{"id":"https://openalex.org/W192639025","doi":"https://doi.org/10.3217/jucs-014-06-0908","title":"The Riemann Integral in Weak Systems of Analysis","display_name":"The Riemann Integral in Weak Systems of Analysis","publication_year":2020,"publication_date":"2020-04-07","ids":{"openalex":"https://openalex.org/W192639025","doi":"https://doi.org/10.3217/jucs-014-06-0908","mag":"192639025"},"language":"en","primary_location":{"id":"pmh:oai:zenodo.org:7000182","is_oa":true,"landing_page_url":"https://zenodo.org/record/7000182","pdf_url":"https://zenodo.org/record/7000182","source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"JUCS - Journal of Universal Computer Science 14((6)) 908-937","raw_type":"info:eu-repo/semantics/article"},"type":"article","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://zenodo.org/record/7000182","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5043193622","display_name":"Fernando Ferreira","orcid":"https://orcid.org/0000-0002-8693-7210"},"institutions":[{"id":"https://openalex.org/I141596103","display_name":"University of Lisbon","ror":"https://ror.org/01c27hj86","country_code":"PT","type":"education","lineage":["https://openalex.org/I141596103"]}],"countries":["PT"],"is_corresponding":false,"raw_author_name":"Fernando Ferreira","raw_affiliation_strings":["University of Lisbon"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Lisbon","institution_ids":["https://openalex.org/I141596103"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5012426547","display_name":"Gilda Ferreira","orcid":"https://orcid.org/0000-0003-1447-9764"},"institutions":[{"id":"https://openalex.org/I141596103","display_name":"University of Lisbon","ror":"https://ror.org/01c27hj86","country_code":"PT","type":"education","lineage":["https://openalex.org/I141596103"]}],"countries":["PT"],"is_corresponding":false,"raw_author_name":"Gilda Ferreira","raw_affiliation_strings":["University of Lisbon"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Lisbon","institution_ids":["https://openalex.org/I141596103"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":35,"citation_normalized_percentile":{"value":0.00106603,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"14","issue":null,"first_page":"908","last_page":"937"},"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9944999814033508,"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"}},{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.992900013923645,"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/hierarchy","display_name":"Hierarchy","score":0.8486530184745789},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.605019211769104},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5807698369026184},{"id":"https://openalex.org/keywords/riemann-hypothesis","display_name":"Riemann hypothesis","score":0.5682878494262695},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.5328586101531982},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5108072757720947},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5046428442001343},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3900381028652191},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3529084026813507},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.32364124059677124},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.31232863664627075},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.13796988129615784},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.0646832287311554}],"concepts":[{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.8486530184745789},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.605019211769104},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5807698369026184},{"id":"https://openalex.org/C199479865","wikidata":"https://www.wikidata.org/wiki/Q205966","display_name":"Riemann hypothesis","level":2,"score":0.5682878494262695},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.5328586101531982},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5108072757720947},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5046428442001343},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3900381028652191},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3529084026813507},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32364124059677124},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.31232863664627075},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.13796988129615784},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0646832287311554},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"pmh:oai:zenodo.org:7000182","is_oa":true,"landing_page_url":"https://zenodo.org/record/7000182","pdf_url":"https://zenodo.org/record/7000182","source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"JUCS - Journal of Universal Computer Science 14((6)) 908-937","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.218.1850","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.218.1850","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://alf1.cii.fc.ul.pt/~ferferr/riemann_ff.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.487.2240","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.487.2240","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.jucs.org/jucs_14_6/the_riemann_integral_in/jucs_14_06_0908_0937_ferreira.pdf","raw_type":"text"},{"id":"doi:10.3217/jucs-014-06-0908","is_oa":true,"landing_page_url":"https://doi.org/10.3217/jucs-014-06-0908","pdf_url":null,"source":{"id":"https://openalex.org/S4306400660","display_name":"TUGraz OPEN Library (Graz University of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4092182","host_organization_name":"Graz University of Technology","host_organization_lineage":["https://openalex.org/I4092182"],"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"},{"id":"mag:192639025","is_oa":false,"landing_page_url":"http://webpages.fc.ul.pt/~fjferreira/riemann_ff.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S58563349","display_name":"JUCS - Journal of Universal Computer Science","issn_l":"0948-695X","issn":["0948-695X","0948-6968"],"is_oa":false,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317875","host_organization_name":"Verlag der Technischen Universit\u00e4t Graz","host_organization_lineage":["https://openalex.org/P4310317875"],"host_organization_lineage_names":["Verlag der Technischen Universit\u00e4t Graz"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":"JUCS - Journal of Universal Computer Science","raw_type":null}],"best_oa_location":{"id":"pmh:oai:zenodo.org:7000182","is_oa":true,"landing_page_url":"https://zenodo.org/record/7000182","pdf_url":"https://zenodo.org/record/7000182","source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"JUCS - Journal of Universal Computer Science 14((6)) 908-937","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W192639025.pdf"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W9698083","https://openalex.org/W133350300","https://openalex.org/W169256259","https://openalex.org/W1533744131","https://openalex.org/W1553743817","https://openalex.org/W1556453281","https://openalex.org/W1983604941","https://openalex.org/W2002385864","https://openalex.org/W2021956337","https://openalex.org/W2068563862","https://openalex.org/W2071204190","https://openalex.org/W2135427238","https://openalex.org/W2135734418","https://openalex.org/W2139227798"],"related_works":["https://openalex.org/W1493859942","https://openalex.org/W1613641260","https://openalex.org/W2060980898","https://openalex.org/W2075272424","https://openalex.org/W2962978894","https://openalex.org/W2475879714","https://openalex.org/W3211112487","https://openalex.org/W2767474523","https://openalex.org/W2999077758","https://openalex.org/W2891016262","https://openalex.org/W2322770856","https://openalex.org/W2051104892","https://openalex.org/W2052851329","https://openalex.org/W3010242050","https://openalex.org/W2054417539","https://openalex.org/W2785200850","https://openalex.org/W2962893614","https://openalex.org/W2894656563","https://openalex.org/W1822430067","https://openalex.org/W3169703920"],"abstract_inverted_index":{"Abstract:":[0],"Taking":[1],"as":[2],"a":[3,9,40,89],"starting":[4],"point":[5],"(a":[6],"modification":[7],"of)":[8],"weak":[10],"theory":[11],"of":[12,14,24,32,91],"arithmetic":[13,34],"Jan":[15],"Johannsen":[16],"and":[17],"Chris":[18],"Pollett":[19],"(connected":[20],"with":[21,51,88],"the":[22,49,52,56,59,62,69,72,79],"hierarchy":[23,54],"counting":[25,53],"functions),":[26],"we":[27],"introduce":[28],"successively":[29],"stronger":[30],"theories":[31,47],"bounded":[33],"in":[35,55,71],"order":[36],"to":[37,65,82],"set":[38],"up":[39],"system":[41],"for":[42,86],"analysis":[43],"(TCA2).":[44],"The":[45],"extended":[46],"preserve":[48],"connection":[50],"sense":[57],"that":[58,76],"algorithms":[60],"which":[61],"systems":[63],"prove":[64],"halt":[66],"are":[67],"exactly":[68],"ones":[70],"hierarchy.":[73],"We":[74],"show":[75],"TCA2":[77],"has":[78],"exact":[80],"strength":[81],"develop":[83],"Riemannian":[84],"integration":[85],"functions":[87],"modulus":[90],"uniform":[92],"continuity.":[93]},"counts_by_year":[{"year":2019,"cited_by_count":27},{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":4}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
