Sentence examples for bound of the set from inspiring English sources

Then the solution ω of VI (4.1) is the least upper bound of the set X. Theorem 5 [2].

Denote by tau = text{the greatest lower bound of the set of possible values of}~a_{0}~text{satisfying} (14).

Then, under the DMP, the solution ω h of VI (4.3) is the least upper bound of the set X h.

where τ denotes the greatest lower bound of the set of values of a 0 for which the inequality (18b) is satisfied.

Let X be a real ordered Banach space with a norm ∥ ⋅ ∥, a normal cone P and a partial ordered relation ≤ defined by the cone P, for arbitrary x, y ∈ X, lub { x, y } and glb { x, y } express the least upper bound of the set { x, y } and the greatest lower bound of the set { x, y } on the partial ordered relation ≤, respectively.

Let X be a real ordered Banach space with norm ∥ ⋅ ∥, a zero θ, a normal cone P, normal constant N and a partial ordered relation ≤ defined by the cone P. For arbitrary x, y ∈ X, lub { x, y } and glb { x, y } express the least upper bound of the set { x, y } and the greatest lower bound of the set { x, y } on the partial ordered relation ≤, respectively.

Finally, a tighter bound of the reachable set is obtained.

First, a priori bound of the solution set is derived.

If the bound of the compact set in which unknown parameter lies is incorporated, the designed finite-time controller can ensure convergence within two stages.

If one nodal injection uncertainty of bus i is ( Delta tilde{P}_{i} in [Delta {underline{P}}_{i},Delta bar{P}_{i} ] ), the maximum contribution of it to transmission constraints for transmission line l will be on the bound of the uncertainty set, depending on the sign of ( varphi_{l,i} ).

Following a robust Bayesian approach, we model uncertainty on prior specification with a class Γ of distributions for θ and we assume that the data yield robust evidence if, as the prior varies in Γ, the lower bound of the credible set inferior limit is sufficiently large.