Sentence examples for manifold structure that from inspiring English sources

Then, the set of all orbits can be given a canonical manifold structure that is independent of the choice of symmetry cell [[6], p. 109].

The Bullet source can be modified to add a user data member to the persistent manifold structure that owns the manifold points.

This leads in a natural way to a smooth manifold structure that we call complex oblique projective manifold, due to its close relation to the oblique manifold which consists of invertible matrices with normalized columns.

The literal reading is that this manifold is an independently existing structure that bears properties.

Thus one might be tempted to identify spacetime with the manifold of events plus some further structure that supplies these spatiotemporal notions.

More generally, manifold substantivalism asserts that the manifold M of local spacetime theories is the mathematical structure that represents spacetime.

An emergent concept, addressed herein and in other Accounts in this special issue, is the presence of a manifold of protein structures that are achieved only transiently and differ from the dominant ground state protein structure.

Manifolds are nonlinear structures that are not vector spaces; hence, Euclidean calculus does not apply.

The geometric term based on graph ensures that the manifold structure of the data within each domain remains unchanged though it does not account for label information.

For dimension reduction, Isomap (Tenenbaum et al., 2000) applies geodesic distance to create a graph that captures the manifold structure to recover the intrinsic dimension of the data.

Numerical results show that the fuel consumption varies from a few kilograms to tens of kilograms, related to the locations and the types of mission orbits as well as the corresponding invariant manifold structures, and indicates that the low-thrust transfers may be a beneficial option for the extended science missions around different libration points.