{"id":"https://openalex.org/W4406376029","doi":"https://doi.org/10.3390/sym17010117","title":"Issues in the Expansion and Contraction of Operators","display_name":"Issues in the Expansion and Contraction of Operators","publication_year":2025,"publication_date":"2025-01-14","ids":{"openalex":"https://openalex.org/W4406376029","doi":"https://doi.org/10.3390/sym17010117"},"language":"en","primary_location":{"id":"doi:10.3390/sym17010117","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17010117","pdf_url":"https://www.mdpi.com/2073-8994/17/1/117/pdf?version=1736913734","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/2073-8994/17/1/117/pdf?version=1736913734","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5079483260","display_name":"\u041c. \u041e\u0442\u0435\u043b\u0431\u0430\u0435\u0432","orcid":"https://orcid.org/0000-0002-5554-4908"},"institutions":[{"id":"https://openalex.org/I4210151480","display_name":"Institute of Mathematics and Mathematical Modeling","ror":"https://ror.org/05xx3wf87","country_code":"KZ","type":"government","lineage":["https://openalex.org/I4210151480"]}],"countries":["KZ"],"is_corresponding":false,"raw_author_name":"Mukhtarbay Otelbaev","raw_affiliation_strings":["Institute of Mathematics and Mathematical Modeling, Almaty 050010, Kazakhstan"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics and Mathematical Modeling, Almaty 050010, Kazakhstan","institution_ids":["https://openalex.org/I4210151480"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5115880470","display_name":"Abdukhali Shynybekov","orcid":null},"institutions":[{"id":"https://openalex.org/I185571130","display_name":"Al-Farabi Kazakh National University","ror":"https://ror.org/03q0vrn42","country_code":"KZ","type":"education","lineage":["https://openalex.org/I185571130"]}],"countries":["KZ"],"is_corresponding":false,"raw_author_name":"Abdukhali Shynybekov","raw_affiliation_strings":["Department of Mathematics, Faculty of Mechanics and Mathematics, Al-Farabi Kazakh National University, Almaty 050040, Kazakhstan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Mechanics and Mathematics, Al-Farabi Kazakh National University, Almaty 050040, Kazakhstan","institution_ids":["https://openalex.org/I185571130"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5016215084","display_name":"Karlygash Dosmagulova","orcid":"https://orcid.org/0000-0001-8289-6573"},"institutions":[{"id":"https://openalex.org/I185571130","display_name":"Al-Farabi Kazakh National University","ror":"https://ror.org/03q0vrn42","country_code":"KZ","type":"education","lineage":["https://openalex.org/I185571130"]},{"id":"https://openalex.org/I2801227569","display_name":"Ghent University Hospital","ror":"https://ror.org/00xmkp704","country_code":"BE","type":"healthcare","lineage":["https://openalex.org/I2801227569"]},{"id":"https://openalex.org/I4210151480","display_name":"Institute of Mathematics and Mathematical Modeling","ror":"https://ror.org/05xx3wf87","country_code":"KZ","type":"government","lineage":["https://openalex.org/I4210151480"]}],"countries":["BE","KZ"],"is_corresponding":true,"raw_author_name":"Karlygash Dosmagulova","raw_affiliation_strings":["Department of Mathematics, Faculty of Mechanics and Mathematics, Al-Farabi Kazakh National University, Almaty 050040, Kazakhstan","Ghent Analysis and PDE Center, Ghent University, 9000 Ghent, Belgium","Institute of Mathematics and Mathematical Modeling, Almaty 050010, Kazakhstan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Mechanics and Mathematics, Al-Farabi Kazakh National University, Almaty 050040, Kazakhstan","institution_ids":["https://openalex.org/I185571130"]},{"raw_affiliation_string":"Ghent Analysis and PDE Center, Ghent University, 9000 Ghent, Belgium","institution_ids":["https://openalex.org/I2801227569"]},{"raw_affiliation_string":"Institute of Mathematics and Mathematical Modeling, Almaty 050010, Kazakhstan","institution_ids":["https://openalex.org/I4210151480"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5016215084"],"corresponding_institution_ids":["https://openalex.org/I185571130","https://openalex.org/I2801227569","https://openalex.org/I4210151480"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.02918054,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"17","issue":"1","first_page":"117","last_page":"117"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9988999962806702,"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/T11262","display_name":"Quantum Mechanics and Non-Hermitian Physics","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.554411768913269},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5359163284301758},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.48746442794799805},{"id":"https://openalex.org/keywords/contraction","display_name":"Contraction (grammar)","score":0.46509185433387756},{"id":"https://openalex.org/keywords/theoretical-physics","display_name":"Theoretical physics","score":0.4159424304962158},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4011513590812683},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.35297873616218567},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.32971078157424927},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3262280523777008},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.276653915643692},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.21070939302444458}],"concepts":[{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.554411768913269},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5359163284301758},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.48746442794799805},{"id":"https://openalex.org/C163415756","wikidata":"https://www.wikidata.org/wiki/Q126473","display_name":"Contraction (grammar)","level":2,"score":0.46509185433387756},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.4159424304962158},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4011513590812683},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.35297873616218567},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.32971078157424927},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3262280523777008},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.276653915643692},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.21070939302444458},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C126322002","wikidata":"https://www.wikidata.org/wiki/Q11180","display_name":"Internal medicine","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym17010117","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17010117","pdf_url":"https://www.mdpi.com/2073-8994/17/1/117/pdf?version=1736913734","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:bfd45f01db48427c8b3b846e8d199f1a","is_oa":true,"landing_page_url":"https://doaj.org/article/bfd45f01db48427c8b3b846e8d199f1a","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 17, Iss 1, p 117 (2025)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/17/1/117/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym17010117","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/sym17010117","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17010117","pdf_url":"https://www.mdpi.com/2073-8994/17/1/117/pdf?version=1736913734","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":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4406376029.pdf","grobid_xml":"https://content.openalex.org/works/W4406376029.grobid-xml"},"referenced_works_count":9,"referenced_works":["https://openalex.org/W1999028772","https://openalex.org/W2045341321","https://openalex.org/W2056134434","https://openalex.org/W2066086134","https://openalex.org/W2090353347","https://openalex.org/W2145586686","https://openalex.org/W3072727749","https://openalex.org/W4206769493","https://openalex.org/W6782226856"],"related_works":["https://openalex.org/W2154204858","https://openalex.org/W3209622820","https://openalex.org/W2382250648","https://openalex.org/W2367363545","https://openalex.org/W2586383879","https://openalex.org/W4231291595","https://openalex.org/W4245609766","https://openalex.org/W1606211735","https://openalex.org/W2329192282","https://openalex.org/W2026588291"],"abstract_inverted_index":{"This":[0,193],"paper":[1,173],"explores":[2],"fundamental":[3],"issues":[4],"in":[5,163,180,204],"the":[6,18,33,45,77,91,109,124,147,165,172,175,181,186],"correct":[7,94,128],"contraction":[8],"and":[9,41,50,64,80,96,131,188,201,210],"expansion":[10],"of":[11,20,35,47,70,93,102,112,123,126,150,167,177,183,190],"operators,":[12,36,104,184],"with":[13,134],"a":[14,73,99,120,138,144,151,160],"primary":[15],"focus":[16],"on":[17,76],"concept":[19],"symmetry":[21,31,107,158,179],"within":[22],"operator":[23],"theory.":[24,212],"Special":[25],"attention":[26],"is":[27,88,154],"given":[28],"to":[29,137],"how":[30,106,157],"influences":[32],"behavior":[34],"particularly":[37],"regarding":[38,90],"their":[39],"approximation":[40],"convergence":[42],"properties.":[43],"In":[44],"domains":[46],"quantum":[48,211],"mechanics":[49],"condensed":[51],"matter":[52],"physics,":[53],"such":[54],"operators":[55,71,113],"are":[56],"essential":[57],"for":[58,98,146,197],"modeling":[59],"phenomena":[60],"like":[61],"superconductivity,":[62],"excitons,":[63],"surface":[65],"states.":[66],"The":[67,117],"symmetric":[68],"properties":[69],"have":[72],"profound":[74],"impact":[75],"physical":[78,169],"interpretations":[79],"predictions":[81],"these":[82],"models":[83],"generate.":[84],"A":[85],"rigorous":[86],"analysis":[87],"provided":[89],"existence":[92],"contractions":[95],"expansions":[97],"specific":[100],"class":[101],"nonlinear":[103,140],"demonstrating":[105],"affects":[108],"structural":[110],"integrity":[111],"under":[114],"natural":[115],"conditions.":[116],"study":[118],"presents":[119],"comprehensive":[121],"description":[122],"set":[125],"all":[127],"contractions,":[129],"expansions,":[130,133],"regular":[132],"an":[135],"application":[136],"third-order":[139],"differential":[141],"expression.":[142],"Additionally,":[143],"condition":[145],"unique":[148],"solvability":[149],"Bitsadze\u2013Samarskii-type":[152],"problem":[153],"derived,":[155],"showcasing":[156],"plays":[159],"crucial":[161],"role":[162],"guiding":[164],"solution":[166],"complex":[168],"models.":[170,192],"Furthermore,":[171],"emphasizes":[174],"importance":[176],"preserving":[178],"construction":[182],"ensuring":[185],"consistency":[187],"accuracy":[189],"mathematical":[191],"has":[194],"significant":[195],"implications":[196],"both":[198],"theoretical":[199],"research":[200],"practical":[202],"applications":[203],"various":[205],"fields,":[206],"including":[207],"nuclear":[208],"physics":[209]},"counts_by_year":[],"updated_date":"2026-03-10T14:07:55.174380","created_date":"2025-10-10T00:00:00"}