Sentence examples for discussed in the proof of from inspiring English sources

As we discussed in the proof of Theorem 3.1, T is compact.

When subcarrier k is in state 3, as discussed in the proof of Lemma 1, we can still improve R ũn k by decreasing the interfering powers of subcarrier k in cell n′ while keeping the minimum user rate of cell n′ non-decreased.

Hence, using a coupling argument as discussed in the proof of Theorem 4.3.5 in [16], we find that there exists a probability space supporting two processes with distributions equivalent to the Poisson process and the Markov chain component such that the Poisson process dominates the second process for all paths.

As discussed in the proof of Lemma 5, there is a simple script from α to w which either starts with a mutation of α or its duplication.

In a sufficiently small vicinity of these intervals on the positive imaginary part of the complex plane, it is discussed in the proof that the imaginary part of z(h) is also positive for all h in this vicinity, therefore this vicinity lies in D h.

Discussing as in the proof of Theorem 5.1, the remaining conclusion is achieved.

which can be done semi-analytically as discussed in "Proof of Proposition 2" in Appendix.

We discuss the proof of Theorem 3 in Section 6.2.

Afterward, we briefly discuss important processing parts, called visual routines, that are used in the proof-of-concept implementation of the described architecture.

Let us briefly discuss the proof of this proposition.

PRHI is in the proof-of-concept phase of development.