{"id":"https://openalex.org/W7203604665","doi":"https://doi.org/10.55041/ijcope.v2i8.137","title":"Distributional Extension of the FKF Transform and Its Relevance to Supply-Chain Systems","display_name":"Distributional Extension of the FKF Transform and Its Relevance to Supply-Chain Systems","publication_year":2026,"publication_date":"2026-08-17","ids":{"openalex":"https://openalex.org/W7203604665","doi":"https://doi.org/10.55041/ijcope.v2i8.137"},"language":"en","primary_location":{"id":"doi:10.55041/ijcope.v2i8.137","doi":"https://doi.org/10.55041/ijcope.v2i8.137","is_oa":true,"landing_page_url":"https://doi.org/10.55041/ijcope.v2i8.137","pdf_url":"https://ijcope.org/wp-content/uploads/2026/08/Distributional-Extension-of-the-FKF-Transform-and-Its-Relevance-to-Supply-Chain-Systems.pdf","source":{"id":"https://openalex.org/S7407055479","display_name":"International Journal of Creative and Open Research in Engineering and Management","issn_l":"3108-1754","issn":["3108-1754"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Creative and Open Research in Engineering and Management","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://ijcope.org/wp-content/uploads/2026/08/Distributional-Extension-of-the-FKF-Transform-and-Its-Relevance-to-Supply-Chain-Systems.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5027139010","display_name":"Akarshan Gulhane","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Akarshan Gulhane","raw_affiliation_strings":["PTC Software Inc"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"PTC Software Inc","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5027139010"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":100.0266,"has_fulltext":true,"cited_by_count":49,"citation_normalized_percentile":{"value":0.99983034,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":100},"biblio":{"volume":"02","issue":"08","first_page":"1","last_page":"9"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9496999979019165,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9496999979019165,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T10328","display_name":"Supply Chain and Inventory Management","score":0.018200000748038292,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11864","display_name":"Supply Chain Resilience and Risk Management","score":0.008899999782443047,"subfield":{"id":"https://openalex.org/subfields/1408","display_name":"Strategy and Management"},"field":{"id":"https://openalex.org/fields/14","display_name":"Business, Management and Accounting"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/kontorovich-lebedev-transform","display_name":"Kontorovich-Lebedev transform","score":0.9179999828338623},{"id":"https://openalex.org/keywords/macdonald-functions","display_name":"Macdonald functions","score":0.828000009059906},{"id":"https://openalex.org/keywords/distributional-analysis","display_name":"distributional analysis","score":0.628000020980835},{"id":"https://openalex.org/keywords/generalized-functions","display_name":"generalized functions","score":0.9369999766349792},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.7350000143051147},{"id":"https://openalex.org/keywords/supply-chain-resilience","display_name":"supply chain resilience","score":0.5249999761581421},{"id":"https://openalex.org/keywords/supply-chain-disruption","display_name":"supply chain disruption","score":0.8029999732971191},{"id":"https://openalex.org/keywords/inventory-intensity","display_name":"inventory intensity","score":0.847000002861023},{"id":"https://openalex.org/keywords/digital-twin","display_name":"digital twin","score":0.6240000128746033},{"id":"https://openalex.org/keywords/spectral-analysis","display_name":"spectral analysis","score":0.6259999871253967}],"concepts":[{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.7815999984741211},{"id":"https://openalex.org/C158154518","wikidata":"https://www.wikidata.org/wiki/Q7310970","display_name":"Relevance (law)","level":2,"score":0.6617000102996826},{"id":"https://openalex.org/C197115733","wikidata":"https://www.wikidata.org/wiki/Q1003136","display_name":"Forcing (mathematics)","level":2,"score":0.6373000144958496},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6039999723434448},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.5878999829292297},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4740000069141388},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.454800009727478},{"id":"https://openalex.org/C57733114","wikidata":"https://www.wikidata.org/wiki/Q1006032","display_name":"Discrete Fourier transform (general)","level":5,"score":0.43779999017715454},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.41359999775886536},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.351500004529953},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3398999869823456},{"id":"https://openalex.org/C200052193","wikidata":"https://www.wikidata.org/wiki/Q877802","display_name":"Integral transform","level":2,"score":0.3296000063419342},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3257000148296356},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.3228999972343445},{"id":"https://openalex.org/C10879293","wikidata":"https://www.wikidata.org/wiki/Q726474","display_name":"Factor analysis","level":2,"score":0.2948000133037567},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2924000024795532},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.28459998965263367},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.28290000557899475},{"id":"https://openalex.org/C93038891","wikidata":"https://www.wikidata.org/wiki/Q1061524","display_name":"Intensity (physics)","level":2,"score":0.2809999883174896},{"id":"https://openalex.org/C2781039887","wikidata":"https://www.wikidata.org/wiki/Q1391724","display_name":"Factor (programming language)","level":2,"score":0.2800000011920929},{"id":"https://openalex.org/C142433447","wikidata":"https://www.wikidata.org/wiki/Q7806653","display_name":"Time\u2013frequency analysis","level":3,"score":0.2797999978065491},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.27079999446868896},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.2700999975204468},{"id":"https://openalex.org/C76563020","wikidata":"https://www.wikidata.org/wiki/Q4817582","display_name":"Fractional Fourier transform","level":4,"score":0.2694999873638153},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.26460000872612},{"id":"https://openalex.org/C30049272","wikidata":"https://www.wikidata.org/wiki/Q6555326","display_name":"Spectral density estimation","level":3,"score":0.2614000141620636},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.26109999418258667},{"id":"https://openalex.org/C99234102","wikidata":"https://www.wikidata.org/wiki/Q7395403","display_name":"S transform","level":5,"score":0.26089999079704285},{"id":"https://openalex.org/C69151251","wikidata":"https://www.wikidata.org/wiki/Q846537","display_name":"Generalized function","level":2,"score":0.25060001015663147},{"id":"https://openalex.org/C168110828","wikidata":"https://www.wikidata.org/wiki/Q1331626","display_name":"Spectral density","level":2,"score":0.25}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.55041/ijcope.v2i8.137","doi":"https://doi.org/10.55041/ijcope.v2i8.137","is_oa":true,"landing_page_url":"https://doi.org/10.55041/ijcope.v2i8.137","pdf_url":"https://ijcope.org/wp-content/uploads/2026/08/Distributional-Extension-of-the-FKF-Transform-and-Its-Relevance-to-Supply-Chain-Systems.pdf","source":{"id":"https://openalex.org/S7407055479","display_name":"International Journal of Creative and Open Research in Engineering and Management","issn_l":"3108-1754","issn":["3108-1754"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Creative and Open Research in Engineering and Management","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.55041/ijcope.v2i8.137","doi":"https://doi.org/10.55041/ijcope.v2i8.137","is_oa":true,"landing_page_url":"https://doi.org/10.55041/ijcope.v2i8.137","pdf_url":"https://ijcope.org/wp-content/uploads/2026/08/Distributional-Extension-of-the-FKF-Transform-and-Its-Relevance-to-Supply-Chain-Systems.pdf","source":{"id":"https://openalex.org/S7407055479","display_name":"International Journal of Creative and Open Research in Engineering and Management","issn_l":"3108-1754","issn":["3108-1754"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Creative and Open Research in Engineering and Management","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.7207000255584717,"display_name":"Industry, innovation and infrastructure","id":"https://metadata.un.org/sdg/9"}],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7203604665.pdf","grobid_xml":"https://content.openalex.org/works/W7203604665.grobid-xml"},"referenced_works_count":6,"referenced_works":["https://openalex.org/W2809983427","https://openalex.org/W3194769965","https://openalex.org/W7165742320","https://openalex.org/W7165780876","https://openalex.org/W7165796887","https://openalex.org/W7171216682"],"related_works":["https://openalex.org/W7203628282","https://openalex.org/W7204845163","https://openalex.org/W7203606182","https://openalex.org/W7203909822","https://openalex.org/W7203948226","https://openalex.org/W7204817135","https://openalex.org/W7204761815","https://openalex.org/W7207804907","https://openalex.org/W7203933543","https://openalex.org/W7204769693"],"abstract_inverted_index":{"This":[0],"paper":[1],"develops":[2],"the":[3,7,15,43,68,75,87],"distributional":[4,92],"theory":[5],"of":[6,17,46,83,89],"FKF":[8,22],"transform":[9,23,76],"and":[10,33,102,125,147],"demonstrates":[11],"its":[12],"relevance":[13],"to":[14,54,79,107,117],"analysis":[16],"modern":[18],"supply-chain":[19,118],"systems.":[20],"The":[21,49,91],"combines":[24],"a":[25,37,80,111],"Fourier":[26],"factor":[27,40],"that":[28,61],"captures":[29],"temporal":[30],"oscillations,":[31],"frequencies":[32],"lead-time":[34],"cycles":[35],"with":[36,142],"Kontorovich\u2013Lebedev":[38],"(KL)":[39],"built":[41],"from":[42],"Macdonald":[44],"function":[45],"imaginary":[47],"order.":[48],"latter":[50],"is":[51,77],"naturally":[52],"adapted":[53],"positive":[55],"scale,":[56],"distance":[57],"or":[58],"intensity":[59,124],"variables":[60],"arise":[62],"throughout":[63],"logistics":[64],"networks.":[65],"After":[66],"reviewing":[67],"classical":[69],"definition":[70],"on":[71],"suitable":[72],"testing-function":[73],"spaces,":[74],"extended":[78],"broad":[81],"class":[82],"generalized":[84],"functions":[85],"in":[86],"sense":[88],"Zemanian.":[90],"extension":[93],"permits":[94],"idealized":[95],"impulses,":[96],"abrupt":[97],"demand":[98],"shocks,":[99],"capacity":[100],"collapses":[101],"other":[103],"singular":[104],"forcing":[105],"terms":[106],"be":[108],"treated":[109],"within":[110],"single":[112],"rigorous":[113],"spectral":[114,127],"framework.":[115],"Applications":[116],"resilience,":[119],"disruption":[120],"modelling,":[121],"multi-scale":[122],"inventory":[123],"digital-twin":[126],"diagnostics":[128],"are":[129,138],"discussed.":[130],"Numerical":[131],"approximation":[132],"formulae":[133],"for":[134,144],"discrete":[135],"operational":[136],"data":[137],"also":[139],"provided,":[140],"together":[141],"recommendations":[143],"future":[145],"research":[146],"computational":[148],"practice.":[149]},"counts_by_year":[{"year":2026,"cited_by_count":46},{"year":2025,"cited_by_count":3}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2026-08-18T00:00:00"}