{"id":"https://openalex.org/W2781637889","doi":"https://doi.org/10.11575/cdm.v12i2.62481","title":"Ball hulls, ball intersections, and 2-center problems for gauges","display_name":"Ball hulls, ball intersections, and 2-center problems for gauges","publication_year":2016,"publication_date":"2016-11-25","ids":{"openalex":"https://openalex.org/W2781637889","doi":"https://doi.org/10.11575/cdm.v12i2.62481","mag":"2781637889"},"language":"en","primary_location":{"id":"doi:10.11575/cdm.v12i2.62481","is_oa":true,"landing_page_url":"https://doi.org/10.11575/cdm.v12i2.62481","pdf_url":null,"source":{"id":"https://openalex.org/S7407053067","display_name":"University of Calgary","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"},"type":"article","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.11575/cdm.v12i2.62481","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5035865191","display_name":"Pedro Mart\u00edn","orcid":"https://orcid.org/0000-0003-4242-0145"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Martin, Pedro","raw_affiliation_strings":["Departamento de Matem\u00e1ticas - Universidad de Extremadura"],"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1ticas - Universidad de Extremadura","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040806028","display_name":"Horst Martini","orcid":null},"institutions":[{"id":"https://openalex.org/I2610724","display_name":"Chemnitz University of Technology","ror":"https://ror.org/00a208s56","country_code":"DE","type":"education","lineage":["https://openalex.org/I2610724"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Martini, Horst","raw_affiliation_strings":["Fakult\u00e4t f\u00fcr Mathematik, TU Chemnitz"],"affiliations":[{"raw_affiliation_string":"Fakult\u00e4t f\u00fcr Mathematik, TU Chemnitz","institution_ids":["https://openalex.org/I2610724"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5076284120","display_name":"Margarita Spirova","orcid":null},"institutions":[{"id":"https://openalex.org/I2610724","display_name":"Chemnitz University of Technology","ror":"https://ror.org/00a208s56","country_code":"DE","type":"education","lineage":["https://openalex.org/I2610724"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Spirova, Margarita","raw_affiliation_strings":["Fakult\u00e4t f\u00fcr Mathematik, TU Chemnitz"],"affiliations":[{"raw_affiliation_string":"Fakult\u00e4t f\u00fcr Mathematik, TU Chemnitz","institution_ids":["https://openalex.org/I2610724"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5035865191"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.26682633,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"12","issue":"2","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11830","display_name":"Point processes and geometric inequalities","score":0.9914000034332275,"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":0.9914000034332275,"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":0.9821000099182129,"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/T12923","display_name":"Digital Image Processing Techniques","score":0.970300018787384,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/ball","display_name":"Ball (mathematics)","score":0.831728994846344},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8056233525276184},{"id":"https://openalex.org/keywords/convex-hull","display_name":"Convex hull","score":0.7736717462539673},{"id":"https://openalex.org/keywords/hull","display_name":"Hull","score":0.6304109692573547},{"id":"https://openalex.org/keywords/convex-body","display_name":"Convex body","score":0.6273666024208069},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.6086092591285706},{"id":"https://openalex.org/keywords/banach-space","display_name":"Banach space","score":0.5836886763572693},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.5711586475372314},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.554573655128479},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5204639434814453},{"id":"https://openalex.org/keywords/euclidean-space","display_name":"Euclidean space","score":0.44387584924697876},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.38227567076683044},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3783224821090698},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.0588146448135376}],"concepts":[{"id":"https://openalex.org/C122041747","wikidata":"https://www.wikidata.org/wiki/Q838611","display_name":"Ball (mathematics)","level":2,"score":0.831728994846344},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8056233525276184},{"id":"https://openalex.org/C206194317","wikidata":"https://www.wikidata.org/wiki/Q1138624","display_name":"Convex