{"id":"https://openalex.org/W3008829513","doi":"https://doi.org/10.1090/mcom/3539","title":"Boolean algebra of two-dimensional continua with arbitrarily complex topology","display_name":"Boolean algebra of two-dimensional continua with arbitrarily complex topology","publication_year":2020,"publication_date":"2020-02-26","ids":{"openalex":"https://openalex.org/W3008829513","doi":"https://doi.org/10.1090/mcom/3539","mag":"3008829513"},"language":"en","primary_location":{"id":"doi:10.1090/mcom/3539","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/3539","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","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/A5051920590","display_name":"Qinghai Zhang","orcid":"https://orcid.org/0000-0002-3655-4190"},"institutions":[{"id":"https://openalex.org/I76130692","display_name":"Zhejiang University","ror":"https://ror.org/00a2xv884","country_code":"CN","type":"education","lineage":["https://openalex.org/I76130692"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qinghai Zhang","raw_affiliation_strings":["School of Mathematical Sciences, Zhejiang University, 38 Zheda Road, Hangzhou, Zhejiang Province, 310027 People\u00e2\u0080\u0099s Republic China","School of Mathematical Sciences, Zhejiang University, 38 Zheda Road, Hangzhou, Zhejiang Province, 310027 People's Republic China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Zhejiang University, 38 Zheda Road, Hangzhou, Zhejiang Province, 310027 People\u00e2\u0080\u0099s Republic China","institution_ids":["https://openalex.org/I76130692"]},{"raw_affiliation_string":"School of Mathematical Sciences, Zhejiang University, 38 Zheda Road, Hangzhou, Zhejiang Province, 310027 People's Republic China","institution_ids":["https://openalex.org/I76130692"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101540014","display_name":"Zhixuan Li","orcid":"https://orcid.org/0009-0003-7215-3209"},"institutions":[{"id":"https://openalex.org/I76130692","display_name":"Zhejiang University","ror":"https://ror.org/00a2xv884","country_code":"CN","type":"education","lineage":["https://openalex.org/I76130692"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhixuan Li","raw_affiliation_strings":["School of Mathematical Sciences, Zhejiang University, 38 Zheda Road, Hangzhou, Zhejiang Province, 310027 People\u00e2\u0080\u0099s Republic China","School of Mathematical Sciences, Zhejiang University, 38 Zheda Road, Hangzhou, Zhejiang Province, 310027 People's Republic China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Zhejiang University, 38 Zheda Road, Hangzhou, Zhejiang Province, 310027 People\u00e2\u0080\u0099s Republic China","institution_ids":["https://openalex.org/I76130692"]},{"raw_affiliation_string":"School of Mathematical Sciences, Zhejiang University, 38 Zheda Road, Hangzhou, Zhejiang Province, 310027 People's Republic China","institution_ids":["https://openalex.org/I76130692"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I76130692"],"apc_list":null,"apc_paid":null,"fwci":3.5332,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.92973614,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"89","issue":"325","first_page":"2333","last_page":"2364"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10481","display_name":"Computer Graphics and Visualization Techniques","score":0.9958000183105469,"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"}},"topics":[{"id":"https://openalex.org/T10481","display_name":"Computer Graphics and Visualization Techniques","score":0.9958000183105469,"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/T13362","display_name":"Slime Mold and Myxomycetes Research","score":0.9764000177383423,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.9649999737739563,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7491112351417542},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.6171954274177551},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.5631492137908936},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.42571669816970825},{"id":"https://openalex.org/keywords/topological-space","display_name":"Topological space","score":0.42165204882621765},{"id":"https://openalex.org/keywords/geometry-and-topology","display_name":"Geometry and topology","score":0.4115281403064728},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.27572354674339294},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1761954426765442},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.15665972232818604}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7491112351417542},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.6171954274177551},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.5631492137908936},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.42571669816970825},{"id":"https://openalex.org/C81332173","wikidata":"https://www.wikidata.org/wiki/Q179899","display_name":"Topological