Sentence examples for manifold lies from inspiring English sources

We believe that the canard-like transition involving saddle-unstable sheets of the critical manifold lies at the heart of any spike-adding mechanism when no invariant saddle-type objects are present.

(a) Since (bar{x}< frac{lambda_{2}-1}{c_{2}}), (E_{0}) is a saddle point with stable manifold lying on the nonnegative x-axis.

When (frac{lambda_{2}-1}{c_{2}}=bar{x}), then (E_{0}) is non-hyperbolic with a stable manifold lying on the nonnegative x-axis by (2.10).

Since the attitude motion is essential in non-Euclidean space, thus, unlike the existing designs which describe the delayed relative attitude via linear algorithm, we treat the attitude error and the local relative attitude on the nonlinear manifold-Lie group, and attempt to obtain coupling attitude information by the natural quaternion multiplication.

The diverging diffuser section of the inlet manifold, which lies immediately upstream the catalytic monolith, induces flow non-uniformity along the transverse direction.

Like all smooth manifolds, a Lie group G has a tangent vector space attached to each element.

By the decomposition of the covariant derivative ∇S, Gray [49] obtained two classes, A Open image in new window and ℬ Open image in new window, of Riemannian manifolds which lie between the class of Ricci symmetric manifolds and the manifolds of constant scalar curvature.

In this survey, we focus on classifying pairs ((X,G)) in the complex setting, i.e., when (X) is a complex manifold and (G) lies in the group (mathrm{Bihol}(X)) of biholomorphic automorphisms of (X).

Thus a Klein geometry (space) consists of, (1) a smooth manifold, (2) a Lie group \(G\) (the principal group of the geometry), and (3) a transitive action of \(G\) on the manifold.

For example, most domesticated chickens grow to at least twice the size of RJF, become sexually mature at a lower age, lay manifold more and larger eggs, show a wide variation in plumage colour and structure, and have a different behaviour in a number of contexts, such as reduced fearfulness [ 3- 6].

Trajectories cannot cross these manifolds and the stable fixed point that any given trajectory tends toward depends on which side of the stable manifold its initial conditions lie upon.