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  • V článku je dokázáno, že variance počtu mřížových bodů v dilatované omezené množině rD s náhodnou polohou je asymptoticky úměrná r^d-1 pokud je rotační průměr absolutní hodnoty Fourierovy transformace tělesa O(r^-d-1). Výsledek má aplikace v odhadu přesnosti odhadů objemu pomocí počítání mřížových bodů v tělese (cs)
  • The aim of the paper is proof, that variance of number of lattice points inside the dilated bounded set rD with random position has asymptotics proportional to r^d-1 if the rotational average of quadrate of the modulus of the Fourier transform of the set is O(r^-d-1). The applications of the results are estimation of precision of estimates of volume by counting lattice points inside the set
  • The aim of the paper is proof, that variance of number of lattice points inside the dilated bounded set rD with random position has asymptotics proportional to r^d-1 if the rotational average of quadrate of the modulus of the Fourier transform of the set is O(r^-d-1). The applications of the results are estimation of precision of estimates of volume by counting lattice points inside the set (en)
Title
  • Asymptotics of variance of the lattice point count
  • Asymptotics of variance of the lattice point count (en)
  • Asymptotika variance počtu mřížových bodů (cs)
skos:prefLabel
  • Asymptotics of variance of the lattice point count
  • Asymptotics of variance of the lattice point count (en)
  • Asymptotika variance počtu mřížových bodů (cs)
skos:notation
  • RIV/67985823:_____/08:00315417!RIV09-AV0-67985823
http://linked.open...avai/riv/aktivita
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  • P(IAA100110502), Z(AV0Z50110509)
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  • 3
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  • 357207
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  • RIV/67985823:_____/08:00315417
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  • point lattice; variance (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...odStatuVydavatele
  • CZ - Česká republika
http://linked.open...ontrolniKodProRIV
  • [E63A6C971F84]
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  • Czechoslovak Mathematical Journal
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  • 58
http://linked.open...iv/tvurceVysledku
  • Janáček, Jiří
http://linked.open...ain/vavai/riv/wos
  • 261955600013
http://linked.open...n/vavai/riv/zamer
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  • 0011-4642
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