Sentence examples for manifold I from inspiring English sources

This paper is concerned with the wave equation on a Zoll manifold, i.e. a compact Riemannian manifold (M, g) all of whose geodesics are closed.

To train the model, we design a two-step maximum likelihood optimization procedure that ensures the orthogonality of the projection matrix by exploiting recent results on the Stiefel manifold, i.e., the manifold of matrices with orthogonal columns.

Especially if η=0, then a QGK n turns out to be a generalized recurrent manifold (i.e., GK n ) by Dubey [11].

The manifold is also symmetric about a plane which divides lip-opening states from lip-closing states, and as a consequence of this speech trajectories are realised as elliptical paths on the manifold (i.e., open-close-open cycles).

However, for many quantities, most notably orientations in 3D, S is not a vector space, but a so-called manifold, i.e. it behaves like a vector space locally but has a more complex global topological structure.

The proposed feedback control law is designed to exponentially stabilize the constraint manifold, i.e. to enforce the virtual holonomic constraints, which allows the convergence of the snake robot to the desired path.

Stein manifolds, i.e., properly embedded submanifolds of ({mathbb C}^N), Projective manifolds, and.

We simplify the proof of the estimates of Bony Häfner and generalize them to the setting of scattering manifolds (i.e. manifolds with large conic ends), by applying a sharp Poincaré inequality.

A torus manifold was also proposed in [36, 37] for the same purpose that is a product of two circular-shaped manifolds, i.e., the view and pose manifolds.

This paper presents a simple and fast procedure that can tear or cut those manifolds, i.e. break their essential loops, in order to make their embedding in a low-dimensional space easier.

Reference metrics are used to define the differential structure on multicube representations of manifolds, i.e., they provide a simple and practical way to define what it means globally for tensor fields and their derivatives to be continuous.