Sentence examples for the previous proof from inspiring English sources
However, as in the previous proof, we obtain a contradiction.
The proof is similar to that of the previous proof.
The proof of strong convergence is different from the previous proof [20].
Proof The proof runs as the previous proof, take α > 0 into account.
The first conclusion is clear by the previous proof (see (15)).
The previous proof will show that { g n } is also ρ-convergent.
Compared to the previous proof-of-concept trial with monohydroxyl coumarin derivatives as the photosensitive groups, the application of dihydroxyl coumarin derivatives in the present work prevented the undesirable gelation during synthesis and enabled properties-oriented structure adjustment of polymerization products.
end{aligned} (13) The remaining part is similar to the previous proofs.
where α = 2, β = 2 p / ( 1 − p ) > 2. Similarly as in the previous proofs, it can be shown that F ( c, μ ) is an increasing function of μ for 0 < μ < 1.
Finally, from all the previous proofs and Zangwill's global convergence theorem, it follows that the limit of any convergent subsequence of B t, C t t = 1 ∞ is in Ω B and Ω C. In this section, we evaluate the performance of the matrix factorization approach and compare it with the Group Lasso regularizer: S ̂ = argmin S 1 2 ∥ AS − Y ∥ F 2 + λ ∑ i = 1 N ∥ S ( i, : ) ∥ 2, λ > 0 (28).
The animal had never before been photographed; the only previous proof of its existence was a specimen collected by Willoughby Lowe, the British explorer for whom the animal is named, in 1932.
