Sentence examples for manifold the first from inspiring English sources

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The key is to find a view-independent space for learning the identity manifold through the commonly-shared conceptual view manifold (the first question raised in Section 3.1).

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In both cases three velocity impulses are needed to perform the transfer: the first at an unknown initial point along the low Earth orbit, the second at injection on the stable manifold, the third at injection in the final (periodic or capture) orbit.

All three divertors employ the same cassette body as the support and the cooling water manifold for the first wall.

Structural parameters such as the distance from the manifold inlet to the first tube electrode, the manifold inlet diameter and the tube electrode length have obvious effects on the electrolyte distribution along the electrode array.

But dazzling comes in manifold shades, and the first work on the program, Fantaisie in A for violin and harp, by Saint-Saëns, was rarely splashy.

In each case, we reduce the system to a two-dimensional center manifold and compute the first Lyapunov constant (L_{1}).

The manifold, M, retains the first- and second-order features of finite-dimensional information geometry: the α-divergences admit first derivatives and mixed second derivatives, enabling the definition of the Fisher metric as a pseudo-Riemannian metric.

To the astonishment of most mathematicians, it turned out that manifolds of the fourth, fifth, and higher dimensions were more tractable than those of the third dimension.

Possible reasons for selecting these synthetic phospholipids instead of natural phospholipids are manifold: First of all, there may not be a natural alternative.

(a) Shape interpolation along the view manifold: the shapes of the first, middle and last columns are training cases that are adjacent on the view manifold, while the others are interpolated.

(b) Shape interpolation along the identity manifold: the shapes of the first, middle and last columns are training cases that are adjacent on the identity manifold, while the others are interpolated.

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