{"id":"https://openalex.org/W3110279720","doi":"https://doi.org/10.1017/s0960129504004359","title":"Domain theory and differential calculus (functions of one variable)","display_name":"Domain theory and differential calculus (functions of one variable)","publication_year":2004,"publication_date":"2004-11-16","ids":{"openalex":"https://openalex.org/W3110279720","doi":"https://doi.org/10.1017/s0960129504004359","mag":"3110279720"},"language":"en","primary_location":{"id":"doi:10.1017/s0960129504004359","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0960129504004359","pdf_url":null,"source":{"id":"https://openalex.org/S101766102","display_name":"Mathematical Structures in Computer Science","issn_l":"0960-1295","issn":["0960-1295","1469-8072"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Structures in Computer Science","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/A5058087229","display_name":"Abbas Edalat","orcid":"https://orcid.org/0000-0002-6211-1991"},"institutions":[{"id":"https://openalex.org/I47508984","display_name":"Imperial College London","ror":"https://ror.org/041kmwe10","country_code":"GB","type":"education","lineage":["https://openalex.org/I47508984"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"ABBAS EDALAT","raw_affiliation_strings":["Department of Computing, Imperial College, London, UK Email:"],"affiliations":[{"raw_affiliation_string":"Department of Computing, Imperial College, London, UK Email:","institution_ids":["https://openalex.org/I47508984"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5032344519","display_name":"Andr\u00e9 Lieutier","orcid":"https://orcid.org/0000-0001-9517-4641"},"institutions":[{"id":"https://openalex.org/I47431100","display_name":"Dassault Syst\u00e8mes (France)","ror":"https://ror.org/038sc5x72","country_code":"FR","type":"company","lineage":["https://openalex.org/I47431100"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"ANDR\u00c9 LIEUTIER","raw_affiliation_strings":["Dassault Systemes Provence and LMC/IMAG, Aix-en-Provence and Grenoble, France"],"affiliations":[{"raw_affiliation_string":"Dassault Systemes Provence and LMC/IMAG, Aix-en-Provence and Grenoble, France","institution_ids":["https://openalex.org/I47431100"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5058087229"],"corresponding_institution_ids":["https://openalex.org/I47508984"],"apc_list":null,"apc_paid":null,"fwci":4.7205,"has_fulltext":false,"cited_by_count":43,"citation_normalized_percentile":{"value":0.95333787,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"14","issue":"6","first_page":"771","last_page":"802"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9664999842643738,"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9664999842643738,"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/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.9549000263214111,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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":0.7077736854553223},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.5610844492912292},{"id":"https://openalex.org/keywords/differential-calculus","display_name":"Differential calculus","score":0.5457264184951782},{"id":"https://openalex.org/keywords/directional-derivative","display_name":"Directional derivative","score":0.5254018902778625},{"id":"https://openalex.org/keywords/generalizations-of-the-derivative","display_name":"Generalizations of the derivative","score":0.514500617980957},{"id":"https://openalex.org/keywords/time-scale-calculus","display_name":"Time-scale calculus","score":0.5098451972007751},{"id":"https://openalex.org/keywords/duality","display_name":"Duality (order theory)","score":0.4951845705509186},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.484060674905777},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.42344406247138977},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.4111579656600952},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3710189163684845},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3586912751197815},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3199060261249542},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2699914574623108},{"id":"https://openalex.org/keywords/multivariable-calculus","display_name":"Multivariable calculus","score":0.15354591608047485},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.11140677332878113}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7077736854553223},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.5610844492912292},{"id":"https://openalex.org/C56802139","wikidata":"https://www.wikidata.org/wiki/Q149999","display_name":"Differential calculus","level":2,"score":0.5457264184951782},{"id":"https://openalex.org/C2011187","wikidata":"https://www.wikidata.org/wiki/Q383851","display_name":"Directional derivative","level":2,"score":0.5254018902778625},{"id":"https://openalex.org/C184537036","wikidata":"https://www.wikidata.org/wiki/Q14163503","display_name":"Generalizations of the derivative","level":3,"score":0.514500617980957},{"id":"https://openalex.org/C33695381","wikidata":"https://www.wikidata.org/wiki/Q7804838","display_name":"Time-scale