Sentence examples for been proven using from inspiring English sources

The stability of the EASFSC has been proven using the Lyapunov stability theorem.

Most of these results have been proven using critical point theory, variational approaches or a fixed point theorem.

Analogues of the above results have been proven using different game models (e.g., epistemic models, epistemic-plausibility models, etc).

The biological role of Grb10 in promoting insulin signaling has been proven using a mouse model (Smith et al., 2007; Wang et al., 2007).

The IL has been proven using XPS to be comprised of a mixture of Ga-O, Ga-O-N, Y-O, and Y-N bonding (HJQ and KYC, unpublished work).

The positive effect of folic acid on dermal fibroblast has already been proven using the Host Cell Reactivation Assay.

The stability and robustness of the proposed controller have been proved using the classic Lyapunov criterion.

The strong bounding theorem of micromixing has been proved using Bellman's principle of optimality.

The finite time stability has been proved using the Lyapunov theory.

Remark 4.2 Equality (28) has been proved, using different method, by Luo [[11], Theorem 2.1].

Later some of these identities have been proved using only elementary techniques.