{"id":"https://openalex.org/W2165846565","doi":"https://doi.org/10.2478/v10037-008-0041-z","title":"Partial Differentiation of Real Binary Functions","display_name":"Partial Differentiation of Real Binary Functions","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W2165846565","doi":"https://doi.org/10.2478/v10037-008-0041-z","mag":"2165846565"},"language":"en","primary_location":{"id":"doi:10.2478/v10037-008-0041-z","is_oa":true,"landing_page_url":"https://doi.org/10.2478/v10037-008-0041-z","pdf_url":"https://sciendo.com/pdf/10.2478/v10037-008-0041-z","source":{"id":"https://openalex.org/S179241345","display_name":"Formalized Mathematics","issn_l":"1426-2630","issn":["1426-2630","1898-9934"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Formalized Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://sciendo.com/pdf/10.2478/v10037-008-0041-z","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5044119075","display_name":"Bing Xie","orcid":"https://orcid.org/0000-0001-6224-6637"},"institutions":[{"id":"https://openalex.org/I143413998","display_name":"Qingdao University of Science and Technology","ror":"https://ror.org/041j8js14","country_code":"CN","type":"education","lineage":["https://openalex.org/I143413998"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Bing Xie","raw_affiliation_strings":["Qingdao University of Science and Technology China"],"affiliations":[{"raw_affiliation_string":"Qingdao University of Science and Technology China","institution_ids":["https://openalex.org/I143413998"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102161473","display_name":"Xiquan Liang","orcid":null},"institutions":[{"id":"https://openalex.org/I143413998","display_name":"Qingdao University of Science and Technology","ror":"https://ror.org/041j8js14","country_code":"CN","type":"education","lineage":["https://openalex.org/I143413998"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiquan Liang","raw_affiliation_strings":["Qingdao University of Science and Technology China"],"affiliations":[{"raw_affiliation_string":"Qingdao University of Science and Technology China","institution_ids":["https://openalex.org/I143413998"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100325345","display_name":"Hongwei Li","orcid":"https://orcid.org/0000-0002-8401-6135"},"institutions":[{"id":"https://openalex.org/I143413998","display_name":"Qingdao University of Science and Technology","ror":"https://ror.org/041j8js14","country_code":"CN","type":"education","lineage":["https://openalex.org/I143413998"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hongwei Li","raw_affiliation_strings":["Qingdao University of Science and Technology China"],"affiliations":[{"raw_affiliation_string":"Qingdao University of Science and Technology China","institution_ids":["https://openalex.org/I143413998"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5044119075"],"corresponding_institution_ids":["https://openalex.org/I143413998"],"apc_list":null,"apc_paid":null,"fwci":1.2963,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.79643036,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"16","issue":"4","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12508","display_name":"Functional Equations Stability Results","score":0.9696999788284302,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12508","display_name":"Functional Equations Stability Results","score":0.9696999788284302,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.9635999798774719,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.942799985408783,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/partial-function","display_name":"Partial function","score":0.8607337474822998},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7501296997070312},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.664726972579956},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.6004924178123474},{"id":"https://openalex.org/keywords/automatic-differentiation","display_name":"Automatic differentiation","score":0.5563748478889465},{"id":"https://openalex.org/keywords/binary-function","display_name":"Binary function","score":0.5385990738868713},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5155856013298035},{"id":"https://openalex.org/keywords/partial-derivative","display_name":"Partial derivative","score":0.4148421287536621},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3292173147201538},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.28701961040496826},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.26465892791748047},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.22797805070877075},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.1934766173362732},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.15401169657707214}],"concepts":[{"id":"https://openalex.org/C182359184","wikidata":"https://www.wikidata.org/wiki/Q1756942","display_name":"Partial function","level":2,"score":0.8607337474822998},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7501296997070312},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.664726972579956},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.6004924178123474},{"id":"https://openalex.org/C133512626","wikidata":"https://www.wikidata.org/wiki/Q787371","display_name":"Automatic differentiation","level":3,"score":0.5563748478889465},{"id":"https://openalex.org/C105462591","wikidata":"https://www.wikidata.org/wiki/Q3737844","display_name":"Binary function","level":3,"score":0.5385990738868713},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5155856013298035},{"id":"https://openalex.org/C53846429","wikidata":"https://www.wikidata.org/wiki/Q186475","display_name":"Partial derivative","level":2,"score":0.4148421287536621},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3292173147201538},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.28701961040496826},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.26465892791748047},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.22797805070877075},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.1934766173362732},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15401169657707214},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.2478/v10037-008-0041-z","is_oa":true,"landing_page_url":"https://doi.org/10.2478/v10037-008-0041-z","pdf_url":"https://sciendo.com/pdf/10.2478/v10037-008-0041-z","source":{"id":"https://openalex.org/S179241345","display_name":"Formalized Mathematics","issn_l":"1426-2630","issn":["1426-2630","1898-9934"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Formalized Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.148.8957","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.148.8957","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://mizar.org/fm/2008-16/pdf16-4/pdiff_2.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.551.7721","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.551.7721","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://fm.uwb.edu.pl/pub/fm/output/8393.pdf","raw_type":"text"},{"id":"pmh:oai:doaj.org/article:c885cad7571149759637bc562ce1018d","is_oa":true,"landing_page_url":"https://doaj.org/article/c885cad7571149759637bc562ce1018d","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Formalized Mathematics, Vol 16, Iss 4, Pp 333-338 (2008)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.2478/v10037-008-0041-z","is_oa":true,"landing_page_url":"https://doi.org/10.2478/v10037-008-0041-z","pdf_url":"https://sciendo.com/pdf/10.2478/v10037-008-0041-z","source":{"id":"https://openalex.org/S179241345","display_name":"Formalized Mathematics","issn_l":"1426-2630","issn":["1426-2630","1898-9934"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Formalized Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.41999998688697815}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2165846565.pdf","grobid_xml":"https://content.openalex.org/works/W2165846565.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W66860599","https://openalex.org/W68895216","https://openalex.org/W79563955","https://openalex.org/W260340778","https://openalex.org/W1483101703","https://openalex.org/W1512393411","https://openalex.org/W1619732349","https://openalex.org/W2070515450","https://openalex.org/W2134057927","https://openalex.org/W2143851127","https://openalex.org/W2150348213","https://openalex.org/W2163641194","https://openalex.org/W2296232473","https://openalex.org/W2548951370","https://openalex.org/W2554327433","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2553993726","https://openalex.org/W2149544075","https://openalex.org/W4394877266","https://openalex.org/W2486169089","https://openalex.org/W3124018042","https://openalex.org/W2127375336","https://openalex.org/W2109371256","https://openalex.org/W2983293055","https://openalex.org/W2162114838","https://openalex.org/W2370856440"],"abstract_inverted_index":{"Partial":[0],"Differentiation":[1],"of":[2,20,26,36],"Real":[3],"Binary":[4],"FunctionsIn":[5],"this":[6],"article,":[7],"we":[8],"define":[9],"two":[10],"single-variable":[11],"functions":[12,23],"SVF1":[13,30],"and":[14,31],"SVF2,":[15],"then":[16],"discuss":[17],"partial":[18,37],"differentiation":[19,38],"real":[21],"binary":[22],"by":[24],"dint":[25],"one":[27],"variable":[28],"function":[29],"SVF2.":[32],"The":[33],"main":[34],"properties":[35],"are":[39],"shown":[40],"[7].MML":[41],"identifier:":[42],"PDIFF":[43],"2,":[44],"version:":[45],"7.9.03":[46],"4.104.1021":[47]},"counts_by_year":[],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
