Sentence examples for some preparatory background from inspiring English sources

We start with some preparatory background on the chemical master equation (CME) and parametric model order reduction.

Some preparatory work has been done.

For this purpose, some preparatory concepts are needed.

This section is devoted to some preparatory results.

Theorem 3.3 will be proved after some preparatory lemmas.

The proof is given at the end of the subsection after some preparatory lemmata.

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

To do this, we need some preparatory knowledge about non-Newtonian calculus.

Next we shall do some preparatory work from Lemma 3.1 to Lemma 3.7.

In order to render the main results as transparently as possible, we also give some preparatory lemmas and theorems.

In Section 4 we collect some preparatory results which will help us to simplify the proof of our main theorems.