{"id":"https://openalex.org/W2809825377","doi":"https://doi.org/10.1007/s00454-019-00169-9","title":"On the Carath\u00e9odory Number for Strong Convexity","display_name":"On the Carath\u00e9odory Number for Strong Convexity","publication_year":2020,"publication_date":"2020-01-17","ids":{"openalex":"https://openalex.org/W2809825377","doi":"https://doi.org/10.1007/s00454-019-00169-9","mag":"2809825377"},"language":"en","primary_location":{"id":"doi:10.1007/s00454-019-00169-9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00454-019-00169-9","pdf_url":null,"source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"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":"Discrete &amp; Computational Geometry","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1806.10937","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Vuong Bui","orcid":null},"institutions":[{"id":"https://openalex.org/I153845743","display_name":"Moscow Institute of Physics and Technology","ror":"https://ror.org/00v0z9322","country_code":"RU","type":"education","lineage":["https://openalex.org/I153845743"]},{"id":"https://openalex.org/I75951250","display_name":"Freie Universit\u00e4t Berlin","ror":"https://ror.org/046ak2485","country_code":"DE","type":"education","lineage":["https://openalex.org/I75951250"]}],"countries":["DE","RU"],"is_corresponding":true,"raw_author_name":"Vuong Bui","raw_affiliation_strings":["Institut f\u00fcr Informatik, Freie Universit\u00e4t Berlin, Takustra\u00dfe 9, 14195, Berlin, Germany","Moscow Institute of Physics and Technology, Institutskiy per. 9, Dolgoprudny, Russia, 141700"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Informatik, Freie Universit\u00e4t Berlin, Takustra\u00dfe 9, 14195, Berlin, Germany","institution_ids":["https://openalex.org/I75951250"]},{"raw_affiliation_string":"Moscow Institute of Physics and Technology, Institutskiy per. 9, Dolgoprudny, Russia, 141700","institution_ids":["https://openalex.org/I153845743"]}]},{"author_position":"last","author":{"id":null,"display_name":"Roman Karasev","orcid":"https://orcid.org/0000-0002-6695-3168"},"institutions":[{"id":"https://openalex.org/I153845743","display_name":"Moscow Institute of Physics and Technology","ror":"https://ror.org/00v0z9322","country_code":"RU","type":"education","lineage":["https://openalex.org/I153845743"]},{"id":"https://openalex.org/I4210107660","display_name":"Institute for Information Transmission Problems","ror":"https://ror.org/013w2d378","country_code":"RU","type":"facility","lineage":["https://openalex.org/I4210107660"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Roman Karasev","raw_affiliation_strings":["Institute for Information Transmission Problems RAS, Bolshoy Karetny per. 19, Moscow, Russia, 127994","Moscow Institute of Physics and Technology, Institutskiy per. 9, Dolgoprudny, Russia, 141700"],"raw_orcid":"https://orcid.org/0000-0002-6695-3168","affiliations":[{"raw_affiliation_string":"Institute for Information Transmission Problems RAS, Bolshoy Karetny per. 19, Moscow, Russia, 127994","institution_ids":["https://openalex.org/I4210107660"]},{"raw_affiliation_string":"Moscow Institute of Physics and Technology, Institutskiy per. 9, Dolgoprudny, Russia, 141700","institution_ids":["https://openalex.org/I153845743"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I153845743","https://openalex.org/I75951250"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00660819,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"65","issue":"3","first_page":"680","last_page":"692"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11830","display_name":"Point processes and geometric inequalities","score":0.7245000004768372,"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/T11830","display_name":"Point processes and geometric inequalities","score":0.7245000004768372,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.07020000368356705,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.05979999899864197,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.8216000199317932},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5317999720573425},{"id":"https://openalex.org/keywords/minkowski-space","display_name":"Minkowski space","score":0.5091999769210815},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.38339999318122864},{"id":"https://openalex.org/keywords/convex-body","display_name":"Convex body","score":0.3749000132083893},{"id":"https://openalex.org/keywords/minkowskis-theorem","display_name":"Minkowski's theorem","score":0.3652999997138977}],"concepts":[{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.8216000199317932},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8007000088691711},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5317999720573425},{"id":"https://openalex.org/C79464548","wikidata":"https://www.wikidata.org/wiki/Q464794","display_name":"Minkowski space","level":2,"score":0.5091999769210815},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.44440001249313354},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4196999967098236},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.38339999318122864},{"id":"https://openalex.org/C134912446","wikidata":"https://www.wikidata.org/wiki/Q5166516","display_name":"Convex body","level":4,"score":0.3749000132083893},{"id":"https://openalex.org/C79013991","wikidata":"https://www.wikidata.org/wiki/Q1097021","display_name":"Minkowski's theorem","level":3,"score":0.3652999997138977},{"id":"https://openalex.org/C136719777","wikidata":"https://www.wikidata.org/wiki/Q3610230","display_name":"Logarithmically convex function","level":5,"score":0.3447999954223633},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2921000123023987},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.2773999869823456},{"id":"https://openalex.org/C10233890","wikidata":"https://www.wikidata.org/wiki/Q1322294","display_name":"Minkowski addition","level":3,"score":0.267300009727478},{"id":"https://openalex.org/C49870271","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex set","level":4,"score":0.267300009727478},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2531000077724457},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.25290000438690186}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s00454-019-00169-9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00454-019-00169-9","pdf_url":null,"source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"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":"Discrete &amp; Computational Geometry","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1806.10937","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1806.10937","pdf_url":"https://arxiv.org/pdf/1806.10937","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1806.10937","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1806.10937","pdf_url":"https://arxiv.org/pdf/1806.10937","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G353943477","display_name":null,"funder_award_id":"18-01-00036","funder_id":"https://openalex.org/F4320321079","funder_display_name":"Russian Foundation for Basic Research"},{"id":"https://openalex.org/G4452723411","display_name":null,"funder_award_id":"19-01-00169","funder_id":"https://openalex.org/F4320321079","funder_display_name":"Russian Foundation for Basic Research"}],"funders":[{"id":"https://openalex.org/F4320321079","display_name":"Russian Foundation for Basic Research","ror":"https://ror.org/02mh1ke95"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W136694183","https://openalex.org/W1540748742","https://openalex.org/W1983127118","https://openalex.org/W1987073789","https://openalex.org/W2003216288","https://openalex.org/W2021394078","https://openalex.org/W2021395899","https://openalex.org/W2036757119","https://openalex.org/W2041308664","https://openalex.org/W2055554649","https://openalex.org/W2133926195","https://openalex.org/W2300651462","https://openalex.org/W2335433420","https://openalex.org/W2504636406","https://openalex.org/W2911873805"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2018-07-10T00:00:00"}
