Sentence examples for introduced as needed from inspiring English sources

Notation: A large proportion of our notation will be introduced as needed.

Lags of (Delta f_{t}^{text{M}}) can be added to Eq. (3) to address autocorrelation and dummy variables can be introduced as needed.

Calculus was introduced, as needed, to understand continuous change.

In a similar manner, predicates or properties used to tag string literals were introduced as needed.

In the Results section, minor extensions and associated statistics derived from the various models, such as influence diagnostics, are introduced as needed.

For our second order algorithm, no adjustment step size needs be introduced as mentioned earlier (i.e., λ = 1), but the number of iterations must be at least L=3.

A threshold is introduced as a design requirement, which needs to be met by a derived upper bound on the probability that all receivers will be successful in recovering a subset of the first most important video layers within the deadline.

Tim is introduced as a self-righteous evangelist ("She needs to hear this," he admonishes Ruth when she tries to stop him from praying with her daughter after the game) but turns out to be ambivalent about his newly found religion, repeatedly slipping up with bouts of adulterous sex, gambling and alcohol.

In order to further investigate how the new educational opportunities are allocated between genders, The Expansion needs to be introduced as a variable as well.

The fourth leg that needs to be introduced as a requirement of fiscal and monetary policy, is a publicly announced planned reduction of interest rates.

Pretesting of patient RS may need to be introduced as an important part of the dose planning strategy.