{"id":"https://openalex.org/W2172114616","doi":"https://doi.org/10.1080/00207160410001712323","title":"Solution of variational problems via Haar orthonormal wavelet direct method","display_name":"Solution of variational problems via Haar orthonormal wavelet direct method","publication_year":2004,"publication_date":"2004-06-29","ids":{"openalex":"https://openalex.org/W2172114616","doi":"https://doi.org/10.1080/00207160410001712323","mag":"2172114616"},"language":"en","primary_location":{"id":"doi:10.1080/00207160410001712323","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160410001712323","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"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/A5101795831","display_name":"Chun\u2010Hui Hsiao","orcid":"https://orcid.org/0000-0003-4136-7450"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Chun-Hui Hsiao","raw_affiliation_strings":["Correspondencehaar.wavelet@msa.hinet.net"],"affiliations":[{"raw_affiliation_string":"Correspondencehaar.wavelet@msa.hinet.net","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5101795831"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.9228,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.73490984,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"81","issue":"7","first_page":"871","last_page":"887"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9997000098228455,"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":0.9997000098228455,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9986000061035156,"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":0.9977999925613403,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/orthonormal-basis","display_name":"Orthonormal basis","score":0.9068772792816162},{"id":"https://openalex.org/keywords/haar","display_name":"Haar","score":0.8325079679489136},{"id":"https://openalex.org/keywords/haar-wavelet","display_name":"Haar wavelet","score":0.7361757755279541},{"id":"https://openalex.org/keywords/wavelet","display_name":"Wavelet","score":0.7189537286758423},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6848815679550171},{"id":"https://openalex.org/keywords/orthonormality","display_name":"Orthonormality","score":0.5314031839370728},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5145934820175171},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.43564358353614807},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.40276095271110535},{"id":"https://openalex.org/keywords/wavelet-transform","display_name":"Wavelet transform","score":0.34547311067581177},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.33757901191711426},{"id":"https://openalex.org/keywords/discrete-wavelet-transform","display_name":"Discrete wavelet transform","score":0.31938502192497253},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.17615574598312378},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.06627717614173889},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0644713044166565}],"concepts":[{"id":"https://openalex.org/C5806529","wikidata":"https://www.wikidata.org/wiki/Q2365325","display_name":"Orthonormal basis","level":2,"score":0.9068772792816162},{"id":"https://openalex.org/C187029792","wikidata":"https://www.wikidata.org/wiki/Q2179112","display_name":"Haar","level":3,"score":0.8325079679489136},{"id":"https://openalex.org/C2780423554","wikidata":"https://www.wikidata.org/wiki/Q766198","display_name":"Haar wavelet","level":5,"score":0.7361757755279541},{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.7189537286758423},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6848815679550171},{"id":"https://openalex.org/C92951342","wikidata":"https://www.wikidata.org/wiki/Q1411166","display_name":"Orthonormality","level":3,"score":0.5314031839370728},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5145934820175171},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.43564358353614807},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.40276095271110535},{"id":"https://openalex.org/C196216189","wikidata":"https://www.wikidata.org/wiki/Q2867","display_name":"Wavelet transform","level":3,"score":0.34547311067581177},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.33757901191711426},{"id":"https://openalex.org/C46286280","wikidata":"https://www.wikidata.org/wiki/Q2414958","display_name":"Discrete wavelet transform","level":4,"score":0.31938502192497253},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.17615574598312378},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.06627717614173889},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0644713044166565},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207160410001712323","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160410001712323","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W1619186981","https://openalex.org/W1971409566","https://openalex.org/W1978063062","https://openalex.org/W1980564965","https://openalex.org/W1986830331","https://openalex.org/W1996021349","https://openalex.org/W1996647346","https://openalex.org/W2007351100","https://openalex.org/W2012024871","https://openalex.org/W2018292279","https://openalex.org/W2037090034","https://openalex.org/W2039216370","https://openalex.org/W2041752335","https://openalex.org/W2059570523","https://openalex.org/W2078433315","https://openalex.org/W2122626572","https://openalex.org/W2129396149","https://openalex.org/W2165591847","https://openalex.org/W4242486132","https://openalex.org/W4255727195"],"related_works":["https://openalex.org/W2013801824","https://openalex.org/W1529452180","https://openalex.org/W1496788307","https://openalex.org/W1591253575","https://openalex.org/W2149054915","https://openalex.org/W2112487673","https://openalex.org/W2013322017","https://openalex.org/W2006729111","https://openalex.org/W1513334449","https://openalex.org/W1749665274"],"abstract_inverted_index":{"This":[0],"article":[1],"establishes":[2],"a":[3,64,68],"clear":[4],"procedure":[5],"for":[6],"the":[7,12,25,29,36,45,54,58],"variational":[8,18],"problem":[9,71],"solution":[10,37],"via":[11],"Haar":[13,30,46],"orthonormal":[14,31,47],"wavelet":[15],"technique.":[16],"The":[17,41],"problems":[19],"are":[20,72],"solved":[21],"by":[22],"means":[23],"of":[24,38,44],"direct":[26],"method":[27],"using":[28],"wavelets":[32,48],"and":[33,63],"reduced":[34],"to":[35,52,67],"algebraic":[39],"equations.":[40],"local":[42],"property":[43],"is":[49],"fully":[50],"applied":[51],"shorten":[53],"calculation":[55],"process":[56],"in":[57],"task.":[59],"Three":[60],"illustrative":[61],"examples":[62],"practical":[65],"application":[66],"heat":[69],"conduction":[70],"included.":[73]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
