Sentence examples for results needed for from inspiring English sources

In this section, we will establish auxiliary results needed for the proofs of the main propositions.

In what follows, we give some preliminary results needed for the convergence analysis of our algorithms.

In this section, we recall some basic results needed for our investigations.

Also, high-risk area analysis with different methods being applied to get the best set of results needed for subsequent operations.

The paper is divided into four sections as follows: After this Introduction, in Section 2, we cite several auxiliary results needed for our study.

In Appendix B some auxiliary results, needed for the study of the generalized solution to problem (mathit {PK}_{2}), are proven.

Last week, Simutowe won the Euwe Stimulans tournament in the Netherlands, the final result needed for the grandmaster title.

The following results are needed for proving our results.

Experimental results are needed for validation of unsteady load analyses.

The following results are needed for the proof of Theorem 3.2.

A thorough analysis of results is needed for deciding which filter to apply.