Sentence examples for be proved using the from inspiring English sources

The last equality can be proved using the polar decomposition.

In the same way, the following result can be proved using the ( O, M ) -compatibility involved in Theorem 33.

This assertion can easily be proved using the Painlevé and Liouville theorems in the Clifford analysis setting, see [1, 15].

Notice that the upper estimate in (3.54) and (3.55) can also be proved using the bounds for Jacobi-Sobolev polynomials given in Corollary 3.5.

Part (a) can be proved using the Poisson summation formula; see, e.g., [75, Chapter VII, Theorem 2.4 and Corollary 2.6]; a recent proof is given in [22].

Further results can be proved using the same plots as those of the earlier theorems in this paper, so we omit them.

That ({mathrm{Tr}} P-Q) in {mathbb {Z} P-Qas finst proven by Effros [134] and can also be proven using the Krein spectral shift [616, Problem 5.9.1].

This converse also appears in Euclid's Elements (Book I, Proposition 48): It can be proven using the law of cosines or as follows: Let ABC be a triangle with side lengths a, b, and c, with a2 + b2 = c2.

On the one hand, one could conclude that risk signatures developed on a mixture of samples perform better, but on the other hand this hypothesis cannot be proven using the HD4 dataset since the signature had been developed on it.

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.