. "H\u00E1jek, Petr Pavel" . . "6" . . "8"^^ . "RIV/67985840:_____/06:00076206!RIV07-AV0-67985840" . "86" . "509838" . . "2"^^ . "[CDD38A59BF3A]" . . . "Pro zadan\u00E1 p\u0159irozen\u00E1 \u010D\u00EDsla k,n, kde n je lich\u00E9, uk\u00E1\u017Eeme existenci \u010D\u00EDsla N = N(k,n) s n\u00E1sleduj\u00EDc\u00ED vlastnost\u00ED. Pro ka\u017Ed\u00FD n-homogenn\u00ED polynom zadan\u00FD na Euklidovsk\u00E9m prostoru dimenze N, existuje k-dimenzion\u00E1ln\u00ED line\u00E1rn\u00ED podprostor, na n\u011Bm\u017E se polynom anuluje."@cs . . "Zero sets of polynomials in several variables"@en . "P(GA201/01/1198), P(GA201/04/0090), P(IAA1019205), Z(AV0Z10190503)" . "Nulov\u00E9 mno\u017Einy polynomu n\u011Bkolika prom\u011Bnn\u00FDch"@cs . "1"^^ . "Zero sets of polynomials in several variables"@en . . "RIV/67985840:_____/06:00076206" . . "Zero sets of polynomials in several variables" . "Let k, n .. N, where n is odd. We show that there is an integer N = N(k,n) such that for every n-homogeneous polynomial P : RN .. R there exists a linear subspace X .. RN, dim X = k, such that P|x .IDENT. 0. This quantitative estimate improves on previous work of Birch et al., who studied this problem from an algebraic viewpoint. The topological method of proof presented here also allows us to obtain a partial solution to the Gromov-Milman problem (in dimension two) on an isometric version of a theorem of Dvoretzky." . "0003-889X" . "Zero sets of polynomials in several variables" . "561;568" . . . "Nulov\u00E9 mno\u017Einy polynomu n\u011Bkolika prom\u011Bnn\u00FDch"@cs . "Archiv der Mathematik" . . . . "Let k, n .. N, where n is odd. We show that there is an integer N = N(k,n) such that for every n-homogeneous polynomial P : RN .. R there exists a linear subspace X .. RN, dim X = k, such that P|x .IDENT. 0. This quantitative estimate improves on previous work of Birch et al., who studied this problem from an algebraic viewpoint. The topological method of proof presented here also allows us to obtain a partial solution to the Gromov-Milman problem (in dimension two) on an isometric version of a theorem of Dvoretzky."@en . . . . "CH - \u0160v\u00FDcarsk\u00E1 konfederace" . "polynomial; zero set"@en . "Aron, R. M." . .