Sentence examples for alternative expressions for from inspiring English sources

Next, we provide three alternative expressions for β s.

Letting in (4.12), we obtain alternative expressions for the identities in (4.10).

Putting further in (4.13), we have the alternative expressions for the identities for (4.11).

The statistical accuracy of our data, however, is insufficient to decide between the two alternative expressions for the function E(f).

Choosing among these alternative expressions for describing a given dataset is an important task that can significantly influence subsequent transport modeling and/or mechanistic interpretation.

An investigation of alternative expressions for this quantity is given, based on which an improved match with the data can be obtained.

From this point of view, we can also express the alternative expression for SINR of MMSE-OSIC.

An alternative expression for the sampling errors in conventional point measurement is derived.

An alternative expression for the random errors of frequency-band estimates of sound intensity is derived.

TDS concentration is an alternative expression for the sum of cations and anions in water.

However, we make further analytical progress below to obtain an alternative expression for the PDF of mutual information.