{"id":"https://openalex.org/W34043516","doi":"https://doi.org/10.1109/tcyb.2020.3004641","title":"A new method and its application to generalized q-Bessel polynomials","display_name":"A new method and its application to generalized q-Bessel polynomials","publication_year":2001,"publication_date":"2001-01-01","ids":{"openalex":"https://openalex.org/W34043516","doi":"https://doi.org/10.1109/tcyb.2020.3004641","mag":"34043516"},"language":"en","primary_location":{"id":"mag:34043516","is_oa":false,"landing_page_url":"http://www.diva-portal.org/smash/record.jsf?pid=diva2:66726","pdf_url":null,"source":{"id":"https://openalex.org/S4210191041","display_name":"IEEE Transactions on Cybernetics","issn_l":"2168-2267","issn":["2168-2267","2168-2275"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE transactions on cybernetics","raw_type":null},"type":"article","indexed_in":[],"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/A5042509034","display_name":"Thomas Ernst","orcid":"https://orcid.org/0000-0002-4687-1667"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Thomas Ernst","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-4687-1667","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5042509034"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.2343,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.72302864,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"52","issue":"7","first_page":"6543","last_page":"6554"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11428","display_name":"Advanced Mathematical Identities","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T11428","display_name":"Advanced Mathematical Identities","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T11191","display_name":"Mathematical functions and polynomials","score":0.9998999834060669,"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/T11166","display_name":"Analytic Number Theory Research","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/mathematics","display_name":"Mathematics","score":0.6609336137771606},{"id":"https://openalex.org/keywords/bessel-polynomials","display_name":"Bessel polynomials","score":0.6405091285705566},{"id":"https://openalex.org/keywords/bessel-function","display_name":"Bessel function","score":0.5404677391052246},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4437004625797272},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.41508013010025024},{"id":"https://openalex.org/keywords/classical-orthogonal-polynomials","display_name":"Classical orthogonal polynomials","score":0.41307342052459717},{"id":"https://openalex.org/keywords/orthogonal-polynomials","display_name":"Orthogonal polynomials","score":0.39852121472358704},{"id":"https://openalex.org/keywords/wilson-polynomials","display_name":"Wilson polynomials","score":0.35255393385887146},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3262762725353241},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2682628631591797},{"id":"https://openalex.org/keywords/medicine","display_name":"Medicine","score":0.07354938983917236}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6609336137771606},{"id":"https://openalex.org/C73295869","wikidata":"https://www.wikidata.org/wiki/Q4896402","display_name":"Bessel polynomials","level":5,"score":0.6405091285705566},{"id":"https://openalex.org/C107706756","wikidata":"https://www.wikidata.org/wiki/Q219637","display_name":"Bessel function","level":2,"score":0.5404677391052246},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4437004625797272},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.41508013010025024},{"id":"https://openalex.org/C21736991","wikidata":"https://www.wikidata.org/wiki/Q17006917","display_name":"Classical orthogonal polynomials","level":3,"score":0.41307342052459717},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.39852121472358704},{"id":"https://openalex.org/C43176163","wikidata":"https://www.wikidata.org/wiki/Q8023263","display_name":"Wilson polynomials","level":4,"score":0.35255393385887146},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3262762725353241},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2682628631591797},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.07354938983917236},{"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":"mag:34043516","is_oa":false,"landing_page_url":"http://www.diva-portal.org/smash/record.jsf?pid=diva2:66726","pdf_url":null,"source":{"id":"https://openalex.org/S4210191041","display_name":"IEEE Transactions on Cybernetics","issn_l":"2168-2267","issn":["2168-2267","2168-2275"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE transactions on cybernetics","raw_type":null},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.65.7729","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.65.7729","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.uu.se/research/pub/Ernst5.