{"id":"https://openalex.org/W4405962801","doi":"https://doi.org/10.3390/axioms14010028","title":"Mappings of a Bounded Dirichlet Integral: The Modulus Method","display_name":"Mappings of a Bounded Dirichlet Integral: The Modulus Method","publication_year":2024,"publication_date":"2024-12-31","ids":{"openalex":"https://openalex.org/W4405962801","doi":"https://doi.org/10.3390/axioms14010028"},"language":"en","primary_location":{"id":"doi:10.3390/axioms14010028","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14010028","pdf_url":"https://www.mdpi.com/2075-1680/14/1/28/pdf?version=1735651174","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/14/1/28/pdf?version=1735651174","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5068001425","display_name":"Mihai Cristea","orcid":"https://orcid.org/0000-0002-2766-8356"},"institutions":[{"id":"https://openalex.org/I141595442","display_name":"University of Bucharest","ror":"https://ror.org/02x2v6p15","country_code":"RO","type":"education","lineage":["https://openalex.org/I141595442"]}],"countries":["RO"],"is_corresponding":true,"raw_author_name":"Mihai Cristea","raw_affiliation_strings":["Faculty of Mathematics and Computer Sciences, University of Bucharest, Str. Academiei 14, R-010014 Bucharest, Romania"],"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics and Computer Sciences, University of Bucharest, Str. Academiei 14, R-010014 Bucharest, Romania","institution_ids":["https://openalex.org/I141595442"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5068001425"],"corresponding_institution_ids":["https://openalex.org/I141595442"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.29591837,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"14","issue":"1","first_page":"28","last_page":"28"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.7426000237464905,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.7426000237464905,"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/bounded-function","display_name":"Bounded function","score":0.7338023781776428},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6298368573188782},{"id":"https://openalex.org/keywords/dirichlet-distribution","display_name":"Dirichlet distribution","score":0.598226010799408},{"id":"https://openalex.org/keywords/modulus","display_name":"Modulus","score":0.5650821924209595},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3791031241416931},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.32898151874542236},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.0681542158126831}],"concepts":[{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.7338023781776428},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6298368573188782},{"id":"https://openalex.org/C169214877","wikidata":"https://www.wikidata.org/wiki/Q981016","display_name":"Dirichlet distribution","level":3,"score":0.598226010799408},{"id":"https://openalex.org/C193867417","wikidata":"https://www.wikidata.org/wiki/Q6889814","display_name":"Modulus","level":2,"score":0.5650821924209595},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3791031241416931},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.32898151874542236},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0681542158126831},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/axioms14010028","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14010028","pdf_url":"https://www.mdpi.com/2075-1680/14/1/28/pdf?version=1735651174","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:3c0a52ed7c6f480d976624357c237068","is_oa":true,"landing_page_url":"https://doaj.org/article/3c0a52ed7c6f480d976624357c237068","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":"Axioms, Vol 14, Iss 1, p 28 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms14010028","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14010028","pdf_url":"https://www.mdpi.com/2075-1680/14/1/28/pdf?version=1735651174","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4405962801.pdf","grobid_xml":"https://content.openalex.org/works/W4405962801.grobid-xml"},"referenced_works_count":46,"referenced_works":["https://openalex.org/W654833068","https://openalex.org/W1491751692","https://openalex.org/W1523004878","https://openalex.org/W1553738528","https://openalex.org/W1578215794","https://openalex.org/W1965274240","https://openalex.org/W1967349178","https://openalex.org/W1970939464","https://openalex.org/W1972738525","https://openalex.org/W1980944118","https://openalex.org/W1982448226","https://openalex.org/W1990935603","https://openalex.org/W1997678332","https://openalex.org/W2012722396","https://openalex.org/W2027649114","https://openalex.org/W2028379019","https://openalex.org/W2041310163","https://openalex.org/W2049109919","https://openalex.org/W2067884470","https://openalex.org/W2100658167","https://openalex.org/W2143809241","https://openalex.org/W2152453197","https://openalex.org/W2238693300","https://openalex.org/W2334104700","https://openalex.org/W2338035356","https://openalex.org/W2763257556","https://openalex.org/W2809502011","https://openalex.org/W2895221729","https://openalex.org/W2925509246","https://openalex.org/W2963322077","https://openalex.org/W2963871974","https://openalex.org/W3002098551","https://openalex.org/W3124028458","https://openalex.org/W3134302776","https://openalex.org/W3202271544","https://openalex.org/W4220674680","https://openalex.org/W4236242570","https://openalex.org/W4239633408","https://openalex.org/W4246954948","https://openalex.org/W4307026300","https://openalex.org/W4382140314","https://openalex.org/W4388784166","https://openalex.org/W6600546786","https://openalex.org/W6643470315","https://openalex.org/W6662769840","https://openalex.org/W6729774627"],"related_works":["https://openalex.org/W3013085049","https://openalex.org/W1560496689","https://openalex.org/W1992739770","https://openalex.org/W4386900933","https://openalex.org/W4229058035","https://openalex.org/W3125672081","https://openalex.org/W2006389905","https://openalex.org/W4297797135","https://openalex.org/W2904666330","https://openalex.org/W82543781"],"abstract_inverted_index":{"We":[0,39],"study":[1],"the":[2,28,35,45],"geometric":[3],"properties":[4],"of":[5,8,21,27,30,47,52],"some":[6,25,42],"classes":[7,20],"mappings":[9,51],"for":[10,44,50],"which":[11],"an":[12],"inverse":[13],"Poletsky":[14],"modular":[15],"inequality":[16],"holds.":[17],"In":[18],"these":[19],"mappings,":[22],"we":[23],"give":[24],"extensions":[26],"theorems":[29],"Lindel\u0151f":[31],"and":[32],"Fatou":[33],"from":[34],"classical":[36],"complex":[37],"analysis.":[38],"also":[40],"find":[41],"conditions":[43],"existence":[46],"injective":[48],"minimizers":[49],"biconformal":[53],"energy.":[54]},"counts_by_year":[],"updated_date":"2026-03-13T14:20:09.374765","created_date":"2025-10-10T00:00:00"}