Sentence examples for are proved using the from inspiring English sources

The unconditional stability and the high-order convergence are proved using the Fourier analysis method.

Almost all such results are proved using the PCP Theorem (and its several variants), one of the deepest theorems in computational complexity.

Robustness and convergence of the proposed schemes are proved using the second method of Lyapunov and the super-twisting algorithm.

The analytical formulas of the models are proved using the finite element method and experimental data, and the formulas are analyzed in the inner soil pressure in the same condition.

The stability and convergence of the finite difference scheme in maximum norm are proved using the energy method, where a new inner product is introduced for the theoretical analysis.

Some of our results are proved using the next well-known results.

The stability and convergence of the scheme are proven using the discrete energy method.

Linear and non-linear stability results, including A-stability, L-stability and B-stability are proven using the energy method for general initial value problems.

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

Finally, the semi-global boundedness of the proposed scheme is proved using the Lyapunov stability theory.

The stability of the closed-loop system is proved using the Lyapunov function analysis method.