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[{"key": "dc.contributor.advisor", "value": "Rajala, Tapio", "language": "", "element": "contributor", "qualifier": "advisor", "schema": "dc"}, {"key": "dc.contributor.author", "value": "Rauhansalo, Akseli", "language": "", "element": "contributor", "qualifier": "author", "schema": "dc"}, {"key": "dc.date.accessioned", "value": "2020-06-01T12:22:33Z", "language": null, "element": "date", "qualifier": "accessioned", "schema": "dc"}, {"key": "dc.date.available", "value": "2020-06-01T12:22:33Z", "language": null, "element": "date", "qualifier": "available", "schema": "dc"}, {"key": "dc.date.issued", "value": "2020", "language": "", "element": "date", "qualifier": "issued", "schema": "dc"}, {"key": "dc.identifier.uri", "value": "https://jyx.jyu.fi/handle/123456789/69349", "language": null, "element": "identifier", "qualifier": "uri", "schema": "dc"}, {"key": "dc.description.abstract", "value": "T\u00e4ss\u00e4 tutkielmassa perehdyt\u00e4\u00e4n massansiirtoteorian perusteisiin, erityisesti niin kutsuttujen liikennesuunnitelmien kautta. Tutkielman p\u00e4\u00e4tuloksena osoitetaan, ett\u00e4 liikennesuunnitelman energialle on olemassa optimaalinen liikennesuunnitelma, joka minimoi energian. \n\nK\u00e4sitelt\u00e4v\u00e4ss\u00e4 massansiirto-ongelmassa tavoitteena on siirt\u00e4\u00e4 massaa yhdelt\u00e4 mitalta toiselle mahdollisimman pienell\u00e4 kokonaiskustannuksella. Mahdolliset kuljetusreitit m\u00e4\u00e4ritell\u00e4\u00e4n Lipschitz-jatkuvina polkuina. Lipschitz-polkujen muodostama metrinen avaruus osoitetaan kompaktiksi sopivalla et\u00e4isyyden valinnalla. Metrist\u00e4 avaruutta kutsutaan kompaktiksi, jos sen jokaisella peitteell\u00e4 on olemassa \u00e4\u00e4rellinen osapeite. \n\nMahdollisista kuljetusreiteist\u00e4 rakennetaan niin kutsuttu liikennesuunnitelma, joka painottaa polkujen avaruutta siten, ett\u00e4 painotetut polut kuljettavat massaa suhteessa annettuun painoon. Liikennesuunnitelma on t\u00e4ll\u00f6in luonnollista m\u00e4\u00e4ritell\u00e4 mittana Lipschitz-polkujen avaruuteen. Liikennesuunnitelmalta vaaditaan, ett\u00e4 \u00e4\u00e4rett\u00f6m\u00e4n pitk\u00e4t polut saavat painokseen nollan, toisin sanoen \u00e4\u00e4rett\u00f6m\u00e4n pitkien polkujen osajoukko on nollamittainen liikennesuunnitelman suhteen.\n\n\nLiikennesuunnitelmalle m\u00e4\u00e4ritell\u00e4\u00e4n energia, joka on yhdenmukainen diskreettien massansiirto-ongelmien kanssa. Energia tulee riippumaan k\u00e4ytettyjen liikennesuunnitelman painottamien polkujen pituuksista ja kertaluvuista. Kertaluku kuvastaa sit\u00e4, kuinka usea polku k\u00e4y samassa pisteess\u00e4. Energian minimoimiseksi pituus ja kertaluku halutaan luonnollisesti minimoida optimaalisen liikennesuunnitelman l\u00f6yt\u00e4misell\u00e4.\n\nOptimaalisen liikennesuunnitelman olemassaolo seuraa polkuavaruuden kompaktiudesta sek\u00e4 energian alhaalta puolijatkuvuudesta. Alhaalta puolijatkuvuuden osoittaminen on yleinen strategia minimointiongelmien ratkaisemisessa. Alhaalta puolijatkuvuus on jatkuvuutta heikompi ehto funktiolle. Rakenteeltaan optimaalinen liikennesuunnitelma tulee olemaan haarautunut eli puumainen, mutta t\u00e4m\u00e4n perustelu sivuutetaan.", "language": "fi", "element": "description", "qualifier": "abstract", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Submitted by Paivi Vuorio (paelvuor@jyu.fi) on 2020-06-01T12:22:33Z\nNo. of bitstreams: 0", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Made available in DSpace on 2020-06-01T12:22:33Z (GMT). No. of bitstreams: 0\n Previous issue date: 2020", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.format.extent", "value": "43", "language": "", "element": "format", "qualifier": "extent", "schema": "dc"}, {"key": "dc.format.mimetype", "value": "application/pdf", "language": null, "element": "format", "qualifier": "mimetype", "schema": "dc"}, {"key": "dc.language.iso", "value": "fin", "language": null, "element": "language", "qualifier": "iso", "schema": "dc"}, {"key": "dc.rights", "value": "In