{"id":"https://openalex.org/W2799201531","doi":"https://doi.org/10.1109/tit.2018.2890208","title":"On the Capacity of the Peak Power Constrained Vector Gaussian Channel: An Estimation Theoretic Perspective","display_name":"On the Capacity of the Peak Power Constrained Vector Gaussian Channel: An Estimation Theoretic Perspective","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2799201531","doi":"https://doi.org/10.1109/tit.2018.2890208","mag":"2799201531"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2018.2890208","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2018.2890208","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1804.08524","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5066257035","display_name":"Alex Dytso","orcid":"https://orcid.org/0000-0003-0625-5306"},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Alex Dytso","raw_affiliation_strings":["Department of Electrical Engineering, Princeton University, Princeton, NJ, USA"],"raw_orcid":"https://orcid.org/0000-0003-0625-5306","affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Princeton University, Princeton, NJ, USA","institution_ids":["https://openalex.org/I20089843"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066716180","display_name":"Mert Al","orcid":"https://orcid.org/0000-0001-6773-0612"},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mert Al","raw_affiliation_strings":["Department of Electrical Engineering, Princeton University, Princeton, NJ, USA"],"raw_orcid":"https://orcid.org/0000-0001-6773-0612","affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Princeton University, Princeton, NJ, USA","institution_ids":["https://openalex.org/I20089843"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5042307561","display_name":"H. Vincent Poor","orcid":"https://orcid.org/0000-0002-2062-131X"},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"H. Vincent Poor","raw_affiliation_strings":["Department of Electrical Engineering, Princeton University, Princeton, NJ, USA"],"raw_orcid":"https://orcid.org/0000-0002-2062-131X","affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Princeton University, Princeton, NJ, USA","institution_ids":["https://openalex.org/I20089843"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5025989795","display_name":"Shlomo Shamai","orcid":"https://orcid.org/0000-0002-6594-3371"},"institutions":[{"id":"https://openalex.org/I174306211","display_name":"Technion \u2013 Israel Institute of Technology","ror":"https://ror.org/03qryx823","country_code":"IL","type":"education","lineage":["https://openalex.org/I174306211"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Shlomo Shamai Shitz","raw_affiliation_strings":["Department of Electrical Engineering, Technion\u2013Israel Institute of Technology, Haifa, Israel"],"raw_orcid":"https://orcid.org/0000-0002-6594-3371","affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Technion\u2013Israel Institute of Technology, Haifa, Israel","institution_ids":["https://openalex.org/I174306211"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5066257035"],"corresponding_institution_ids":["https://openalex.org/I20089843"],"apc_list":null,"apc_paid":null,"fwci":0.1211,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.4334522,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"65","issue":"6","first_page":"3907","last_page":"3921"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10964","display_name":"Wireless Communication Security Techniques","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10964","display_name":"Wireless Communication Security Techniques","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/T10968","display_name":"Statistical Distribution Estimation and Applications","score":0.9894000291824341,"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/T10125","display_name":"Advanced Wireless Communication Techniques","score":0.9740999937057495,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/ball","display_name":"Ball (mathematics)","score":0.639839768409729},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.6139971613883972},{"id":"https://openalex.org/keywords/spheres","display_name":"SPHERES","score":0.6115872263908386},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.6103395819664001},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5861377120018005},{"id":"https://openalex.org/keywords/bar","display_name":"Bar (unit)","score":0.5489087104797363},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.5272067189216614},{"id":"https://openalex.org/keywords/radius","display_name":"RADIUS","score":0.5198565125465393},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4803829789161682},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.4797871708869934},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.45576557517051697},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2891307473182678},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2255360186100006},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14200618863105774},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.10018044710159302}],"concepts":[{"id":"https://openalex.org/C122041747","wikidata":"https://www.wikidata.org/wiki/Q838611","display_name":"Ball (mathematics)","level":2,"score":0.639839768409729},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.6139971613883972},{"id":"https://openalex.org/C72422203","wikidata":"https://www.wikidata.org/wiki/Q7392545","display_name":"SPHERES","level":2,"score":0.6115872263908386},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.6103395819664001},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5861377120018005},{"id":"https://openalex.org/C188721877","wikidata":"https://www.wikidata.org/wiki/Q103510","display_name":"Bar (unit)","level":2,"score":0.5489087104797363},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.5272067189216614},{"id":"https://openalex.org/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"score":0.5198565125465393},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4803829789161682},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.4797871708869934},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.45576557517051697},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2891307473182678},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2255360186100006},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14200618863105774},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.10018044710159302},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0},{"id":"https://openalex.org/C153294291","wikidata":"https://www.wikidata.org/wiki/Q25261","display_name":"Meteorology","level":1,"score":0.0}],"mesh":[],"locations_count":9,"locations":[{"id":"doi:10.1109/tit.2018.2890208","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2018.2890208","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1804.08524","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1804.08524","pdf_url":"https://arxiv.org/pdf/1804.08524","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:2799201531","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1804.08524v1","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:zenodo.org:2590228","is_oa":true,"landing_page_url":"https://zenodo.org/record/2590228","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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":"","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:zenodo.org:3247011","is_oa":true,"landing_page_url":"https://zenodo.org/record/3247011","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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":"","raw_type":"info:eu-repo/semantics/article"},{"id":"doi:10.48550/arxiv.1804.08524","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1804.08524","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"},{"id":"doi:10.5281/zenodo.2590227","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.2590227","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"},{"id":"doi:10.5281/zenodo.2590228","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.2590228","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"},{"id":"doi:10.5281/zenodo.3247011","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.3247011","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1804.08524","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1804.08524","pdf_url":"https://arxiv.org/pdf/1804.08524","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1449290724","display_name":"CIF: Medium: Collaborative Research: Feedback Communication: Models, Designs, and Fundamental Limits","funder_award_id":"1513915","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3515941858","display_name":null,"funder_award_id":"CNS-1702808","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3911631480","display_name":"Cloud Wireless Networks: An Information Theoretic Framework","funder_award_id":"694630","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G5214133963","display_name":null,"funder_award_id":"CCF\u20131513915","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5844803823","display_name":"WiFiUS: Collaborative Research: Secure Inference in the Internet of Things","funder_award_id":"1702808","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6095009616","display_name":null,"funder_award_id":"CCF-1513915","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W1532769753","https://openalex.org/W1964052676","https://openalex.org/W1965797870","https://openalex.org/W1982804608","https://openalex.org/W1988458057","https://openalex.org/W2025137987","https://openalex.org/W2031724611","https://openalex.org/W2041475782","https://openalex.org/W2055356928","https://openalex.org/W2071061952","https://openalex.org/W2071511936","https://openalex.org/W2077144549","https://openalex.org/W2081338783","https://openalex.org/W2105204872","https://openalex.org/W2111616148","https://openalex.org/W2128705329","https://openalex.org/W2154750699","https://openalex.org/W2164714023","https://openalex.org/W2174000564","https://openalex.org/W2400075630","https://openalex.org/W2542437104","https://openalex.org/W2565206597","https://openalex.org/W2742239311","https://openalex.org/W2751666153","https://openalex.org/W2804224960","https://openalex.org/W2887561091","https://openalex.org/W2895077731","https://openalex.org/W2908899249","https://openalex.org/W2962719762","https://openalex.org/W2963918213","https://openalex.org/W2964018106","https://openalex.org/W2964248347","https://openalex.org/W3001978909","https://openalex.org/W6770510577"],"related_works":["https://openalex.org/W2908899249","https://openalex.org/W2094726556","https://openalex.org/W2064517065","https://openalex.org/W2534568398","https://openalex.org/W1974936036","https://openalex.org/W2953338282","https://openalex.org/W2132551315","https://openalex.org/W3173663981","https://openalex.org/W2088816860","https://openalex.org/W2055104190","https://openalex.org/W3102271552","https://openalex.org/W2625147455","https://openalex.org/W1971590827","https://openalex.org/W2013528585","https://openalex.org/W2073683055","https://openalex.org/W2969922848","https://openalex.org/W2962864013","https://openalex.org/W3084756427","https://openalex.org/W2126419612","https://openalex.org/W2765556718"],"abstract_inverted_index":{"This":[0,65],"paper":[1,66],"studies":[2],"the":[3,14,22,29,38,52,54,57,60,73,78,124],"capacity":[4],"of":[5,24,48,59,110,127],"an":[6,17,111],"n-dimensional":[7],"vector":[8],"Gaussian":[9],"noise":[10],"channel":[11],"subject":[12],"to":[13,106],"constraint":[15,74],"that":[16,34,77,96,118],"input":[18,40,79],"must":[19],"lie":[20],"in":[21,35],"ball":[23],"radius":[25],"R":[26],"centered":[27],"at":[28],"origin.":[30],"It":[31],"is":[32,42,86,102,104,116,133],"known":[33],"this":[36],"setting,":[37],"optimizing":[39],"distribution":[41,80],"supported":[43,81],"on":[44,72,82],"a":[45,83,99,108],"finite":[46],"number":[47],"concentric":[49],"spheres.":[50],"However,":[51],"number,":[53],"positions,":[55],"and":[56,69,123],"probabilities":[58],"spheres":[61],"are":[62],"generally":[63],"unknown.":[64],"characterizes":[67],"necessary":[68],"sufficient":[70],"conditions":[71],"R,":[75],"such":[76,95],"single":[84,100],"sphere":[85,101],"optimal.":[87],"The":[88],"maximum":[89],"R\u0305":[90,128],"<sub":[91,129],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[92,130],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">n</sub>":[93],",":[94],"using":[97],"only":[98],"optimal,":[103],"shown":[105,117],"be":[107],"solution":[109],"integral":[112],"equation.":[113],"Moreover,":[114],"it":[115],"\u0305Rn":[119],"scales":[120],"as":[121],"\u221an":[122,132],"exact":[125],"limit":[126],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">n/</sub>":[131],"found.":[134]},"counts_by_year":[{"year":2019,"cited_by_count":1}],"updated_date":"2026-05-23T08:51:43.019350","created_date":"2025-10-10T00:00:00"}