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G11847706","display_name":null,"funder_award_id":"61632018","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3732680637","display_name":"\u6df1\u5ea6\u89c6\u89c9\u96f6\u6837\u672c\u5b66\u4e60\u5173\u952e\u6280\u672f\u7814\u7a76","funder_award_id":"61771329","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G601340942","display_name":null,"funder_award_id":"2020QNA5010","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W230523020","https://openalex.org/W1495550473","https://openalex.org/W1510348186","https://openalex.org/W1522793004","https://openalex.org/W1594563152","https://openalex.org/W1966268321","https://openalex.org/W1971123899","https://openalex.org/W1975085551","https://openalex.org/W1976159081","https://openalex.org/W1978495773","https://openalex.org/W1981220623","https://openalex.org/W1996965099","https://openalex.org/W2002357000","https://openalex.org/W2003325493","https://openalex.org/W2008052995","https://openalex.org/W2027018061","https://openalex.org/W2028017249","https://openalex.org/W2031356832","https://openalex.org/W2033151001","https://openalex.org/W2044740790","https://openalex.org/W2052621205","https://openalex.org/W2058017258","https://openalex.org/W2064786715","https://openalex.org/W2077290892","https://openalex.org/W2078984934","https://openalex.org/W2080261998","https://openalex.org/W2088802737","https://openalex.org/W2123952220","https://openalex.org/W2145552616","https://openalex.org/W2146098404","https://openalex.org/W2318152807","https://openalex.org/W2599604731","https://openalex.org/W2605520562","https://openalex.org/W3040464464"],"related_works":["https://openalex.org/W2885890865","https://openalex.org/W1479708902","https://openalex.org/W3022096402","https://openalex.org/W2046913223","https://openalex.org/W2071157507","https://openalex.org/W2332331898","https://openalex.org/W2022600882","https://openalex.org/W3204466845","https://openalex.org/W1969966400","https://openalex.org/W2747635820","https://openalex.org/W2949834558","https://openalex.org/W2044230273","https://openalex.org/W2998899482","https://openalex.org/W2600367300","https://openalex.org/W1532702160","https://openalex.org/W2963752488","https://openalex.org/W151796810","https://openalex.org/W1541597676","https://openalex.org/W2027018061","https://openalex.org/W2068075982"],"abstract_inverted_index":{"In":[0,28,54],"this":[1],"article,":[2],"we":[3,108,127,176],"focus":[4],"on":[5,207,213,252],"the":[6,19,31,40,49,55,58,70,74,83,88,95,103,123,130,150,166,169,187,193,203,236,244,249,258,263,267],"task":[7],"of":[8,61,133],"zero-shot":[9],"image":[10,33],"classification":[11,264],"(ZSIC)":[12],"that":[13,149,165,228,239,257],"equips":[14],"a":[15,66,99,110,144],"learning":[16],"system":[17],"with":[18,48,158],"ability":[20,98],"to":[21,30,80,82,114,119,122,142,147,185,202,243],"recognize":[22],"visual":[23,190],"images":[24,134],"from":[25,39,135,168],"unseen":[26,85,237],"classes.":[27],"contrast":[29],"traditional":[32,89,221],"classification,":[34],"ZSIC":[35,216,222,225],"more":[36,46],"easily":[37],"suffers":[38],"class-imbalance":[41,104],"issue":[42,105],"since":[43],"it":[44],"is":[45,78],"concerned":[47],"class-level":[50],"knowledge":[51],"transferring":[52],"capability.":[53],"real":[56],"world,":[57],"sample":[59],"numbers":[60],"different":[62,200],"categories":[63,238],"generally":[64],"follow":[65],"long-tailed":[67],"distribution,":[68],"and":[69,223],"discriminative":[71,188],"information":[72],"in":[73,87,106,173],"sample-scarce":[75,151,245],"seen":[76,246],"classes":[77,86,118,141,152,157],"hard":[79],"transfer":[81],"related":[84,242],"batch-based":[90],"training":[91,112,117,140,145],"manner,":[92],"which":[93],"degrades":[94],"overall":[96],"generalization":[97],"lot.":[100],"To":[101],"alleviate":[102],"ZSIC,":[107],"propose":[109],"sample-balanced":[111],"process":[113,197],"encourage":[115],"all":[116,139],"contribute":[120,153],"equally":[121,154],"learned":[124],"model.":[125,269],"Specifically,":[126],"randomly":[128],"select":[129],"same":[131,170],"number":[132],"each":[136,162],"class":[137,171,174,189,209],"across":[138],"form":[143],"batch":[146],"ensure":[148],"as":[155],"those":[156],"sufficient":[159],"samples":[160,205],"during":[161],"iteration.":[163],"Considering":[164],"instances":[167],"differ":[172],"representativeness,":[175],"further":[177],"develop":[178],"an":[179],"efficient":[180],"semantic-guided":[181],"feature":[182],"fusion":[183],"model":[184],"obtain":[186],"prototype":[191],"for":[192,219,235],"following":[194],"visual-semantic":[195],"interaction":[196],"via":[198],"distributing":[199],"weights":[201],"selected":[204],"based":[206],"their":[208],"representativeness.":[210],"Extensive":[211],"experiments":[212],"three":[214],"imbalanced":[215],"benchmark":[217],"datasets":[218,255],"both":[220],"generalized":[224],"tasks":[226],"demonstrate":[227],"our":[229],"approach":[230,260],"achieves":[231],"promising":[232],"results,":[233],"especially":[234],"are":[240],"closely":[241],"categories.":[247],"Besides,":[248],"experimental":[250],"results":[251],"two":[253],"class-balanced":[254],"show":[256],"proposed":[259],"also":[261],"improves":[262],"performance":[265],"against":[266],"baseline":[268]},"counts_by_year":[{"year":2014,"cited_by_count":1}],"updated_date":"2025-07-23T07:26:32.042638","created_date":"2016-06-24T00:00:00"}