],"showed":[32],"that":[33,51,60,78,103],"for":[34,104],"any":[35],"there":[37],"exists":[38],"a":[39,41,46,70,72,82,105,112],"constant":[40],"0":[42,68,73,83,113],"\u2267":[43],"3":[44,85],"continuous":[47],"function":[48],"\u03bb(a)":[49],"such":[50],"a,\u03bb(a)":[53],"possesses":[54],"Herman":[56,65],"ring":[57,66],"also":[59],"modulus":[61],"M(a)":[62],"approaches":[67,71],"as":[69],".":[74],"It":[75],"is":[76,89,114],"remarked":[77],"question":[80],"whether":[81],"holds":[86],"or":[87],"not":[88],"open.":[90],"According":[91],"to":[92],"idea":[94],"Fagella":[96],"Geyer":[98],"[2003]":[99],"we":[100],"can":[101],"show":[102],"certain":[106],"set":[107],"rotation":[110],"numbers,":[111],"strictly":[115],"larger":[116],"than":[117],"3.":[118]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
