Sentence examples for we replaced with from inspiring English sources

It even had a hole in the wall for a coffee machine, which we replaced with our designed-to-fit pill dispenser.

If, we replace with.

First, we replace with the equivalent decision statistic.

We replace with, with, with, with, and with in Theorem 7.

that is, we obtain the same expression in (2.4) if we replace with.

for all and We replace with in (2.20) to obtain (2.21).

In the above proof, if we replace with, then the following result can be obtained.

In the case of fractional derivative, we will use the notation instead of and we replace with with, and with.

In this state we will repeatedly find 'A's, which we replace with '1's, and move to the left.

Considering Aubin's compactness theorem, we conclude that there is a subsequence,,,, so that,,,   and Now we replace with.

For, we replace with and with, substitute < for >, then the dual version of the above induction principle is also true.