The simplest function (which is realizable as a MAK system) f(x) with three zeros is the cubic polynomial.
Investigations (by Ara and Goodearl, see [32]) continue into whether or not every finitely generated refinement monoid is realizable; whether or not the realization passes to direct limits; and whether or not there are wild monoids which are not realizable.
Structuralist computationalism emphasizes organizationally invariant descriptions, which are multiply realizable.
It is well known that the synergistic combination of nanofillers and polymer matrix offers materials with exceptional properties, which are not realizable by using an individual component.
In the language of analysis, Markov's Principle and the negative translation of the countable axiom of choice are among the many non-intuitionistic principles which are function-realizable (by classical arguments) and hence consistent with FIM; cf. Kleene [1965], Vesley [1972] and Moschovakis [2003].
Furthermore, these same input/output approaches allow inputs to span the whole space often assuming values which are not physically realizable.
This example also, illustrates the difficulty to find the least mean squares estimator which is physically realizable.
However, in contrast to former work here we use a simple phase-reversal grating for the modulation, which is practically realizable and has already been fabricated.
The constraint imposed is that the resulting function contains smooth practical filters, which are assumed to be physically realizable.
In particular, anisotropic viscosity can lead to regular convective structures that mimic naturally realizable Rayleigh Bénard cells, which are unphysical for the specified external parameter range.
One consequence of our structural results rules out the existence of certain Koopman-realizable measures arising from semidirect products which are absolutely continuous, but not Lebesgue.
