Sentence examples for manifold by from inspiring English sources

It may be mentioned that the notion of weakly symmetric manifold by Selberg is different from that by Tamássy and Binh, and the pseudosymmetric manifold by Chaki is also different from the pseudosymmetric manifold by Deszcz.

Denote the surgically altered manifold by M* and the restriction of gab to M* by g*ab.

The wells and pipelines are connected to the manifold by jumpers.

The method considers many simple-structured smooth manifolds associated with the original manifold by local diffeomorphisms.

In the following, we confirm numerically this firing threshold manifold by calculating the canard.

Isomap aims to recover the intrinsic geometric structure of manifold by preserving geodesic distances between all pairs of data points.

However, when it comes to the manifold hazardous by-blows of an overheating planet, and especially those involving the ground we stand on, we must also be prepared to expect the unexpected.

Thus, (G'_{infty} u neq0) for any (uinmathcal{M}_{infty}), and (mathcal{M}_{infty}) is a (C^{1} -manifold by the implicit function theorem.

Moreover, we define pseudo-slant submanifolds of almost contact manifolds by using the slant distribution given in [10].

Extending the notion of generalized quasi-Einstein manifolds by Chaki [43], recently Shaikh et al. [47] introduced the notion of hyper-generalized quasi-Einstein manifold.

In this paper, we propose a new approach to define the penalty term on manifolds by the sparse representations instead of the adjacency graphs of data.