Sentence examples for manifold it is from inspiring English sources

Since the metric described above is a model of pseudo quasi-Einstein manifold, it is significant geometrically and relevant physically.

Given a concept of distance on a manifold it is possible to talk about geodesics—a geodesic joining two points is a curve of shortest length between those two points.

When the range of is a manifold, it is easy to prove that this number is independent of the selected point, and, from [1, Propositions  2.10 and  2.12], is a finite number, providing that is a finite CW complex.

This is important because all objects within the real world are manifold: it is impossible to manufacture a perfect plane (single fold) of 0 thickness, or two shapes that touch in a single, mathematically discrete dot – these are abstract concepts.

Read for context and emphasis: does Kant mean " synthetic unity of the manifold", "synthetic unity of the manifold", or "synthetic unity of the manifold "? It's not that the concepts are different, but the author is pointing out something different about the concept depending on where and how he uses the phrase.

Though Davenport et al.[3] offers theoretical bounds on the number of measurements necessary to preserve distances among different manifolds, it is not clear how the performance scales with K or how to incorporate background models into this setup.

In order to extend the use of these algorithms to images painted on manifolds it is necessary to devise numerical schemes for the implementation of the geodesic generalizations of these equations.

Examining these shadow manifolds, it is evident that both are immersions of the Lorenz attractor, because zooming in on a particular piece of either will reveal that the tangent spaces have the same dimensionality as the original.

For Anosov flows on smooth compact manifolds it was first established by Giulietti Liverani Pollicott [109] and then by Dyatlov Zworski [78].

We compute the critical manifold for this situation and study the associated slow flow to explain this phenomenon; we find that the saddle equilibrium point lies in the middle of a saddle-unstable sheet of the critical manifold, and it is an attractor with respect to the slow flow on the critical manifold.

Just as the pathogenesis of the disease is manifold, it may be this multilateral approach that eventually leads us to a breakthrough in finding neuroprotective agents for PD, if they exist.