{"id":"https://openalex.org/W2078295123","doi":"https://doi.org/10.1007/s00454-004-1104-8","title":"The Mixed Volume of Two Finite Vector Sets","display_name":"The Mixed Volume of Two Finite Vector Sets","publication_year":2004,"publication_date":"2004-06-04","ids":{"openalex":"https://openalex.org/W2078295123","doi":"https://doi.org/10.1007/s00454-004-1104-8","mag":"2078295123"},"language":"en","primary_location":{"id":"doi:10.1007/s00454-004-1104-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-004-1104-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-004-1104-8.pdf","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 & Computational Geometry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://link.springer.com/content/pdf/10.1007/s00454-004-1104-8.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100459387","display_name":"Xiaoyan Li","orcid":"https://orcid.org/0000-0001-6295-2072"},"institutions":[{"id":"https://openalex.org/I113940042","display_name":"Shanghai University","ror":"https://ror.org/006teas31","country_code":"CN","type":"education","lineage":["https://openalex.org/I113940042"]},{"id":"https://openalex.org/I173759888","display_name":"Hunan Normal University","ror":"https://ror.org/053w1zy07","country_code":"CN","type":"education","lineage":["https://openalex.org/I173759888"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Li Xiaoyan","raw_affiliation_strings":["Department of Mathematics, Hunan Normal University, Changsha\n410081, People\u2019s Republic of China \nand Department of Mathematics, Shanghai\nUniversity,\n Shanghai 200436, People\u2019s Republic of China","Department of Mathematics, Hunan Normal University, Changsha#N#410081, People\u2019s Republic of China #N#and Department of Mathematics, Shanghai#N#University,#N# Shanghai 200436"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Hunan Normal University, Changsha\n410081, People\u2019s Republic of China \nand Department of Mathematics, Shanghai\nUniversity,\n Shanghai 200436, People\u2019s Republic of China","institution_ids":["https://openalex.org/I173759888","https://openalex.org/I113940042"]},{"raw_affiliation_string":"Department of Mathematics, Hunan Normal University, Changsha#N#410081, People\u2019s Republic of China #N#and Department of Mathematics, Shanghai#N#University,#N# Shanghai 200436","institution_ids":["https://openalex.org/I173759888"]}]},{"author_position":"last","author":{"id":null,"display_name":"Leng Gangsong","orcid":null},"institutions":[{"id":"https://openalex.org/I113940042","display_name":"Shanghai University","ror":"https://ror.org/006teas31","country_code":"CN","type":"education","lineage":["https://openalex.org/I113940042"]},{"id":"https://openalex.org/I173759888","display_name":"Hunan Normal University","ror":"https://ror.org/053w1zy07","country_code":"CN","type":"education","lineage":["https://openalex.org/I173759888"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Leng Gangsong","raw_affiliation_strings":["Department of Mathematics, Hunan Normal University, Changsha\n410081, People\u2019s Republic of China \nand Department of Mathematics, Shanghai\nUniversity,\n Shanghai 200436, People\u2019s Republic of China","Department of Mathematics, Hunan Normal University, Changsha#N#410081, People\u2019s Republic of China #N#and Department of Mathematics, Shanghai#N#University,#N# Shanghai 200436"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Hunan Normal University, Changsha\n410081, People\u2019s Republic of China \nand Department of Mathematics, Shanghai\nUniversity,\n Shanghai 200436, People\u2019s Republic of China","institution_ids":["https://openalex.org/I173759888","https://openalex.org/I113940042"]},{"raw_affiliation_string":"Department of Mathematics, Hunan Normal University, Changsha#N#410081, People\u2019s Republic of China #N#and Department of Mathematics, Shanghai#N#University,#N# Shanghai 200436","institution_ids":["https://openalex.org/I173759888"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100459387"],"corresponding_institution_ids":["https://openalex.org/I113940042","https://openalex.org/I173759888"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.17601487,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"33","issue":"3","first_page":"403","last_page":"421"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11830","display_name":"Point processes and geometric inequalities","score":0.9991000294685364,"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":0.9991000294685364,"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/T11564","display_name":"Mathematical Inequalities and Applications","score":0.9970999956130981,"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/T12504","display_name":"Mathematics and Applications","score":0.995199978351593,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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":0.8454275131225586},{"id":"https://openalex.org/keywords/finite-volume-method","display_name":"Finite volume method","score":0.6388832330703735},{"id":"https://openalex.org/keywords/volume","display_name":"Volume (thermodynamics)","score":0.4524872601032257},{"id":"https://openalex.org/keywords/finite-set","display_name":"Finite set","score":0.43722736835479736},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.43204444646835327},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.4204573631286621},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.40338003635406494},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.25452905893325806}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8454275131225586},{"id":"https://openalex.org/C50478463","wikidata":"https://www.wikidata.org/wiki/Q1401936","display_name":"Finite volume method","level":2,"score":0.6388832330703735},{"id":"https://openalex.org/C20556612","wikidata":"https://www.wikidata.org/wiki/Q4469374","display_name":"Volume (thermodynamics)","level":2,"score":0.4524872601032257},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.43722736835479736},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.43204444646835327},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.4204573631286621},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.40338003635406494},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.25452905893325806},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00454-004-1104-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-004-1104-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-004-1104-8.pdf","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 & Computational Geometry","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s00454-004-1104-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-004-1104-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-004-1104-8.pdf","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 & Computational Geometry","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.5600000023841858}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2078295123.pdf","grobid_xml":"https://content.openalex.org/works/W2078295123.grobid-xml"},"referenced_works_count":23,"referenced_works":["https://openalex.org/W1494380125","https://openalex.org/W1966241133","https://openalex.org/W1977287551","https://openalex.org/W1984330686","https://openalex.org/W2002523572","https://openalex.org/W2020177148","https://openalex.org/W2025820172","https://openalex.org/W2030837997","https://openalex.org/W2033477070","https://openalex.org/W2038153565","https://openalex.org/W2057088638","https://openalex.org/W2061748236","https://openalex.org/W2065714235","https://openalex.org/W2082867153","https://openalex.org/W2123774638","https://openalex.org/W2313503213","https://openalex.org/W2330625556","https://openalex.org/W2610857016","https://openalex.org/W4248378484","https://openalex.org/W4253558876","https://openalex.org/W4254502176","https://openalex.org/W6606310112","https://openalex.org/W6823364988"],"related_works":["https://openalex.org/W1978042415","https://openalex.org/W3086542228","https://openalex.org/W2017331178","https://openalex.org/W2976797620","https://openalex.org/W4313276337","https://openalex.org/W3106133691","https://openalex.org/W4249580765","https://openalex.org/W2325664614","https://openalex.org/W2096753949","https://openalex.org/W1966522846"],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2026-06-19T15:47:20.252518","created_date":"2025-10-10T00:00:00"}