{"id":"https://openalex.org/W2029691756","doi":"https://doi.org/10.1215/00294527-1306172","title":"Euclidean Functions of Computable Euclidean Domains","display_name":"Euclidean Functions of Computable Euclidean Domains","publication_year":2011,"publication_date":"2011-04-01","ids":{"openalex":"https://openalex.org/W2029691756","doi":"https://doi.org/10.1215/00294527-1306172","mag":"2029691756"},"language":"en","primary_location":{"id":"doi:10.1215/00294527-1306172","is_oa":true,"landing_page_url":"https://doi.org/10.1215/00294527-1306172","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-52/issue-2/Euclidean-Functions-of-Computable-Euclidean-Domains/10.1215/00294527-1306172.pdf","source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal Logic","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-52/issue-2/Euclidean-Functions-of-Computable-Euclidean-Domains/10.1215/00294527-1306172.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5071503687","display_name":"Rodney G. Downey","orcid":"https://orcid.org/0000-0003-4381-2845"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Rodney G. Downey","raw_affiliation_strings":["Department of Mathematics Victoria University of Wellington Wellington NEW ZEALAND"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics Victoria University of Wellington Wellington NEW ZEALAND","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5079381390","display_name":"Asher M. Kach","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Asher M. Kach","raw_affiliation_strings":["Department of Mathematics Victoria University of Wellington Wellington NEW ZEALAND"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics Victoria University of Wellington Wellington NEW ZEALAND","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5071503687"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.3214,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.59898422,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"52","issue":"2","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9998999834060669,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9998999834060669,"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/T13720","display_name":"Benford\u2019s Law and Fraud Detection","score":0.9749000072479248,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T12162","display_name":"Cellular Automata and Applications","score":0.9645000100135803,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.8441523313522339},{"id":"https://openalex.org/keywords/euclidean-domain","display_name":"Euclidean domain","score":0.7948670983314514},{"id":"https://openalex.org/keywords/euclidean-distance-matrix","display_name":"Euclidean distance matrix","score":0.7217125296592712},{"id":"https://openalex.org/keywords/euclidean-group","display_name":"Euclidean group","score":0.6389952301979065},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.630154550075531},{"id":"https://openalex.org/keywords/euclidean-distance","display_name":"Euclidean distance","score":0.6175013780593872},{"id":"https://openalex.org/keywords/non-euclidean-geometry","display_name":"Non-Euclidean geometry","score":0.5738598704338074},{"id":"https://openalex.org/keywords/euclidean-shortest-path","display_name":"Euclidean shortest path","score":0.49889564514160156},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4904155433177948},{"id":"https://openalex.org/keywords/seven-dimensional-space","display_name":"Seven-dimensional space","score":0.46373051404953003},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.38699308037757874},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.35670924186706543},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.34524089097976685},{"id":"https://openalex.org/keywords/affine-space","display_name":"Affine space","score":0.3329974114894867},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3318721055984497},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.056163251399993896}],"concepts":[{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.8441523313522339},{"id":"https://openalex.org/C23719512","wikidata":"https://www.wikidata.org/wiki/Q867345","display_name":"Euclidean domain","level":4,"score":0.7948670983314514},{"id":"https://openalex.org/C171558263","wikidata":"https://www.wikidata.org/wiki/Q5406122","display_name":"Euclidean distance matrix","level":3,"score":0.7217125296592712},{"id":"https://openalex.org/C19939924","wikidata":"https://www.wikidata.org/wiki/Q852195","display_name":"Euclidean group","level":4,"score":0.6389952301979065},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.630154550075531},{"id":"https://openalex.org/C120174047","wikidata":"https://www.wikidata.org/wiki/Q847073","display_name":"Euclidean distance","level":2,"score":0.6175013780593872},{"id":"https://openalex.org/C10784197","wikidata":"https://www.wikidata.org/wiki/Q233858","display_name":"Non-Euclidean geometry","level":3,"score":0.5738598704338074},{"id":"https://openalex.org/C170836113","wikidata":"https://www.wikidata.org/wiki/Q5406126","display_name":"Euclidean shortest path","level":5,"score":0.49889564514160156},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4904155433177948},{"id":"https://openalex.org/C74802450","wikidata":"https://www.wikidata.org/wiki/Q2070474","display_name":"Seven-dimensional space","level":4,"score":0.46373051404953003},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.38699308037757874},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.35670924186706543},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.34524089097976685},{"id":"https://openalex.org/C173110770","wikidata":"https://www.wikidata.org/wiki/Q382698","display_name":"Affine space","level":3,"score":0.3329974114894867},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3318721055984497},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.056163251399993896},{"id":"https://openalex.org/C1465435","wikidata":"https://www.wikidata.org/wiki/Q2916352","display_name":"Longest path problem","level":4,"score":0.0},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"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/C22590252","wikidata":"https://www.wikidata.org/wiki/Q1058754","display_name":"Shortest path problem","level":3,"score":0.0},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1215/00294527-1306172","is_oa":true,"landing_page_url":"https://doi.org/10.1215/00294527-1306172","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-52/issue-2/Euclidean-Functions-of-Computable-Euclidean-Domains/10.1215/00294527-1306172.pdf","source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal Logic","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.ndjfl/1303995712","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.ndjfl/1303995712","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.184.9711","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.184.9711","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.mcs.vuw.ac.nz/%7Edowney/publications/domain.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1215/00294527-1306172","is_oa":true,"landing_page_url":"https://doi.org/10.1215/00294527-1306172","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-52/issue-2/Euclidean-Functions-of-Computable-Euclidean-Domains/10.1215/00294527-1306172.pdf","source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal Logic","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320335369","display_name":"Marsden Fund","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2029691756.pdf","grobid_xml":"https://content.openalex.org/works/W2029691756.grobid-xml"},"referenced_works_count":10,"referenced_works":["https://openalex.org/W27930116","https://openalex.org/W1556453281","https://openalex.org/W1590434062","https://openalex.org/W1966637286","https://openalex.org/W2053184952","https://openalex.org/W2056217991","https://openalex.org/W2059568104","https://openalex.org/W2063706894","https://openalex.org/W3199165616","https://openalex.org/W4242679002"],"related_works":["https://openalex.org/W4300430248","https://openalex.org/W2095047739","https://openalex.org/W3037672488","https://openalex.org/W2105228010","https://openalex.org/W2749646986","https://openalex.org/W2150084168","https://openalex.org/W2029691756","https://openalex.org/W2884694964","https://openalex.org/W2036683229","https://openalex.org/W4242350006"],"abstract_inverted_index":{"We":[0,14],"study":[1],"the":[2,17,20,34],"complexity":[3,18],"of":[4,19,37,43],"(finitely-valued":[5],"and":[6,24],"transfinitely-valued)":[7],"Euclidean":[8,12,22,26,39],"functions":[9,40],"for":[10],"computable":[11],"domains.":[13],"examine":[15],"both":[16],"minimal":[21,38],"function":[23],"any":[25],"function.":[27],"Additionally,":[28],"we":[29],"draw":[30],"some":[31],"conclusions":[32],"about":[33],"proof-theoretical":[35],"strength":[36],"in":[41],"terms":[42],"reverse":[44],"mathematics.":[45]},"counts_by_year":[{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
