Sentence examples similar to any assumed compact set from inspiring English sources

We shall further assume that S is the union of a decreasing sequence of countable family of compact sets { C n } such that for any other compact set in S there is a C i which contains it (see [44]).

A simple learning control algorithm is designed which guarantees asymptotic output tracking for any initial condition belonging to any given connected compact set.

uniformly for in any compact set.

Since is continuous, it is uniformly continuous on any compact set.

if for any compact set K ⊂ M ⊂ R n, we have.

Then is bounded and uniformly continuous on for any compact set in.

For any compact set there exists a constant such that for all for all for all and.

Suppose that, for any compact set (mathcal {D}subsetmathcal{Z}), let (d =sup{Vert z-z^{0}Vert _{G}vert zinmathcal {D}}).

and, for any compact set, we denote by the set of all the functions such that (1.7) is replaced by (2.2).

As a result, for any, Since is a weak* compact set, we have (2.28).

Perhaps the most germane property is given by the universal function approximation theorem [ 20], which states that a sufficiently complex neural network is capable of modeling any smooth function on a compact set to an arbitrary degree of precision.