For simplicity, only the major steps of derivation are presented in this section.
A new concept called shale number (SN) is developed and detailed steps of derivation using mathematical technique of dimensional analysis is presented in "Appendix" as Eq. 21, and given below by Eq. 11.
Therefore, given a sequence of I n t e r f a c e/ O u t e r f a c e symbols used in the derivation between Start and Turn, the number of residues originating from each helix at each step of the derivation is known, e.g. S t a r t⇒ O u t e r f a c e DD ⇒ D o u b l e I n t e r f a c e DS S i n g l e⇒ S i n g l e O u t e r f a c e SD D o u b l e⇒ T u r n.
2) A far analogical problem in which the surface features were drawn from visually distinct categories in the derivation and application panels, for example, if the number of dots incremented by 2 in each step of the derivation panel, then the application panel could contain shapes with a variable numbers of sides (Fig. 1, right).
Each rule derivation panel was included in 2 types of problem. 1) A near-analogy problem, in which surface features were drawn from the same category in the derivation and the application panels, for example, if number of dots incremented by 2 in each step of the derivation panel, then the application panel would also consist of objects with a variable number of dots (Fig. 1, left).
where Eq. (44) has been used in the last step of the derivation.
These examples have been augmented with comments explaining, in each step of a derivation by Boole, which aspect of his methods is being employed.
In the above each step of the derivation process is reversible, so we only need (g_{11},g_{22},g_{33}) to satisfy inequality (3.15); eventually inequality (3.12) is true.
The last step of the derivation is based on unit rank matrices decomposition and analysis on the R-transform domain, as presented in [6, 10].
The first step of the derivation is to quantify the change in all states x at the end of the pulse perturbation, i.e. at time τ + Δ τ, using the Taylor series expansion: (10) In the next step, the change Δ x is translated to the change in the state x i at time t using the Green's function matrix (GFM) S x (t, τ + Δ τ) [ 47].
