To prove the proposition, we use the same technique as in [17].
To examine this proposition, we use Pinkowitz et al. (2006)'s value regression.
In [4], section 3, we stated some properties of σ -approximate contractibility when A has an identity and considered some corollaries when σ ( A ) is dense in A. In proof of the following proposition we use those results.
To prove this proposition, we use the idea of the proof of Theorem 1.1 in [19], in which the extinction of the solution for the equation u t = div ( | ∇ u m | p − 2 ∇ u m ). was studied.
For forming propositions we use this type structure: thus R a1,…,an) is a proposition if R is of type (A1,…,An) and ai is of type Ai for i = 1,…,n.
Moreover, as in the proof of Proposition 4.3 we use again Remark 4.4 to shorten the presentation.
To prove Proposition 3, we use the diversity equivalence between a block BEC and the BF channel.
Based on Proposition 1, we use Heff,k[n - D] with the delayed CSIT to replace the H ^ eff, k [ n ] in (11).
where we used Proposition 2.1, Proposition 2.3, the embedding F p, q s − 1 ↪ L ∞, and the boundedness of the Calderón-Zygmund singular integral operator on F p, q s.
To prove the proposition, we will use mathematical induction.
