{"id":"https://openalex.org/W2787475915","doi":"https://doi.org/10.1080/00029890.2018.1401832","title":"A New Extension of the Riemann Integral","display_name":"A New Extension of the Riemann Integral","publication_year":2018,"publication_date":"2018-01-30","ids":{"openalex":"https://openalex.org/W2787475915","doi":"https://doi.org/10.1080/00029890.2018.1401832","mag":"2787475915"},"language":"en","primary_location":{"id":"doi:10.1080/00029890.2018.1401832","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00029890.2018.1401832","pdf_url":null,"source":{"id":"https://openalex.org/S156280010","display_name":"American Mathematical Monthly","issn_l":"0002-9890","issn":["0002-9890","1930-0972"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The American Mathematical Monthly","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/A5068876210","display_name":"C. Bryan Dawson","orcid":"https://orcid.org/0000-0002-8023-1591"},"institutions":[{"id":"https://openalex.org/I155673605","display_name":"Union University","ror":"https://ror.org/02c561939","country_code":"US","type":"education","lineage":["https://openalex.org/I155673605"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"C. Bryan Dawson","raw_affiliation_strings":["Department of Mathematics, Union University, Jackson, TN 38305"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Union University, Jackson, TN 38305","institution_ids":["https://openalex.org/I155673605"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5068876210"],"corresponding_institution_ids":["https://openalex.org/I155673605"],"apc_list":null,"apc_paid":null,"fwci":0.7326,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.64107884,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"125","issue":"2","first_page":"130","last_page":"140"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.9998999834060669,"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9896000027656555,"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9796000123023987,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/extension","display_name":"Extension (predicate logic)","score":0.77248215675354},{"id":"https://openalex.org/keywords/integrable-system","display_name":"Integrable system","score":0.7589243650436401},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7524615526199341},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6790793538093567},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.6594792604446411},{"id":"https://openalex.org/keywords/riemann-integral","display_name":"Riemann integral","score":0.5726802945137024},{"id":"https://openalex.org/keywords/locally-integrable-function","display_name":"Locally integrable function","score":0.5693333745002747},{"id":"https://openalex.org/keywords/riemann-hypothesis","display_name":"Riemann hypothesis","score":0.5387241840362549},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5269611477851868},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.47164076566696167},{"id":"https://openalex.org/keywords/riemann\u2013stieltjes-integral","display_name":"Riemann\u2013Stieltjes integral","score":0.4348967373371124},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4145504832267761},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.27333739399909973},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07274842262268066},{"id":"https://openalex.org/keywords/fourier-integral-operator","display_name":"Fourier integral operator","score":0.04693269729614258}],"concepts":[{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.77248215675354},{"id":"https://openalex.org/C200741047","wikidata":"https://www.wikidata.org/wiki/Q1957758","display_name":"Integrable system","level":2,"score":0.7589243650436401},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7524615526199341},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6790793538093567},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.6594792604446411},{"id":"https://openalex.org/C41833934","wikidata":"https://www.wikidata.org/wiki/Q697181","display_name":"Riemann integral","level":4,"score":0.5726802945137024},{"id":"https://openalex.org/C83295520","wikidata":"https://www.wikidata.org/wiki/Q1318586","display_name":"Locally integrable function","level":3,"score":0.5693333745002747},{"id":"https://openalex.org/C199479865","wikidata":"https://www.wikidata.org/wiki/Q205966","display_name":"Riemann hypothesis","level":2,"score":0.5387241840362549},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5269611477851868},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.47164076566696167},{"id":"https://openalex.org/C167211080","wikidata":"https://www.wikidata.org/wiki/Q285771","display_name":"Riemann\u2013Stieltjes integral","level":3,"score":0.4348967373371124},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4145504832267761},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.27333739399909973},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07274842262268066},{"id":"https://openalex.org/C191832335","wikidata":"https://www.wikidata.org/wiki/Q4262191","display_name":"Fourier integral operator","level":3,"score":0.04693269729614258},{"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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":1,"locations":[{"id":"doi:10.1080/00029890.2018.1401832","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00029890.2018.1401832","pdf_url":null,"source":{"id":"https://openalex.org/S156280010","display_name":"American Mathematical Monthly","issn_l":"0002-9890","issn":["0002-9890","1930-0972"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The American Mathematical Monthly","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.4699999988079071}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W28883802","https://openalex.org/W1990465732","https://openalex.org/W2069787050","https://openalex.org/W2488999146","https://openalex.org/W2952148567","https://openalex.org/W3159837299","https://openalex.org/W4212778169","https://openalex.org/W4300453772","https://openalex.org/W4366574676"],"related_works":["https://openalex.org/W2784778011","https://openalex.org/W3156464835","https://openalex.org/W4244844931","https://openalex.org/W1970788826","https://openalex.org/W4248085762","https://openalex.org/W4386761228","https://openalex.org/W2372686356","https://openalex.org/W2169920639","https://openalex.org/W2151625979","https://openalex.org/W2592770093"],"abstract_inverted_index":{"Using":[0],"an":[1],"equivalence":[2],"relation":[3],"on":[4,49],"the":[5,13],"hyperreals":[6],"called":[7],"approximation,":[8],"a":[9,32],"new":[10],"extension":[11],"of":[12,52],"Riemann":[14],"integral":[15],"is":[16,25,43,47,58],"motivated":[17],"and":[18,27,55],"introduced":[19],"in":[20],"which":[21,29],"every":[22,50],"bounded":[23],"function":[24,33],"integrable":[26],"for":[28],"there":[30],"exists":[31],"g:":[34],"[0,":[35,53],"1]":[36],"\u2192":[37],"R":[38],"simultaneously":[39],"satisfying":[40],"(1)":[41],"g":[42,46,57],"integrable,":[44],"(2)":[45],"unbounded":[48],"subinterval":[51],"1],":[54],"(3)":[56],"identical":[59],"to":[60],"its":[61],"average":[62],"value":[63],"function.":[64]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2019,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}