Sentence examples for are proved based on from inspiring English sources

These strong monotonicity results are proved based on explicit computations for measures in relevant Lévy Khintchine (or actually Kolmogorov) formulas.

Some related mathematical theorems are proved, based on which the basic ideas of the generalized wavelet-Galerkin method are described in details.

The complexation between the corn starch and LiClO4 in the matrix polymers are proven based on the presence of the change in intensity, shape of peaks and shift in peaks as observed in Fourier transform infrared spectroscopy (FTIR) analysis.

Furthermore, the boundedness of covariance matrix and the convergence of the proposed filter are proven based on the strong connectivity of directed network topology and the global observability which permits the sub-system with local sensor's measurements to be unobservable.

High-ranking Nazi officers were often charged with lesser offenses only because their direct responsibility for the killing of one or more individuals could not be proved based on the narrow German jurisdiction.

Then, the asymptotic stability of the system is proved based on the Lyapunov method.

The convergence of the switching control is proved based on state sample trajectories.

The significance of velocity uniformity is proved based on the analysis and experiment.

The stability of the proposed scheme is proved based on the Lyapunov analysis method.

Their robustness is proved based on the proposed Lyapunov equation approach.

The stability of the overall closed-loop system is proved based on Lyapunov theory.