{"id":"https://openalex.org/W4409174584","doi":"https://doi.org/10.1155/jama/5976163","title":"SVD\u2010Krylov\u2013Based Structure\u2010Preserving Techniques for Approximation of a Class of Second\u2010Order Index\u20101 Descriptor Systems","display_name":"SVD\u2010Krylov\u2013Based Structure\u2010Preserving Techniques for Approximation of a Class of Second\u2010Order Index\u20101 Descriptor Systems","publication_year":2025,"publication_date":"2025-01-01","ids":{"openalex":"https://openalex.org/W4409174584","doi":"https://doi.org/10.1155/jama/5976163"},"language":"en","primary_location":{"id":"doi:10.1155/jama/5976163","is_oa":true,"landing_page_url":"https://doi.org/10.1155/jama/5976163","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1155/jama/5976163","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1155/jama/5976163","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5040369140","display_name":"Mahtab Uddin","orcid":"https://orcid.org/0000-0002-6526-9276"},"institutions":[{"id":"https://openalex.org/I157386601","display_name":"North South University","ror":"https://ror.org/05wdbfp45","country_code":"BD","type":"education","lineage":["https://openalex.org/I157386601"]},{"id":"https://openalex.org/I183697816","display_name":"Bangladesh University of Engineering and Technology","ror":"https://ror.org/05a1qpv97","country_code":"BD","type":"education","lineage":["https://openalex.org/I183697816"]},{"id":"https://openalex.org/I63169043","display_name":"United International University","ror":"https://ror.org/01tqv1p28","country_code":"BD","type":"education","lineage":["https://openalex.org/I63169043"]}],"countries":["BD"],"is_corresponding":false,"raw_author_name":"Mahtab Uddin","raw_affiliation_strings":["Department of Mathematics ,  Bangladesh University of Engineering & Technology ,  Dhaka ,  Bangladesh , buet.ac.bd","Department of Mathematics and Physics ,  North South University ,  Dhaka ,  Bangladesh , northsouth.edu","Institute of Natural Sciences ,  United International University ,  Dhaka ,  Bangladesh , uiu.ac.bd"],"raw_orcid":"https://orcid.org/0000-0002-6526-9276","affiliations":[{"raw_affiliation_string":"Department of Mathematics ,  Bangladesh University of Engineering & Technology ,  Dhaka ,  Bangladesh , buet.ac.bd","institution_ids":["https://openalex.org/I183697816"]},{"raw_affiliation_string":"Department of Mathematics and Physics ,  North South University ,  Dhaka ,  Bangladesh , northsouth.edu","institution_ids":["https://openalex.org/I157386601"]},{"raw_affiliation_string":"Institute of Natural Sciences ,  United International University ,  Dhaka ,  Bangladesh , uiu.ac.bd","institution_ids":["https://openalex.org/I63169043"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040369140","display_name":"Mahtab Uddin","orcid":"https://orcid.org/0000-0002-6526-9276"},"institutions":[{"id":"https://openalex.org/I157386601","display_name":"North South University","ror":"https://ror.org/05wdbfp45","country_code":"BD","type":"education","lineage":["https://openalex.org/I157386601"]},{"id":"https://openalex.org/I183697816","display_name":"Bangladesh University of Engineering and Technology","ror":"https://ror.org/05a1qpv97","country_code":"BD","type":"education","lineage":["https://openalex.org/I183697816"]},{"id":"https://openalex.org/I63169043","display_name":"United International University","ror":"https://ror.org/01tqv1p28","country_code":"BD","type":"education","lineage":["https://openalex.org/I63169043"]}],"countries":["BD"],"is_corresponding":true,"raw_author_name":"Mahtab Uddin","raw_affiliation_strings":["Department of Mathematics ,  Bangladesh University of Engineering & Technology ,  Dhaka ,  Bangladesh , buet.ac.bd","Department of Mathematics and Physics ,  North South University ,  Dhaka ,  Bangladesh , northsouth.edu","Institute of Natural Sciences ,  United International University ,  Dhaka ,  Bangladesh , uiu.ac.bd"],"raw_orcid":"https://orcid.org/0000-0002-6526-9276","affiliations":[{"raw_affiliation_string":"Department of Mathematics ,  Bangladesh University of Engineering & Technology ,  Dhaka ,  Bangladesh , buet.ac.bd","institution_ids":["https://openalex.org/I183697816"]},{"raw_affiliation_string":"Department of Mathematics and Physics ,  North South University ,  Dhaka ,  Bangladesh , northsouth.edu","institution_ids":["https://openalex.org/I157386601"]},{"raw_affiliation_string":"Institute