{"id":"https://openalex.org/W4385839977","doi":"https://doi.org/10.3390/s23167179","title":"Extended Higher-Order Elements with Frequency-Doubled Parameters: The Hysteresis Loops Are Always of Type II","display_name":"Extended Higher-Order Elements with Frequency-Doubled Parameters: The Hysteresis Loops Are Always of Type II","publication_year":2023,"publication_date":"2023-08-15","ids":{"openalex":"https://openalex.org/W4385839977","doi":"https://doi.org/10.3390/s23167179","pmid":"https://pubmed.ncbi.nlm.nih.gov/37631716"},"language":"en","primary_location":{"id":"doi:10.3390/s23167179","is_oa":true,"landing_page_url":"https://doi.org/10.3390/s23167179","pdf_url":"https://www.mdpi.com/1424-8220/23/16/7179/pdf?version=1692171913","source":{"id":"https://openalex.org/S101949793","display_name":"Sensors","issn_l":"1424-8220","issn":["1424-8220"],"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":"Sensors","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1424-8220/23/16/7179/pdf?version=1692171913","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5048440535","display_name":"Zden\u011bk Biolek","orcid":"https://orcid.org/0000-0003-3055-4621"},"institutions":[{"id":"https://openalex.org/I96415178","display_name":"University of Defence","ror":"https://ror.org/04arkmn57","country_code":"CZ","type":"education","lineage":["https://openalex.org/I96415178"]}],"countries":["CZ"],"is_corresponding":false,"raw_author_name":"Zden\u011bk Biolek","raw_affiliation_strings":["Department of Electrical Engineering, University of Defence, 662 10 Brno, Czech Republic"],"raw_orcid":"https://orcid.org/0000-0003-3055-4621","affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, University of Defence, 662 10 Brno, Czech Republic","institution_ids":["https://openalex.org/I96415178"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5069658742","display_name":"Dalibor Biolek","orcid":"https://orcid.org/0000-0002-7607-6146"},"institutions":[{"id":"https://openalex.org/I60587646","display_name":"Brno University of Technology","ror":"https://ror.org/03613d656","country_code":"CZ","type":"education","lineage":["https://openalex.org/I60587646"]},{"id":"https://openalex.org/I96415178","display_name":"University of Defence","ror":"https://ror.org/04arkmn57","country_code":"CZ","type":"education","lineage":["https://openalex.org/I96415178"]}],"countries":["CZ"],"is_corresponding":true,"raw_author_name":"Dalibor Biolek","raw_affiliation_strings":["Department of Electrical Engineering, University of Defence, 662 10 Brno, Czech Republic","Department of Microelectronics, Brno University of Technology, 616 00 Brno, Czech Republic"],"raw_orcid":"https://orcid.org/0000-0002-7607-6146","affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, University of Defence, 662 10 Brno, Czech Republic","institution_ids":["https://openalex.org/I96415178"]},{"raw_affiliation_string":"Department of Microelectronics, Brno University of Technology, 616 00 Brno, Czech Republic","institution_ids":["https://openalex.org/I60587646"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083744068","display_name":"Viera Biolkov\u00e1","orcid":"https://orcid.org/0000-0003-2589-2722"},"institutions":[{"id":"https://openalex.org/I60587646","display_name":"Brno University of Technology","ror":"https://ror.org/03613d656","country_code":"CZ","type":"education","lineage":["https://openalex.org/I60587646"]}],"countries":["CZ"],"is_corresponding":false,"raw_author_name":"Viera Biolkov\u00e1","raw_affiliation_strings":["Department of Radio Electronics, Brno University of Technology, 616 00 Brno, Czech Republic"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Radio Electronics, Brno University of Technology, 616 00 Brno, Czech Republic","institution_ids":["https://openalex.org/I60587646"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5066848813","display_name":"Zden\u011bk Kolka","orcid":"https://orcid.org/0000-0002-7034-9430"},"institutions":[{"id":"https://openalex.org/I60587646","display_name":"Brno University of Technology","ror":"https://ror.org/03613d656","country_code":"CZ","type":"education","lineage":["https://openalex.org/I60587646"]}],"countries":["CZ"],"is_corresponding":false,"raw_author_name":"Zden\u011bk Kolka","raw_affiliation_strings":["Department of Radio Electronics, Brno University of Technology, 616 00 Brno, Czech Republic"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Radio Electronics, Brno University of Technology, 616 00 Brno, Czech