Sentence examples for establish rigorously from inspiring English sources

In classical geometry Archimedes had advanced farthest in this part of mathematics, having used the method of exhaustion to establish rigorously various results on areas and volumes and having derived for some curves (e.g., the spiral) significant results concerning tangents.

There are several reasons why it should be interesting to establish rigorously that spectral thinness provides a low variance.

This is maybe not so easy to do, but is certainly a very important thing to establish rigorously as it is the key part of the authors' model.

Stability and convergence of the method are established rigorously.

The existence, stability and convergence of numerical solutions of the proposed numerical schemes are established rigorously.

(This can be established rigorously with an argument based on random sampling of gametes, analogous to the argument used in the one-locus case).

Accuracy, stability, and convergence of the semidiscrete approximation to Maxwell's equations is established rigorously and bounds on the growth of the global divergence error are provided.

Water purification, meat inspection, corporate accounting oversight, stocks and mutual fund trading limitations, natural resources preservation -- relaxation of controls in these and other areas all tell one story: human greed leads inevitably to sacrifice of safety for profit, unless protective regulations are established and rigorously enforced.

The situation changed, however, once the Stoics had established a rigorously physicalist system ruled by an all-pervasive divine mind.

Secondly, on the basis of gas-water two phase conservation equations of mass and momentum, the relationship between pressure and saturation is established through rigorously derivation.

But this sensitivity will have to be established more rigorously by simulations.