{"id":"https://openalex.org/W4405781620","doi":"https://doi.org/10.3390/sym17010011","title":"On [r, s]-Superporosity","display_name":"On [r, s]-Superporosity","publication_year":2024,"publication_date":"2024-12-25","ids":{"openalex":"https://openalex.org/W4405781620","doi":"https://doi.org/10.3390/sym17010011"},"language":"en","primary_location":{"id":"doi:10.3390/sym17010011","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17010011","pdf_url":"https://www.mdpi.com/2073-8994/17/1/11/pdf?version=1735119777","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/2073-8994/17/1/11/pdf?version=1735119777","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5079288666","display_name":"Stanis\u0142aw Kowalczyk","orcid":"https://orcid.org/0000-0001-8404-3427"},"institutions":[{"id":"https://openalex.org/I4210092219","display_name":"Uniwersytet Pomorski w S\u0142upsku","ror":"https://ror.org/00h8nar58","country_code":"PL","type":"education","lineage":["https://openalex.org/I4210092219"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Stanis\u0142aw Kowalczyk","raw_affiliation_strings":["Stanis\u0142aw Kowalczyk Institute of Exact and Technical Sciences, Pomeranian University in S\u0142upsk, ul. Bohater\u00f3w Westerplatte 64, 76-200 S\u0142upsk, Poland"],"affiliations":[{"raw_affiliation_string":"Stanis\u0142aw Kowalczyk Institute of Exact and Technical Sciences, Pomeranian University in S\u0142upsk, ul. Bohater\u00f3w Westerplatte 64, 76-200 S\u0142upsk, Poland","institution_ids":["https://openalex.org/I4210092219"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5053834718","display_name":"Ma\u0142gorzata Turowska","orcid":"https://orcid.org/0000-0001-9802-7874"},"institutions":[{"id":"https://openalex.org/I4210092219","display_name":"Uniwersytet Pomorski w S\u0142upsku","ror":"https://ror.org/00h8nar58","country_code":"PL","type":"education","lineage":["https://openalex.org/I4210092219"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Ma\u0142gorzata Turowska","raw_affiliation_strings":["Stanis\u0142aw Kowalczyk Institute of Exact and Technical Sciences, Pomeranian University in S\u0142upsk, ul. Bohater\u00f3w Westerplatte 64, 76-200 S\u0142upsk, Poland"],"affiliations":[{"raw_affiliation_string":"Stanis\u0142aw Kowalczyk Institute of Exact and Technical Sciences, Pomeranian University in S\u0142upsk, ul. Bohater\u00f3w Westerplatte 64, 76-200 S\u0142upsk, Poland","institution_ids":["https://openalex.org/I4210092219"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5053834718"],"corresponding_institution_ids":["https://openalex.org/I4210092219"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.9143,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.76116963,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"17","issue":"1","first_page":"11","last_page":"11"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11545","display_name":"Advanced Banach Space Theory","score":0.9994999766349792,"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/T11545","display_name":"Advanced Banach Space Theory","score":0.9994999766349792,"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/T12062","display_name":"Approximation Theory and Sequence Spaces","score":0.998199999332428,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9945999979972839,"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/porosity","display_name":"Porosity","score":0.8218735456466675},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5320706367492676},{"id":"https://openalex.org/keywords/focus","display_name":"Focus (optics)","score":0.4654479920864105},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.36417120695114136},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1759805977344513},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.16437667608261108},{"id":"https://openalex.org/keywords/composite-material","display_name":"Composite