Wyniki wyszukiwania - BazTech

Ograniczanie wyników

Znaleziono wyników: 2

Liczba wyników na stronie

Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych: differential groups

Sortuj według:

Ogranicz wyniki do:

On homogeneous functions in second-order field theory

Brajercík J., Urban Z.

Systemy Wspomagania w Inżynierii Produkcji

2017

Vol. 6, iss. 4

230--236

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.

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.

Hopf-Sikorski algebras

Heller M., Odrzygóźdź Z., Pysiak L., Sasin W.

Demonstratio Mathematica

2011

Vol. 44, nr 2

213-221

The dual category with respect to the category of differential groups is defined and investigated. The objects of this category are algebras, called Hopf-Sikorski (H-S) algebras, the axioms of which combine the axioms of Sikorski's algebras with modified axiomas of Hopf algebras. Morphisms of this category are structural mappings corresponding to Hopf algebras that are smooth in the sense of Sikorski. As an example, we discuss the H-S algebra of the Lorentz group.