From (23), (24), and the chain rule of derivation, we know that ∂ I ( x ; y ) ∂ B = H † HBT.
The resulting general equilibrium model has much in common with derivations of Marshall's rules of derived demand.
In the first stage, a set of elementary periodic patterns (mathcal {P}_e) and a set of derivation rules described earlier are used to discover a set (mathcal {P}) of more complex periodic patterns.
Discovery of elementary periodic patterns is followed by application of derivation rules to create complex periodic patterns that span over the longer periods of time and that have complex repetition characteristics.
Evaluation of the developed system was performed in terms of derivation of new rules by the machine learning process, WSN performance and mote lifetime.
Albert Dragalin refined in the late 1970s the calculus into one in which the structural rules are moreover "height-preserving admissible", meaning that whenever the premiss of such a rule is derivable, the conclusion is derivable without the rule and with at most the same size (maximum number of rule instances in a derivation branch) of derivation.
Then application of the chain rule for derivations with respect to x i, x j and x k leads to the following set of partial differential equations (PDEs) for the output function y = y ( x ̲ ) : y x i = ∂ i P i ∂ x i u l, y x j = ∂ j P j ∂ x j u l. (1).
The two new things in our study is the use of only basic rules and the derivation of explicit bounds.
The dominant strain of current syntactic theory takes the lexicon as primitive and studies the rule-governed derivation of syntactic forms, which are structures known as LFs (or, more misleadingly, Logical Forms).
Table 4 shows the results of the analysis of derivation and validation data sets of the new TOR rule for predicting a one-month unfavorable neurological outcome.
