invariant function

invariant function

[in′ver·ē·ənt ′fəŋk·shən]
(mathematics)
A function ƒ on a set S is said to be invariant under a transformation T of S into itself if ƒ(Tx) = ƒ(x) for all x in S.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
System (1) can be disturbance decoupled by feedback (2) if and only if there exist an controlled invariant function [phi] and an (h, f)-invariant function y such that
Bayoumi, "A dyadic wavelet affine invariant function for 2D shape recognition," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.
In Section 3 we give a cyclically invariant function with sensitivity [THETA]([n.sup.1/3]).
The second invariant function (i.e., function g) is clearly needed in order to fit experimental data as well in compression as in tension.
Conversely, given any r-conjugacy invariant function [xi](t) on D', equivalently a function on the union of T' = T(E) with T ranging over {T}, whose restriction to T' vanishes on a neighborhood of the r-singular part of T', and which is locally constant and transforms via [[omega].sup.-1] under Z', there exists f [epsilon] [H.sub.D] which is zero in a neighborhood of the r-singular set of D' with [xi](t,f) = [xi](t) on D'.
Considering the approach presented in [6], one can easily show that each class of transitions can be described by only one invariant function. The main advantage of this approach is that relations among the invariant functions become structure independent although the expression of the invariant function is structure dependent.
We denote the corresponding invariant functions [[PI].sub.1], [[PI].sub.2], [[PI].sub.3], [[PI].sub.4] and [[PI].sup.*.sub.1], [[PI].sup.*.sub.2], [[PI].sup.*.sub.3], and [[PI].sup.*.sub.4], respectively.
These varieties families (joint invariant functions) will be solutions of the Stoka equations [17,18]:
We will extend the lagrangian with auxiliary fields so that this is not necessary but only that the gauge invariant functions of the collective reality of these fields evolve causally.
In this paper Gaussian is utilized as the spread function since the function phases can stay invariant functioned by Gaussian.