TY - GEN
T1 - Prime Basis Factorials and Systematic Sampling
AU - Francisco, Carla
AU - Oliveira, Manuela
AU - Carvalho, Francisco
AU - Mexia, João Tiago
N1 - Publisher Copyright:
© 2024 American Institute of Physics Inc.. All rights reserved.
PY - 2024/6/7
Y1 - 2024/6/7
N2 - 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].
AB - 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].
KW - Factorials
KW - Multi-alphabetic hypercubes
KW - Systematic sampling
UR - http://www.scopus.com/inward/record.url?scp=85196553340&partnerID=8YFLogxK
U2 - 10.1063/5.0210674
DO - 10.1063/5.0210674
M3 - Conference contribution
AN - SCOPUS:85196553340
T3 - AIP Conference Proceedings
BT - International Conference on Numerical Analysis and Applied Mathematics
A2 - Simos, Theodore E.
A2 - Tsitouras, Charalambos
PB - AIP - American Institute of Physics
T2 - International Conference of Numerical Analysis and Applied Mathematics 2022, ICNAAM 2022
Y2 - 19 September 2022 through 25 September 2022
ER -