In fact, the operators H ˜ and ℋ enjoy the same boundedness property for L p → L p and L 1 → L 1, ∞, but they do not have the same property involving the Hardy space H 1. For instance, the operator H ˜ is bounded from H 1 to L 1 ; but the operator ℋ is not since ℋ is nonnegative (cf. [13]).
The resulting structure will satisfy all the axioms of Zermelo set theory except Separation, and will satisfy all instances of Separation in which each quantifier is bounded in a set (this boundedness comes in because each instance of Comprehension in TST has each quantifier bounded in a type, which becomes a bounding set for that quantifier in the interpretation of Mac Lane set theory).
This problem is NP-complete and the instances are so large that with current technology any agent's rationality is bounded by computational complexity.
For instance, if f i ∈ C r d ( J ) and f i is bounded, the existence holds.
If is bounded, closed, and convex and is a nonexpansive mapping of into itself, then ; see, for instance, [1].
An instance (C,U) of the set-cover problem is k-bounded if the number of occurrences in C of any element is bounded by a constant k⩾2.
Our free will is bounded.
As established by the fixed-parameter tractability of AH-Cut, if a simple greedy algorithm does not produce a solution with a sufficiently high objective value, then the instance size must be bounded by an relatively simple function of the parameters.
Other types of networks, however, may allow for similar approaches as the ranges of outcome values of, e.g., L and C, are bounded; see for instance the scale-free networks in Klemm and Eguíluz [48].
Remark Frequently activation functions f j are assumed to be bounded and monotonic; see, for instance, [18, 28].
For instance, one of the results shows that the forecasting error of the new algorithm can be bounded by (11).
