{"id":"https://openalex.org/W1488784459","doi":"https://doi.org/10.1007/978-3-540-70666-3_23","title":"Reconfirmation of Two Results on Disjoint Empty Convex Polygons","display_name":"Reconfirmation of Two Results on Disjoint Empty Convex Polygons","publication_year":2007,"publication_date":"2007-06-26","ids":{"openalex":"https://openalex.org/W1488784459","doi":"https://doi.org/10.1007/978-3-540-70666-3_23","mag":"1488784459"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-540-70666-3_23","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-540-70666-3_23","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"conference-paper","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/A5070293387","display_name":"Liping Wu","orcid":"https://orcid.org/0000-0002-3416-6645"},"institutions":[{"id":"https://openalex.org/I43337087","display_name":"Hebei University","ror":"https://ror.org/01p884a79","country_code":"CN","type":"education","lineage":["https://openalex.org/I43337087"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Liping Wu","raw_affiliation_strings":["College of Physical Science and Technology, Hebei University, Baoding 071002, China","College of Physical Science and Technology, Hebei University, baoding, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Physical Science and Technology, Hebei University, Baoding 071002, China","institution_ids":["https://openalex.org/I43337087"]},{"raw_affiliation_string":"College of Physical Science and Technology, Hebei University, baoding, China","institution_ids":["https://openalex.org/I43337087"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5068866876","display_name":"\u0420\u0435\u043d \u0414\u0438\u043d\u0433","orcid":null},"institutions":[{"id":"https://openalex.org/I94611258","display_name":"Hebei Normal University","ror":"https://ror.org/004rbbw49","country_code":"CN","type":"education","lineage":["https://openalex.org/I94611258"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ren Ding","raw_affiliation_strings":["College of Mathematics, Hebei Normal University, Shijiazhuang, 050016, China","College of Mathematics, Hebei Normal University, Shijiazhuang, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mathematics, Hebei Normal University, Shijiazhuang, 050016, China","institution_ids":["https://openalex.org/I94611258"]},{"raw_affiliation_string":"College of Mathematics, Hebei Normal University, Shijiazhuang, China","institution_ids":["https://openalex.org/I94611258"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"216","last_page":"220"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11830","display_name":"Point processes and geometric inequalities","score":0.9819999933242798,"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":0.9819999933242798,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9146999716758728,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/T12508","display_name":"Functional Equations Stability Results","score":0.9057999849319458,"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/combinatorics","display_name":"Combinatorics","score":0.8489818572998047},{"id":"https://openalex.org/keywords/convex-hull","display_name":"Convex hull","score":0.7909338474273682},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.7586808800697327},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.6557669043540955},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6327461004257202},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.48487576842308044},{"id":"https://openalex.org/keywords/convex-set","display_name":"Convex set","score":0.47263428568840027},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.16865107417106628},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.14837199449539185}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8489818572998047},{"id":"https://openalex.org/C206194317","wikidata":"https://www.wikidata.org/wiki/Q1138624","display_name":"Convex hull","level":3,"score":0.7909338474273682},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.7586808800697327},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.6557669043540955},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6327461004257202},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.48487576842308044},{"id":"https://openalex.org/C49870271","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex set","level":4,"score":0.47263428568840027},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.16865107417106628},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.14837199449539185}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-540-70666-3_23","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-540-70666-3_23","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W134663479","https://openalex.org/W1487872891","https://openalex.org/W1561962265","https://openalex.org/W1970934335","https://openalex.org/W1977266879","https://openalex.org/W2007033927","https://openalex.org/W2152525037","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2374624997","https://openalex.org/W2363904277","https://openalex.org/W868123585","https://openalex.org/W2578380588","https://openalex.org/W4386395423","https://openalex.org/W2375652826","https://openalex.org/W981962503","https://openalex.org/W4296997005","https://openalex.org/W2300145982","https://openalex.org/W2128601753"],"abstract_inverted_index":null,"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}