On Homogeneous Functions in Second-Order Field Theory

• Autorzy: Jan Brajercík , Zbynek Urban

Warianty tytułu

O homogenních funkcích v teorii pole druhého rˇ ádu

• Języki publikacji: EN

Abstrakty

EN

The classical concept of a homogeneous function is introduced and extended within the theory of differential groups, known in the theory of differential invariants. Invariance under reparametrizations of solutions of partial differential equations is studied. On this basis the wellknown generalizations of the Euler theorem are obtained (the Zermelo conditions). The positive homogeneity concept is then applied to second-order variational equations in field theory. (original abstract)

Standardní koncept homogenní funkce je zaveden a zobecnen pomocí užití diferenciálních grup, známých v teorii diferenciálních invariantu. Studujeme invarianci vzhledem k reparametrizacím integrálních krivek parciálních diferenciálních rovnic. Na základe tohoto prístupu obdržíme známé zobecnení Eulerova teorému, tzv. Zermelovy podmínky. Koncept pozitivní homogenity aplikujeme na variacní rovnice druhého rádu v teorii pole. (abstrakt oryginalny)

Słowa kluczowe

EN

Mathematics; Lagrange multiplier; Calculus; Differential equations

PL

Matematyka; Mnożniki Lagrange'a; Rachunek różniczkowy i całkowy; Równania różniczkowe

• Czasopismo: Systems Supporting Production Engineering
• Rocznik: 2017
• Numer: 6(4) Cross-Border Exchange of Experience in Production Engineering Using Principles of Mathematics
• Strony: 230--236

Twórcy

autor

Jan Brajercík

• University of Prešov, Slovakia

autor

Zbynek Urban

• VŠB-Technical University of Ostrava, Czech Republic

Bibliografia

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• K. Kondo. "On the physical meaning of the Zermelo conditions of Kawaguchi space", Tensor, N.S., Vol. 14, 1963, p. 191-215.
• D. Krupka and J. Janyška. Lectures on Differential Invariants, J. E. Purkyne University, Faculty of Science, Brno, Czechoslovakia, 1990, p. 193.
• R. Matsyuk. "Autoparallel variational description of the free relativistic top third order dynamics", in: Diff. Geom. Appl., Proc. Conf., Opava, Czech Republic, August 2001, Silesian University in Opava, Czech Republic, 2001, p. 447-459.
• M. A. McKiernan. "Sufficiency of parameter invariance conditions in areal and higherorder Kawaguchi spaces", Publ. Math. Debrecen, Vol. 13, 1966, p. 77-85.
• Z. Urban, D. Krupka. "The Zermelo conditions and higher order homogeneous functions", Publ. Math. Debrecen, Vol. 82, No. 1, 2013, p. 59-76.