Sentence examples for needed for the analysis from inspiring English sources

First, we obtain preliminary results that are needed for the analysis of the average measure (pi _{t}^{M times N}).

These auxiliary problems are needed for the analysis and not for the computation, to get the estimate.

In the following section, we consider concrete examples and will give theformulas needed for the analysis of those examples.

Modification of conventional statistical methodologies or devise of new methodologies is needed for the analysis of colon cancer.

That is, the material parameters needed for the analysis are limited to invariant material properties that can be measured with standard test methods.

Only flowing bottomhole pressure (BHP) and rate data are needed for the analysis; the knowledge of reservoir geometry or shape factor and average-reservoir pressure is not required.

Good quality post-stall aerofoil force data at low Reynolds numbers is needed for the analysis of vertical-axis wind turbines (VAWTs).

The examples discussed suggest that the notion of minimality that is needed for the analysis of donkey conditionals also accounts for exhaustive interpretations of answers.

It seems that rather more efficient tools are needed for the analysis and design of the future smart electric grids, especially at the distribution part.

It was shown that robust estimators of the auto and pseudo cross-variograms were needed for the analysis of these data.

Quantitative Structure-Activity Relationships (QSARs), needed for the analysis/drug-design, are in the form of structural alerts that incorporate molecular substructures, presence/absence of activity, structural relationships, etc.