{"?xml":{"@version":"1.0"},"edm:RDF":{"@xmlns:dc":"http://purl.org/dc/elements/1.1/","@xmlns:edm":"http://www.europeana.eu/schemas/edm/","@xmlns:wgs84_pos":"http://www.w3.org/2003/01/geo/wgs84_pos","@xmlns:foaf":"http://xmlns.com/foaf/0.1/","@xmlns:rdaGr2":"http://rdvocab.info/ElementsGr2","@xmlns:oai":"http://www.openarchives.org/OAI/2.0/","@xmlns:owl":"http://www.w3.org/2002/07/owl#","@xmlns:rdf":"http://www.w3.org/1999/02/22-rdf-syntax-ns#","@xmlns:ore":"http://www.openarchives.org/ore/terms/","@xmlns:skos":"http://www.w3.org/2004/02/skos/core#","@xmlns:dcterms":"http://purl.org/dc/terms/","edm:WebResource":[{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-C64T57UA/da1486e8-e1f6-40f2-a39b-1cde797f9cf6/PDF","dcterms:extent":"354 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-C64T57UA/8b88b2b5-a7b6-4391-8570-8aeccc08d925/TEXT","dcterms:extent":"47 KB"}],"edm:TimeSpan":{"@rdf:about":"2008-2025","edm:begin":{"@xml:lang":"en","#text":"2008"},"edm:end":{"@xml:lang":"en","#text":"2025"}},"edm:ProvidedCHO":{"@rdf:about":"URN:NBN:SI:doc-C64T57UA","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2020","dc:creator":["Prezelj-Perman, Jasna","Vlacci, Fabio"],"dc:format":[{"@xml:lang":"sl","#text":"letnik:19"},{"@xml:lang":"sl","#text":"številka:2"},{"@xml:lang":"sl","#text":"str. 189-208"}],"dc:identifier":["ISSN:1855-3974","COBISSID_HOST:42362883","URN:URN:NBN:SI:doc-C64T57UA"],"dc:language":"en","dc:publisher":{"@xml:lang":"sl","#text":"Univerza na Primorskem, Fakulteta za matematiko, naravoslovje in informacijske tehnologije"},"dc:subject":[{"@xml:lang":"en","#text":"bidegree full functions"},{"@xml:lang":"sl","#text":"bistopenjsko polne funkcije"},{"@xml:lang":"en","#text":"Hamming graph"},{"@xml:lang":"sl","#text":"Hammingov graf"},{"@xml:lang":"sl","#text":"kvaternionske potenčne vrste"},{"@xml:lang":"en","#text":"linearly independent quaternionic monomials"},{"@xml:lang":"sl","#text":"linearno neodvisni kvaternionski monomi"},{"@xml:lang":"en","#text":"quaternionic power series"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Divergence zero quaternionic vector fields and Hamming graphs|"},"dc:description":[{"@xml:lang":"sl","#text":"We give a possible extension of the definition of quaternionic power series, partial derivatives and vector fields in the case of two (and then several) non commutative (quaternionic) variables. In this setting we also investigate the problem of describing zero functions which are not null functions in the formal sense. A connection between an analytic condition and a graph theoretic property of a subgraph of a Hamming graph is shown, namely the condition that polynomial vector field has formal divergence zero is equivalent to connectedness of subgraphs of Hamming graphs ?$H(d, 2)$?. We prove that monomials in variables ?$z$? and ?$w$? are always linearly independent as functions only in bidegrees ?$(p, 0)$?, ?$(p, 1)$?, ?$(0, q)$?, ?$(1, q)$? and ?$(2, 2)$?"},{"@xml:lang":"sl","#text":"V članku je predlagana možna razširitev definicije kvaternionskih potenčnih vrst, parcialnih odvodov in vektorskih polj za dve oz. več nekomutativnih (kvaternionskih) spremenljivk. Obravnavan je problem ničelnih funkcij, ki jih popisujejo vrste, ki niso formalno ničelne. Podana je povezava med analitičnim pogojem in pogojem na podgraf Hammingovega grafa. Natančneje, polinomsko vektorsko polje ima formalno divergenco nič natanko tedaj, ko je določen podgraf Hammingovega grafa ?$H(d, 2)$? povezan. Dokazano je, da so monomi v spremenljivkah ?$z$? in ?$w$? vedno linearno neodvisni kot funkcije samo v bistopnjah ?$(p, 0)$?, ?$(p, 1)$?, ?$(0, q)$?, ?$(1, q)$? in ?$(2, 2)$?"}],"edm:type":"TEXT","dc:type":[{"@xml:lang":"sl","#text":"znanstveno časopisje"},{"@xml:lang":"en","#text":"journals"},{"@rdf:resource":"http://www.wikidata.org/entity/Q361785"}]},"ore:Aggregation":{"@rdf:about":"http://www.dlib.si/?URN=URN:NBN:SI:doc-C64T57UA","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-C64T57UA"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-C64T57UA/da1486e8-e1f6-40f2-a39b-1cde797f9cf6/PDF"},"edm:rights":{"@rdf:resource":"http://creativecommons.org/licenses/by/4.0/"},"edm:provider":"Slovenian National E-content Aggregator","edm:intermediateProvider":{"@xml:lang":"en","#text":"National and University Library of Slovenia"},"edm:dataProvider":{"@xml:lang":"sl","#text":"Univerza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije"},"edm:object":{"@rdf:resource":"http://www.dlib.si/streamdb/URN:NBN:SI:doc-C64T57UA/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-C64T57UA"}}}}