Sentence examples for a parallel transport from inspiring English sources

A controller is designed using transverse feedback linearization and a parallel transport frame that is suitable for regular paths with parametrized fivefold continuously differentiable representation.

Such a massive transport is possible only when it occurs in electroneutral manner, so that cations (e.g., K+) transport needs to be accompanied by a parallel transport of anions via anion channels.

Theorem A.3 If for every point \(p\) in a neighborhood \(U\) of \(M\), there exists a geodesic coordinate system \(\overline{x}\) such that the change in the components of a vector under parallel transport to an infinitesimally near point \ q\) is given by then locally in any other coordinate system \(x\), where \ \Gamma^{i}_{jk}(x) = \Gamma^{i}_{kj}(x)\), and conversely.

We'll see that the Kato dynamics defines a notion of parallel transport on the natural vector bundle over the manifold of all k-dimensional subspaces of a Hilbert space, ({mathcal H}), and so a connection.

The Kato dynamics, W s), tells you how to "parallel transport" a vector (v in {text {ran}}, P gamma (0))) along a curve (gamma (s);,0 le s le 1) in ({mathcal M}).

Figure 5: The parallel transport of a vector by a two-dimensional creature, from \(A \rightarrow B \rightarrow C \rightarrow A\) around a geodesic triangle on a two-dimensional surface \(S^{2}\), ends up pointing in a different direction upon returning to \(A\).

In particular, we require a formula for the parallel transport and the geodesics of the COP manifold.

The numerical implementation is based on an operator-split formulation, with two straightforward steps: a perpendicular transport step (including sources), and a Lagrangian (field-line integral) parallel transport step.

These are based on discrete geodesic interpolation, a discrete geometric logarithm, a discrete exponential map, and discrete parallel transport.

In our context, stochastic parallel transport provides a canonical moving frame on the path space.

Levi-Civita's construction of infinitesimal parallel transport on a manifold required the process of embedding the manifold into a flat higher-dimensional metric space.