About: The variational sequence: Local and global properties

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	The aim of this paper is to discuss some aspects of local and global properties of the Euler-Lagrange and Helmholtz-Sonin mappings of the calculus of variations in the r-th order field theory, i.e. on r-jet prolongations of fibered manifolds over a n-dimensional base with n>1, within the framework of the variational sequence, i.e. the quotient of the De Rham sequence with respect to its subsequence of contact differential forms. Such a discussion is, in general, based on the concept of sheaves of differential forms. In the paper a globally defined representation of the variational sequence by forms is constructed which is closely related to the standard concepts in the calculus of variations. There is a close relationship between elements of the quotient sheaves (classes of forms) and the quotient mappings on one hand and the standard objects of the calculus of variations, as lagrangians, Euler-Lagrange and Helmholtz-Sonin forms, and Euler-Lagrange and Helmholtz-Sonin mappings on the other hand. The aim of this paper is to discuss some aspects of local and global properties of the Euler-Lagrange and Helmholtz-Sonin mappings of the calculus of variations in the r-th order field theory, i.e. on r-jet prolongations of fibered manifolds over a n-dimensional base with n>1, within the framework of the variational sequence, i.e. the quotient of the De Rham sequence with respect to its subsequence of contact differential forms. Such a discussion is, in general, based on the concept of sheaves of differential forms. In the paper a globally defined representation of the variational sequence by forms is constructed which is closely related to the standard concepts in the calculus of variations. There is a close relationship between elements of the quotient sheaves (classes of forms) and the quotient mappings on one hand and the standard objects of the calculus of variations, as lagrangians, Euler-Lagrange and Helmholtz-Sonin forms, and Euler-Lagrange and Helmholtz-Sonin mappings on the other hand. (en)
Title	The variational sequence: Local and global properties The variational sequence: Local and global properties (en)
skos:prefLabel	The variational sequence: Local and global properties The variational sequence: Local and global properties (en)
skos:notation	RIV/47813059:19610/00:00000047!RIV/2001/MSM/196101/N
http://linked.open.../vavai/riv/strany	15
http://linked.open...avai/riv/aktivita	Z
http://linked.open...avai/riv/aktivity	Z(MSM 192400002)
http://linked.open...vai/riv/dodaniDat	2001
http://linked.open...aciTvurceVysledku	Musilová, Jana
http://linked.open.../riv/druhVysledku	D - Článek ve sborníku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Slezská univerzita v Opavě / Matematický ústav v Opavě
http://linked.open...dnocenehoVysledku	730622
http://linked.open...ai/riv/idVysledku	RIV/47813059:19610/00:00000047
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Fibered manifold, r-jet prolongation, contact form, De Rham sequence, variational sequence, Euler-La (en)
http://linked.open.../riv/klicoveSlovo	variational sequence Fibered manifold De Rham sequence Euler-La r-jet prolongation contact form
http://linked.open...ontrolniKodProRIV	[24A379B62057]
http://linked.open...i/riv/mistoVydani	Opava, ČR
http://linked.open...i/riv/nazevZdroje	Proceedings of the Seminar on Differential Geometry
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	3 (xsd:int)
http://linked.open...UplatneniVysledku	2000
http://linked.open...iv/tvurceVysledku	Kašparová, Jana Musilová, Jana Krbek, Michael
http://linked.open...n/vavai/riv/zamer	http://linked.opendata.cz/resource/domain/vavai/zamer/MSM%20192400002
number of pages	24 (xsd:int)
http://purl.org/ne...btex#hasPublisher	Slezská univerzita v Opavě
https://schema.org/isbn	80-7248-104-5
http://localhost/t...ganizacniJednotka	19610

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