Republic","institution_ids":["https://openalex.org/I60587646"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5069658742"],"corresponding_institution_ids":["https://openalex.org/I60587646","https://openalex.org/I96415178"],"apc_list":{"value":2400,"currency":"CHF","value_usd":2598},"apc_paid":{"value":2400,"currency":"CHF","value_usd":2598},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.09520681,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"23","issue":"16","first_page":"7179","last_page":"7179"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10923","display_name":"Force Microscopy Techniques and Applications","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"}},"topics":[{"id":"https://openalex.org/T10923","display_name":"Force Microscopy Techniques and Applications","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"}},{"id":"https://openalex.org/T11525","display_name":"Piezoelectric Actuators and Control","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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/T10502","display_name":"Advanced Memory and Neural Computing","score":0.9980000257492065,"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/hysteresis","display_name":"Hysteresis","score":0.7234739661216736},{"id":"https://openalex.org/keywords/inductor","display_name":"Inductor","score":0.6261714696884155},{"id":"https://openalex.org/keywords/resistor","display_name":"Resistor","score":0.6150447130203247},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.5663560628890991},{"id":"https://openalex.org/keywords/element","display_name":"Element (criminal law)","score":0.5136563181877136},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5114396810531616},{"id":"https://openalex.org/keywords/capacitor","display_name":"Capacitor","score":0.5075005888938904},{"id":"https://openalex.org/keywords/electrical-element","display_name":"Electrical element","score":0.4859074652194977},{"id":"https://openalex.org/keywords/loop","display_name":"Loop (graph theory)","score":0.45341524481773376},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.37211519479751587},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.36645954847335815},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.32328057289123535},{"id":"https://openalex.org/keywords/voltage","display_name":"Voltage","score":0.2962912321090698},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2766556143760681},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2457360029220581},{"id":"https://openalex.org/keywords/electrical-engineering","display_name":"Electrical engineering","score":0.1797780692577362},{"id":"https://openalex.org/keywords/condensed-matter-physics","display_name":"Condensed matter physics","score":0.16960859298706055}],"concepts":[{"id":"https://openalex.org/C123299182","wikidata":"https://www.wikidata.org/wiki/Q190837","display_name":"Hysteresis","level":2,"score":0.7234739661216736},{"id":"https://openalex.org/C144534570","wikidata":"https://www.wikidata.org/wiki/Q5325","display_name":"Inductor","level":3,"score":0.6261714696884155},{"id":"https://openalex.org/C137488568","wikidata":"https://www.wikidata.org/wiki/Q5321","display_name":"Resistor","level":3,"score":0.6150447130203247},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5663560628890991},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.5136563181877136},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5114396810531616},{"id":"https://openalex.org/C52192207","wikidata":"https://www.wikidata.org/wiki/Q5322","display_name":"Capacitor","level":3,"score":0.5075005888938904},{"id":"https://openalex.org/C113089479","wikidata":"https://www.wikidata.org/wiki/Q210729","display_name":"Electrical element","level":2,"score":0.4859074652194977},{"id":"https://openalex.org/C184670325","wikidata":"https://www.wikidata.org/wiki/Q512604","display_name":"Loop (graph theory)","level":2,"score":0.45341524481773376},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.37211519479751587},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.36645954847335815},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.32328057289123535},{"id":"https://openalex.org/C165801399","wikidata":"https://www.wikidata.org/wiki/Q25428","display_name":"Voltage","level":2,"score":0.2962912321090698},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2766556143760681},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2457360029220581},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.1797780692577362},{"id":"https://openalex.org/C26873012","wikidata":"https://www.wikidata.org/wiki/Q214781","display_name":"Condensed matter