Copyright", "language": "en", "element": "rights", "qualifier": null, "schema": "dc"}, {"key": "dc.subject.other", "value": "massansiirto", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "liikennesuunnitelma", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.title", "value": "Optimaalisten liikennesuunnitelmien olemassaolo", "language": "", "element": "title", "qualifier": null, "schema": "dc"}, {"key": "dc.type", "value": "master thesis", "language": null, "element": "type", "qualifier": null, "schema": "dc"}, {"key": "dc.identifier.urn", "value": "URN:NBN:fi:jyu-202006013606", "language": "", "element": "identifier", "qualifier": "urn", "schema": "dc"}, {"key": "dc.type.ontasot", "value": "Pro gradu -tutkielma", "language": "fi", "element": "type", "qualifier": "ontasot", "schema": "dc"}, {"key": "dc.type.ontasot", "value": "Master\u2019s thesis", "language": "en", "element": "type", "qualifier": "ontasot", "schema": "dc"}, {"key": "dc.contributor.faculty", "value": "Matemaattis-luonnontieteellinen tiedekunta", "language": "fi", "element": "contributor", "qualifier": "faculty", "schema": "dc"}, {"key": "dc.contributor.faculty", "value": "Faculty of Sciences", "language": "en", "element": "contributor", "qualifier": "faculty", "schema": "dc"}, {"key": "dc.contributor.department", "value": "Matematiikan ja tilastotieteen laitos", "language": "fi", "element": "contributor", "qualifier": "department", "schema": "dc"}, {"key": "dc.contributor.department", "value": "Department of Mathematics and Statistics", "language": "en", "element": "contributor", "qualifier": "department", "schema": "dc"}, {"key": "dc.contributor.organization", "value": "Jyv\u00e4skyl\u00e4n yliopisto", "language": "fi", "element": "contributor", "qualifier": "organization", "schema": "dc"}, {"key": "dc.contributor.organization", "value": "University of Jyv\u00e4skyl\u00e4", "language": "en", "element": "contributor", "qualifier": "organization", "schema": "dc"}, {"key": "dc.subject.discipline", "value": "Matematiikan opettajankoulutus", "language": "fi", "element": "subject", "qualifier": "discipline", "schema": "dc"}, {"key": "dc.subject.discipline", "value": "Teacher education programme in Mathematics", "language": "en", "element": "subject", "qualifier": "discipline", "schema": "dc"}, {"key": "yvv.contractresearch.funding", "value": "0", "language": "", "element": "contractresearch", "qualifier": "funding", "schema": "yvv"}, {"key": "dc.type.coar", "value": "http://purl.org/coar/resource_type/c_bdcc", "language": null, "element": "type", "qualifier": "coar", "schema": "dc"}, {"key": "dc.rights.accesslevel", "value": "openAccess", "language": null, "element": "rights", "qualifier": "accesslevel", "schema": "dc"}, {"key": "dc.type.publication", "value": "masterThesis", "language": null, "element": "type", "qualifier": "publication", "schema": "dc"}, {"key": "dc.subject.oppiainekoodi", "value": "4041", "language": "", "element": "subject", "qualifier": "oppiainekoodi", "schema": "dc"}, {"key": "dc.subject.yso", "value": "matematiikka", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "mittateoria", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "metriset avaruudet", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.format.content", "value": "fulltext", "language": null, "element": "format", "qualifier": "content", "schema": "dc"}, {"key": "dc.rights.url", "value": "https://rightsstatements.org/page/InC/1.0/", "language": null, "element": "rights", "qualifier": "url", "schema": "dc"}, {"key": "dc.type.okm", "value": "G2", "language": null, "element": "type", "qualifier": "okm", "schema": "dc"}]
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