{"id":"https://openalex.org/W2733906233","doi":"https://doi.org/10.3390/axioms6030020","title":"Quincunx Fundamental Refinable Functions in Arbitrary Dimensions","display_name":"Quincunx Fundamental Refinable Functions in Arbitrary Dimensions","publication_year":2017,"publication_date":"2017-07-06","ids":{"openalex":"https://openalex.org/W2733906233","doi":"https://doi.org/10.3390/axioms6030020","mag":"2733906233"},"language":"en","primary_location":{"id":"doi:10.3390/axioms6030020","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms6030020","pdf_url":"https://www.mdpi.com/2075-1680/6/3/20/pdf?version=1499681396","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"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":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/6/3/20/pdf?version=1499681396","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5073172471","display_name":"Xiaosheng Zhuang","orcid":"https://orcid.org/0000-0001-7238-0143"},"institutions":[{"id":"https://openalex.org/I168719708","display_name":"City University of Hong Kong","ror":"https://ror.org/03q8dnn23","country_code":"HK","type":"education","lineage":["https://openalex.org/I168719708"]}],"countries":["HK"],"is_corresponding":true,"raw_author_name":"Xiaosheng Zhuang","raw_affiliation_strings":["Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon Tong, Hong Kong"],"raw_orcid":"https://orcid.org/0000-0001-7238-0143","affiliations":[{"raw_affiliation_string":"Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon Tong, Hong Kong","institution_ids":["https://openalex.org/I168719708"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5073172471"],"corresponding_institution_ids":["https://openalex.org/I168719708"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.0,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.08989512,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"6","issue":"3","first_page":"20","last_page":"20"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12923","display_name":"Digital Image Processing Techniques","score":0.9857000112533569,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10481","display_name":"Computer Graphics and Visualization Techniques","score":0.9797000288963318,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8145314455032349},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.7185118198394775},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5899641513824463},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.5340584516525269},{"id":"https://openalex.org/keywords/dilation","display_name":"Dilation (metric space)","score":0.48201265931129456},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.34333378076553345},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.33198821544647217},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.22876602411270142}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8145314455032349},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.7185118198394775},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5899641513824463},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.5340584516525269},{"id":"https://openalex.org/C2780757906","wikidata":"https://www.wikidata.org/wiki/Q5276676","display_name":"Dilation (metric space)","level":2,"score":0.48201265931129456},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.34333378076553345},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.33198821544647217},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.22876602411270142},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/axioms6030020","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms6030020","pdf_url":"https://www.mdpi.com/2075-1680/6/3/20/pdf?version=1499681396","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"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":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:db4a51a1c7c04e6dbb865a512387fe51","is_oa":false,"landing_page_url":"https://doaj.org/article/db4a51a1c7c04e6dbb865a512387fe51","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 6, Iss 3, p 20 (2017)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/6/3/20/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms6030020","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":"Axioms; Volume 6; Issue 3; Pages: 20","raw_type":"Text"},{"id":"pmh:oai:pure.atira.dk:publications/77ffa5e5-dc92-4440-9533-0c0fa44c91dd","is_oa":true,"landing_page_url":"https://hdl.handle.net/2031/77ffa5e5-dc92-4440-9533-0c0fa44c91dd","pdf_url":null,"source":{"id":"https://openalex.org/S7407055387","display_name":"CityU Scholars","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"Zhuang, X 2017, 'Quincunx fundamental refinable functions in arbitrary dimensions', Axioms, vol. 6, no. 3, 20. https://doi.org/10.3390/axioms6030020","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.3390/axioms6030020","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms6030020","pdf_url":"https://www.mdpi.com/2075-1680/6/3/20/pdf?version=1499681396","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"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":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1520570889","display_name":null,"funder_award_id":"7004445","funder_id":"https://openalex.org/F4320309893","funder_display_name":"City University of Hong Kong"},{"id":"https://openalex.org/G6041244236","display_name":null,"funder_award_id":"7200462","funder_id":"https://openalex.org/F4320309893","funder_display_name":"City University of Hong Kong"}],"funders":[{"id":"https://openalex.org/F4320309893","display_name":"City University of Hong Kong","ror":"https://ror.org/03q8dnn23"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2733906233.pdf","grobid_xml":"https://content.openalex.org/works/W2733906233.grobid-xml"},"referenced_works_count":21,"referenced_works":["https://openalex.org/W1758200638","https://openalex.org/W1973537402","https://openalex.org/W1973858921","https://openalex.org/W1987996534","https://openalex.org/W1990032047","https://openalex.org/W1991963339","https://openalex.org/W1997381877","https://openalex.org/W2029204039","https://openalex.org/W2043737174","https://openalex.org/W2051121810","https://openalex.org/W2051656206","https://openalex.org/W2053362192","https://openalex.org/W2065661959","https://openalex.org/W2070372935","https://openalex.org/W2103965347","https://openalex.org/W2315820111","https://openalex.org/W2485137799","https://openalex.org/W4242546747","https://openalex.org/W4251619700","https://openalex.org/W4255272544","https://openalex.org/W6663744050"],"related_works":["https://openalex.org/W3132983279","https://openalex.org/W2495356367","https://openalex.org/W1522520750","https://openalex.org/W2392687107","https://openalex.org/W3124990892","https://openalex.org/W2944641486","https://openalex.org/W3207208339","https://openalex.org/W2182121179","https://openalex.org/W2130323728","https://openalex.org/W2497538886"],"abstract_inverted_index":{"In":[0,63],"this":[1],"paper,":[2],"we":[3,69],"generalize":[4],"the":[5,20,59,71,82],"family":[6,27,40,50,88],"of":[7,28,41,51,54,74,85,89],"Deslauriers\u2013Dubuc\u2019s":[8],"interpolatory":[9,44,78],"masks":[10,45,52],"from":[11],"dimension":[12,64],"one":[13],"to":[14,19],"arbitrary":[15,34],"dimensions":[16],"with":[17],"respect":[18],"quincunx":[21,29,43,77],"dilation":[22],"matrices,":[23],"thereby":[24],"providing":[25],"a":[26,39,49,87],"fundamental":[30],"refinable":[31],"functions":[32],"in":[33],"dimensions.":[35],"We":[36],"show":[37],"that":[38],"unique":[42,76],"exists":[46],"and":[47,57],"such":[48,75,86],"is":[53],"real":[55],"value":[56],"has":[58],"full-axis":[60],"symmetry":[61],"property.":[62],"d":[65],"=":[66],"2":[67],",":[68],"give":[70],"explicit":[72],"form":[73],"masks,":[79],"which":[80],"implies":[81],"nonnegativity":[83],"property":[84],"masks.":[90]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}