The Steep Nekhoroshev’s Theorem

Quasiplanar steep water waves.

A unique description for highly nonlinear potential water waves is suggested, where weak three-dimensional effects are included as small corrections to exact two-dimensional equations written in conformal variables. Contrary to the traditional approach, a small parameter in this theory is not a surface slope, but it is the ratio of a typical wavelength to a large transversal scale along the sec...

Antidunes on steep slopes

16 When increasing the rates of subcritical flow on gentle slopes, the bed successively produces 17 ripples, dunes and flat beds. Antidunes (defined here as all bed undulations for which the 18 surface gravity waves are in phase with the bed profile) appear only in high flow rates and 19 may be found in some extreme natural flow events. Inversely, on steep slopes flume 20 experiment (S≥1% appro...

Generation of the Ahlfors Five Islands Theorem

The steep dose-response curves of anesthesia.

To the Editor:—The critique by Eger et al. on the article by Eckenhoff and Johansson concerns combining the dose–response curves of several ion channels to make them steeper. The slopes of the in vivo studies are steep, whereas those of the in vitro studies are gradual. Both groups anticipate that when several binding sites among ion channels are combined, the dose–response curves may become st...

The Basic Theorem and its Consequences

Let T be a compact Hausdorff topological space and let M denote an n–dimensional subspace of the space C(T ), the space of real–valued continuous functions on T and let the space be equipped with the uniform norm. Zukhovitskii [7] attributes the Basic Theorem to E.Ya.Remez and gives a proof by duality. He also gives a proof due to Shnirel’man, which uses Helly’s Theorem, now the paper obtains a...