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Statements

Subject Item
n2:RIV%2F67985840%3A_____%2F06%3A00076206%21RIV07-AV0-67985840
rdf:type
skos:Concept n15:Vysledek
dcterms:description
Pro zadaná přirozená čísla k,n, kde n je liché, ukážeme existenci čísla N = N(k,n) s následující vlastností. Pro každý n-homogenní polynom zadaný na Euklidovském prostoru dimenze N, existuje k-dimenzionální lineární podprostor, na němž se polynom anuluje. 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. 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.
dcterms:title
Zero sets of polynomials in several variables Zero sets of polynomials in several variables Nulové množiny polynomu několika proměnných
skos:prefLabel
Zero sets of polynomials in several variables Nulové množiny polynomu několika proměnných Zero sets of polynomials in several variables
skos:notation
RIV/67985840:_____/06:00076206!RIV07-AV0-67985840
n3:strany
561;568
n3:aktivita
n12:Z n12:P
n3:aktivity
P(GA201/01/1198), P(GA201/04/0090), P(IAA1019205), Z(AV0Z10190503)
n3:cisloPeriodika
6
n3:dodaniDat
n13:2007
n3:domaciTvurceVysledku
n11:4599071
n3:druhVysledku
n18:J
n3:duvernostUdaju
n14:S
n3:entitaPredkladatele
n17:predkladatel
n3:idSjednocenehoVysledku
509838
n3:idVysledku
RIV/67985840:_____/06:00076206
n3:jazykVysledku
n8:eng
n3:klicovaSlova
polynomial; zero set
n3:klicoveSlovo
n5:zero%20set n5:polynomial
n3:kodStatuVydavatele
CH - Švýcarská konfederace
n3:kontrolniKodProRIV
[CDD38A59BF3A]
n3:nazevZdroje
Archiv der Mathematik
n3:obor
n16:BA
n3:pocetDomacichTvurcuVysledku
1
n3:pocetTvurcuVysledku
2
n3:projekt
n4:IAA1019205 n4:GA201%2F04%2F0090 n4:GA201%2F01%2F1198
n3:rokUplatneniVysledku
n13:2006
n3:svazekPeriodika
86
n3:tvurceVysledku
Hájek, Petr Pavel Aron, R. M.
n3:zamer
n9:AV0Z10190503
s:issn
0003-889X
s:numberOfPages
8