Sentence examples for derivations are given from inspiring English sources

Under this assumption, it was shown in [3] that the probability of message reception can be analytically derived from the Nakagami model (for completeness, the derivations are given in the appendix) as follows: (1).

Detailed derivations are given.

Corresponding theoretical derivations are given subsequently.

Detailed mathematics derivations are given below.

The derivations are given in an easy to follow procedure.

Finally, some analytical derivations are given in the Appendix.

A glossary of terms relating to diagnostic test performance, together with their derivations, is given in Table S1.

Hourly mean time series of external SHE coefficients in a geomagnetic dipole coordinate system (up to degree 3 and order 1) have been derived by analysis of 4.5 years of observatory data (July 1998-December 2002), details of the derivation are given in Olsen et al. (2005).

Again, details of the derivation are given in the Appendix.

Hourly mean time series of external coefficients in a geomagnetic dipole coordinate system (up to degree n = 3 and order m = 1) have been obtained by analysis of 4.5 years of observatory data (July 1998 December 2002), details of the derivation are given in Olsen et al. (2006).

Details of the derivation are given in the Supplementary Material.