{"id":"https://openalex.org/W2777410790","doi":"https://doi.org/10.1142/s0219691318500200","title":"Some crystallographic Haar type composite dilation wavelets for P4 = C4 \u22c9 \u21242","display_name":"Some crystallographic Haar type composite dilation wavelets for P4 = C4 \u22c9 \u21242","publication_year":2017,"publication_date":"2017-12-18","ids":{"openalex":"https://openalex.org/W2777410790","doi":"https://doi.org/10.1142/s0219691318500200","mag":"2777410790"},"language":"en","primary_location":{"id":"doi:10.1142/s0219691318500200","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219691318500200","pdf_url":null,"source":{"id":"https://openalex.org/S56986848","display_name":"International Journal of Wavelets Multiresolution and Information Processing","issn_l":"0219-6913","issn":["0219-6913","1793-690X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Wavelets, Multiresolution and Information Processing","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/A5019658405","display_name":"Rupali Deshpande","orcid":"https://orcid.org/0000-0002-6558-1294"},"institutions":[{"id":"https://openalex.org/I878213199","display_name":"Savitribai Phule Pune University","ror":"https://ror.org/044g6d731","country_code":"IN","type":"education","lineage":["https://openalex.org/I878213199"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"R. Deshpande","raw_affiliation_strings":["Department of Mathematics, Savitribai Phule Pune University, Pune, India","Vishwakarma Institute of Technology, Department of Engineering Sciences and Humanities, Pune, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Savitribai Phule Pune University, Pune, India","institution_ids":["https://openalex.org/I878213199"]},{"raw_affiliation_string":"Vishwakarma Institute of Technology, Department of Engineering Sciences and Humanities, Pune, India","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5005377501","display_name":"Hemant Bhate","orcid":null},"institutions":[{"id":"https://openalex.org/I878213199","display_name":"Savitribai Phule Pune University","ror":"https://ror.org/044g6d731","country_code":"IN","type":"education","lineage":["https://openalex.org/I878213199"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"H. Bhate","raw_affiliation_strings":["Department of Mathematics, Savitribai Phule Pune University, Pune, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Savitribai Phule Pune University, Pune, India","institution_ids":["https://openalex.org/I878213199"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I878213199"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.22695104,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"16","issue":"03","first_page":"1850020","last_page":"1850020"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","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/T11034","display_name":"Digital Filter Design and Implementation","score":0.9878000020980835,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T11191","display_name":"Mathematical functions and polynomials","score":0.9800999760627747,"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/dilation","display_name":"Dilation (metric space)","score":0.7837756872177124},{"id":"https://openalex.org/keywords/haar","display_name":"Haar","score":0.7122571468353271},{"id":"https://openalex.org/keywords/wavelet","display_name":"Wavelet","score":0.6774685978889465},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6323424577713013},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.5581402778625488},{"id":"https://openalex.org/keywords/haar-wavelet","display_name":"Haar wavelet","score":0.5577650666236877},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.540708601474762},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.47184064984321594},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.457286536693573},{"id":"https://openalex.org/keywords/composite-number","display_name":"Composite number","score":0.4482356905937195},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4285893142223358},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4156896770000458},{"id":"https://openalex.org/keywords/wavelet-transform","display_name":"Wavelet transform","score":0.2738400101661682},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1913047730922699},{"id":"https://openalex.org/keywords/discrete-wavelet-transform","display_name":"Discrete wavelet transform","score":0.1626405417919159},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.13042721152305603},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.12807106971740723},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.11825239658355713},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09891852736473083},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.07413622736930847},{"id":"https://openalex.org/keywords/composite-material","display_name":"Composite material","score":0.0701046884059906}],"concepts":[{"id":"https://openalex.org/C2780757906","wikidata":"https://www.wikidata.org/wiki/Q5276676","display_name":"Dilation (metric space)","level":2,"score":0.7837756872177124},{"id":"https://openalex.org/C187029792","wikidata":"https://www.wikidata.org/wiki/Q2179112","display_name":"Haar","level":3,"score":0.7122571468353271},{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.6774685978889465},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6323424577713013},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.5581402778625488},{"id":"https://openalex.org/C2780423554","wikidata":"https://www.wikidata.org/wiki/Q766198","display_name":"Haar wavelet","level":5,"score":0.5577650666236877},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.540708601474762},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.47184064984321594},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.457286536693573},{"id":"https://openalex.org/C104779481","wikidata":"https://www.wikidata.org/wiki/Q50707","display_name":"Composite number","level":2,"score":0.4482356905937195},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4285893142223358},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4156896770000458},{"id":"https://openalex.org/C196216189","wikidata":"https://www.wikidata.org/wiki/Q2867","display_name":"Wavelet transform","level":3,"score":0.2738400101661682},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1913047730922699},{"id":"https://openalex.org/C46286280","wikidata":"https://www.wikidata.org/wiki/Q2414958","display_name":"Discrete wavelet transform","level":4,"score":0.1626405417919159},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.13042721152305603},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.12807106971740723},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.11825239658355713},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09891852736473083},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.07413622736930847},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0701046884059906},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0219691318500200","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219691318500200","pdf_url":null,"source":{"id":"https://openalex.org/S56986848","display_name":"International Journal of Wavelets Multiresolution and Information Processing","issn_l":"0219-6913","issn":["0219-6913","1793-690X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Wavelets, Multiresolution and Information Processing","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":15,"referenced_works":["https://openalex.org/W66786174","https://openalex.org/W168640205","https://openalex.org/W200633896","https://openalex.org/W1545817210","https://openalex.org/W1965935638","https://openalex.org/W1990805796","https://openalex.org/W1992907556","https://openalex.org/W2027037828","https://openalex.org/W2059391811","https://openalex.org/W2065575984","https://openalex.org/W2078163802","https://openalex.org/W2088728841","https://openalex.org/W2152083855","https://openalex.org/W2154507364","https://openalex.org/W2165368396"],"related_works":["https://openalex.org/W2766849256","https://openalex.org/W4361795924","https://openalex.org/W984746159","https://openalex.org/W1523827626","https://openalex.org/W1999916501","https://openalex.org/W4232769230","https://openalex.org/W2005569824","https://openalex.org/W111100742","https://openalex.org/W4239324723","https://openalex.org/W2043338154"],"abstract_inverted_index":{"Composite":[0],"dilation":[1,63,69],"wavelets":[2,64],"generate":[3],"bases":[4],"or":[5],"frames":[6],"using":[7],"two":[8,68],"groups":[9,70],"of":[10,47],"dilations.":[11],"One":[12],"group":[13,38],"is":[14,26,39],"associated":[15,40,71],"with":[16,30,41,52,72],"a":[17],"set":[18],"[Formula:":[19,23,31,44,49,53,73],"see":[20,24,32,45,50,54,74],"text]":[21,25,33,46,51,55,75],"where":[22],"an":[27,34],"expanding":[28],"matrix":[29],"integer.":[35],"The":[36],"second":[37],"the":[42],"subgroup":[43],"matrices":[48],"Here,":[56],"we":[57,77],"present":[58],"crystallographic":[59],"Haar":[60],"type":[61],"composite":[62],"generated":[65],"by":[66],"such":[67],"Further,":[76],"provide":[78],"matricial":[79],"filters":[80],"and":[81],"reconstruction":[82],"formulae":[83],"at":[84],"various":[85],"scales.":[86]},"counts_by_year":[],"updated_date":"2026-06-26T08:34:08.712188","created_date":"2025-10-10T00:00:00"}