Prime Basis Factorials and Systematic Sampling

Carla Francisco, Manuela Oliveira, Francisco Carvalho, João Tiago Mexia

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Abstract

In [p] = {0, ..., p − 1} with a p prime, we can define m od (p) a ddition a nd m ultiplication r eplacing t he results of the usual operations by the remains of their division by p. We then get a Galois Field G[P] = ([p], (+p)(×p)). With [p]n = {(x1, ..., xn), xj ε [p], j = 1, ..., n} we have the linear space G[p]n = {x; (+p)(×p)} with the operations x+y = (x1 (+p)y1, ..., xn (+p)yn) and c(x) = ((cx1), ..., (cxn) on [p]n. (p) (p) The dual of this space will be constituted by the linear applications L(x|a) = (Σ ajxj)(p) where a, x ε G[p]n n j=1 These algebraic structures have important applications to experimental designs, (see for instance Dey & Mukargee [12] and Mukargee & Wu [11]). We now present a new field of applications to systematic sampling, see Cochran [1].
Original languageEnglish
Title of host publicationInternational Conference on Numerical Analysis and Applied Mathematics
Subtitle of host publicationICNAAM2022
EditorsTheodore E. Simos, Charalambos Tsitouras
PublisherAIP - American Institute of Physics
Number of pages7
Edition1
ISBN (Electronic)978-073544954-1
DOIs
Publication statusPublished - 7 Jun 2024
EventInternational Conference of Numerical Analysis and Applied Mathematics 2022, ICNAAM 2022 - Heraklion, Greece
Duration: 19 Sept 202225 Sept 2022

Publication series

NameAIP Conference Proceedings
PublisherAIP - American Institute of Physics
Number1
Volume3094
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Conference

ConferenceInternational Conference of Numerical Analysis and Applied Mathematics 2022, ICNAAM 2022
Country/TerritoryGreece
CityHeraklion
Period19/09/2225/09/22

Keywords

  • Factorials
  • Multi-alphabetic hypercubes
  • Systematic sampling

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