{"id":"https://openalex.org/W2052773451","doi":"https://doi.org/10.1007/s11590-013-0680-z","title":"A note on the trace quotient problem","display_name":"A note on the trace quotient problem","publication_year":2013,"publication_date":"2013-07-26","ids":{"openalex":"https://openalex.org/W2052773451","doi":"https://doi.org/10.1007/s11590-013-0680-z","mag":"2052773451"},"language":"en","primary_location":{"id":"doi:10.1007/s11590-013-0680-z","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11590-013-0680-z","pdf_url":null,"source":{"id":"https://openalex.org/S12647387","display_name":"Optimization Letters","issn_l":"1862-4472","issn":["1862-4472","1862-4480"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Letters","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5113461594","display_name":"Lei-Hong Zhang","orcid":null},"institutions":[{"id":"https://openalex.org/I181679659","display_name":"Shanghai University of Finance and Economics","ror":"https://ror.org/00wtvfq62","country_code":"CN","type":"education","lineage":["https://openalex.org/I181679659"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Lei-Hong Zhang","raw_affiliation_strings":["Department of Applied Mathematics, Shanghai University of Finance and Economics, 777 Guoding Road, Shanghai,  200433, People\u2019s Republic of China","Department of Applied Mathematics, Shanghai University of Finance and Economics, 777 Guoding Road, Shanghai, \u00a0200433, People\u2019s Republic of China","SHANGHAI UNIVERSITY OF FINANCE AND ECONOMICS"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Shanghai University of Finance and Economics, 777 Guoding Road, Shanghai,  200433, People\u2019s Republic of China","institution_ids":["https://openalex.org/I181679659"]},{"raw_affiliation_string":"Department of Applied Mathematics, Shanghai University of Finance and Economics, 777 Guoding Road, Shanghai, \u00a0200433, People\u2019s Republic of China","institution_ids":["https://openalex.org/I181679659"]},{"raw_affiliation_string":"SHANGHAI UNIVERSITY OF FINANCE AND ECONOMICS","institution_ids":["https://openalex.org/I181679659"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077741971","display_name":"Wei Hong Yang","orcid":"https://orcid.org/0000-0002-4585-9682"},"institutions":[{"id":"https://openalex.org/I24943067","display_name":"Fudan University","ror":"https://ror.org/013q1eq08","country_code":"CN","type":"education","lineage":["https://openalex.org/I24943067"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wei Hong Yang","raw_affiliation_strings":["Mathematical Sciences, Fudan University, Shanghai,  200433, People\u2019s Republic of China","Mathematical Sciences, Fudan University, Shanghai, \u00a0200433, People\u2019s Republic of China","Fudan University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematical Sciences, Fudan University, Shanghai,  200433, People\u2019s Republic of China","institution_ids":["https://openalex.org/I24943067"]},{"raw_affiliation_string":"Mathematical Sciences, Fudan University, Shanghai, \u00a0200433, People\u2019s Republic of China","institution_ids":["https://openalex.org/I24943067"]},{"raw_affiliation_string":"Fudan University","institution_ids":["https://openalex.org/I24943067"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5079973146","display_name":"Li\u2010Zhi Liao","orcid":"https://orcid.org/0000-0002-0588-7953"},"institutions":[{"id":"https://openalex.org/I141568987","display_name":"Hong Kong Baptist University","ror":"https://ror.org/0145fw131","country_code":"HK","type":"education","lineage":["https://openalex.org/I141568987"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Li-Zhi Liao","raw_affiliation_strings":["Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong, People\u2019s Republic of China","Hong Kong Baptist University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong, People\u2019s Republic of China","institution_ids":["https://openalex.org/I141568987"]},{"raw_affiliation_string":"Hong Kong Baptist University","institution_ids":["https://openalex.org/I141568987"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5113461594"],"corresponding_institution_ids":["https://openalex.org/I181679659"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":1.8623,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.85745051,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"8","issue":"5","first_page":"1637","last_page":"1645"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9940999746322632,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9940999746322632,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9901999831199646,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T11476","display_name":"Graph theory and applications","score":0.980400025844574,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/quotient","display_name":"Quotient","score":0.8060373067855835},{"id":"https://openalex.org/keywords/trace","display_name":"TRACE (psycholinguistics)","score":0.6962016224861145},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6610597372055054},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5526189208030701},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5208038091659546},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.5089325904846191},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.44675305485725403},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4414171576499939},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.4275687336921692},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4229242503643036},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4018791913986206},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.34807467460632324},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.18354889750480652}],"concepts":[{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.8060373067855835},{"id":"https://openalex.org/C75291252","wikidata":"https://www.wikidata.org/wiki/Q1315756","display_name":"TRACE (psycholinguistics)","level":2,"score":0.6962016224861145},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6610597372055054},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5526189208030701},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5208038091659546},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5089325904846191},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.44675305485725403},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4414171576499939},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.4275687336921692},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4229242503643036},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4018791913986206},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.34807467460632324},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.18354889750480652},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s11590-013-0680-z","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11590-013-0680-z","pdf_url":null,"source":{"id":"https://openalex.org/S12647387","display_name":"Optimization Letters","issn_l":"1862-4472","issn":["1862-4472","1862-4480"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Letters","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.4399999976158142}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1712224752","https://openalex.org/W1804110266","https://openalex.org/W2000286736","https://openalex.org/W2017530772","https://openalex.org/W2024283886","https://openalex.org/W2033478416","https://openalex.org/W2061987257","https://openalex.org/W2090579338","https://openalex.org/W2152004476","https://openalex.org/W2158281641","https://openalex.org/W2762384127","https://openalex.org/W3029645440","https://openalex.org/W4205293427","https://openalex.org/W4301014524"],"related_works":["https://openalex.org/W2077314575","https://openalex.org/W4315701745","https://openalex.org/W1990290471","https://openalex.org/W4380682190","https://openalex.org/W2102386043","https://openalex.org/W2945307361","https://openalex.org/W2116636209","https://openalex.org/W4311529015","https://openalex.org/W2382785608","https://openalex.org/W3028475238"],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2}],"updated_date":"2026-06-19T15:47:20.252518","created_date":"2025-10-10T00:00:00"}
