Sentence examples for bounded we can define from inspiring English sources

Since is bounded, we can define a function by for all.

Proof Since {x n } is bounded, we can define a function f on H by f ( x ) = limsup n → ∞ x n - x 2, ∀ x ∈ H.

For | y ˙ k ( t ) − y ˙ k ( t 0 ) |, since x k ( t ) is bounded, we can define max | f ( x k ( t ) ) | : = r 1 ≥ 0. By the conditions (H2), we can get the estimation as follows.

If is bounded, we can easily know that is bounded [16].

for all If is bounded, we can take.

In other words, for this bounded, we can write:.

By exploiting the different time scales in the dynamics and neglecting the amount of DNA-bound protein, we can define the dimensionless variables as x = X1/ θ with, i = I/ θ I, y = Y1/(K4 θ Y )1/2, and a = A/K3.

Although the distributions of asset returns are uncertain, in the robust optimization framework, we may assert that μ or σ, or both, belong to an uncertainty set, the bounds of which we can define.

For and its Hodge decomposition we can define a bounded linear operator from to by.

In the same way as the Hausdorff distance defined on the family of bounded closed subsets of a metric space, we can define the analogue to the Hausdorff distance for modular function spaces.

We can define the scenario bounds, the test time, node mobility, and the routing protocol used.