{"id":"https://openalex.org/W2112612564","doi":"https://doi.org/10.3390/a5040604","title":"Laplace\u2013Fourier Transform of the Stretched Exponential Function: Analytic Error Bounds, Double Exponential Transform, and Open-Source Implementation \u201clibkww\u201d","display_name":"Laplace\u2013Fourier Transform of the Stretched Exponential Function: Analytic Error Bounds, Double Exponential Transform, and Open-Source Implementation \u201clibkww\u201d","publication_year":2012,"publication_date":"2012-11-22","ids":{"openalex":"https://openalex.org/W2112612564","doi":"https://doi.org/10.3390/a5040604","mag":"2112612564"},"language":"en","primary_location":{"id":"doi:10.3390/a5040604","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a5040604","pdf_url":"https://www.mdpi.com/1999-4893/5/4/604/pdf?version=1353572518","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1999-4893/5/4/604/pdf?version=1353572518","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5019903097","display_name":"Joachim Wuttke","orcid":"https://orcid.org/0000-0002-4028-1447"},"institutions":[{"id":"https://openalex.org/I171892758","display_name":"Forschungszentrum J\u00fclich","ror":"https://ror.org/02nv7yv05","country_code":"DE","type":"facility","lineage":["https://openalex.org/I1305996414","https://openalex.org/I171892758"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Joachim Wuttke","raw_affiliation_strings":["Forschungszentrum J\u00fclich GmbH, J\u00fclich Centre for Neutron Science at FRM II, Lichtenbergstra\u00dfe 1, 85747 Garching, Germany"],"affiliations":[{"raw_affiliation_string":"Forschungszentrum J\u00fclich GmbH, J\u00fclich Centre for Neutron Science at FRM II, Lichtenbergstra\u00dfe 1, 85747 Garching, Germany","institution_ids":["https://openalex.org/I171892758"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5019903097"],"corresponding_institution_ids":["https://openalex.org/I171892758"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":1.9764,"has_fulltext":true,"cited_by_count":41,"citation_normalized_percentile":{"value":0.86689747,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"5","issue":"4","first_page":"604","last_page":"628"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13126","display_name":"Scientific Research and Discoveries","score":0.9908000230789185,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T13126","display_name":"Scientific Research and Discoveries","score":0.9908000230789185,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10474","display_name":"Material Dynamics and Properties","score":0.9830999970436096,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11890","display_name":"Scientific Measurement and Uncertainty Evaluation","score":0.9632999897003174,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/laplace-transform","display_name":"Laplace transform","score":0.7639845013618469},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.7618720531463623},{"id":"https://openalex.org/keywords/stretched-exponential-function","display_name":"Stretched exponential function","score":0.6748124361038208},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.6490333080291748},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.6096807718276978},{"id":"https://openalex.org/keywords/transformation","display_name":"Transformation (genetics)","score":0.583956778049469},{"id":"https://openalex.org/keywords/double-exponential-function","display_name":"Double exponential function","score":0.5584946870803833},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4918839931488037},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.451923131942749},{"id":"https://openalex.org/keywords/two-sided-laplace-transform","display_name":"Two-sided Laplace transform","score":0.42722123861312866},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3291893005371094},{"id":"https://openalex.org/keywords/fourier-analysis","display_name":"Fourier analysis","score":0.2098887860774994},{"id":"https://openalex.org/keywords/fractional-fourier-transform","display_name":"Fractional Fourier transform","score":0.15104371309280396}],"concepts":[{"id":"https://openalex.org/C97937538","wikidata":"https://www.wikidata.org/wiki/Q199691","display_name":"Laplace transform","level":2,"score":0.7639845013618469},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.7618720531463623},{"id":"https://openalex.org/C2777404744","wikidata":"https://www.wikidata.org/wiki/Q849591","display_name":"Stretched exponential function","level":3,"score":0.6748124361038208},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.6490333080291748},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.6096807718276978},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.583956778049469},{"id":"https://openalex.org/C49016629","wikidata":"https://www.wikidata.org/wiki/Q3075235","display_name":"Double exponential function","level":3,"score":0.5584946870803833},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4918839931488037},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.451923131942749},{"id":"https://openalex.org/C10288518","wikidata":"https://www.wikidata.org/wiki/Q1785576","display_name":"Two-sided