Sentence examples for be proved using a from inspiring English sources
The proposition can be proved using a similar method as that in [25].
The following lemma can be proved using a similar argument as in the proof of Theorem 2.6 in [4].
The second claim that the expanding slope must be bounded below by (gamma') can be proved using a similar contradiction argument to above.
Notice that "any hyperconvex norm on " means essentially (i.e., up to an isometric isomorphism) the maximum norm; this follows from Theorem 2.6 and can also be proved using a geometric argument (see [19, Theorem 4.1]).
Furthermore, it is a convex function in S and its global minimum is (21) S = S ∼ ○ α (W T W ) + + 2 γ S 0 2 γ S ∼ + α (W T W ) − + α diag (W T W J J K. can be proved using a similar idea to that in (Ding et al., 2006) by validating (i) L (S ) ≤ Z (S, S ∼ ), (ii) L (S ) = Z (S, S ) (iii) Z (S, S ∼ ) is convex with respect to S. The formal proof is provided in the Supplementary Material.
The operator T is clearly p-concave, but T is not Fatou, which can be proved using an argument similar to the one given in Example 3.
If so, author' claim "the main argument is based on the difference between distributions and was shown to be significant" should be proved using an appropriate sampling and statistical testing (may be not only by visual inspection of the functions on the plots).
Instead, non-conserved miRNAs must be proven using a combination of detailed analyses of their sequence, biogenesis, secondary structure, expression patterns, and silencing functions.
The stability analysis in the paper is proved using a well-known Lyapunov stability theory.
The existence of a variational solution is proved, using a special property of the nonlinear operator.
