Sentence examples for manifold examples of from inspiring English sources

Natural molecular evolution supplies us with manifold examples of protein engineering.

Different modes of system operating and manifold examples of its application to the molecular structure elucidation of new complex organic compounds (mostly natural products) have been described in our earlier articles [23 30, 43, 44].

Diamond [1] also provided manifold examples of how consequent advantages lead to a recurring pattern of cultural or physical genocide of hunter-and-gatherers by agriculturalists throughout history [see also 12], [13].

Polyhedra and differentiable manifolds are examples of ANRs.

Hadamard manifolds are examples of hyperbolic spaces and geodesics; see [1, 3 5, 19, 20, 26 28] and the references therein.

In [12], Bishop and O'Neill, defined the notion of warped product manifolds to construct examples of Riemannian manifolds with a negative curvature.

Besides manifolds, other important examples of global NPC spaces are the Bruhat-Tits buildings (in particular, the trees).

Lie groups are, in a sense, the nicest examples of manifolds and are good spaces on which to test conjectures[1].

Remark 1.6 Examples of manifolds satisfying the hypotheses of the theorem are the gauged G -complexifications of [6] for unimodular Lie groups.

See also [13] (where the G -Fredholm property is extended to a wider class of invariant operators), [12] and [14] (where the Laplacian is studied without unimodularity assumptions on G ). Examples of manifolds satisfying the hypotheses of the theorem are the gauged G-complexifications of [6] for unimodular Lie groups.

Homogeneous manifolds satisfy this condition, but we exhibit examples of locally homogeneous manifolds which are not critical points in dimensions ≥ 3.