{"id":"https://openalex.org/W2811463075","doi":"https://doi.org/10.3390/sym10070239","title":"On the Convolution Quadrature Rule for Integral Transforms with Oscillatory Bessel Kernels","display_name":"On the Convolution Quadrature Rule for Integral Transforms with Oscillatory Bessel Kernels","publication_year":2018,"publication_date":"2018-06-25","ids":{"openalex":"https://openalex.org/W2811463075","doi":"https://doi.org/10.3390/sym10070239","mag":"2811463075"},"language":"en","primary_location":{"id":"doi:10.3390/sym10070239","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym10070239","pdf_url":"https://www.mdpi.com/2073-8994/10/7/239/pdf?version=1529909348","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/2073-8994/10/7/239/pdf?version=1529909348","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5018872719","display_name":"Junjie Ma","orcid":"https://orcid.org/0000-0001-7868-827X"},"institutions":[{"id":"https://openalex.org/I178232147","display_name":"Guizhou University","ror":"https://ror.org/02wmsc916","country_code":"CN","type":"education","lineage":["https://openalex.org/I178232147"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Junjie Ma","raw_affiliation_strings":["Guizhou Provincial Key Laboratory of Public Big Data, Guizhou University, Guiyang 550025, China","School of Mathematics and Statistics, Guizhou University, Guiyang 550025, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Guizhou Provincial Key Laboratory of Public Big Data, Guizhou University, Guiyang 550025, China","institution_ids":["https://openalex.org/I178232147"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Guizhou University, Guiyang 550025, China","institution_ids":["https://openalex.org/I178232147"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5090527349","display_name":"Huilan Liu","orcid":"https://orcid.org/0000-0001-5388-0986"},"institutions":[{"id":"https://openalex.org/I178232147","display_name":"Guizhou University","ror":"https://ror.org/02wmsc916","country_code":"CN","type":"education","lineage":["https://openalex.org/I178232147"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Huilan Liu","raw_affiliation_strings":["Guizhou Provincial Key Laboratory of Public Big Data, Guizhou University, Guiyang 550025, China","School of Mathematics and Statistics, Guizhou University, Guiyang 550025, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Guizhou Provincial Key Laboratory of Public Big Data, Guizhou University, Guiyang 550025, China","institution_ids":["https://openalex.org/I178232147"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Guizhou University, Guiyang 550025, China","institution_ids":["https://openalex.org/I178232147"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5018872719","https://openalex.org/A5090527349"],"corresponding_institution_ids":["https://openalex.org/I178232147"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.9452,"has_fulltext":true,"cited_by_count":14,"citation_normalized_percentile":{"value":0.73665049,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"10","issue":"7","first_page":"239","last_page":"239"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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":0.9980999827384949,"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9973999857902527,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/quadrature","display_name":"Quadrature (astronomy)","score":0.7805489897727966},{"id":"https://openalex.org/keywords/numerical-integration","display_name":"Numerical integration","score":0.7096192240715027},{"id":"https://openalex.org/keywords/clenshaw\u2013curtis-quadrature","display_name":"Clenshaw\u2013Curtis quadrature","score":0.6999301910400391},{"id":"https://openalex.org/keywords/gauss\u2013kronrod-quadrature-formula","display_name":"Gauss\u2013Kronrod quadrature formula","score":0.6898621320724487},{"id":"https://openalex.org/keywords/tanh-sinh-quadrature","display_name":"Tanh-sinh quadrature","score":0.6196308732032776},{"id":"https://openalex.org/keywords/gauss\u2013jacobi-quadrature","display_name":"Gauss\u2013Jacobi quadrature","score":0.6054068207740784},{"id":"https://openalex.org/keywords/convolution","display_name":"Convolution (computer science)","score":0.5873565673828125},{"id":"https://openalex.org/keywords/gaussian-quadrature","display_name":"Gaussian