The phrase "as any function" is correct and usable in written English.
It can be used in contexts where you are comparing or relating something to the behavior or characteristics of any function in mathematics or programming.
Example: "The algorithm behaves as any function would when given a specific input."
Alternatives: "like any function" or "similar to any function".
In fact, in ref (232), g1 and g2 are defined as "any function" of b "normalized so that g(1/2) = 1".
The sigmoid function is defined as any function that is bounded and has a direct relation between the input variable and the output variable (Smith 1993).
We define the kernel function K as any function satisfies (int _ K x), dx =1 ) and: begin{array}rcl@ widetilde{f}(x;h) &=& frac{1}{N h} sumlimits_{i=1}^{N} Kleft(frac{x-x_{i}}{h}right).
Section 11(1) allows for trustees "[to] authorise any person to exercise any or all of their delegable functions as their agent", with Section 11(2) defining "delegable functions" as any function other than the powers to distribute or dispose of trust assets, allocating fees or other payments, appointing a trustee or further delegating duties.
The last example can indeed be generalized and used as an alternative demonstration of equation (21), as any function can be seen as a superposition of Dirac's deltas: p 0 (y ) = ∫ ℝ p 0 (u ) δ (u − y ) d u.
For a given monotone increasing property Q (such as the appearance of a certain subgraph), we define a threshold function t(n) for Q as any function which satisfies Threshold functions are not unique although they are so within certain factors (Bollobás, 2001, p. 40).
An example is that of canalyzing Boolean functions that were introduced by Kauffman as "any Boolean function having the property that it has at least one input having at least one value (1 or 0) which suffices to guarantee that the regulated element assumes a specific value (1 or 0)" [ 81].
We define and as any utility function with any resource allocation vector over the convex set : (14).
Alternatively, CTT may be formulated as follows: any function that is "naturally regarded as computable" (Turing 1936 7, 135) is Turing-computable.
(One early term for abstraction, "non-objective," is especially fallacious in this light — as if any function of the human brain, let alone a work of art, could evade subjectivity).
Finally, as with any function prediction method, the primary limitation is the comprehensiveness of experimental annotations.
