where [I.sub.S](x) is defined as the Schrodinger

invariant [1, 4].

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).