Sentence examples for preparatory result for from inspiring English sources

First, we have the following preparatory result for later use.

A second point of interest emerges from the analysis of the preparatory results of this study.

Now, we give the following important preparatory result.

This section is devoted to some preparatory results.

The theorems of the following section require some preparatory results which we group together here.

In Section 3, the reader can find preparatory lemmas, results, and corollaries.

Results are used as preparatory material for decision making.

The Preparatory Sketch for Portrait of Luther Burbank is displayed in tandem with the resulting oil painting.

The resulting data were normalized with the quantile normalization method as a preparatory step for the application of the Split-Factor ANOVA.

They are never just "preparatory studies" for paintings.

They are either practice exercises or preparatory studies for paintings.