"41"^^ . "1"^^ . . "41"^^ . . . . . "Projekt je zam\u011B\u0159en na z\u00E1kladn\u00ED v\u00FDzkum v oblasti geometrick\u00E9 anal\u00FDzy a jejich aplikac\u00ED ve fyzice, a to zejm\u00E9na na varia\u010Dn\u00ED anal\u00FDzu na hladk\u00FDch variet\u00E1ch, geometrickou teorii parci\u00E1ln\u00EDch diferenci\u00E1ln\u00EDch rovnic a geometrick\u00E9 struktury v mechanice a obecn\u00E9 teorii relativity. Navazuje na projekty GA \u010CR 201/93/2245, 201/96/0845 a 201/98/0853, \u0159e\u0161en\u00E9 v obdob\u00ED 1993-1999. C\u00EDlem je p\u0159isp\u011Bt k \u0159e\u0161en\u00ED t\u011Bchto probl\u00E9m\u016F: - dal\u0161\u00ED rozvoj glob\u00E1ln\u00ED varia\u010Dn\u00ED anal\u00FDzy a teorie varia\u010Dn\u00EDch rovnic na variet\u00E1ch (roz\u0161\u00ED\u0159en\u00ED obecn\u00E9teorie varia\u010Dn\u00EDch posloupnost\u00ED kone\u010Dn\u00E9ho \u0159\u00E1du na oblast syst\u00E9m\u016F s vazbami, vybudov\u00E1n\u00ED teorie na Grassmannov\u00FDch variet\u00E1ch, studium aplikac\u00ED ve fyzice), - uplatn\u011Bn\u00ED geometrick\u00FDch metod p\u0159i \u0159e\u0161en\u00ED probl\u00E9m\u016F v teoretick\u00E9 fyzice (unit\u00E1rn\u00ED teorie gravitace a elektromagnetizmu, z\u00E1kony zachov\u00E1n\u00ED v teorii pole, exaktn\u00ED \u0159e\u0161en\u00ED Einsteinov\u00FDch rovnic, geometrick\u00E1 struktura mechaniky s vazbami), - vyjasn\u011Bn\u00ED geometrick\u00FDch struktur v teorii diferenci\u00E1ln\u00EDch rovnic, geometrick\u00E9 metody \u0159e\u0161en\u00ED." . . "Geometrick\u00E1 anal\u00FDza" . "http://www.isvav.cz/projectDetail.do?rowId=GA201/00/0724"^^ . . . . . "Neuvedeno."@en . "2008-05-19+02:00"^^ . "Geometric analysis"@en . "GA201/00/0724" . . . . . "0"^^ . . "V\u011Bdeck\u00FD p\u0159\u00EDnos projektu je vynikaj\u00EDc\u00ED. \u00DAdaje v z\u00E1v\u011Bre\u010Dn\u00E9 kart\u011B jasn\u011B popisuj\u00ED dosa\u017Een\u00E9 v\u00FDsledky. P\u016Fvodn\u00ED v\u00FDsledky teoretick\u00E9ho charakteru maj\u00ED sv\u016Fj p\u0159irozen\u00FD dopad v aplikac\u00EDch ve fyzice. V\u00FDznamn\u00E1 je i bohat\u00E1 \u010Dinnost pedagogick\u00E1 a \u0161kolitelsk\u00E1. Rozs\u00E1hl\u00E1 p"@cs . "The aim of the project is basic research in geometric analysis and its applications in mathematical physics, in particular, in variational analysis on smooth manifolds, geometric theory of differential equations and geometric structures in mechanics and general relativity theory. It is a continuation of the projects GACR 201/93/2245, 201/96/0845, and 201/98/0853 of the Grant Agency of the Czech Republic. The project is focused on the following problems: - further development of global variational analysis and the theory of variational equations on manifolds (variational sequences and bicomplexes, constrained systems, variational calculus on Grassmann manifolds) - applications of geometrical methods to problems of mathematical physics (unitary theories of gravity and electromagnetism, conservation laws in field theory, exact solutions of Einstein equations, geometric structure of constrained systems) - geometric structures for ordinary and partial differential equations, geometric methods of"@en . . "1"^^ .