material","score":0.06676670908927917}],"concepts":[{"id":"https://openalex.org/C6648577","wikidata":"https://www.wikidata.org/wiki/Q622669","display_name":"Porosity","level":2,"score":0.8218735456466675},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5320706367492676},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.4654479920864105},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.36417120695114136},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1759805977344513},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.16437667608261108},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.06676670908927917},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/sym17010011","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17010011","pdf_url":"https://www.mdpi.com/2073-8994/17/1/11/pdf?version=1735119777","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:93ee8b34bc1f4822a5482df1c2b1e4c0","is_oa":true,"landing_page_url":"https://doaj.org/article/93ee8b34bc1f4822a5482df1c2b1e4c0","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 11 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/sym17010011","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17010011","pdf_url":"https://www.mdpi.com/2073-8994/17/1/11/pdf?version=1735119777","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/W4405781620.pdf","grobid_xml":"https://content.openalex.org/works/W4405781620.grobid-xml"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W1605794153","https://openalex.org/W2030820976","https://openalex.org/W2117277357","https://openalex.org/W2937060374","https://openalex.org/W2958731657","https://openalex.org/W3007409605","https://openalex.org/W3008334032","https://openalex.org/W3009035647","https://openalex.org/W3197643999","https://openalex.org/W3208320373","https://openalex.org/W3208557700","https://openalex.org/W4292508250","https://openalex.org/W4294718794","https://openalex.org/W4296964700"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2962838298","https://openalex.org/W2600246793"],"abstract_inverted_index":{"The":[0,45],"main":[1],"goal":[2],"of":[3,10,14,20,25,27,32,40,55,61,96,110,128,162,172,187,197,200,206,239,246],"the":[4,56,59,134,183,204,213,237],"paper":[5],"is":[6,50,78,82,100,105,114,119,149,166,176],"to":[7,36,51,107,121,144,230,241],"characterize":[8],"families":[9,205],"[r,s]-(upper)":[11],"superporous":[12,70,79],"subsets":[13,26,54],"R,":[15],"which":[16],"generalize":[17],"well-known":[18],"notions":[19],"superporosity":[21,24,41,189,192,231],"and":[22,30,38,42,68,89,155,185,190,195,232,244],"strong":[23,43,73,191,233],"R.":[28],"Definitions":[29],"properties":[31,39,186],"[r,s]-superporosity":[33,139,229,240],"are":[34,193,209],"symmetric":[35,135,194],"definitions":[37],"superporosity.":[44,234],"purpose":[46],"in":[47],"all":[48,196],"cases":[49],"define":[52],"small":[53,202],"line":[57],"using":[58],"notion":[60,238],"porosity.":[62],"Superporous":[63],"sets":[64,71,208,221],"preserve":[65,72],"positive":[66,125],"porosity,":[67,126],"strongly":[69,83],"porosity;":[74],"i.e.,":[75,146],"if":[76,147],"E":[77,81,148],"(correspondingly,":[80,104,118],"superporous),":[84],"then":[85,151],"for":[86,90,140,152,156,222],"every":[87,91,153,157],"x\u2208E":[88,154],"F":[92,97,158,163],"such":[93,159],"that":[94,160],"porosity":[95,109,161,171],"at":[98,112,164,174],"x":[99,113,165,175],"greater":[101,115],"than":[102,116,169,179],"0":[103,117,129],"equal":[106,120],"1),":[108],"E\u222aF":[111,173],"1).":[122],"Taking":[123],"arbitrary":[124],"instead":[127],"or":[130],"1,":[131],"we":[132,215,227],"obtain":[133],"definition":[136,184],"as":[137],"follows:":[138],"0<r\u2264s<1":[141],"transfers":[142],"s-porosity":[143],"r-porosity;":[145],"[r,s]-superporous,":[150],"not":[167,177],"less":[168,178],"s,":[170],"r.":[180],"Even":[181],"though":[182],"[r,s]-superporosity,":[188],"them":[198],"consist":[199],"very":[201],"sets,":[203],"these":[207],"essentially":[210],"different.":[211],"In":[212],"paper,":[214],"focus":[216],"on":[217],"relationships":[218],"between":[219],"[r,s]-superporous":[220],"different":[223],"indices":[224],"[r,s].":[225],"Furthermore,":[226],"compare":[228],"We":[235],"apply":[236],"find":[242],"multipliers":[243],"adders":[245],"porouscontinuous":[247],"functions.":[248]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-03-13T14:20:09.374765","created_date":"2024-12-26T00:00:00"}