Sentence examples for analysis of the proof from inspiring English sources

The stability analysis of the proof mass motion is performed by transformation of the simplified model into the standard form of the Mathieu differential equation.

By the careful analysis of the proof of Theorem 3.3, we can obtain the desired result.

By the careful analysis of the proof of Theorem 3.1, we can obtain the following result.

If and f is strictly convex (strictly mid-convex), then the analysis of the proof of Theorem 1 shows that.

By the careful analysis of the proof of Corollary 3.3 and Theorem 3.5, it is not hard to derive the following result.

Similarly to the analysis of the proof of Theorem 3.1, by Barbalat's lemma (see [30]) we have lim_{trightarrowinfty}bigl(x_{2}(t -x_{2}^ bigr)^{2}=0,qquad lim_{t -x_{2}rowinfty}bigl(u(t)-u^ bigr)^{2}=0,qquad is, lim_{trightarrowinfty}bigl ut -u^{2}^, qquad lim_{t -u^tarrowinfty}u(t)=u^.

By some further analysis on the proof of Theorem 2.4 in [6], we can obtain the conclusion of Lemma 2.2 when (P (z, f )) is a differential-difference polynomial in f. ([13]).

Secondary analysis of the proof-of-concept study with Souvenaid [ 9] pointed to a potential benefit on ADAS-cog in patients with higher ADAS-cog scores (more impaired cognition) at baseline.

In this context, the fight over Nakamoto looks more like the jostling of courtiers to install a sympathetic heir to the throne than an objective analysis of the cryptographic proof.

The quantitative analysis of the convergence proof for (5) has to be left for future research.

For similar reasons, predicative mathematics does not permit the Least Upper Bound Axiom of analysis (the proof of this axiom in a set theoretical implementation of the reals as Dedekind cuts fails for the same kind of reason).