Sentence examples for substituted equation from inspiring English sources

Equation 3 substituted Equation 1 in the algorithm 2 and was run in the same cross-validation scheme yielding (100 folds, 100 repetitions, 6 proportions of SNPs) 6000 replicates per SNP-chip.

Substituting Equation 2 yields (6).

Substituting Equation 7 into Equation 8 obtains Theorem 1.

Substituting Equation A12 into Equation A13 yields (A14).

Substituting Equation 19 into Equation 18, we have (21).

By substituting Equation (1) in Equation (9), becomes (10).

Substituting Equation (20) into (18), leads to: (21).

The first line above is obtained by substituting Equation (30) in the expectation, and, the second line is obtained by substituting Equation (29) into the first line.

Substituting Equation 7 into Equation 15 and after simplification, Equation 14 follows.

Proof: Substituting Equation 9 into Equation 1.30 in [5], we have Equa-tion 16.

Introducing this variable in subsequent equations, and substituting Equation (5) into (4) then yields: (6).