Sentence examples for the above representations from inspiring English sources

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.

The above representation can be used to define an integer approximation of the DCT.

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.

The above representation, in this article, is named as LMD-based TFR by IDLMD-TFR.

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.

In the above representation, the kernel (G(P,Q)) is said to be the Green's function for the homogeneous problem corresponding to that of (7) and (8).