of Natural Sciences ,  United International University ,  Dhaka ,  Bangladesh , uiu.ac.bd","institution_ids":["https://openalex.org/I63169043"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088467986","display_name":"M. Monir Uddin","orcid":"https://orcid.org/0000-0002-9817-6156"},"institutions":[{"id":"https://openalex.org/I157386601","display_name":"North South University","ror":"https://ror.org/05wdbfp45","country_code":"BD","type":"education","lineage":["https://openalex.org/I157386601"]},{"id":"https://openalex.org/I183697816","display_name":"Bangladesh University of Engineering and Technology","ror":"https://ror.org/05a1qpv97","country_code":"BD","type":"education","lineage":["https://openalex.org/I183697816"]},{"id":"https://openalex.org/I63169043","display_name":"United International University","ror":"https://ror.org/01tqv1p28","country_code":"BD","type":"education","lineage":["https://openalex.org/I63169043"]}],"countries":["BD"],"is_corresponding":false,"raw_author_name":"M. Monir Uddin","raw_affiliation_strings":["Department of Mathematics ,  Bangladesh University of Engineering & Technology ,  Dhaka ,  Bangladesh , buet.ac.bd","Department of Mathematics and Physics ,  North South University ,  Dhaka ,  Bangladesh , northsouth.edu","Institute of Natural Sciences ,  United International University ,  Dhaka ,  Bangladesh , uiu.ac.bd"],"raw_orcid":"https://orcid.org/0000-0002-9817-6156","affiliations":[{"raw_affiliation_string":"Department of Mathematics ,  Bangladesh University of Engineering & Technology ,  Dhaka ,  Bangladesh , buet.ac.bd","institution_ids":["https://openalex.org/I183697816"]},{"raw_affiliation_string":"Department of Mathematics and Physics ,  North South University ,  Dhaka ,  Bangladesh , northsouth.edu","institution_ids":["https://openalex.org/I157386601"]},{"raw_affiliation_string":"Institute of Natural Sciences ,  United International University ,  Dhaka ,  Bangladesh , uiu.ac.bd","institution_ids":["https://openalex.org/I63169043"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088467986","display_name":"M. Monir Uddin","orcid":"https://orcid.org/0000-0002-9817-6156"},"institutions":[{"id":"https://openalex.org/I157386601","display_name":"North South University","ror":"https://ror.org/05wdbfp45","country_code":"BD","type":"education","lineage":["https://openalex.org/I157386601"]},{"id":"https://openalex.org/I183697816","display_name":"Bangladesh University of Engineering and Technology","ror":"https://ror.org/05a1qpv97","country_code":"BD","type":"education","lineage":["https://openalex.org/I183697816"]},{"id":"https://openalex.org/I63169043","display_name":"United International University","ror":"https://ror.org/01tqv1p28","country_code":"BD","type":"education","lineage":["https://openalex.org/I63169043"]}],"countries":["BD"],"is_corresponding":true,"raw_author_name":"M. Monir Uddin","raw_affiliation_strings":["Department of Mathematics ,  Bangladesh University of Engineering & Technology ,  Dhaka ,  Bangladesh , buet.ac.bd","Department of Mathematics and Physics ,  North South University ,  Dhaka ,  Bangladesh , northsouth.edu","Institute of Natural Sciences ,  United International University ,  Dhaka ,  Bangladesh , uiu.ac.bd"],"raw_orcid":"https://orcid.org/0000-0002-9817-6156","affiliations":[{"raw_affiliation_string":"Department of Mathematics ,  Bangladesh University of Engineering & Technology ,  Dhaka ,  Bangladesh , buet.ac.bd","institution_ids":["https://openalex.org/I183697816"]},{"raw_affiliation_string":"Department of Mathematics and Physics ,  North South University ,  Dhaka ,  Bangladesh , northsouth.edu","institution_ids":["https://openalex.org/I157386601"]},{"raw_affiliation_string":"Institute of Natural Sciences ,  United International University ,  Dhaka ,  Bangladesh , uiu.ac.bd","institution_ids":["https://openalex.org/I63169043"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5060278833","display_name":"Md. Abdul Hakim Khan","orcid":"https://orcid.org/0000-0003-2700-6261"},"institutions":[{"id":"https://openalex.org/I183697816","display_name":"Bangladesh University of Engineering and Technology","ror":"https://ror.org/05a1qpv97","country_code":"BD","type":"education","lineage":["https://openalex.org/I183697816"]}],"countries":["BD"],"is_corresponding":false,"raw_author_name":"Md. Abdul