Sentence examples for are equivalent in a from inspiring English sources

(3.15) It follows from (3.14) and (3.15) that ({z^{0}_{k}}) is also bounded in E since all norms are equivalent in a finite dimensional space.

Since all norms are equivalent in a finite dimensional normed space, there exists a positive constant C 2 such that C 2 ∥ u ∥ ≤ ∥ u ∥ L ν for  u ∈ E n. (3.15).

Since all norms are equivalent in a finite dimensional space, there is a constant C 4 > 0 such that ∥ u ∥ 4 ≥ C 4 ∥ u ∥ E, ∀ u ∈ E k. (3.8).

Moreover, since ∥ z k ∥ L 2 2 = ∥ z k + ∥ L 2 2 + ∥ z k 0 ∥ L 2 2 + ∥ z k − ∥ L 2 2, we have Ψ ( z k ) ≥ c 1 ∥ z k ∥ L 2 2 − c 2 ∥ z k ∥ L 2 ≥ ∥ z k ∥ L 2 − c 4 ≥ ∥ z k 0 ∥ L 2 − c 4. It follows from (3.11) and the above inequality that { z k 0 } is also bounded in E since all norms are equivalent in a finite dimensional space.

The data provided here demonstrate that sCUR and nCUR are equivalent in a number of in vitro biological assays, which are designed to mimic bacteria-induced mucosal surface inflammation.

Theorem 4. The following are equivalent in an L-ts (X,τ): (i) X is normal.

On the one hand, the axiom is equivalent (in a theory that allows only sets) to the statement that every set appears in the iterative hierarchy informally described above there are no other sets.

The state constraint AWBT and MPC strategies are shown to be equivalent in a non-trivial region of the state space.

It is equivalent in a first approach to an impact on a sandwich panel comprising a foam core and a thin woven composite skin.

data dropouts, we first show that such a channel is equivalent, in a second order moment sense, to an additive white noise channel subject to an instantaneous signal-to-noise ratio constraint.

In general, the term duality refers to a situation where two seemingly different physical theories turn out to be equivalent in a nontrivial way.