space","level":2,"score":0.42165204882621765},{"id":"https://openalex.org/C156135169","wikidata":"https://www.wikidata.org/wiki/Q5535522","display_name":"Geometry and topology","level":2,"score":0.4115281403064728},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.27572354674339294},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1761954426765442},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.15665972232818604},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1090/mcom/3539","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/3539","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities","score":0.5400000214576721}],"awards":[{"id":"https://openalex.org/G2990233989","display_name":null,"funder_award_id":"11871429","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7795245716","display_name":null,"funder_award_id":"#11871429","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":47,"referenced_works":["https://openalex.org/W47500126","https://openalex.org/W203809554","https://openalex.org/W626407659","https://openalex.org/W642107583","https://openalex.org/W1024421181","https://openalex.org/W1496383623","https://openalex.org/W1507144431","https://openalex.org/W1579213680","https://openalex.org/W1593821512","https://openalex.org/W1874694348","https://openalex.org/W1975847612","https://openalex.org/W1982799443","https://openalex.org/W1991113069","https://openalex.org/W1995222467","https://openalex.org/W1996285926","https://openalex.org/W2008547560","https://openalex.org/W2020156682","https://openalex.org/W2023248330","https://openalex.org/W2027940660","https://openalex.org/W2028638323","https://openalex.org/W2033139573","https://openalex.org/W2044540217","https://openalex.org/W2063484453","https://openalex.org/W2070444191","https://openalex.org/W2074849287","https://openalex.org/W2079210173","https://openalex.org/W2083548344","https://openalex.org/W2086636341","https://openalex.org/W2086969205","https://openalex.org/W2092886188","https://openalex.org/W2100185791","https://openalex.org/W2148713284","https://openalex.org/W2155657794","https://openalex.org/W2181920740","https://openalex.org/W2320067553","https://openalex.org/W2324049880","https://openalex.org/W2330586106","https://openalex.org/W2609170234","https://openalex.org/W2900537138","https://openalex.org/W4233291103","https://openalex.org/W4234555707","https://openalex.org/W4236797139","https://openalex.org/W4237713727","https://openalex.org/W4245557876","https://openalex.org/W4251391716","https://openalex.org/W4251723445","https://openalex.org/W4298410530"],"related_works":["https://openalex.org/W4309710663","https://openalex.org/W2116865742","https://openalex.org/W2081579710","https://openalex.org/W2371641196","https://openalex.org/W2000850197","https://openalex.org/W3100864178","https://openalex.org/W3217271750","https://openalex.org/W4286849932","https://openalex.org/W4376620824","https://openalex.org/W2166411899"],"abstract_inverted_index":{"We":[0],"propose":[1],"a":[2,12,135,138,143,169,173],"mathematical":[3],"model":[4,71],"for":[5,16],"two-dimensional":[6],"continua":[7],"in":[8,32,86,125,172],"order":[9],"to":[10,115,137,167],"establish":[11],"solid":[13],"theoretical":[14],"foundation":[15],"the":[17,33,42,131,158,162],"study":[18],"of":[19,35,46,63,69,76,92,134,145,150],"their":[20],"complex":[21,117,170],"topology,":[22],"large":[23],"geometric":[24],"deformations,":[25],"and":[26,54,60,102,113,123,141,152],"topological":[27,74,90],"changes":[28,91],"such":[29,78],"as":[30,79],"merging":[31],"context":[34],"multiphase":[36],"flows.":[37],"Our":[38],"modeling":[39],"space,":[40,44],"named":[41],"Yin":[43,159],"consists":[45],"regular":[47],"open":[48],"semianalytic":[49],"sets":[50],"with":[51,58,161],"bounded":[52],"boundaries,":[53,101],"is":[55],"further":[56],"equipped":[57],"constructive":[59],"algebraic":[61],"definitions":[62],"Boolean":[64,104],"operations.":[65],"Major":[66],"distinguishing":[67],"features":[68],"our":[70],"include":[72],"(a)":[73,151],"information":[75],"fluids":[77,93,107],"Betti":[80],"numbers":[81],"can":[82],"be":[83],"easily":[84],"extracted":[85],"constant":[87],"time,":[88],"(b)":[89],"are":[94,121,154],"captured":[95],"by":[96,156],"nonmanifold":[97],"points":[98],"on":[99,106],"fluid":[100,171],"(c)":[103,153],"operations":[105],"correctly":[108],"handle":[109],"all":[110],"degenerate":[111],"cases":[112],"apply":[114],"arbitrarily":[116],"topologies,":[118],"yet":[119],"they":[120,127],"simple":[122],"efficient":[124],"that":[126],"only":[128],"involve":[129],"determining":[130],"relative":[132],"position":[133],"point":[136],"Jordan":[139],"curve":[140,146],"intersecting":[142],"number":[144],"segments.":[147],"Finally,":[148],"utilities":[149],"demonstrated":[155],"combining":[157],"space":[160],"recent":[163],"cubic":[164],"MARS":[165],"method":[166],"track":[168],"single":[174],"vortex":[175],"flow.":[176]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}