where [I.sub.S](x) is defined as the Schrodinger invariant
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  of two invariant
The twisted Alexander invariant
can be computed using the Fox calculus ([1,2,10]).
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
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 , 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).