Sentence examples for by replacing with another from inspiring English sources

One word is revised by replacing with another word.

By replacing with in (2.10), respectively, we deduce that (211).

(i) Estimate and by replacing with in (22) and (23): (33)  .

Estimate and by replacing with in (22) and (23): (33).

and similarly for, by replacing with in (30).

Based on an analogy with (7), we define nonnegative tensor principal component analysis by replacing with.

Note that an accurate expression (with no approximation) may be obtained by replacing with.

We can then obtain from (A.6) by replacing with, with, and setting, thus yielding (A.7).

The original construction in [12] easily extends to -nets by replacing with.

Using Theorem 2.1, we obtain the estimate about by replacing with.

by replacing with within (2), the watermarked pixel values and are got.