The phrase "a hard upper bound" is correct and usable in written English.
It is typically used in mathematical or computational contexts to refer to a limit that cannot be exceeded.
Example: "In this algorithm, we have established a hard upper bound on the number of iterations to ensure efficiency."
Alternatives: "a strict upper limit" or "a definitive upper bound".
Improved blade load regulation via the blade pitch angle control guarantees a hard upper bound on the flapwise bending moment.
Both purported ancestral islands of each group (Tenerife and Gran Canaria, 12 and 14 Ma, respectively) and the oldest Macaronesian islands (Fuerteventura, 21 Ma) were used as root calibration points; the date of the oldest island (21 Ma) was used as a hard upper bound at the root of each tree.
A binomial distribution also serves this purpose, but it imposes a hard upper bound on the number of successes.
This distribution is suitable for modeling fossil calibrations, because it allows us to avoid a hard upper bound while providing an increased probability with the age range of fossil discovery [ 121].
To account for the uncertainty in fossil calibrations and the likelihood of the true age of a node being older than the first fossil record, the age constraint was set with a hard upper bound of 228 Mya and soft lower bound of 239.4 Mya.
Significant upgrades to the design include a hard upper torso and greater hip and shoulder mobility.
Ching et al. [ 110] looked at hard constraints for an upper bound on the number of controls, and proposed a novel approach that requires minimising the distance between terminal and desirable states.
In both models, the goal is to minimize the makespan and the total completion time of agent A respectively, subject to an upper bound on the makespan of agent B. We prove that these two problems are NP-hard and can be solved in pseudo-polynomial time.
Given an arbitrary cut (L, R), we propose that r will be the least upper bound of L. The Least Upper Bound Axiom of the usual theory of the reals tells us that L has a least upper bound (L is nonempty and any element of R (which is also nonempty) is an upper bound of L, so L has a least upper bound).
With rapidly varying, hard to predict energy and data arrivals, these offline policies can still be used as a benchmark since the sum throughput achieved by an offline policy is an upper bound on the sum throughput achieved by the online policy for the same setup.
We now discuss a useful upper bound.
