Sentence examples for proposition we use from inspiring English sources

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.

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.

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.

In the proof of the previous proposition, we used some interesting properties of the iterates.

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).

In his important 1880 paper, "On the Algebra of Logic", Peirce quietly broke with the traditional extensional semantics and introduced a usual assumption of modern semantics: the extension of a concept, understood as a class, could be empty (as well as the universe), and stated the truth values of the categorical propositions that we use today.

To prove the proposition, we will use mathematical induction.