quadrature","score":0.5446502566337585},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5163551568984985},{"id":"https://openalex.org/keywords/bessel-function","display_name":"Bessel function","score":0.5038401484489441},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.475144624710083},{"id":"https://openalex.org/keywords/adaptive-quadrature","display_name":"Adaptive quadrature","score":0.45813798904418945},{"id":"https://openalex.org/keywords/gauss\u2013laguerre-quadrature","display_name":"Gauss\u2013Laguerre quadrature","score":0.4256131649017334},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.37607520818710327},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.3106074035167694},{"id":"https://openalex.org/keywords/nystr\u00f6m-method","display_name":"Nystr\u00f6m method","score":0.28269314765930176},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2504481077194214},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.08057916164398193},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07353657484054565}],"concepts":[{"id":"https://openalex.org/C62869609","wikidata":"https://www.wikidata.org/wiki/Q28137","display_name":"Quadrature (astronomy)","level":2,"score":0.7805489897727966},{"id":"https://openalex.org/C127349201","wikidata":"https://www.wikidata.org/wiki/Q753445","display_name":"Numerical integration","level":2,"score":0.7096192240715027},{"id":"https://openalex.org/C172657837","wikidata":"https://www.wikidata.org/wiki/Q5131618","display_name":"Clenshaw\u2013Curtis quadrature","level":5,"score":0.6999301910400391},{"id":"https://openalex.org/C14103991","wikidata":"https://www.wikidata.org/wiki/Q5527852","display_name":"Gauss\u2013Kronrod quadrature formula","level":4,"score":0.6898621320724487},{"id":"https://openalex.org/C162046254","wikidata":"https://www.wikidata.org/wiki/Q7683194","display_name":"Tanh-sinh quadrature","level":5,"score":0.6196308732032776},{"id":"https://openalex.org/C54691486","wikidata":"https://www.wikidata.org/wiki/Q5527851","display_name":"Gauss\u2013Jacobi quadrature","level":5,"score":0.6054068207740784},{"id":"https://openalex.org/C45347329","wikidata":"https://www.wikidata.org/wiki/Q5166604","display_name":"Convolution (computer science)","level":3,"score":0.5873565673828125},{"id":"https://openalex.org/C167196314","wikidata":"https://www.wikidata.org/wiki/Q767680","display_name":"Gaussian quadrature","level":4,"score":0.5446502566337585},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5163551568984985},{"id":"https://openalex.org/C107706756","wikidata":"https://www.wikidata.org/wiki/Q219637","display_name":"Bessel function","level":2,"score":0.5038401484489441},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.475144624710083},{"id":"https://openalex.org/C184599523","wikidata":"https://www.wikidata.org/wiki/Q4680758","display_name":"Adaptive quadrature","level":4,"score":0.45813798904418945},{"id":"https://openalex.org/C6866599","wikidata":"https://www.wikidata.org/wiki/Q4218412","display_name":"Gauss\u2013Laguerre quadrature","level":5,"score":0.4256131649017334},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.37607520818710327},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.3106074035167694},{"id":"https://openalex.org/C48265008","wikidata":"https://www.wikidata.org/wiki/Q7071295","display_name":"Nystr\u00f6m method","level":3,"score":0.28269314765930176},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2504481077194214},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.08057916164398193},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07353657484054565},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3390/sym10070239","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym10070239","pdf_url":"https://www.mdpi.com/2073-8994/10/7/239/pdf?version=1529909348","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"}],"best_oa_location":{"id":"doi:10.3390/sym10070239","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym10070239","pdf_url":"https://www.mdpi.com/2073-8994/10/7/239/pdf?version=1529909348","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/G1292200566","display_name":"COLLABORATIVE RESEARCH: Multimodal signaling in rhinoceros