# 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.
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This means that for a rock element subjected to tri-axial stresses, 0x, 0y, 0z, it will be assumed that failure is a function of the second stress invariant function (i.
In Section 3 we give a cyclically invariant function with sensitivity [THETA]([n.
Note that a cyclically invariant function is invariant under the group of cyclic shifts.
Comparing the minimum and maximum invariant function values, it can be seen that results for both types of samples mostly overlap, which makes it difficult to use the invariant moments as a classifier tool, except for those cases when the objects in the images have the same size.
Table 1: Experimental values for a hollowed object RTS Invariant function table Object: Hollowed Wrench (hollowed) [[phi].
With the first invariant function f estimated, we are able to plot the second invariant function g from the compression stress values [[sigma].
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].
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.
that has, as solution, the invariant functions y = t and v = u, taking
3]) into invariant functions along the characteristics (10) and zero average functions i.
Appendixes cover topics that are not standard parts of an average science of engineering undergraduate curriculum: Green's functions, real spherical harmonics, spherical modified Bessel functions, plane groups and invariant functions, and elementary elasticity theory.
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