Sentence examples for analytical proof is from inspiring English sources
In contrast, an analytical proof is provided to show that MIL and GST methods are strictly equivalent.
An analytical proof is presented showing that the marginal or neutral state for surface-tension-driven convection in infinite liquid layers is stationary so that the principle of exchange of stabilities is valid.
This equivalence was suggested in[12], by numerical results, but the analytical proof was missing.
This was first suggested in[12], but the analytical proof was missing, and we provided it in the 'Results and discussion' Section of this work.
We present a unified soft-core technique that ensures the monotonicity of the numerically integrated function (analytical proof) which is important for the selection of intermediates.
An analytical proof has been conducted to prove that, in the worst case, the proposed algorithm has a complexity of O(n log m).
A mathematical proof is offered that the optimization problem is convex with well-known analytical conditions (specifically, KarushKuhnTucker conditions).
Proof The proof is by contradiction.
