Sentence examples for above representation from inspiring English sources

It is clear that in the above representation, matrix A is a stochastic matrix.

In [19], it is shown that the above representation can be extended to deterministic signals.

Then, by using the above representation and in view of Theorem A1, we obtain the assertion of Theorem 1.

It is clear that is a subspace of, and the above representation of in the form is unique.

If n < K and D is a full-rank matrix, an infinite number of solutions are available for the above representation problem.

If φ ( t ) ≡ C in the above representation, then we speak of normalized regularly varying functions of index ϑ; we write f ∈ NRV.

You hereby acknowledge that the above representations, warranties and undertakings are express conditions of this Agreement and that in the event that You are in breach of any of them, GNM shall have the right to terminate the Agreement forthwith without any liability to You whatsoever.

Comparing the above representations of, we require that the kernel is (17).

If the assumption of boundedness of S is dropped, then in all specified settings the above representations hold with intersections of conv Sz in place of cl conv Sz.

We then use an SEIR process to model the spread of an infectious disease in a structured hospital population whose contact patterns are described by using all of the above representations, computed from the raw proximity data.

For complex polynomials, the above convex representation is not available.