{"id":"https://openalex.org/W2011995705","doi":"https://doi.org/10.4064/ap87-0-22","title":"Volume and multiplicities of real analytic sets","display_name":"Volume and multiplicities of real analytic sets","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W2011995705","doi":"https://doi.org/10.4064/ap87-0-22","mag":"2011995705"},"language":"en","primary_location":{"id":"doi:10.4064/ap87-0-22","doi":"https://doi.org/10.4064/ap87-0-22","is_oa":true,"landing_page_url":"https://doi.org/10.4064/ap87-0-22","pdf_url":"https://www.impan.pl/shop/publication/transaction/download/product/84791?download.pdf","source":{"id":"https://openalex.org/S179694389","display_name":"Annales Polonici Mathematici","issn_l":"0066-2216","issn":["0066-2216","1730-6272"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","jufo-1","norway-1"],"host_organization":"https://openalex.org/P4310317485","host_organization_name":"Polish Academy of Sciences","host_organization_lineage":["https://openalex.org/P4310317485"],"host_organization_lineage_names":["Polish Academy of Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annales Polonici Mathematici","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.impan.pl/shop/publication/transaction/download/product/84791?download.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5067470130","display_name":"Guillaume Valette","orcid":"https://orcid.org/0000-0002-5461-1312","observed_orcids":["https://orcid.org/0000-0002-5461-1312"]},"institutions":[{"id":"https://openalex.org/I126596746","display_name":"Jagiellonian University","ror":"https://ror.org/03bqmcz70","country_code":"PL","type":"education","lineage":["https://openalex.org/I126596746"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Guillaume Valette","raw_affiliation_strings":["Institute of Mathematics Jagiellonian University Reymonta 4 30-059 Krak\u00f3w, Poland","Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Krak\u00f3w , Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Mathematics Jagiellonian University Reymonta 4 30-059 Krak\u00f3w, Poland","institution_ids":["https://openalex.org/I126596746"]},{"raw_affiliation_string":"Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Krak\u00f3w , Poland","institution_ids":["https://openalex.org/I126596746"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5067470130"],"corresponding_institution_ids":["https://openalex.org/I126596746"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.14998404,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"87","issue":null,"first_page":"265","last_page":"276"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9106000065803528,"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"}},"topics":[{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9106000065803528,"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/T12351","display_name":"Geometry and complex manifolds","score":0.041099999099969864,"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/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.030899999663233757,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/real-analytic-sets","display_name":"real analytic sets","score":0.968999981880188},{"id":"https://openalex.org/keywords/multiplicity","display_name":"multiplicity","score":0.7239999771118164},{"id":"https://openalex.org/keywords/finite-determinacy","display_name":"finite determinacy","score":0.9909999966621399}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8781055212020874},{"id":"https://openalex.org/C58468513","wikidata":"https://www.wikidata.org/wiki/Q1201165","display_name":"Determinacy","level":2,"score":0.8591600060462952},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.6693791747093201},{"id":"https://openalex.org/C20556612","wikidata":"https://www.wikidata.org/wiki/Q4469374","display_name":"Volume (thermodynamics)","level":2,"score":0.62224280834198},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.48587673902511597},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.47586721181869507},{"id":"https://openalex.org/C50478463","wikidata":"https://www.wikidata.org/wiki/Q1401936","display_name":"Finite volume method","level":2,"score":0.41100630164146423},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.38130754232406616},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.33696889877319336},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.32926177978515625},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.056122660636901855},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.4064/ap87-0-22","doi":"https://doi.org/10.4064/ap87-0-22","is_oa":true,"landing_page_url":"https://doi.org/10.4064/ap87-0-22","pdf_url":"https://www.impan.pl/shop/publication/transaction/download/product/84791?download.pdf","source":{"id":"https://openalex.org/S179694389","display_name":"Annales Polonici Mathematici","issn_l":"0066-2216","issn":["0066-2216","1730-6272"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","jufo-1","norway-1"],"host_organization":"https://openalex.org/P4310317485","host_organization_name":"Polish Academy of Sciences","host_organization_lineage":["https://openalex.org/P4310317485"],"host_organization_lineage_names":["Polish Academy of Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annales Polonici Mathematici","raw_type":"journal-article"},{"id":"pmh:oai:ruj.uj.edu.pl:item/81933","doi":null,"is_oa":true,"landing_page_url":"https://ruj.uj.edu.pl/xmlui/handle/item/81933","pdf_url":null,"source":{"id":"https://openalex.org/S4306400316","display_name":"Homo Politicus (Academy of Humanities and Economics in Lodz)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"artyku\u0142 w czasopi\u015bmie"}],"best_oa_location":{"id":"doi:10.4064/ap87-0-22","doi":"https://doi.org/10.4064/ap87-0-22","is_oa":true,"landing_page_url":"https://doi.org/10.4064/ap87-0-22","pdf_url":"https://www.impan.pl/shop/publication/transaction/download/product/84791?download.pdf","source":{"id":"https://openalex.org/S179694389","display_name":"Annales Polonici Mathematici","issn_l":"0066-2216","issn":["0066-2216","1730-6272"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","jufo-1","norway-1"],"host_organization":"https://openalex.org/P4310317485","host_organization_name":"Polish Academy of Sciences","host_organization_lineage":["https://openalex.org/P4310317485"],"host_organization_lineage_names":["Polish Academy of Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annales Polonici Mathematici","raw_type":"journal-article"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2011995705.pdf","grobid_xml":"https://content.openalex.org/works/W2011995705.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2088108327","https://openalex.org/W3037524176","https://openalex.org/W45652848","https://openalex.org/W1521335825","https://openalex.org/W2505787881","https://openalex.org/W1482555883","https://openalex.org/W4213060090","https://openalex.org/W4301421734","https://openalex.org/W4236657165","https://openalex.org/W2063305408"],"abstract_inverted_index":{"We":[0],"give":[1],"criteria":[2],"of":[3,26,29,32],"finite":[4],"determinacy":[5],"for":[6],"the":[7,23,27,30,33],"volume":[8,28],"and":[9,35],"multiplicities.":[10],"Given":[11],"an":[12],"analytic":[13],"set":[14,34],"described":[15],"by":[16],"$\\{":[17],"v=0\\}":[18],"$,":[19],"we":[20],"prove":[21],"that":[22],"log-analytic":[24],"expansion":[25],"intersection":[31],"a":[36],"\u201clittle":[37],"ball\u201d":[38],"is":[39],"determined":[40]},"counts_by_year":[],"updated_date":"2026-09-19T00:03:45.406941","created_date":"2025-10-10T00:00:00"}
