{"id":"https://openalex.org/W7536951","doi":"https://doi.org/10.1007/978-3-642-03816-7_62","title":"Points on Computable Curves of Computable Lengths","display_name":"Points on Computable Curves of Computable Lengths","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W7536951","doi":"https://doi.org/10.1007/978-3-642-03816-7_62","mag":"7536951"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-642-03816-7_62","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-03816-7_62","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","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/A5076334612","display_name":"Robert Rettinger","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":true,"raw_author_name":"Robert Rettinger","raw_affiliation_strings":["Lehrgebiet Algorithmen und Komplexit\u00e4t, FernUniversit\u00e4t Hagen, 58084, Hagen, Germany"],"affiliations":[{"raw_affiliation_string":"Lehrgebiet Algorithmen und Komplexit\u00e4t, FernUniversit\u00e4t Hagen, 58084, Hagen, Germany","institution_ids":["https://openalex.org/I120691247"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102089636","display_name":"Xizhong Zheng","orcid":null},"institutions":[{"id":"https://openalex.org/I51204116","display_name":"Arcadia University","ror":"https://ror.org/00ff4bt20","country_code":"US","type":"education","lineage":["https://openalex.org/I51204116"]},{"id":"https://openalex.org/I115592961","display_name":"Jiangsu University","ror":"https://ror.org/03jc41j30","country_code":"CN","type":"education","lineage":["https://openalex.org/I115592961"]}],"countries":["CN","US"],"is_corresponding":false,"raw_author_name":"Xizhong Zheng","raw_affiliation_strings":["Department of Computer Science and Mathematics, Arcadia University, Glenside, PA, 19038, USA","Department of Mathematics, Jiangsu University, Zhenjiang, 212013, China"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Mathematics, Arcadia University, Glenside, PA, 19038, USA","institution_ids":["https://openalex.org/I51204116"]},{"raw_affiliation_string":"Department of Mathematics, Jiangsu University, Zhenjiang, 212013, China","institution_ids":["https://openalex.org/I115592961"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5076334612"],"corresponding_institution_ids":["https://openalex.org/I120691247"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.3288,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.57334434,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"736","last_page":"743"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9995999932289124,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9995999932289124,"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/T12923","display_name":"Digital Image Processing Techniques","score":0.9613000154495239,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T11567","display_name":"semigroups and automata theory","score":0.9329000115394592,"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/computable-function","display_name":"Computable function","score":0.8211987614631653},{"id":"https://openalex.org/keywords/computable-analysis","display_name":"Computable analysis","score":0.7104782462120056},{"id":"https://openalex.org/keywords/computable-number","display_name":"Computable number","score":0.5717824697494507},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.534807562828064},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.47324615716934204},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.44066154956817627},{"id":"https://openalex.org/keywords/computable-general-equilibrium","display_name":"Computable general equilibrium","score":0.4338175058364868},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.431508868932724},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.34688496589660645},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.30191153287887573},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2228076457977295}],"concepts":[{"id":"https://openalex.org/C54271186","wikidata":"https://www.wikidata.org/wiki/Q1148456","display_name":"Computable function","level":2,"score":0.8211987614631653},{"id":"https://openalex.org/C27318111","wikidata":"https://www.wikidata.org/wiki/Q5157264","display_name":"Computable analysis","level":3,"score":0.7104782462120056},{"id":"https://openalex.org/C156382255","wikidata":"https://www.wikidata.org/wiki/Q818895","display_name":"Computable number","level":4,"score":0.5717824697494507},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.534807562828064},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.47324615716934204},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.44066154956817627},{"id":"https://openalex.org/C20522121","wikidata":"https://www.wikidata.org/wiki/Q3589458","display_name":"Computable general equilibrium","level":2,"score":0.4338175058364868},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.431508868932724},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34688496589660645},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.30191153287887573},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2228076457977295},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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/C139719470","wikidata":"https://www.wikidata.org/wiki/Q39680","display_name":"Macroeconomics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-642-03816-7_62","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-03816-7_62","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","score":0.4699999988079071,"display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1497475168","https://openalex.org/W1503133286","https://openalex.org/W1506292197","https://openalex.org/W1509579779","https://openalex.org/W1545819195","https://openalex.org/W1546826212","https://openalex.org/W1964473643","https://openalex.org/W1966996896","https://openalex.org/W1980550011","https://openalex.org/W1990962533","https://openalex.org/W2077769760","https://openalex.org/W4243563333","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W197714092","https://openalex.org/W2150482238","https://openalex.org/W153068418","https://openalex.org/W2527631632","https://openalex.org/W1577501449","https://openalex.org/W1994403863","https://openalex.org/W2108904240","https://openalex.org/W1987175852","https://openalex.org/W1498085647","https://openalex.org/W2099946855"],"abstract_inverted_index":null,"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
