Sentence examples for propositions above from inspiring English sources

Next we turn to strictly show the two propositions above.

Following Lemma 1 and the propositions above, (34) can be recast as SDP (35).

In fact, the verification of propositions above can be found in pp.23-26 pp.23-26and pp.59-62 in [13].

▪ The bounds in the proposition above are tight, as the following example shows.

Choosing suitable functions γ in the propositions stated above, we can derive several efficient conditions sufficient for the validity of the inclusion ℓ ∈ V ˜ a b − ( h ).

In this case, it properly extends [1, Proposition 3.15] as in that proposition, the above decomposition has been obtained for a square-free automorphism-invariant module of finite Goldie dimension.

In fact, according to the next proposition, the above three conditions can be easily verified, and the detail the omitted here.

Consequently (omega_{i}) satisfies the properties in Proposition A above uniformly in (x_{1}, ldots, x_{i-1}, x_{i+1}, ldots, x_{n}) if (mu_{i}) is a Radon measure without mass-point.

It is worth noting that the proposition stated above can also be considered for the case of relay networks with more than two hops or more than one relays.

This is the inverse of the proposition above, and it's hard to pull off.

We need two lemmas for the proof of the proposition above.