Sentence examples for proved using this from inspiring English sources

We show that various Poisson formulas for the heat kernel can be proved using this interpolation by methods of local index theory.

Decidability of type checking is proved using this syntax directed version and a correct type checker can be extracted from this proof.

Statistical significance was proved using the paired t-test.

A spectral gap can be proved using Poincaré type inequalities; this idea has been developed in [1, 4, 5] and is for smooth kernels K.

Equivalence is proved using test E2 if this confidence interval falls entirely within the equivalence interval [ EL L, EL U ]. Non-equivalence is proved using test E3 if the confidence interval falls entirely outside the equivalence interval [ EL L, EL U ].

This we prove using the decidability of Skolem Arithmetic.

This can be proved using elimination procedure [18].

Unconditional stability is proved using Von-Neumann approach.

Stability is proved using a Lyapunov approach.

Prior bounds are proved using Lyapunov function.

This can be proven using your state-issued ID.