{"?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-5MNBQ2OK/247e608f-dc8c-4126-90fd-671e77622b66/PDF","dcterms:extent":"401 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-5MNBQ2OK/7a69df63-fdc6-4c8f-a9f8-08b4a1bac0f3/TEXT","dcterms:extent":"60 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-5MNBQ2OK","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2017","dc:creator":["Beveridge, Andrew","Cai, Yiqing"],"dc:format":[{"@xml:lang":"sl","#text":"številka:1"},{"@xml:lang":"sl","#text":"letnik:13"},{"@xml:lang":"sl","#text":"str. 187-206"}],"dc:identifier":["COBISSID:18199897","ISSN:1855-3966","URN:URN:NBN:SI:doc-5MNBQ2OK"],"dc:language":"en","dc:publisher":{"@xml:lang":"sl","#text":"Univerza na Primorskem, Fakulteta za matematiko, naravoslovje in informacijske tehnologije"},"dc:subject":[{"@xml:lang":"sl","#text":"CAT(0) prosto"},{"@xml:lang":"sl","#text":"izogibanje zasledovanju"},{"@xml:lang":"sl","#text":"lev in človek"},{"@xml:lang":"sl","#text":"načrtovanje premikanja"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Pursuit-evasion in a two-dimensional domain|"},"dc:description":[{"@xml:lang":"sl","#text":"In a pursuit-evasion game, a team of pursuers attempt to capture an evader. The players alternate turns, move with equal speed, and have full information about the state of the game. We consider the most restrictive capture condition: a pursuer must become colocated with the evader to win the game. We prove two general results about this adversarial motion planning problem in geometric spaces. First, we show that one pursuer has a winning strategy in any compact CAT(0) space. This complements a result of Alexander, Bishop and Ghrist, who provide a winning strategy for a game with positive capture radius. Second, we consider the game played in a compact domain in Euclidean two-space with piecewise analytic boundary and arbitrary Euler characteristic. We show that three pursuers always have a winning strategy by extending recent work of Bhadauria, Klein, Isler and Suri from polygonal environments to our more general setting"},{"@xml:lang":"sl","#text":"V igri izogibanja zasledovanju skupina zasledovalcev poskuša ujeti ubežnika. Igralci so izmenično na potezi, premikajo se z enako hitrostjo in imajo popolno informacijo o statusu igre. Obravnavamo najbolj omejujoči pogoj lovljenja: zasledovalec mora zavzeti isti položaj kot ubežnik, da zmaga v igri. Dokažemo dva splošna rezultata v zvezi s tem problemom načrtovanja gibanja nasprotnikov v geometrijskih prostorih. Najprej pokažemo, da ima en zasledovalec zmagovalno strategijo v vsakem kompaktnem CAT(0) prostoru. To dopolnjuje rezultat Alexandra, Bishopa and Ghrista, ki so opisali zmagovalno stretegijo za igro s pozitivnim radijem lovljenja. Nato obravnavamo igro, ki se igra na kompaktnem območju v evklidskem dvodimenzionalnem prostoru z odsekoma analitičnim robom in poljubno Eulerjevo karakteristiko. Pokažemo, da trije zasledovalci vselej imajo zmagovalno strategijo, in s tem posplošimo nedavni rezultat, ki so ga podali Bhadauria, Klein, Isler in Suri, s poligonskega okolja na naš splošnejši okvir"}],"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-5MNBQ2OK","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-5MNBQ2OK"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-5MNBQ2OK/247e608f-dc8c-4126-90fd-671e77622b66/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-5MNBQ2OK/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-5MNBQ2OK"}}}}