{"id":"https://openalex.org/W2994896855","doi":"https://doi.org/10.3390/sym11121530","title":"Kim, T. et al. Degenerate Stirling Polynomials of the Second Kind and Some Applications. Symmetry, 2019, 11(8), 1046","display_name":"Kim, T. et al. Degenerate Stirling Polynomials of the Second Kind and Some Applications. Symmetry, 2019, 11(8), 1046","publication_year":2019,"publication_date":"2019-12-17","ids":{"openalex":"https://openalex.org/W2994896855","doi":"https://doi.org/10.3390/sym11121530","mag":"2994896855"},"language":"en","primary_location":{"id":"doi:10.3390/sym11121530","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym11121530","pdf_url":"https://www.mdpi.com/2073-8994/11/12/1530/pdf?version=1576615031","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/11/12/1530/pdf?version=1576615031","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100653780","display_name":"Taekyun Kim","orcid":"https://orcid.org/0000-0002-3731-7023"},"institutions":[{"id":"https://openalex.org/I161024014","display_name":"Kwangwoon University","ror":"https://ror.org/02e9zc863","country_code":"KR","type":"education","lineage":["https://openalex.org/I161024014"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Taekyun Kim","raw_affiliation_strings":["Department of Mathematics, Kwangwoon University, Seoul 139-701, Korea"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Kwangwoon University, Seoul 139-701, Korea","institution_ids":["https://openalex.org/I161024014"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003571699","display_name":"Dae San Kim","orcid":"https://orcid.org/0000-0001-9599-7015"},"institutions":[{"id":"https://openalex.org/I148751991","display_name":"Sogang University","ror":"https://ror.org/056tn4839","country_code":"KR","type":"education","lineage":["https://openalex.org/I148751991"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Dae San Kim","raw_affiliation_strings":["Department of Mathematics, Sogang University, Seoul 121-742, Korea"],"raw_orcid":"https://orcid.org/0000-0001-9599-7015","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Sogang University, Seoul 121-742, Korea","institution_ids":["https://openalex.org/I148751991"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029305363","display_name":"Han Young Kim","orcid":"https://orcid.org/0000-0002-5585-9272"},"institutions":[{"id":"https://openalex.org/I161024014","display_name":"Kwangwoon University","ror":"https://ror.org/02e9zc863","country_code":"KR","type":"education","lineage":["https://openalex.org/I161024014"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Han Young Kim","raw_affiliation_strings":["Department of Mathematics, Kwangwoon University, Seoul 139-701, Korea"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Kwangwoon University, Seoul 139-701, Korea","institution_ids":["https://openalex.org/I161024014"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5081051998","display_name":"Jongkyum Kwon","orcid":"https://orcid.org/0000-0002-3470-5020"},"institutions":[{"id":"https://openalex.org/I189442560","display_name":"Gyeongsang National University","ror":"https://ror.org/00saywf64","country_code":"KR","type":"education","lineage":["https://openalex.org/I189442560"]}],"countries":["KR"],"is_corresponding":true,"raw_author_name":"Jongkyum Kwon","raw_affiliation_strings":["Department of Mathematics Education and ERI, Gyeongsang National University, Jinju 52828, Korea"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics Education and ERI, Gyeongsang National University, Jinju 52828, Korea","institution_ids":["https://openalex.org/I189442560"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5081051998"],"corresponding_institution_ids":["https://openalex.org/I189442560"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.0854,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.49228747,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"11","issue":"12","first_page":"1530","last_page":"1530"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10407","display_name":"Lipid Membrane Structure and Behavior","score":0.9855999946594238,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T10407","display_name":"Lipid Membrane Structure and Behavior","score":0.9855999946594238,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T12084","display_name":"Synthesis and properties of polymers","score":0.9814000129699707,"subfield":{"id":"https://openalex.org/subfields/2507","display_name":"Polymers and Plastics"},"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/T10721","display_name":"Surfactants and Colloidal Systems","score":0.9671000242233276,"subfield":{"id":"https://openalex.org/subfields/1605","display_name":"Organic Chemistry"},"field":{"id":"https://openalex.org/fields/16","display_name":"Chemistry"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/degenerate-energy-levels","display_name":"Degenerate energy levels","score":0.7553826570510864},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.7207733988761902},{"id":"https://openalex.org/keywords/stirling-engine","display_name":"Stirling engine","score":0.526552677154541},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.49085289239883423},{"id":"https://openalex.org/keywords/stirling-number","display_name":"Stirling number","score":0.48270630836486816},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.4619596004486084},{"id":"https://openalex.org/keywords/wish","display_name":"Wish","score":0.4401628077030182},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4197123050689697},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.39397960901260376},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.39006805419921875},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.37850913405418396},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3657785654067993},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.34796521067619324},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.32199111580848694},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.24985918402671814},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.16732719540596008},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.09766837954521179},{"id":"https://openalex.org/keywords/medicine","display_name":"Medicine","score":0.09212860465049744}],"concepts":[{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.7553826570510864},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.7207733988761902},{"id":"https://openalex.org/C27134321","wikidata":"https://www.wikidata.org/wiki/Q186212","display_name":"Stirling engine","level":2,"score":0.526552677154541},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49085289239883423},{"id":"https://openalex.org/C168902406","wikidata":"https://www.wikidata.org/wiki/Q80918","display_name":"Stirling number","level":2,"score":0.48270630836486816},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.4619596004486084},{"id":"https://openalex.org/C2781298115","wikidata":"https://www.wikidata.org/wiki/Q241625","display_name":"Wish","level":2,"score":0.4401628077030182},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4197123050689697},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.39397960901260376},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.39006805419921875},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.37850913405418396},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3657785654067993},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34796521067619324},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.32199111580848694},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.24985918402671814},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.16732719540596008},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.09766837954521179},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.09212860465049744},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0},{"id":"https://openalex.org/C19165224","wikidata":"https://www.wikidata.org/wiki/Q23404","display_name":"Anthropology","level":1,"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:10.3390/sym11121530","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym11121530","pdf_url":"https://www.mdpi.com/2073-8994/11/12/1530/pdf?version=1576615031","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:mdpi.com:/2073-8994/11/12/1530/","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/sym11121530","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":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym11121530","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym11121530","pdf_url":"https://www.mdpi.com/2073-8994/11/12/1530/pdf?version=1576615031","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5781575782","display_name":null,"funder_award_id":"2017R1E1A1A03070882","funder_id":"https://openalex.org/F4320322120","funder_display_name":"National Research Foundation of Korea"}],"funders":[{"id":"https://openalex.org/F4320322120","display_name":"National Research Foundation of Korea","ror":"https://ror.org/013aysd81"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":1,"referenced_works":["https://openalex.org/W2968744016"],"related_works":["https://openalex.org/W4281748020","https://openalex.org/W4313148216","https://openalex.org/W4313403335","https://openalex.org/W2786724599","https://openalex.org/W4221162632","https://openalex.org/W4295116579","https://openalex.org/W2000880393","https://openalex.org/W3088269311","https://openalex.org/W4229049803","https://openalex.org/W4360977521"],"abstract_inverted_index":{"The":[0],"authors":[1],"wish":[2],"to":[3,8],"make":[4],"the":[5,9],"following":[6],"corrections":[7],"published":[10],"paper":[11],"[...]":[12]},"counts_by_year":[{"year":2021,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}