beetles","funder_award_id":"2016125","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G418668863","display_name":null,"funder_award_id":"QKH[2017]5788","funder_id":"https://openalex.org/F4320322272","funder_display_name":"Guizhou Science and Technology Department"},{"id":"https://openalex.org/G4540527285","display_name":null,"funder_award_id":"[2017]5788","funder_id":"https://openalex.org/F4320326674","funder_display_name":"Department of Education of Guizhou Province"},{"id":"https://openalex.org/G6239680297","display_name":"\u7f3a\u5931\u6570\u636e\u4e0b\u534a\u53c2\u6570\u56de\u5f52\u6a21\u578b\u7684\u7a33\u5065\u4f30\u8ba1\u53ca\u53d8\u91cf\u9009\u62e9\u65b9\u6cd5\u7814\u7a76","funder_award_id":"11761020","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8147327638","display_name":null,"funder_award_id":"[2017]5788","funder_id":"https://openalex.org/F4320322272","funder_display_name":"Guizhou Science and Technology Department"},{"id":"https://openalex.org/G8267787854","display_name":null,"funder_award_id":"[2017]5788","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322272","display_name":"Guizhou Science and Technology Department","ror":"https://ror.org/00kwnh405"},{"id":"https://openalex.org/F4320326674","display_name":"Department of Education of Guizhou Province","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2811463075.pdf","grobid_xml":"https://content.openalex.org/works/W2811463075.grobid-xml"},"referenced_works_count":31,"referenced_works":["https://openalex.org/W1974613178","https://openalex.org/W1979313496","https://openalex.org/W1986853328","https://openalex.org/W1989095828","https://openalex.org/W1993395418","https://openalex.org/W1999416634","https://openalex.org/W2009986244","https://openalex.org/W2010311824","https://openalex.org/W2019979782","https://openalex.org/W2021297049","https://openalex.org/W2029837441","https://openalex.org/W2031966155","https://openalex.org/W2061749829","https://openalex.org/W2064079660","https://openalex.org/W2065529515","https://openalex.org/W2073377075","https://openalex.org/W2081260656","https://openalex.org/W2081814612","https://openalex.org/W2090616302","https://openalex.org/W2092552789","https://openalex.org/W2112658815","https://openalex.org/W2116266506","https://openalex.org/W2126358436","https://openalex.org/W2129647233","https://openalex.org/W2147983461","https://openalex.org/W2169806412","https://openalex.org/W2463002925","https://openalex.org/W2779980829","https://openalex.org/W2791387702","https://openalex.org/W2801203067","https://openalex.org/W3148434010"],"related_works":["https://openalex.org/W2289189603","https://openalex.org/W4294281846","https://openalex.org/W2106219619","https://openalex.org/W2032097736","https://openalex.org/W4390128132","https://openalex.org/W4317584040","https://openalex.org/W4377005030","https://openalex.org/W2125520544","https://openalex.org/W2765175526","https://openalex.org/W1992170928"],"abstract_inverted_index":{"Lubich\u2019s":[0],"convolution":[1,43,61,92,110],"quadrature":[2,44,62,93,111],"rule":[3,45,63,94,112],"provides":[4],"efficient":[5,119],"approximations":[6],"to":[7,17,36,66,74,86],"integrals":[8],"with":[9,64],"special":[10],"kernels.":[11],"Particularly,":[12],"when":[13],"it":[14,25],"is":[15,34,69,79,101,118],"applied":[16],"computing":[18],"highly":[19,47,75,97,115],"oscillatory":[20,48,76,98,116],"integrals,":[21],"numerical":[22,106],"tests":[23],"show":[24],"does":[26],"not":[27],"suffer":[28],"from":[29,103],"fast":[30],"oscillation.":[31],"This":[32],"paper":[33],"devoted":[35],"studying":[37],"the":[38,42,51,56,60,67,88,91,109],"convergence":[39,57],"property":[40],"of":[41,53,59,90],"for":[46,113],"problems.":[49,99],"With":[50],"help":[52],"operational":[54],"calculus,":[55],"rate":[58],"respect":[65],"frequency":[68],"derived.":[70],"Furthermore,":[71],"its":[72],"application":[73],"integral":[77],"equations":[78],"also":[80],"investigated.":[81],"Numerical":[82],"results":[83,107],"are":[84],"presented":[85],"verify":[87],"effectiveness":[89],"in":[95],"solving":[96,114],"It":[100],"found":[102],"theoretical":[104],"and":[105,120],"that":[108],"problems":[117],"high-potential.":[121]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1}],"updated_date":"2026-06-06T09:05:17.133730","created_date":"2025-10-10T00:00:00"}