Laplace transform","level":5,"score":0.42722123861312866},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3291893005371094},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.2098887860774994},{"id":"https://openalex.org/C76563020","wikidata":"https://www.wikidata.org/wiki/Q4817582","display_name":"Fractional Fourier transform","level":4,"score":0.15104371309280396},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","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/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","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:10.3390/a5040604","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a5040604","pdf_url":"https://www.mdpi.com/1999-4893/5/4/604/pdf?version=1353572518","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:0911.4796","is_oa":true,"landing_page_url":"http://arxiv.org/abs/0911.4796","pdf_url":"https://arxiv.org/pdf/0911.4796","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"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":null,"raw_type":"text"},{"id":"pmh:oai:mdpi.com:/1999-4893/5/4/604/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/a5040604","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Algorithms; Volume 5; Issue 4; Pages: 604-628","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/a5040604","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a5040604","pdf_url":"https://www.mdpi.com/1999-4893/5/4/604/pdf?version=1353572518","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2112612564.pdf","grobid_xml":"https://content.openalex.org/works/W2112612564.grobid-xml"},"referenced_works_count":50,"referenced_works":["https://openalex.org/W58044373","https://openalex.org/W1509335871","https://openalex.org/W1600066014","https://openalex.org/W1620449130","https://openalex.org/W1636787203","https://openalex.org/W1860287188","https://openalex.org/W1974150790","https://openalex.org/W1974811801","https://openalex.org/W1979765007","https://openalex.org/W1981316513","https://openalex.org/W1983998946","https://openalex.org/W1987523927","https://openalex.org/W1987815728","https://openalex.org/W1992755218","https://openalex.org/W1993620328","https://openalex.org/W1995802502","https://openalex.org/W1995844781","https://openalex.org/W2003923484","https://openalex.org/W2015247909","https://openalex.org/W2019453149","https://openalex.org/W2022304570","https://openalex.org/W2031501875","https://openalex.org/W2034369159","https://openalex.org/W2038674878","https://openalex.org/W2039669017","https://openalex.org/W2042153002","https://openalex.org/W2060753810","https://openalex.org/W2062067039","https://openalex.org/W2070403522","https://openalex.org/W2070904040","https://openalex.org/W2071615689","https://openalex.org/W2076602648","https://openalex.org/W2091570098","https://openalex.org/W2094811987","https://openalex.org/W2098103126","https://openalex.org/W2107713043","https://openalex.org/W2121378814","https://openalex.org/W2122202311","https://openalex.org/W2163683882","https://openalex.org/W2171643765","https://openalex.org/W2480068994","https://openalex.org/W2949525215","https://openalex.org/W3099511948","https://openalex.org/W3120882506","https://openalex.org/W3122675353","https://openalex.org/W4240324102","https://openalex.org/W4292165848","https://openalex.org/W6651157047","https://openalex.org/W6684120608","https://openalex.org/W6788363180"],"related_works":["https://openalex.org/W3126199408","https://openalex.org/W4283576291","https://openalex.org/W3022275705","https://openalex.org/W3166878184","https://openalex.org/W3023736802","https://openalex.org/W4213365297","https://openalex.org/W4387738947","https://openalex.org/W2112612564","https://openalex.org/W2763003374","https://openalex.org/W2745659514"],"abstract_inverted_index":{"The":[0,64,78],"C":[1],"library":[2],"libkww":[3],"provides":[4],"functions":[5],"to":[6,91],"compute":[7],"the":[8,13,17,41,51,59,67,72],"Kohlrausch\u2013Williams\u2013":[9],"Watts":[10],"function,":[11],"i.e.,":[12],"Laplace\u2013Fourier":[14],"transform":[15,69],"of":[16,66],"stretched":[18],"(or":[19],"compressed)":[20],"exponential":[21,62],"function":[22],"exp(-t\u03b2":[23],")":[24],"for":[25,40,71],"exponents":[26],"\u03b2":[27],"between":[28],"0.1":[29],"and":[30,43],"1.9":[31],"with":[32],"double":[33,61],"precision.":[34],"Analytic":[35],"error":[36],"bounds":[37],"are":[38],"derived":[39],"low":[42],"high":[44],"frequency":[45],"series":[46],"expansions.":[47],"For":[48],"intermediate":[49],"frequencies,":[50],"numeric":[52],"integration":[53],"is":[54,75,80,86],"enormously":[55],"accelerated":[56],"by":[57],"using":[58],"Ooura\u2013Mori":[60],"transformation.":[63],"primitive":[65],"cosine":[68],"needed":[70],"convolution":[73],"integrals":[74],"also":[76],"implemented.":[77],"software":[79],"hosted":[81],"at":[82],"http://apps.jcns.fz-juelich.de/kww;":[83],"version":[84],"3.0":[85],"deposited":[87],"as":[88],"supplementary":[89],"material":[90],"this":[92],"article.":[93]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-03-29T08:15:47.926485","created_date":"2016-06-24T00:00:00"}