Hakim Khan","raw_affiliation_strings":["Department of Mathematics ,  Bangladesh University of Engineering & Technology ,  Dhaka ,  Bangladesh , buet.ac.bd"],"raw_orcid":"https://orcid.org/0000-0003-2700-6261","affiliations":[{"raw_affiliation_string":"Department of Mathematics ,  Bangladesh University of Engineering & Technology ,  Dhaka ,  Bangladesh , buet.ac.bd","institution_ids":["https://openalex.org/I183697816"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5040369140","https://openalex.org/A5088467986"],"corresponding_institution_ids":["https://openalex.org/I157386601","https://openalex.org/I183697816","https://openalex.org/I63169043"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.04943682,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"2025","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11236","display_name":"Control Systems and Identification","score":0.9959999918937683,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9886000156402588,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/class","display_name":"Class (philosophy)","score":0.6751250624656677},{"id":"https://openalex.org/keywords/singular-value-decomposition","display_name":"Singular value decomposition","score":0.5987425446510315},{"id":"https://openalex.org/keywords/index","display_name":"Index (typography)","score":0.5606297254562378},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5494276881217957},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5475344657897949},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.517616868019104},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4622717797756195},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3577123284339905},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1765013039112091}],"concepts":[{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.6751250624656677},{"id":"https://openalex.org/C22789450","wikidata":"https://www.wikidata.org/wiki/Q420904","display_name":"Singular value decomposition","level":2,"score":0.5987425446510315},{"id":"https://openalex.org/C2777382242","wikidata":"https://www.wikidata.org/wiki/Q6017816","display_name":"Index (typography)","level":2,"score":0.5606297254562378},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5494276881217957},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5475344657897949},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.517616868019104},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4622717797756195},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3577123284339905},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1765013039112091},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C136764020","wikidata":"https://www.wikidata.org/wiki/Q466","display_name":"World Wide Web","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1155/jama/5976163","is_oa":true,"landing_page_url":"https://doi.org/10.1155/jama/5976163","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1155/jama/5976163","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:a9e55d0b68d24ac4abf95017aa2f2afc","is_oa":true,"landing_page_url":"https://doaj.org/article/a9e55d0b68d24ac4abf95017aa2f2afc","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Applied Mathematics, Vol 2025 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/jama/5976163","is_oa":true,"landing_page_url":"https://doi.org/10.1155/jama/5976163","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1155/jama/5976163","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320319006","display_name":"United International University","ror":"https://ror.org/01tqv1p28"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4409174584.pdf","grobid_xml":"https://content.openalex.org/works/W4409174584.grobid-xml"},"referenced_works_count":48,"referenced_works":["https://openalex.org/W80445920","https://openalex.org/W578411849","https://openalex.org/W1493329061","https://openalex.org/W1506342804","https://openalex.org/W1509586029","https://openalex.org/W1561849568","https://openalex.org/W1987009281","https://openalex.org/W2012198279","https://openalex.org/W2028703352","https://openalex.org/W2030310690","https://openalex.org/W2042029506","https://openalex.org/W2044931959","https://openalex.org/W2049154285","https://openalex.org/W2082029992","https://openalex.org/W2083642242","https://openalex