Publikation:

Smooth coalgebra : testing vector analysis

Lade...
Vorschaubild

Dateien

Zu diesem Dokument gibt es keine Dateien.

Datum

2017

Autor:innen

Pavlovic, Dusko

Herausgeber:innen

Kontakt

ISSN der Zeitschrift

Electronic ISSN

ISBN

Bibliografische Daten

Verlag

Schriftenreihe

Auflagebezeichnung

URI (zitierfähiger Link)

Internationale Patentnummer

Angaben zur Forschungsförderung

Projekt

Open Access-Veröffentlichung
Core Facility der Universität Konstanz

Gesperrt bis

Titel in einer weiteren Sprache

Publikationstyp
Zeitschriftenartikel
Publikationsstatus
Published

Erschienen in

Mathematical Structures in Computer Science. 2017, 27(7), pp. 1195-1235. ISSN 0960-1295. eISSN 1469-8072. Available under: doi: 10.1017/S0960129515000511

Zusammenfassung

Processes are often viewed as coalgebras, with the structure maps specifying the state transitions. In the simplest case, the state spaces are discrete, and the structure map simply takes each state to the next states. But the coalgebraic view is also quite effective for studying processes over structured state spaces, e.g. measurable, or continuous. In the present paper, we consider coalgebras over manifolds. This means that the captured processes evolve over state spaces that are not just continuous, but also locally homeomorphic to normed vector spaces, and thus carry a differential structure. Both dynamical systems and differential forms arise as coalgebras over such state spaces, for two different endofunctors over manifolds. A duality induced by these two endofunctors provides a formal underpinning for the informal geometric intuitions linking differential forms and dynamical systems in the various practical applications, e.g. in physics. This joint functorial reconstruction of tangent bundles and cotangent bundles uncovers the universal properties and a high-level view of these fundamental structures, which are implemented rather intricately in their standard form. The succinct coalgebraic presentation provides unexpected insights even about the situations as familiar as Newton's laws.

Zusammenfassung in einer weiteren Sprache

Fachgebiet (DDC)
530 Physik

Schlagwörter

Konferenz

Rezension
undefined / . - undefined, undefined

Forschungsvorhaben

Organisationseinheiten

Zeitschriftenheft

Zugehörige Datensätze in KOPS

Zitieren

ISO 690PAVLOVIC, Dusko, Bertfried FAUSER, 2017. Smooth coalgebra : testing vector analysis. In: Mathematical Structures in Computer Science. 2017, 27(7), pp. 1195-1235. ISSN 0960-1295. eISSN 1469-8072. Available under: doi: 10.1017/S0960129515000511
BibTex
@article{Pavlovic2017Smoot-41158,
  year={2017},
  doi={10.1017/S0960129515000511},
  title={Smooth coalgebra : testing vector analysis},
  number={7},
  volume={27},
  issn={0960-1295},
  journal={Mathematical Structures in Computer Science},
  pages={1195--1235},
  author={Pavlovic, Dusko and Fauser, Bertfried}
}
RDF
<rdf:RDF
    xmlns:dcterms="http://purl.org/dc/terms/"
    xmlns:dc="http://purl.org/dc/elements/1.1/"
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:bibo="http://purl.org/ontology/bibo/"
    xmlns:dspace="http://digital-repositories.org/ontologies/dspace/0.1.0#"
    xmlns:foaf="http://xmlns.com/foaf/0.1/"
    xmlns:void="http://rdfs.org/ns/void#"
    xmlns:xsd="http://www.w3.org/2001/XMLSchema#" > 
  <rdf:Description rdf:about="https://kops.uni-konstanz.de/server/rdf/resource/123456789/41158">
    <dc:creator>Fauser, Bertfried</dc:creator>
    <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/>
    <dcterms:abstract xml:lang="eng">Processes are often viewed as coalgebras, with the structure maps specifying the state transitions. In the simplest case, the state spaces are discrete, and the structure map simply takes each state to the next states. But the coalgebraic view is also quite effective for studying processes over structured state spaces, e.g. measurable, or continuous. In the present paper, we consider coalgebras over manifolds. This means that the captured processes evolve over state spaces that are not just continuous, but also locally homeomorphic to normed vector spaces, and thus carry a differential structure. Both dynamical systems and differential forms arise as coalgebras over such state spaces, for two different endofunctors over manifolds. A duality induced by these two endofunctors provides a formal underpinning for the informal geometric intuitions linking differential forms and dynamical systems in the various practical applications, e.g. in physics. This joint functorial reconstruction of tangent bundles and cotangent bundles uncovers the universal properties and a high-level view of these fundamental structures, which are implemented rather intricately in their standard form. The succinct coalgebraic presentation provides unexpected insights even about the situations as familiar as Newton's laws.</dcterms:abstract>
    <dc:contributor>Fauser, Bertfried</dc:contributor>
    <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2018-01-25T10:30:31Z</dc:date>
    <dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/41"/>
    <dc:language>eng</dc:language>
    <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2018-01-25T10:30:31Z</dcterms:available>
    <dcterms:title>Smooth coalgebra : testing vector analysis</dcterms:title>
    <dcterms:issued>2017</dcterms:issued>
    <dcterms:isPartOf rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/41"/>
    <dc:contributor>Pavlovic, Dusko</dc:contributor>
    <dc:creator>Pavlovic, Dusko</dc:creator>
    <bibo:uri rdf:resource="https://kops.uni-konstanz.de/handle/123456789/41158"/>
    <foaf:homepage rdf:resource="http://localhost:8080/"/>
  </rdf:Description>
</rdf:RDF>

Interner Vermerk

xmlui.Submission.submit.DescribeStep.inputForms.label.kops_note_fromSubmitter

Kontakt
URL der Originalveröffentl.

Prüfdatum der URL

Prüfungsdatum der Dissertation

Finanzierungsart

Kommentar zur Publikation

Allianzlizenz
Corresponding Authors der Uni Konstanz vorhanden
Internationale Co-Autor:innen
Universitätsbibliographie
Nein
Begutachtet
Diese Publikation teilen