physics","level":1,"score":0.16960859298706055},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.3390/s23167179","is_oa":true,"landing_page_url":"https://doi.org/10.3390/s23167179","pdf_url":"https://www.mdpi.com/1424-8220/23/16/7179/pdf?version=1692171913","source":{"id":"https://openalex.org/S101949793","display_name":"Sensors","issn_l":"1424-8220","issn":["1424-8220"],"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":"Sensors","raw_type":"journal-article"},{"id":"pmid:37631716","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/37631716","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Sensors (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:dspace.vut.cz:11012/245042","is_oa":true,"landing_page_url":"http://hdl.handle.net/11012/245042","pdf_url":"https://dspace.vut.cz/bitstreams/e046e4ab-6740-4e66-b5a5-9946413d5ae1/download","source":{"id":"https://openalex.org/S4306400317","display_name":"Brno University of Technology Digital Library (Brno University of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I60587646","host_organization_name":"Brno University of Technology","host_organization_lineage":["https://openalex.org/I60587646"],"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":null,"raw_type":"publishedVersion"},{"id":"pmh:oai:pubmedcentral.nih.gov:10458208","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/10458208","pdf_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC10458208/pdf/sensors-23-07179.pdf","source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"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":"Sensors (Basel)","raw_type":"Text"},{"id":"pmh:oai:doaj.org/article:d988d9b1842e466f9caf925b050664ff","is_oa":true,"landing_page_url":"https://doaj.org/article/d988d9b1842e466f9caf925b050664ff","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Sensors, Vol 23, Iss 16, p 7179 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1424-8220/23/16/7179/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/s23167179","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":"Sensors; Volume 23; Issue 16; Pages: 7179","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/s23167179","is_oa":true,"landing_page_url":"https://doi.org/10.3390/s23167179","pdf_url":"https://www.mdpi.com/1424-8220/23/16/7179/pdf?version=1692171913","source":{"id":"https://openalex.org/S101949793","display_name":"Sensors","issn_l":"1424-8220","issn":["1424-8220"],"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":"Sensors","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy","score":0.46000000834465027}],"awards":[{"id":"https://openalex.org/G5666851053","display_name":null,"funder_award_id":"20-26849S","funder_id":"https://openalex.org/F4320321006","funder_display_name":"Grantov\u00e1 Agentura \u010cesk\u00e9 Republiky"}],"funders":[{"id":"https://openalex.org/F4320321006","display_name":"Grantov\u00e1 Agentura \u010cesk\u00e9 Republiky","ror":"https://ror.org/01pv73b02"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4385839977.pdf"},"referenced_works_count":95,"referenced_works":["https://openalex.org/W605875166","https://openalex.org/W1554296272","https://openalex.org/W1578560839","https://openalex.org/W1598338247","https://openalex.org/W1964179363","https://openalex.org/W1966025990","https://openalex.org/W1975229527","https://openalex.org/W1979425945","https://openalex.org/W1983560850","https://openalex.org/W1999184785","https://openalex.org/W2005482522","https://openalex.org/W2015248366","https://openalex.org/W2018258488","https://openalex.org/W2022947725","https://openalex.org/W2033592371","https://openalex.org/W2037438538","https://openalex.org/W2044207434","https://openalex.org/W2045009304","https://openalex.org/W2057866825","https://openalex.org/W2066539612","https://openalex.org/W2069717653","https://openalex.org/W2071119949","https://openalex.org/W2082989704","https://openalex.org/W2087661690","https://openalex.org/W2103282475","https://openalex.org/W2103920070","https://openalex.org/W2109052923","https://openalex.org/W2112181056","https://openalex.org/W2125453397","https://openalex.org/W2147073959","https://openalex.org/W2150039047","https://openalex.org/W2150055511","https://openalex.org/W2162651880","https://openalex.org/W2264574174","https://openalex.org/W2279614360","https://openalex.org/W2288560260","https://openalex.org/W2298162613","https://openalex.org/W2330593779","https://openalex.org/W2336471101","https://openalex.org/W2472275516","https://openalex.org/W2477921776","https://openalex.org/W2493028547","https://openalex.org/W2518581802","https://openalex.org/W2531422891","https://openalex.org/W2540973205","https://openalex.org/W2605154112","https://openalex.org/W2767485082","https://openalex.org/W2789881329","https://openalex.org/W2792860014","https://openalex.org/W2794375783","https://openalex.org/W2797509433","https://openalex.org/W2803045744","https://openalex.org/W2805745475","https://openalex.org/W2807631060","https://openalex.org/W2884757872","https://openalex.org/W2900178210","https://openalex.org/W2902283950","https://openalex.org/W2920814391","https://openalex.org/W2954654523","https://openalex.org/W2962697549","https://openalex.org/W2963972125","https://openalex.org/W2997199178","https://openalex.org/W3004441219","https://openalex.org/W3046373265","https://openalex.org/W3093430078","https://openalex.org/W3104276615","https://openalex.org/W3106113239","https://openalex.org/W3111875997","https://openalex.org/W3131267969","https://openalex.org/W3169064244","https://openalex.org/W3187729430","https://openalex.org/W3194591345","https://openalex.org/W4205892980","https://openalex.org/W4206061765","https://openalex.org/W4206899403","https://openalex.org/W4207017185","https://openalex.org/W4233712419","https://openalex.org/W4280496126","https://openalex.org/W4281381295","https://openalex.org/W4290072581","https://openalex.org/W4296079213","https://openalex.org/W4306963816","https://openalex.org/W4318830934","https://openalex.org/W4320917551","https://openalex.org/W4321770440","https://openalex.org/W4365453305","https://openalex.org/W4375844907","https://openalex.org/W4382790897","https://openalex.org/W6633094287","https://openalex.org/W6658807841","https://openalex.org/W6682630956","https://openalex.org/W6693238461","https://openalex.org/W6696336959","https://openalex.org/W6728750200","https://openalex.org/W6747756577"],"related_works":["https://openalex.org/W3200817179","https://openalex.org/W1960166976","https://openalex.org/W1992708211","https://openalex.org/W2380067098","https://openalex.org/W1548152478","https://openalex.org/W2137172615","https://openalex.org/W2106247205","https://openalex.org/W2789898315","https://openalex.org/W2189302854","https://openalex.org/W2359779428"],"abstract_inverted_index":{"Current":[0],"MEMS":[1],"(Micro":[2],"Electro":[3],"Mechanical":[4],"Systems)":[5],"can":[6,56],"be":[7,57,178],"modeled":[8],"by":[9,168,201],"state-dependent":[10],"elements":[11,43,134],"that":[12,135,171],"exhibit":[13,38],"hysteretic":[14,75],"behavior.":[15],"Examples":[16],"include":[17],"capacitors":[18],"and":[19,23,66,80,156,190,199],"inductors":[20],"whose":[21,36],"capacitances":[22],"inductances":[24],"are":[25,44,166,195],"dependent":[26],"on":[27,128],"the":[28,32,42,50,61,96,113,119,150,157,173,181,185],"instantaneous":[29],"state":[30],"of":[31,49,64,74,92,115,122,132,153,159,175,184],"electromechanical":[33],"system,":[34],"resistors":[35],"resistances":[37],"temperature":[39],"changes":[40],"when":[41],"actually":[45],"heated,":[46],"etc.":[47],"Regardless":[48],"physical":[51],"background,":[52],"such":[53],"hysteresis":[54,161,176],"manifestations":[55],"studied":[58],"uniformly":[59],"in":[60,70],"broader":[62],"framework":[63],"generic":[65],"extended":[67,133],"higher-order":[68],"elements,":[69],"which":[71],"a":[72],"classification":[73],"loops":[76,139],"into":[77],"types":[78],"I":[79],"II":[81,138],"is":[82,87,107],"established.":[83],"The":[84,143,163],"loop":[85,117],"type":[86,114,137,158,174],"an":[88,93,123,154],"important":[89],"dynamical":[90],"parameter":[91,187],"element,":[94],"having":[95],"potential":[97],"to":[98,111,177],"indicate,":[99],"for":[100],"example,":[101],"its":[102,160],"(in)volatility.":[103],"Thus":[104],"far,":[105],"there":[106],"no":[108],"reliable":[109],"criterion":[110],"determine":[112],"steady":[116],"from":[118,180],"defining":[120],"relations":[121],"element.":[124],"This":[125],"work":[126],"reports":[127],"one":[129],"special":[130],"class":[131],"produces":[136],"under":[140],"all":[141],"circumstances.":[142],"paper":[144],"presents":[145],"hitherto":[146],"unpublished":[147],"connections":[148],"between":[149],"frequency-doubling":[151],"parameters":[152],"element":[155,186],"loop.":[162],"new":[164],"findings":[165],"expressed":[167],"several":[169],"theorems":[170],"allow":[172],"inferred":[179],"frequency":[182],"behavior":[183],"or":[188],"state,":[189],"vice":[191],"versa.":[192],"These":[193],"procedures":[194],"demonstrated":[196],"with":[197],"examples":[198],"verified":[200],"computer":[202],"simulations.":[203]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
