{"id":"https://openalex.org/W2014662707","doi":"https://doi.org/10.1016/s0885-064x(02)00005-5","title":"Probabilistic and average linear widths of Sobolev space with Gaussian measure","display_name":"Probabilistic and average linear widths of Sobolev space with Gaussian measure","publication_year":2003,"publication_date":"2003-01-30","ids":{"openalex":"https://openalex.org/W2014662707","doi":"https://doi.org/10.1016/s0885-064x(02)00005-5","mag":"2014662707"},"language":"en","primary_location":{"id":"doi:10.1016/s0885-064x(02)00005-5","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0885-064x(02)00005-5","pdf_url":null,"source":{"id":"https://openalex.org/S42286584","display_name":"Journal of Complexity","issn_l":"0885-064X","issn":["0885-064X","1090-2708"],"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":"Journal of 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/A5051724745","display_name":"Fang Gensun","orcid":null},"institutions":[{"id":"https://openalex.org/I25254941","display_name":"Beijing Normal University","ror":"https://ror.org/022k4wk35","country_code":"CN","type":"education","lineage":["https://openalex.org/I25254941"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Fang Gensun","raw_affiliation_strings":["Department of Mathematics,Beijing Normal University,Beijing 100875,China)"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics,Beijing Normal University,Beijing 100875,China)","institution_ids":["https://openalex.org/I25254941"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5010523186","display_name":"Peixin Ye","orcid":"https://orcid.org/0000-0002-4706-3223"},"institutions":[{"id":"https://openalex.org/I25254941","display_name":"Beijing Normal University","ror":"https://ror.org/022k4wk35","country_code":"CN","type":"education","lineage":["https://openalex.org/I25254941"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ye Peixin","raw_affiliation_strings":["Department of Mathematics,Beijing Normal University,Beijing 100875,China)"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics,Beijing Normal University,Beijing 100875,China)","institution_ids":["https://openalex.org/I25254941"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5051724745"],"corresponding_institution_ids":["https://openalex.org/I25254941"],"apc_list":{"value":2200,"currency":"USD","value_usd":2200},"apc_paid":null,"fwci":2.1701,"has_fulltext":false,"cited_by_count":28,"citation_normalized_percentile":{"value":0.86530612,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"19","issue":"1","first_page":"73","last_page":"84"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12404","display_name":"Mathematical Approximation and Integration","score":0.9951000213623047,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T12404","display_name":"Mathematical Approximation and Integration","score":0.9951000213623047,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9776999950408936,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11830","display_name":"Point processes and geometric inequalities","score":0.9538999795913696,"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/mathematics","display_name":"Mathematics","score":0.8025761842727661},{"id":"https://openalex.org/keywords/sobolev-space","display_name":"Sobolev space","score":0.7761132717132568},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.700037956237793},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.6452203392982483},{"id":"https://openalex.org/keywords/gaussian-measure","display_name":"Gaussian measure","score":0.5740548372268677},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.5402194857597351},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4808419644832611},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.36405062675476074},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.35600924491882324},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.32685720920562744},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.23762795329093933},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.095807284116745},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07650390267372131}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8025761842727661},{"id":"https://openalex.org/C99730327","wikidata":"https://www.wikidata.org/wiki/Q1501536","display_name":"Sobolev space","level":2,"score":0.7761132717132568},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.700037956237793},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.6452203392982483},{"id":"https://openalex.org/C2777630202","wikidata":"https://www.wikidata.org/wiki/Q5527840","display_name":"Gaussian measure","level":3,"score":0.5740548372268677},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5402194857597351},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4808419644832611},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.36405062675476074},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.35600924491882324},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.32685720920562744},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.23762795329093933},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.095807284116745},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07650390267372131},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1016/s0885-064x(02)00005-5","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0885-064x(02)00005-5","pdf_url":null,"source":{"id":"https://openalex.org/S42286584","display_name":"Journal of Complexity","issn_l":"0885-064X","issn":["0885-064X","1090-2708"],"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":"Journal of Complexity","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.576.8774","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.576.8774","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://math.bnu.edu.cn/~fanggs/papers/fy4pre.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W361765212","https://openalex.org/W1168782874","https://openalex.org/W1480774962","https://openalex.org/W1583497601","https://openalex.org/W1598589417","https://openalex.org/W2004485838","https://openalex.org/W2028230285","https://openalex.org/W2030550240","https://openalex.org/W2032241300","https://openalex.org/W2070221980","https://openalex.org/W2078561759","https://openalex.org/W2116932878","https://openalex.org/W2137224975","https://openalex.org/W2160858274","https://openalex.org/W3021898623","https://openalex.org/W4299521717","https://openalex.org/W4301425558","https://openalex.org/W6658446460"],"related_works":["https://openalex.org/W1978391200","https://openalex.org/W2093451591","https://openalex.org/W2092426748","https://openalex.org/W2952469878","https://openalex.org/W2070221980","https://openalex.org/W3143702020","https://openalex.org/W2011691693","https://openalex.org/W4297806059","https://openalex.org/W1841698145","https://openalex.org/W3089991925"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}