Sentence examples for proven using from inspiring English sources

Convergence is proven, using a Lyapounov function.

Finite time stability and convergence are proven using Lyapunov theory.

Each question is divided into two articles, the first proven using rational premises and the second proven using premises drawn from faith.

Case 1. ∥ u ∥ p = 1 ⇔ ρ p ( u ) = 1 is proven using Proposition 2.2.

They can be proven using standard techniques applied to the present matrix context.

The correctness of these rules can be proven using their respective decision tables.

The validity and effectiveness of the proposed method are proven using simulation and laboratory tests.

The corollaries can all be proven using standard Aizenman Lieb arguments from [1].

Equation (6) can be alternatively and more rigorously proven using an inductive argument.

The performance and efficiency of the method was proven using several simulations.

The structure of the compounds was proven using spectral methods (IR, 1H-NMR, 13C-NMR, MS).