This equations can be simplified by substituting the rights-hand side of the equations into the left-hand side to obtain: x^{ k)} = A^{T}A x^{ k-1)} (12).
The DC algorithm performs successive optimization of the convex problem obtained by substituting the right-hand side of (30) for the concave part in (29) until convergence.
Proof By substituting the right-hand side of (2) into (15), we get ∑ n = 0 ∞ ( d l B k n ( x ) d x l ) t n n !
Proof By substituting the right-hand side of (2) into (23), we get ∑ n = 0 ∞ B k 1 n ( x ) t n n !
The theorem follows by substituting the right-hand side of this expression for the partial derivatives in Equation 15, and then by recognizing the fractions in the resulting expression in terms of the equilibrium probabilities Equation 2. We point out that the expression (16).
In the implementation, this is simplified to an unconstrained optimization problem by substituting the right-hand side of Eq. 2 for v i 0. For reactions with multiple substrates and products, there are two possible mechanisms, namely single-displacement and double-displacement.
We attempted to fit the observed electron density data by substituting the most commonly observed cysteine side chain oxidation products at position 113 and carried out one round of refinement.
Although calcium activation was compromised by substituting the acidic residue with a longer side chain, D734E was still more sensitive to calcium than other mutants possessing substitutions at this residue.
Once high molecular weight linear poly(dichlorophosphazene) is synthesized, the polymer can be modified by substituting the phosphorus-bound chlorine atoms with organic side groups.
109, 110 The developers of idoxifene tried to minimize the negative side effects of tamoxifen by substituting the dimethylamino group found on tamoxifen with a pyrrolidino group to avoid the production of a desmethyl metabolite and formaldehyde after metabolism in the liver.
