Sentence examples for for arbitrary k from inspiring English sources

(The argument shows that an ok is a cloud for arbitrary k, we can easily generalize to the claim that for every i, oi is a cloud).

Suppose m<K<2m (we will later generalize the achievability scheme for arbitrary K), let m ′=K−m.

A natural problem is to try to generalize the results by using the procedure for arbitrary k, which is technically not so easy.

For arbitrary k, we can thus let δ=δ k)→0 as a function of k to see that this is always bounded.

Stationary solutions of these doubly nonlinear problems are explicitly and analytically derived for arbitrary k and a general axial load p applied at the ends of the bridge.

In this section, we will derive the general form of the CDF of the SCN of central semi-correlated Wishart matrix for arbitrary K and N.

Then, for arbitrary m ∈ K T, there exists an element y m ∈ K T such that T ( m, ⋅ ) : [ 0, 1 ] → [ 0, m ] or T ( y m, ⋅ ) : [ 0, 1 ] → [ 0, y m ] is not continuous.

Therefore, for arbitrary m ∈ K T, there exists an element y m ∈ K T such that T ( m, ⋅ ) : [ 0, 1 ] → [ 0, m ] or T ( y m, ⋅ ) : [ 0, 1 ] → [ 0, y m ] is not continuous.

Thus, we obtain that the equivalence class of the weakest t-norm T D contains a t-norm which is different from a t-norm T D. We obtain that for arbitrary m ∈ K T, there exists an element y m ∈ K T such that T ( m, ⋅ ) : [ 0, 1 ] → [ 0, m ] or T ( y m, ⋅ ) : [ 0, 1 ] → [ 0, y m ] is not continuous.

The model used enables us to consider the instability pattern for an arbitrary k y.

The cylindrical model has enabled us to consider the stability for an arbitrary k y, which showed that even an azimu-tally large-scale mode, k y a ≪ 1, can be destabilized.