{"id":"https://openalex.org/W4288054960","doi":"https://doi.org/10.1007/s10957-026-03041-y","title":"Blaschke and Separation Theorems for Orthogonal Convex Sets and Some Applications","display_name":"Blaschke and Separation Theorems for Orthogonal Convex Sets and Some Applications","publication_year":2026,"publication_date":"2026-06-18","ids":{"openalex":"https://openalex.org/W4288054960","doi":"https://doi.org/10.1007/s10957-026-03041-y"},"language":"en","primary_location":{"id":"doi:10.1007/s10957-026-03041-y","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10957-026-03041-y","pdf_url":null,"source":{"id":"https://openalex.org/S52430896","display_name":"Journal of Optimization Theory and Applications","issn_l":"0022-3239","issn":["0022-3239","1573-2878"],"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 Optimization Theory and Applications","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2207.11973","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5060713170","display_name":"Nguyen Thi Le","orcid":"https://orcid.org/0000-0002-7880-6624"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Nguyen Thi Le","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Phan Thanh An","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Phan Thanh An","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":3190,"currency":"USD","value_usd":3190},"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00254662,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"210","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.97079998254776,"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"}},"topics":[{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.97079998254776,"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"}},{"id":"https://openalex.org/T11830","display_name":"Point processes and geometric inequalities","score":0.9585000276565552,"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/intersection","display_name":"Intersection (aeronautics)","score":0.6470327973365784},{"id":"https://openalex.org/keywords/convex-set","display_name":"Convex set","score":0.6241660118103027},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.608216404914856},{"id":"https://openalex.org/keywords/convex-analysis","display_name":"Convex analysis","score":0.5972780585289001},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5301350355148315},{"id":"https://openalex.org/keywords/convex-combination","display_name":"Convex combination","score":0.4810805022716522},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.4713674783706665},{"id":"https://openalex.org/keywords/convex-hull","display_name":"Convex hull","score":0.47021034359931946},{"id":"https://openalex.org/keywords/subderivative","display_name":"Subderivative","score":0.4625534117221832},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4510178565979004},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.4495566487312317},{"id":"https://openalex.org/keywords/separation","display_name":"Separation (statistics)","score":0.4165421426296234},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.35500237345695496},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.3486180901527405},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.22448033094406128},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.20419663190841675},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.20064592361450195},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.07264646887779236}],"concepts":[{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.6470327973365784},{"id":"https://openalex.org/C49870271","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex set","level":4,"score":0.6241660118103027},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.608216404914856},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.5972780585289001},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5301350355148315},{"id":"https://openalex.org/C111110010","wikidata":"https://www.wikidata.org/wiki/Q2627315","display_name":"Convex combination","level":4,"score":0.4810805022716522},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.4713674783706665},{"id":"https://openalex.org/C206194317","wikidata":"https://www.wikidata.org/wiki/Q1138624","display_name":"Convex hull","level":3,"score":0.47021034359931946},{"id":"https://openalex.org/C200661725","wikidata":"https://www.wikidata.org/wiki/Q289500","display_name":"Subderivative","level":4,"score":0.4625534117221832},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4510178565979004},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.4495566487312317},{"id":"https://openalex.org/C2776061190","wikidata":"https://www.wikidata.org/wiki/Q7451805","display_name":"Separation (statistics)","level":2,"score":0.4165421426296234},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.35500237345695496},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3486180901527405},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.22448033094406128},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.20419663190841675},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.20064592361450195},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.07264646887779236},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s10957-026-03041-y","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10957-026-03041-y","pdf_url":null,"source":{"id":"https://openalex.org/S52430896","display_name":"Journal of Optimization Theory and Applications","issn_l":"0022-3239","issn":["0022-3239","1573-2878"],"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 Optimization Theory and Applications","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2207.11973","is_oa":true,"landing_page_url":"https://arxiv.org/abs/2207.11973","pdf_url":"https://arxiv.org/pdf/2207.11973","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2207.11973","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2207.11973","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2207.11973","is_oa":true,"landing_page_url":"https://arxiv.org/abs/2207.11973","pdf_url":"https://arxiv.org/pdf/2207.11973","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11","score":0.6600000262260437}],"awards":[],"funders":[{"id":"https://openalex.org/F4320326592","display_name":"Viet Nam National University Ho Chi Minh City","ror":"https://ror.org/00waaqh38"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4288054960.pdf","grobid_xml":"https://content.openalex.org/works/W4288054960.grobid-xml"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W3092256677","https://openalex.org/W4303982821","https://openalex.org/W3092768451","https://openalex.org/W2008950554","https://openalex.org/W7132855595","https://openalex.org/W2004570919","https://openalex.org/W2083269131","https://openalex.org/W4281297356","https://openalex.org/W1966214606","https://openalex.org/W2609231990","https://openalex.org/W2012357692","https://openalex.org/W2017227406","https://openalex.org/W2965622787","https://openalex.org/W2016037484","https://openalex.org/W2065065327","https://openalex.org/W2070165907","https://openalex.org/W1966720998","https://openalex.org/W4301171592","https://openalex.org/W1993029499","https://openalex.org/W2015783949","https://openalex.org/W1973628836","https://openalex.org/W1992508337"],"related_works":["https://openalex.org/W868123585","https://openalex.org/W2026600343","https://openalex.org/W2374624997","https://openalex.org/W2133925519","https://openalex.org/W2356261519","https://openalex.org/W4382519084","https://openalex.org/W2478309485","https://openalex.org/W2913596570","https://openalex.org/W2002037426","https://openalex.org/W3092518081"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-08-29T07:29:34.045763","created_date":"2022-07-28T00:00:00"}