Sentence examples for is proven by using from inspiring English sources

This result is proven by using an inductive argument.

The invertibility of this matrix and its submatrices is proven by using brute force simulations.

The non-negativity of R ( t ) ∀ t ∈ [ 0, t f ] is proven by using continuity arguments.

The finite-time stability nature of the TSMC law is proven by using a Lyapunov-based approach.

Theoretically, its weak convergence is proven by using Markov theory, while the experimental results demonstrate its strong convergence.

Property (iii) is proven by using, in addition, [[35], Lemma 3.8], one gets ∃ lim n → ∞ d ( x 2 n + 3, x 2 n + 2 ) = lim n → ∞ d ( x 2 n + 2, x 2 n + 1 ) = D ⇒ lim n → ∞ d ( x 2 n + 3, x 2 n + 1 ) = 0. for any sequence { x n } with x 1 ∈ A ∪ B and x n + 1 ∈ T x n since ( X, d ) is a uniformly convex Banach space, A and B are nonempty and disjoint closed subsets of X and A is convex.

Thus the theorem is proved by using Theorem 5.2.

This result is proved by using the implicit function theorem.

The asymptotic stability of the closed-loop MRR system is proved by using the Lyapunov theory.

Then, the stability of controlled system is proved by using Lyapunov's direct method.

The convergence of the identification error is proved by using the Lyapunov theory.