Sentence examples for convergence implies from inspiring English sources

Pointwise convergence implies pointwise convergence.

In certain cases (i.e, for special families of convex constraints), this weak convergence implies norm convergence.

Since finite-time convergence implies nonuniqueness of system solutions in reverse time, such systems possess non-Lipschitzian dynamics.

On the other hand, the wide-spread occurrence of evolutionary convergence implies that similar phenotypes can be found again with relative ease.

For continuous-time dynamical systems finite-time convergence implies nonuniqueness of system solutions in reverse time, and hence, such systems possess non-Lipschitzian dynamics.

Here, stable convergence implies that the use of more materials can yield better system performance and a distinct void solid distribution is favored over an intermediate material distribution during the optimization process.

We show that, in most cases, the convergence implied in such decompositions holds not only in the distributions sense, but also in the function spaces themselves.

[[14], Proposition 2.5] For sequences in a complete CAT 0) space X, w-convergence implies Δ-convergence (to the same limit).

Edely and Mursaleen [14] introduced statistical A-summability (or, (A_{S} -summability) A_{S} -summability_{and-convergence implieshowedS})-summabilithatnder the aS_{mption of bounded sequence but the converse is not vA} -convergence

It is obvious that convergence in the metric implies w-convergence, and it is easy to check that w-convergence implies Δ-convergence [[6], Proposition 2.5], but it is showed in ([[19], Example 4.7]) that the converse is not valid.

As in the proof of Proposition 6.1, a priori convergence already implies convergence U (T ℓ ) → u as ℓ → ∞.