Hence, if ℛ K) is sufficiently small for all K ∈ B δ * (K0) the system admits a stable periodic orbit in B δ * (K0) (having ℛ K) small enough in the box B δ * (K0) implies that the Taylor expansion of the system on the center manifold passing through and x e is such that the terms of order higher than three are negligible in B δ * (K0)).
In the dimensional reduction, 1-D smooth symmetries induce orbits that are 1-D manifolds passing through every symmetry cell.
The aim was to either modify or eliminate the defect by manipulating those parameters so that the lower inlet manifold casting would pass a leak test.
If the singular limit trajectory passes this manifold, the singular limit predicts a spike event.
Another scheme utilizes a series of miniature probes released from a multi-probe carrier vehicle from a parking halo orbit, to travel on that halo orbit invariant unstable manifold in successive single passes through the surveillance zone, requiring continuing replenishment.
At the same time, he clearly admires the man's manifold journalistic contributions and laments the passing of both his style of genteel journalism and the Washington of his glory days.
Moreover, let us consider the unperturbed trajectory to pass through the switching manifold when (xi = xi^{m}(t)), (m in mathbb{Z}).
It is possible that between times s and (t_{i+1}), the cell passes through other switching manifolds, in which case, the procedure for identifying switching times and updating the region variable is repeated as many times as necessary.
In Laplacian SVM, it assumes that the data of each class, which follow a manifold and decision function must avoid passing through the manifold.
Starting at Hulme End, it is a gentle amble through the picturesque valleys of the Hamps and Manifold rivers, via the hamlet of Ecton, passing beneath the famous Thor's Cave gaping over the trail from its position up in the limestone spur.
