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 ?
In the next section, we prove that the switching system (1) has an invariant conic [x.sup.2] + [cy.sup.2] = 1, c [member of] R, and there exists a large limit cycle in switching system (1); half attracting invariant conic [x.sup.2] + [cy.sup.2] = 1, c [member of] R, is found in switching systems.
We set [mathematical expression not reproducible], the first inequality of (44) is required that it has the regularity at [alpha] = 0, and moreover, the second one is an additional nondegeneracy condition for the bifurcation [7] of two invariant closed curves,
The twisted Alexander invariant can be computed using the Fox calculus ([1,2,10]).
Firsov: Invariant Einstein metrics on three-locally-symmetric spaces, Matem.
However we are showing in Theorem 3 that a richer theory is obtained if we restrict the sample space to those [omega] whose weak ergodic limit is a [theta] null invariant probability.
In this paper, the phase feature [[LAMBDA].sub.f](x, y) is considered as the illumination invariant. Figure 2 shows the illumination normalized face images and the obtained illumination invariant.
This gives the following invariant representation and associated canonical form for the system of three 2nd-order ODEs admitting Lie algebra [A.sup.sub.3,5]:
For a fully invariant submodule N of a QTAG-module M and an endomorphism f of M, it induces an endomorphism [bar.f] of M/N such that [bar.f] (x + N) = f(x) + N.
Compared to [12], improved proofs are provided and an explicit formula is found for the computation of the controlled invariant vector function [epsilon] on which the solution of the DDDPM depends.
Then, we compare these two invariant curves given by both the methods.
As for features selection, low-order shifted moment with TRS-invariant (invariant to 2D translation, 2D rotation and scale) properties were proposed (Tahri, 2015), Spherical invariants to rotational motions based on unified projection model were proposed (Fomena, 2011), and hybrid projected features was proposed to decouple the translational and rotational motions (Ye, 2015).