{"id":"https://openalex.org/W4386219852","doi":"https://doi.org/10.3390/sym15091658","title":"On Primary Decomposition of Hermite Projectors","display_name":"On Primary Decomposition of Hermite Projectors","publication_year":2023,"publication_date":"2023-08-28","ids":{"openalex":"https://openalex.org/W4386219852","doi":"https://doi.org/10.3390/sym15091658"},"language":"en","primary_location":{"id":"doi:10.3390/sym15091658","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/sym15091658","pdf_url":"https://www.mdpi.com/2073-8994/15/9/1658/pdf?version=1693216407","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","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/15/9/1658/pdf?version=1693216407","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5090062378","display_name":"Boris Shekhtman","orcid":null},"institutions":[{"id":"https://openalex.org/I2613432","display_name":"University of South Florida","ror":"https://ror.org/032db5x82","country_code":"US","type":"education","lineage":["https://openalex.org/I2613432"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Boris Shekhtman","raw_affiliation_strings":["Department of Mathematics and Statistics, University of South Florida, 4202 East Fowler ave, CMC 342, Tampa, FL 33620, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of South Florida, 4202 East Fowler ave, CMC 342, Tampa, FL 33620, USA","institution_ids":["https://openalex.org/I2613432"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5052713898","display_name":"Les\u0142aw Skrzypek","orcid":"https://orcid.org/0000-0002-4705-8440"},"institutions":[{"id":"https://openalex.org/I2613432","display_name":"University of South Florida","ror":"https://ror.org/032db5x82","country_code":"US","type":"education","lineage":["https://openalex.org/I2613432"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Les\u0142aw Skrzypek","raw_affiliation_strings":["Department of Mathematics and Statistics, University of South Florida, 4202 East Fowler ave, CMC 342, Tampa, FL 33620, USA"],"raw_orcid":"https://orcid.org/0000-0002-4705-8440","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of South Florida, 4202 East Fowler ave, CMC 342, Tampa, FL 33620, USA","institution_ids":["https://openalex.org/I2613432"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5018183482","display_name":"Brian Tuesink","orcid":null},"institutions":[{"id":"https://openalex.org/I2613432","display_name":"University of South Florida","ror":"https://ror.org/032db5x82","country_code":"US","type":"education","lineage":["https://openalex.org/I2613432"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Brian Tuesink","raw_affiliation_strings":["Department of Mathematics and Statistics, University of South Florida, 4202 East Fowler ave, CMC 342, Tampa, FL 33620, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of South Florida, 4202 East Fowler ave, CMC 342, Tampa, FL 33620, USA","institution_ids":["https://openalex.org/I2613432"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5052713898"],"corresponding_institution_ids":["https://openalex.org/I2613432"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.11808329,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"15","issue":"9","first_page":"1658","last_page":"1658"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9991000294685364,"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"}},"topics":[{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9991000294685364,"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"}},{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9988999962806702,"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/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9973000288009644,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/ideal","display_name":"Ideal (ethics)","score":0.794586181640625},{"id":"https://openalex.org/keywords/projector","display_name":"Projector","score":0.7611278295516968},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7378960847854614},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.6206207275390625},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.4361411929130554},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.4328486919403076},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4300583004951477},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.4205361604690552},{"id":"https://openalex.org/keywords/hermite-polynomials","display_name":"Hermite polynomials","score":0.4172023832798004},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3081066906452179},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.16999253630638123},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.09256422519683838}],"concepts":[{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.794586181640625},{"id":"https://openalex.org/C2776865275","wikidata":"https://www.wikidata.org/wiki/Q311666","display_name":"Projector","level":2,"score":0.7611278295516968},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7378960847854614},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.6206207275390625},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.4361411929130554},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.4328486919403076},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4300583004951477},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.4205361604690552},{"id":"https://openalex.org/C201362023","wikidata":"https://www.wikidata.org/wiki/Q658574","display_name":"Hermite polynomials","level":2,"score":0.4172023832798004},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3081066906452179},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.16999253630638123},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.09256422519683838},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","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},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","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},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym15091658","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/sym15091658","pdf_url":"https://www.mdpi.com/2073-8994/15/9/1658/pdf?version=1693216407","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"},{"id":"pmh:oai:doaj.org/article:40b7a35a1533423ebee603285874978e","is_oa":false,"landing_page_url":"https://doaj.org/article/40b7a35a1533423ebee603285874978e","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":"Symmetry, Vol 15, Iss 9, p 1658 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/15/9/1658/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym15091658","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":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym15091658","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/sym15091658","pdf_url":"https://www.mdpi.com/2073-8994/15/9/1658/pdf?version=1693216407","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":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4386219852.pdf"},"referenced_works_count":15,"referenced_works":["https://openalex.org/W589984754","https://openalex.org/W1481556851","https://openalex.org/W1529743226","https://openalex.org/W1586478237","https://openalex.org/W1698169260","https://openalex.org/W1963813458","https://openalex.org/W1974087575","https://openalex.org/W2019127701","https://openalex.org/W2026749500","https://openalex.org/W2028133475","https://openalex.org/W2047928154","https://openalex.org/W2075832453","https://openalex.org/W2155065327","https://openalex.org/W4292096448","https://openalex.org/W6628672169"],"related_works":["https://openalex.org/W2366989203","https://openalex.org/W2013995543","https://openalex.org/W2547954852","https://openalex.org/W2800812882","https://openalex.org/W3198360760","https://openalex.org/W2388454722","https://openalex.org/W4388488814","https://openalex.org/W2373608992","https://openalex.org/W2918931022","https://openalex.org/W2324517116"],"abstract_inverted_index":{"An":[0],"ideal":[1,16,20,30,47,75],"projector":[2,11,21,76],"on":[3],"the":[4,35,46],"space":[5],"of":[6,29,37,45,59,90],"polynomials":[7],"C[x]=C[x1,\u2026,xd]":[8],"is":[9,14,41,56,80,86],"a":[10,27,42,57,81,88],"whose":[12,78],"kernel":[13,79],"an":[15,70,74],"in":[17],"C[x].":[18],"Every":[19],"P":[22,55,77,85],"can":[23],"be":[24],"written":[25],"as":[26],"sum":[28],"projectors":[31,61],"P(k)":[32,67],"such":[33],"that":[34,54],"intersection":[36],"their":[38],"kernels":[39],"kerP(k)":[40],"primary":[43],"decomposition":[44],"kerP.":[48],"In":[49],"this":[50],"paper,":[51],"we":[52,72],"show":[53],"limit":[58,89],"Lagrange":[60,91],"if":[62,65],"and":[63],"only":[64],"each":[66],"is.":[68],"As":[69],"application,":[71],"construct":[73],"symmetric":[82],"ideal,":[83],"yet":[84],"not":[87],"projectors.":[92]},"counts_by_year":[],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}