hull","level":3,"score":0.7736717462539673},{"id":"https://openalex.org/C37423430","wikidata":"https://www.wikidata.org/wiki/Q6750281","display_name":"Hull","level":2,"score":0.6304109692573547},{"id":"https://openalex.org/C134912446","wikidata":"https://www.wikidata.org/wiki/Q5166516","display_name":"Convex body","level":4,"score":0.6273666024208069},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.6086092591285706},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.5836886763572693},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.5711586475372314},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.554573655128479},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5204639434814453},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.44387584924697876},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.38227567076683044},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3783224821090698},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0588146448135376},{"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/C199104240","wikidata":"https://www.wikidata.org/wiki/Q118291","display_name":"Marine engineering","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.11575/cdm.v12i2.62481","is_oa":true,"landing_page_url":"https://doi.org/10.11575/cdm.v12i2.62481","pdf_url":null,"source":{"id":"https://openalex.org/S7407053067","display_name":"University of Calgary","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"article-journal"},{"id":"mag:2781637889","is_oa":true,"landing_page_url":"https://cdm.ucalgary.ca/article/download/62481/46805","pdf_url":null,"source":{"id":"https://openalex.org/S2498033248","display_name":"Contributions to Discrete Mathematics","issn_l":"1715-0868","issn":["1715-0868"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310312896","host_organization_name":"University of Calgary Press","host_organization_lineage":["https://openalex.org/P4310312896"],"host_organization_lineage_names":["University of Calgary Press"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":"Contributions to Discrete Mathematics","raw_type":null}],"best_oa_location":{"id":"doi:10.11575/cdm.v12i2.62481","is_oa":true,"landing_page_url":"https://doi.org/10.11575/cdm.v12i2.62481","pdf_url":null,"source":{"id":"https://openalex.org/S7407053067","display_name":"University of Calgary","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"},"sustainable_development_goals":[{"score":0.6700000166893005,"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2173272578","https://openalex.org/W3098341223","https://openalex.org/W1981398010","https://openalex.org/W2964234751","https://openalex.org/W2075979998","https://openalex.org/W2072822417","https://openalex.org/W1994476198","https://openalex.org/W2075507388","https://openalex.org/W1594635667","https://openalex.org/W2086520051","https://openalex.org/W1992715252","https://openalex.org/W1967098823","https://openalex.org/W1968836767","https://openalex.org/W1521686223","https://openalex.org/W2026157097","https://openalex.org/W2000253480","https://openalex.org/W1886463601","https://openalex.org/W1499764222","https://openalex.org/W2065224676","https://openalex.org/W2503751940"],"abstract_inverted_index":{"The":[0],"notions":[1,48],"of":[2,8,67,96,115],"ball":[3,6,97,100],"hull":[4],"and":[5,49,63,75,99,102,119],"intersection":[7],"nite":[9],"sets,":[10],"important":[11],"in":[12,78,113],"Banach":[13],"space":[14],"theory,":[15],"are":[16,32,126],"extended":[17],"from":[18,69,81],"normed":[19,23],"planes":[20],"to":[21,26,52,73,84,105],"generalized":[22],"planes,":[24],"i.e.,":[25],"(asymmetric)":[27],"convex":[28,87,117],"distance":[29],"functions":[30],"which":[31],"also":[33,127],"called":[34],"gauges.":[35],"In":[36],"this":[37],"more":[38],"general":[39],"setting":[40],"we":[41,57],"derive":[42,90],"various":[43],"new":[44],"results":[45,92],"about":[46],"these":[47],"their":[50],"relations":[51],"each":[53],"other.":[54],"Further":[55],"on,":[56],"extend":[58],"the":[59,70,94,106,122],"known":[60],"2-center":[61,107,124],"problem":[62,108,125],"a":[64],"modified":[65],"version":[66],"it":[68],"Euclidean":[71,82],"situation":[72],"norms":[74,118],"gauges":[76],"or,":[77],"other":[79],"words,":[80],"circles":[83,111],"arbitrary":[85],"closed":[86],"curves.":[88],"We":[89],"algorithmical":[91],"on":[93],"construction":[95],"hulls":[98],"intersections,":[101],"computational":[103],"approaches":[104],"with":[109],"constrained":[110],"and,":[112],"case":[114],"strictly":[116],"gauges,":[120],"for":[121],"fixed":[123],"given.":[128]},"counts_by_year":[],"updated_date":"2025-11-06T06:51:31.235846","created_date":"2025-10-10T00:00:00"}