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13.
▫$Y$▫-compatible and strict ▫$Y$▫-compatible functions
Hvala, Bojan ; Klavžar, Sandi ; Novak, Franc, 1950-
Naj bo ▫$Y \in \RR^n$▫. Funkcija ▫$f : \RR^n \to \RR^k$▫ ▫$Y$▫-kompatibilna, če je za vsak ▫$Z \in \RR^n$▫ ▫$Z \le Y$▫ natanko tedaj, ko je ▫$f(Z) \le f(Y)$▫. Funkcija ▫$f$▫ je strogo ...▫$Y$▫-kompatibilna, če je ▫$Z < Y$▫ natanko tedaj, ko je ▫$f(Z) < f(Y)$▫. Dokazano je, da za vsak ▫$Y \in \RR^n$▫, ▫$n \ge 2$▫, ne obstaja ▫$Y$▫-kompatibilna funkcija ▫$f : \RR^n \to \RR^k$▫, ▫$1 \le k < n$▫. Dokazano je tudi, da je ▫$J_f(Y) = 0$▫ za odvedljivo strogo ▫$Y$▫-kompatibilno preslikavo ▫$f$▫. Pri tem je ▫$J_f(Y)$▫ Jacobijeva matrika preslikave ▫$f$▫ v ▫$Y$▫. Gornji problemi se pojavijo pri stiskanju podatkov analognih signatur.
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