calculus","level":3,"score":0.5098451972007751},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.4951845705509186},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.484060674905777},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.42344406247138977},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.4111579656600952},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3710189163684845},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3586912751197815},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3199060261249542},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2699914574623108},{"id":"https://openalex.org/C117312493","wikidata":"https://www.wikidata.org/wiki/Q2035437","display_name":"Multivariable calculus","level":2,"score":0.15354591608047485},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.11140677332878113},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C133731056","wikidata":"https://www.wikidata.org/wiki/Q4917288","display_name":"Control engineering","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1017/s0960129504004359","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0960129504004359","pdf_url":null,"source":{"id":"https://openalex.org/S101766102","display_name":"Mathematical Structures in Computer Science","issn_l":"0960-1295","issn":["0960-1295","1469-8072"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Structures in Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:spiral.imperial.ac.uk:10044/1/569","is_oa":false,"landing_page_url":"http://hdl.handle.net/10044/1/569","pdf_url":null,"source":{"id":"https://openalex.org/S4306401396","display_name":"Spiral (Imperial College London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I47508984","host_organization_name":"Imperial College London","host_organization_lineage":["https://openalex.org/I47508984"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"802","raw_type":"Journal Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W1506173494","https://openalex.org/W1509579779","https://openalex.org/W1547926009","https://openalex.org/W1551360398","https://openalex.org/W1582269801","https://openalex.org/W1696720702","https://openalex.org/W1719974439","https://openalex.org/W1960239420","https://openalex.org/W1984190214","https://openalex.org/W2000621909","https://openalex.org/W2007275810","https://openalex.org/W2028924965","https://openalex.org/W2044454977","https://openalex.org/W2065193326","https://openalex.org/W2073030937","https://openalex.org/W2075490047","https://openalex.org/W2079735866","https://openalex.org/W2114953769","https://openalex.org/W2115154197","https://openalex.org/W2149945624","https://openalex.org/W2166644419","https://openalex.org/W3096424428"],"related_works":["https://openalex.org/W2055261210","https://openalex.org/W3095008505","https://openalex.org/W2285567317","https://openalex.org/W1532118721","https://openalex.org/W3023610599","https://openalex.org/W4256146081","https://openalex.org/W2060735178","https://openalex.org/W4252875744","https://openalex.org/W2207627920","https://openalex.org/W607781286"],"abstract_inverted_index":{"We":[0,8,76,152,179],"introduce":[1],"a":[2,65,79,86,132,182,194,202],"domain-theoretic":[3,69,195],"framework":[4],"for":[5,60,81,134,185,205],"differential":[6,136,186,207],"calculus.":[7,55,187],"define":[9],"the":[10,18,27,42,51,68,73,94,115,135],"set":[11,102,116],"of":[12,20,29,41,45,54,64,85,103,117,120,138,148,156,197],"primitive":[13],"maps":[14],"as":[15,17,49],"well":[16],"derivative":[19,70,160],"an":[21,39,176,189],"interval-valued":[22],"Scott":[23],"continuous":[24,126,150],"function":[25,95,157],"on":[26,164],"domain":[28,80,129,172],"intervals,":[30],"and":[31,47,96,145,159],"show":[32],"that":[33,154,170],"they":[34],"are":[35],"dually":[36],"related,":[37],"providing":[38],"extension":[40],"classical":[43,104],"duality":[44],"differentiation":[46],"integration":[48],"in":[50],"fundamental":[52],"theorem":[53],"It":[56],"is":[57,112,162],"shown":[58],"that,":[59],"locally":[61,142],"Lipschitz":[62,143],"functions":[63,84,144],"real":[66,87],"variable,":[67],"coincides":[71],"with":[72,108],"Clarke's":[74],"derivative.":[75,100],"then":[77],"construct":[78],"differentiable":[82],"real-valued":[83],"variable":[88],"by":[89],"pairing":[90],"consistent":[91],"information":[92,97,158,161],"about":[93,98],"its":[99,109],"The":[101],"$C^1$":[105,110,140],"functions,":[106,141,167],"equipped":[107],"norm,":[111],"embedded":[113],"into":[114],"maximal":[118],"elements":[119],"this":[121],"countably":[122],"based,":[123],"bounded":[124],"complete":[125],"domain.":[127],"This":[128],"also":[130],"provides":[131,201],"model":[133],"properties":[137],"piecewise":[139],"more":[146],"generally":[147],"all":[149],"functions.":[151],"prove":[153],"consistency":[155],"decidable":[163],"rational":[165],"step":[166],"which":[168,200],"shows":[169],"our":[171],"can":[173],"be":[174],"given":[175],"effective":[177],"structure.":[178],"thus":[180],"obtain":[181],"data":[183,203],"type":[184,204],"As":[188],"immediate":[190],"application,":[191],"we":[192],"present":[193],"formulation":[196],"Picard's":[198],"theorem,":[199],"solving":[206],"equations.":[208]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
