{"id":"https://openalex.org/W1983398636","doi":"https://doi.org/10.1007/bf01589397","title":"Survey of solved and open problems in the degeneracy phenomenon","display_name":"Survey of solved and open problems in the degeneracy phenomenon","publication_year":1988,"publication_date":"1988-04-01","ids":{"openalex":"https://openalex.org/W1983398636","doi":"https://doi.org/10.1007/bf01589397","mag":"1983398636"},"language":"en","primary_location":{"id":"doi:10.1007/bf01589397","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf01589397","pdf_url":null,"source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"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":"Mathematical Programming","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/A5039513667","display_name":"Tom\u00e1\u0161 G\u00e1l","orcid":"https://orcid.org/0000-0001-7383-5672"},"institutions":[{"id":"https://openalex.org/I120691247","display_name":"University of Hagen","ror":"https://ror.org/04tkkr536","country_code":"DE","type":"education","lineage":["https://openalex.org/I120691247"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Tomas Gal","raw_affiliation_strings":["Department of OR, FernUniversit\u00e4t Hagen, FR Germany","Hagen Germany"],"affiliations":[{"raw_affiliation_string":"Department of OR, FernUniversit\u00e4t Hagen, FR Germany","institution_ids":["https://openalex.org/I120691247"]},{"raw_affiliation_string":"Hagen Germany","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109333618","display_name":"Hermann-Josef Kruse","orcid":null},"institutions":[{"id":"https://openalex.org/I120691247","display_name":"University of Hagen","ror":"https://ror.org/04tkkr536","country_code":"DE","type":"education","lineage":["https://openalex.org/I120691247"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Hermann-Josef Kruse","raw_affiliation_strings":["Department of OR, FernUniversit\u00e4t Hagen, FR Germany","Hagen Germany"],"affiliations":[{"raw_affiliation_string":"Department of OR, FernUniversit\u00e4t Hagen, FR Germany","institution_ids":["https://openalex.org/I120691247"]},{"raw_affiliation_string":"Hagen Germany","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5105852145","display_name":"Peter Z\u00f6rnig","orcid":null},"institutions":[{"id":"https://openalex.org/I120691247","display_name":"University of Hagen","ror":"https://ror.org/04tkkr536","country_code":"DE","type":"education","lineage":["https://openalex.org/I120691247"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Peter Z\u00f6rnig","raw_affiliation_strings":["Department of OR, FernUniversit\u00e4t Hagen, FR Germany","Hagen Germany"],"affiliations":[{"raw_affiliation_string":"Department of OR, FernUniversit\u00e4t Hagen, FR Germany","institution_ids":["https://openalex.org/I120691247"]},{"raw_affiliation_string":"Hagen Germany","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5039513667"],"corresponding_institution_ids":["https://openalex.org/I120691247"],"apc_list":{"value":2190,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":5.55294906,"has_fulltext":false,"cited_by_count":32,"citation_normalized_percentile":{"value":0.95989577,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"42","issue":"1-3","first_page":"125","last_page":"133"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12709","display_name":"Optimization and Mathematical Programming","score":0.9932000041007996,"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"}},"topics":[{"id":"https://openalex.org/T12709","display_name":"Optimization and Mathematical Programming","score":0.9932000041007996,"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/T11777","display_name":"Fixed Point Theorems Analysis","score":0.9632999897003174,"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"}},{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9629999995231628,"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/mathematics","display_name":"Mathematics","score":0.6830638647079468},{"id":"https://openalex.org/keywords/phenomenon","display_name":"Phenomenon","score":0.6257005929946899},{"id":"https://openalex.org/keywords/degeneracy","display_name":"Degeneracy (biology)","score":0.5855228900909424},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.5099226236343384},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.39752423763275146},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3740540146827698},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.32014280557632446},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.21228370070457458},{"id":"https://openalex.org/keywords/epistemology","display_name":"Epistemology","score":0.11819502711296082}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6830638647079468},{"id":"https://openalex.org/C50335755","wikidata":"https://www.wikidata.org/wiki/Q483247","display_name":"Phenomenon","level":2,"score":0.6257005929946899},{"id":"https://openalex.org/C2777727622","wikidata":"https://www.wikidata.org/wiki/Q5251772","display_name":"Degeneracy (biology)","level":2,"score":0.5855228900909424},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.5099226236343384},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.39752423763275146},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3740540146827698},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.32014280557632446},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.21228370070457458},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.11819502711296082},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"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/C60644358","wikidata":"https://www.wikidata.org/wiki/Q128570","display_name":"Bioinformatics","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/bf01589397","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf01589397","pdf_url":null,"source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"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":"Mathematical Programming","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W32221055","https://openalex.org/W317084220","https://openalex.org/W622962059","https://openalex.org/W976146572","https://openalex.org/W1573502202","https://openalex.org/W1862519416","https://openalex.org/W1971258090","https://openalex.org/W1974142055","https://openalex.org/W2009005114","https://openalex.org/W2016853911","https://openalex.org/W2027341106","https://openalex.org/W2043732800","https://openalex.org/W2053732480","https://openalex.org/W2066018928","https://openalex.org/W2071549198","https://openalex.org/W2082824470","https://openalex.org/W2087817570","https://openalex.org/W2089315616","https://openalex.org/W2091467991","https://openalex.org/W2119822193","https://openalex.org/W2124163050","https://openalex.org/W2129506323","https://openalex.org/W2162703724","https://openalex.org/W2166016858","https://openalex.org/W2321503613","https://openalex.org/W2326954772","https://openalex.org/W2504537197","https://openalex.org/W3023019763","https://openalex.org/W4230134808","https://openalex.org/W6643736426","https://openalex.org/W6721860123"],"related_works":["https://openalex.org/W2372940580","https://openalex.org/W4300450609","https://openalex.org/W4386931570","https://openalex.org/W2391010541","https://openalex.org/W2357367123","https://openalex.org/W2387276901","https://openalex.org/W2385953334","https://openalex.org/W2101113459","https://openalex.org/W2130834282","https://openalex.org/W2351303360"],"abstract_inverted_index":null,"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
