Sentence examples for manifold of all from inspiring English sources

Consider now the linear manifold of all which satisfy the condition.

Let ({mathcal M}) be the manifold of all k-dimensional subspaces of some Hilbert space, ({mathcal H}).

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.

Certain construction methods, such as harmonic frames and spectral tetris, are known in the special case of unit norm tight frames, but even these provide but a few examples from the manifold of all such frames, the dimension of which is known and nontrivial.

A quantitative version of the standard Sobolev inequality, with sharp constant, for functions u in W1,1(Rn) (or BV(Rn)) is established in terms of a distance of u from the manifold of all multiples of characteristic functions of balls.

To create the latent input space, a larger matrix model is created that represents and captures the joint manifold union of all input domains.

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

Edelman et al. [25] proved that for Stiefel manifolds (set of all orthonormal k-frames in (mathbb {R}^{N}), (V_{k}(mathbb {R}^{n}) = left {mathbf {A} in mathbb {R}^{n times k}: mathbf {A}^{top } mathbf {A} = mathbf {I}right })), e.g., SO(3), their canonical Riemannian structure makes possible to generalize a Riemannian Newton's method on them.

The Grassmann manifold Gk,m−k consists of k-dimensional hyperplanes in Rm and is equivalent to the manifold Pk,m−k of all m×m orthogonal projection matrices idempotent of rank k.

A manifold of connections among all DNA repair proteins highlights the complex set of mechanisms that were developed by cells to preserve the genome integrity.

In this respect, the global approach in our study to assess the expression data in the manifold of metastatic tumors, all in the screening phase by microarrays, in the validation phase by RT-qPCR and response validation by target protein expressions and their miRNA dependent regulation, as mentioned above, proved to be advantageous.