Sentence examples for fs for all from inspiring English sources

Here, we should point out that data for the longer probing wavelengths (550 980 nm) show a rise time of approximately 300 fs for all the samples involved in this work.

SBS values for FZ250 were significantly higher than for FS for all of the underlying materials tested (P < 0.05).

The time-step of integration was chosen to be 2 fs for all simulations performed in this study.

SBS values are given in Table 2. SBS values of FZ250 were significantly higher than SBS values of FS for all underlying test materials (P < 0.05).

Covalent bond lengths to hydrogen atoms were constrained using the SHAKE algorithm [ 21], which allowed a time step of 2 fs for all the MD simulations.

The classification accuracies achieved by this method in combination with the BioHEL rule-based machine learning method were better than other machine learning methods used (without FS) for all datasets and better or equal for the majority of datasets with feature selection also applied.

It implies that f ( x ) ≤ f ( y ) for all f ∈ F ⪯ ′ and so x ⪯ y.

In accordance with Proposition 2, it holds that x ⪯ y when f ( x ) ≤ f ( y ) for all f ∈ F ⪯ ′.

The first condition implies that f ( x ) ≤ f ( y ) for all f ∈ R, or equivalently, ∫ f d P x ≤ ∫ f d P y for all  f ∈ R, where P w ∈ P denotes the probability distribution degenerated at the point w ∈ X.

Thus, f ( x ) ≤ f ( y ) for all f ∈ R 1, or equivalently, ∫ f d P x ≤ ∫ f d P y for all  f ∈ R 1, that is, P x ⪯ ˜ P y.

∥ A X f ∥ ⩽ ∥ f ∥ for all f ∈ K. ∥ A X f + A Y f ∥ ⩽ ∥ A X f ∥ + ∥ A Y f ∥ for all f ∈ K. Suppose that A X and A Y are operators associated with two independent random variables X, Y and f ∈ K. Then A X A Y f = A Y A X f = A X + Y f.