Sentence examples for be bounded as from inspiring English sources

Ohno in [39] devoted most of the paper to finding necessary and sufficient conditions for (C_{varphi}D) to be bounded as well as for (C_{varphi}D) to be compact on the Hardy space (H^{2}).

The first term can be bounded as follows: (D.132).

Therefore, error probability can be bounded as (D.28).

Finally, using (2.26), can be bounded as follows: (2.36).

The second term can be bounded as (E.46).

Consequently, the conditional probability can be bounded as (40).

Otherwise there is a sequence such that and is bounded as, where.

If ({z(n)}) is bounded, then, by Lemma 2, ({x_{1}(n)}) is bounded as well and, therefore, there exists a finite (lim_{ntoinfty}x_{1}(n)).

Assume also that |bar{p}| < 1. (14) If the sequence ({z(n)}) defined by (12) is bounded, then the sequence ({x_{1}(n)}) is bounded as well.

This permits to calculate the region of reachable marking vectors, when the considered Petri net is bounded, as the projection of an integral polyhedron.

Its energy is bounded as follows.