{"id":"https://openalex.org/W4415360804","doi":"https://doi.org/10.4213/sm10188e","title":"Density functions with respect to a model growth function","display_name":"Density functions with respect to a model growth function","publication_year":2025,"publication_date":"2025-01-01","ids":{"openalex":"https://openalex.org/W4415360804","doi":"https://doi.org/10.4213/sm10188e"},"language":"en","primary_location":{"id":"doi:10.4213/sm10188e","doi":"https://doi.org/10.4213/sm10188e","is_oa":true,"landing_page_url":"https://doi.org/10.4213/sm10188e","pdf_url":"https://www.mathnet.ru/php/getFT.phtml?jrnid=sm&paperid=10188&what=fullteng&option_lang=eng","source":{"id":"https://openalex.org/S89900327","display_name":"Sbornik Mathematics","issn_l":"1064-5616","issn":["1064-5616","1468-4802"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-1","norway-1","poland-70","russia-white-list-1"],"host_organization":"https://openalex.org/P4310320083","host_organization_name":"IOP Publishing","host_organization_lineage":["https://openalex.org/P4310320083","https://openalex.org/P4310311669"],"host_organization_lineage_names":["IOP Publishing","Institute of Physics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Sbornik: Mathematics","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.mathnet.ru/php/getFT.phtml?jrnid=sm&paperid=10188&what=fullteng&option_lang=eng","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5073830589","display_name":"\u041c\u0438\u0445\u0430\u0438\u043b \u0412\u043b\u0430\u0434\u0438\u043c\u0438\u0440\u043e\u0432\u0438\u0447 \u041a\u0430\u0431\u0430\u043d\u043a\u043e","orcid":"https://orcid.org/0000-0002-9537-3699","observed_orcids":["https://orcid.org/0000-0002-9537-3699"]},"institutions":[{"id":"https://openalex.org/I140141371","display_name":"Kursk State University","ror":"https://ror.org/05yjqdn82","country_code":"RU","type":"education","lineage":["https://openalex.org/I140141371"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Mikhail Vladimirovich Kabanko","raw_affiliation_strings":["Faculty of Physics, Mathematics, Computer Science, Kursk State University, Kursk, Russia"],"raw_orcid":"https://orcid.org/0000-0002-9537-3699","affiliations":[{"raw_affiliation_string":"Faculty of Physics, Mathematics, Computer Science, Kursk State University, Kursk, Russia","institution_ids":["https://openalex.org/I140141371"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073823623","display_name":"Konstantin Gennadyevich Malyutin","orcid":"https://orcid.org/0000-0001-5480-0722","observed_orcids":["https://orcid.org/0000-0001-5480-0722"]},"institutions":[{"id":"https://openalex.org/I140141371","display_name":"Kursk State University","ror":"https://ror.org/05yjqdn82","country_code":"RU","type":"education","lineage":["https://openalex.org/I140141371"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Konstantin Gennadyevich Malyutin","raw_affiliation_strings":["Faculty of Physics, Mathematics, Computer Science, Kursk State University, Kursk, Russia"],"raw_orcid":"https://orcid.org/0000-0001-5480-0722","affiliations":[{"raw_affiliation_string":"Faculty of Physics, Mathematics, Computer Science, Kursk State University, Kursk, Russia","institution_ids":["https://openalex.org/I140141371"]}]},{"author_position":"last","author":{"id":null,"display_name":"Taisiya Ivanovna Malyutina","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I140141371","display_name":"Kursk State University","ror":"https://ror.org/05yjqdn82","country_code":"RU","type":"education","lineage":["https://openalex.org/I140141371"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Taisiya Ivanovna Malyutina","raw_affiliation_strings":["Faculty of Physics, Mathematics, Computer Science, Kursk State University, Kursk, Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Physics, Mathematics, Computer Science, Kursk State University, Kursk, Russia","institution_ids":["https://openalex.org/I140141371"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I140141371"],"apc_list":null,"apc_paid":null,"fwci":0.603,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.51140491,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"216","issue":"12","first_page":"1664","last_page":"1692"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12812","display_name":"Meromorphic and Entire Functions","score":0.9336000084877014,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T12812","display_name":"Meromorphic and Entire Functions","score":0.9336000084877014,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T11166","display_name":"Analytic Number Theory Research","score":0.04230000078678131,"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/T12062","display_name":"Approximation Theory and Sequence Spaces","score":0.006099999882280827,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/density-function","display_name":"density function","score":0.9169999957084656},{"id":"https://openalex.org/keywords/additive-functions","display_name":"additive functions","score":0.6740000247955322},{"id":"https://openalex.org/keywords/lower-density","display_name":"lower density","score":0.847000002861023},{"id":"https://openalex.org/keywords/upper-density","display_name":"upper density","score":0.6370000243186951},{"id":"https://openalex.org/keywords/polya-s-theorem","display_name":"P\u00f3lya's theorem","score":0.9020000100135803}],"concepts":[{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.19949999451637268},{"id":"https://openalex.org/C116834253","wikidata":"https://www.wikidata.org/wiki/Q2039217","display_name":"Identification (biology)","level":2,"score":0.19539999961853027},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.19169999659061432},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.18780000507831573},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.1860000044107437},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.1687999963760376},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.1662999987602234},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.16359999775886536},{"id":"https://openalex.org/C2776608160","wikidata":"https://www.wikidata.org/wiki/Q4785462","display_name":"Natural (archaeology)","level":2,"score":0.15790000557899475},{"id":"https://openalex.org/C81917197","wikidata":"https://www.wikidata.org/wiki/Q628760","display_name":"Selection (genetic algorithm)","level":2,"score":0.1573999971151352}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.4213/sm10188e","doi":"https://doi.org/10.4213/sm10188e","is_oa":true,"landing_page_url":"https://doi.org/10.4213/sm10188e","pdf_url":"https://www.mathnet.ru/php/getFT.phtml?jrnid=sm&paperid=10188&what=fullteng&option_lang=eng","source":{"id":"https://openalex.org/S89900327","display_name":"Sbornik Mathematics","issn_l":"1064-5616","issn":["1064-5616","1468-4802"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-1","norway-1","poland-70","russia-white-list-1"],"host_organization":"https://openalex.org/P4310320083","host_organization_name":"IOP Publishing","host_organization_lineage":["https://openalex.org/P4310320083","https://openalex.org/P4310311669"],"host_organization_lineage_names":["IOP Publishing","Institute of Physics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Sbornik: Mathematics","raw_type":"journal-article"},{"id":"doi:10.4213/sm10188","doi":"https://doi.org/10.4213/sm10188","is_oa":false,"landing_page_url":"https://doi.org/10.4213/sm10188","pdf_url":null,"source":{"id":"https://openalex.org/S4210187849","display_name":"\u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0439 \u0441\u0431\u043e\u0440\u043d\u0438\u043a","issn_l":"0368-8666","issn":["0368-8666","2305-2783"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":["russia-white-list-1"],"host_organization":"https://openalex.org/P4310312733","host_organization_name":"Moscow Mathematical Society","host_organization_lineage":["https://openalex.org/P4310312733"],"host_organization_lineage_names":["Moscow Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"\u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0439 \u0441\u0431\u043e\u0440\u043d\u0438\u043a","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.4213/sm10188e","doi":"https://doi.org/10.4213/sm10188e","is_oa":true,"landing_page_url":"https://doi.org/10.4213/sm10188e","pdf_url":"https://www.mathnet.ru/php/getFT.phtml?jrnid=sm&paperid=10188&what=fullteng&option_lang=eng","source":{"id":"https://openalex.org/S89900327","display_name":"Sbornik Mathematics","issn_l":"1064-5616","issn":["1064-5616","1468-4802"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-1","norway-1","poland-70","russia-white-list-1"],"host_organization":"https://openalex.org/P4310320083","host_organization_name":"IOP Publishing","host_organization_lineage":["https://openalex.org/P4310320083","https://openalex.org/P4310311669"],"host_organization_lineage_names":["IOP Publishing","Institute of Physics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Sbornik: Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G4895159231","display_name":null,"funder_award_id":"24-21-00006","funder_id":"https://openalex.org/F4320324099","funder_display_name":"Russian Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320324099","display_name":"Russian Science Foundation","ror":"https://ror.org/03y2gwe85"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4415360804.pdf","grobid_xml":"https://content.openalex.org/works/W4415360804.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W627954411","https://openalex.org/W817595593","https://openalex.org/W2027719260","https://openalex.org/W2078860713","https://openalex.org/W2154886869","https://openalex.org/W2523218725","https://openalex.org/W2657334474","https://openalex.org/W2914656778","https://openalex.org/W4206769493","https://openalex.org/W4245336091","https://openalex.org/W4395087314","https://openalex.org/W4396799392"],"related_works":["https://openalex.org/W7128631583","https://openalex.org/W4408620886","https://openalex.org/W2319969583","https://openalex.org/W7113333737","https://openalex.org/W2320034932","https://openalex.org/W893372728","https://openalex.org/W7007083665","https://openalex.org/W7025691299","https://openalex.org/W2329801251","https://openalex.org/W2728815842"],"abstract_inverted_index":{"The":[0,20,52,102],"properties":[1,67,104],"of":[2,22,24,54,68,79,82,91,105,120,134,140,149,163],"general":[3],"density":[4,84,88,168],"functions":[5,17,70,74,109,164,169],"with":[6,27,48,57,110],"respect":[7,28,49,58,111],"to":[8,29,50,59,112,145],"a":[9,45,77,92,125,146],"model":[10,31,114,158],"growth":[11,26,32,47,152,159],"function":[12,23,33,42,56,93,115,160],"$M$":[13,34,60,116],"and":[14,64,86,107,142,166],"related":[15],"semiadditive":[16],"are":[18,71,75,117,170],"discussed.":[19],"concept":[21,53],"slow":[25,46],"the":[30,41,65,80,83,113,121,138],"is":[35,38,61,95,100,124,153],"introduced;":[36],"it":[37],"shown":[39],"that":[40,127],"$L(r)=M^{-\\rho}(r)V(r))$":[43],"has":[44],"$M$.":[51,161],"$\\rho$-semiadditive":[55,108],"also":[62],"introduced,":[63],"main":[66,103],"such":[69],"established.":[72],"Density":[73],"studied;":[76],"criterion":[78],"continuity":[81],"$N_M(\\alpha)$":[85],"lower":[87],"$\\underline":[89],"N_M(\\alpha)$":[90],"$f$":[94,165],"obtained.":[96],"A":[97],"uniformity":[98],"theorem":[99,126,136],"proved.":[101],"$\\rho$-additive":[106],"presented.":[118,171],"One":[119],"central":[122],"results":[123],"can":[128],"be":[129],"viewed":[130],"as":[131],"an":[132,156],"extension":[133],"Po\u0301lya's":[135],"on":[137],"existence":[139],"minimal":[141],"maximal":[143],"densities":[144],"wider":[147],"class":[148],"functions,":[150],"whose":[151],"bounded":[154],"by":[155],"arbitrary":[157],"Examples":[162],"their":[167],"Bibliography:":[172],"17":[173],"titles.":[174]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2025-10-21T00:00:00"}