# invariant

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## invariant

[in′ver·ē·ənt]
(mathematics)
An element x of a set E is said to be invariant with respect to a group G of mappings acting on E if g (x) = x for all g in G.
A subset F of a set E is said to be invariant with respect to a group G of mappings acting on E if g (x) is in F for all x in F and all g in G.
For an algebraic equation, an expression involving the coefficients that remains unchanged under a rotation or translation of the coordinate axes in the cartesian space whose coordinates are the unknown quantities.

## invariant

(programming)
A rule, such as the ordering of an ordered list or heap, that applies throughout the life of a data structure or procedure. Each change to the data structure must maintain the correctness of the invariant.
References in periodicals archive ?
A good method for constructing local feature descriptor [13] is proposed and two descriptors, MROGH (multi-support region order-based gradient histogram) and MRRID (multi-support region rotation and intensity monotonic invariant descriptor), are presented.
Therefore, we plan to extend UOTSDF in our quaternion based face image correlator for the recognition of view invariant person face since it is less complicated in computational viewpoint than conventional MACE filter and achieve good performance.
Invariant Analysis Technologies: These technologies automatically extract and model universal relationships that represent the characteristics of a system (invariant) based on massive quantities of sensor data, without relying on domain knowledge of the plant system.
m are termed the invariant polynomials of D(z) and have the following property
Chandok: Common fixed points, invariant approximation and generalized weak contractions, Internat.
G] the ring formed by all polynomials invariant under the action of G.
Since a partial differential equation is invariant under a group of transformations, if their solutions are transformed in solutions under the action of the group, it is reasonable the possibility that some solutions of the equation also be invariant under the group.
In Section 3 we also construct a cyclically invariant Boolean function for which the product of 0-sensitivity and 1-sensitivity is [THETA]([square root of (n)]).
The focused results in the azimuth invariant and variant cases are shown in Fig.
In other words, any other polynomial loop invariant of Figure 1(b) is proved to be a logical consequence of xy - 1 = 0.
A graph G order p is a 3-path invariant graph if, and only if, it is isomorphic to any of the following graphs:

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