.org/W2086590360","https://openalex.org/W2088244796","https://openalex.org/W2088809856","https://openalex.org/W2088925018","https://openalex.org/W2090292347","https://openalex.org/W2091325846","https://openalex.org/W2094371111","https://openalex.org/W2099629311","https://openalex.org/W2137362177","https://openalex.org/W2145616692","https://openalex.org/W2152896489","https://openalex.org/W2168386575","https://openalex.org/W2169328438","https://openalex.org/W2211802523","https://openalex.org/W2224208171","https://openalex.org/W2356092338","https://openalex.org/W2962706012","https://openalex.org/W2963997708","https://openalex.org/W3016043850","https://openalex.org/W3103837813","https://openalex.org/W3109186751","https://openalex.org/W3109747096","https://openalex.org/W3175148902","https://openalex.org/W3185029070","https://openalex.org/W3193914487","https://openalex.org/W3216304349","https://openalex.org/W4206549555","https://openalex.org/W4211222663","https://openalex.org/W4251369476","https://openalex.org/W4286486944","https://openalex.org/W4300666158","https://openalex.org/W4361281559","https://openalex.org/W4392653592"],"related_works":["https://openalex.org/W3121932492","https://openalex.org/W4232638561","https://openalex.org/W1997544008","https://openalex.org/W2954752069","https://openalex.org/W1607100495","https://openalex.org/W3004137470","https://openalex.org/W131378092","https://openalex.org/W2938523900","https://openalex.org/W1598328844","https://openalex.org/W2348093013"],"abstract_inverted_index":{"This":[0],"work":[1,136],"is":[2,50,72,137],"aimed":[3],"at":[4],"deriving":[5],"a":[6,51,58,73,81,87,91],"computationally":[7,59],"efficient":[8],"approach":[9,77],"to":[10,79,86,138,177],"approximate":[11],"the":[12,19,23,28,31,34,41,65,99,110,119,127,140,145,150,153,157,165,174,180,185,193,197,205,213,216,224,228],"second\u2010order":[13,146],"Index\u20101":[14],"descriptor":[15],"systems":[16,147],"without":[17],"exploiting":[18],"fundamental":[20],"structure":[21],"of":[22,30,36,134,144,152,156,184,192,196,201,208,215],"systems,":[24],"which":[25,49],"ensures":[26],"both":[27],"accuracy":[29],"approximation":[32],"and":[33,64,148,182,199,231],"feasibility":[35],"computation":[37],"time.":[38],"It":[39],"demonstrates":[40],"structure\u2010preserving":[42],"iterative":[43,67],"singular\u2010value":[44],"decomposition":[45],"(SVD)\u2010Krylov":[46],"algorithm":[47],"(ISKA)":[48],"hybrid":[52],"two\u2010sided":[53],"projections":[54],"strategy":[55,187],"combined":[56],"with":[57,90,223],"feasible":[60],"Krylov":[61,129],"subspace":[62],"technique":[63,68],"stability\u2010preserving":[66],"based":[69],"SVD.":[70],"ISKA":[71],"model\u2010order":[74],"reduction":[75],"(MOR)":[76],"utilized":[78,172],"get":[80],"reduced\u2010order":[82],"model":[83,89,162,176],"(ROM)":[84],"corresponding":[85],"target":[88,175],"desired":[92],"size,":[93],"where":[94],"two":[95],"projector":[96,104,121],"matrices":[97],"are":[98,204],"main":[100,132],"constituent.":[101],"The":[102,131],"left":[103],"matrix":[105,122],"will":[106,123,170,220],"be":[107,124,171,221],"constructed":[108,125],"using":[109],"low\u2010rank":[111],"Cholesky\u2010factor":[112],"alternative":[113],"direction":[114],"implicit":[115],"(LRCF\u2010ADI)":[116],"technique,":[117],"whereas":[118],"right":[120],"utilizing":[126],"well\u2010known":[128],"subspace.":[130],"focus":[133],"this":[135,209],"avoid":[139],"so\u2010called":[141],"first\u2010order":[142],"conversion":[143],"ensure":[149],"invariance":[151],"matrix\u2010vector":[154],"operations":[155],"original":[158],"systems.":[159],"A":[160],"real\u2010world":[161],"derived":[163],"from":[164],"adaptive":[166],"spindle":[167],"support":[168],"system":[169],"as":[173],"numerically":[178],"validate":[179],"competency":[181],"efficiency":[183],"proposed":[186,217],"through":[188],"MATLAB":[189],"simulations.":[190],"Accuracy":[191],"approximation,":[194],"stability":[195],"ROMs,":[198],"optimization":[200],"computational":[202],"time":[203],"prime":[206],"concerns":[207],"work.":[210],"To":[211],"confirm":[212],"advancement":[214],"approach,":[218],"it":[219],"compared":[222],"existing":[225],"approaches":[226],"employing":[227],"necessary":[229],"figures":[230],"tables.":[232]},"counts_by_year":[],"updated_date":"2026-06-16T07:32:37.131356","created_date":"2025-10-10T00:00:00"}
