Helmholtz conditions and their generalizations
Identifikátory výsledku
Kód výsledku v IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17310%2F10%3AA1100Z84" target="_blank" >RIV/61988987:17310/10:A1100Z84 - isvavai.cz</a>
Výsledek na webu
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DOI - Digital Object Identifier
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Alternativní jazyky
Jazyk výsledku
angličtina
Název v původním jazyce
Helmholtz conditions and their generalizations
Popis výsledku v původním jazyce
The Euler-Lagrange morphism E1 is well-understood. It is also known that the kernel of the Helmholtz morphism E2 consists of locally variational dynamical forms, and is characterized by Helmholtz conditions. We study the image of E2 and the kernel of thenext morphism E3, and solve the corresponding local and global inverse problem when a three-form comes from a dynamical form, i.e., corresponds to a system of diferential equations. We find identities, that are a generalization of the Helmholtz conditions to this situation, and show that the problem is closely related to the question on existence of a closed three-form. The obtained results extend known results on Lagrangians and locally variational dynamical forms to general dynamical forms, and opena new possibility to study non-variational equations by means of closed three-forms, as a parallel to extremal problems (variational equations) that are studied by means of closed two-forms (Cartan forms, symplectic geometry).
Název v anglickém jazyce
Helmholtz conditions and their generalizations
Popis výsledku anglicky
The Euler-Lagrange morphism E1 is well-understood. It is also known that the kernel of the Helmholtz morphism E2 consists of locally variational dynamical forms, and is characterized by Helmholtz conditions. We study the image of E2 and the kernel of thenext morphism E3, and solve the corresponding local and global inverse problem when a three-form comes from a dynamical form, i.e., corresponds to a system of diferential equations. We find identities, that are a generalization of the Helmholtz conditions to this situation, and show that the problem is closely related to the question on existence of a closed three-form. The obtained results extend known results on Lagrangians and locally variational dynamical forms to general dynamical forms, and opena new possibility to study non-variational equations by means of closed three-forms, as a parallel to extremal problems (variational equations) that are studied by means of closed two-forms (Cartan forms, symplectic geometry).
Klasifikace
Druh
J<sub>x</sub> - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
CEP obor
BA - Obecná matematika
OECD FORD obor
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Návaznosti výsledku
Projekt
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Návaznosti
S - Specificky vyzkum na vysokych skolach
Ostatní
Rok uplatnění
2010
Kód důvěrnosti údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Údaje specifické pro druh výsledku
Název periodika
Balkan Journal of Geometry and Its Applications
ISSN
1843-2875
e-ISSN
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Svazek periodika
15
Číslo periodika v rámci svazku
1
Stát vydavatele periodika
RO - Rumunsko
Počet stran výsledku
10
Strana od-do
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Kód UT WoS článku
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EID výsledku v databázi Scopus
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