Spectral gaps for water waves above a corrugated bottom

In this paper, the essential spectrum of the linear problem on water waves in a water layer and in a channel with a gently corrugated bottom is studied. We show that, under a certain geometric condition, the essential spectrum has spectral gaps. In other words, there exist intervals in the positive real semi-axis that are free of the spectrum but have their endpoints in it. The position and the length of the gaps are found out by applying an asymptotic analysis to the model problem in the periodicity cell

The loyal dissident: N.A. Bernstein and the double-edged sword of Stalinism

Nikolai Aleksandrovich Bernstein (1896-1966) studied movement in order to understand the brain. Contra Pavlov, he saw movements (thus, the brain) as coordinated. For Bernstein, the cortex was a stochastic device; the more cortexes an animal species has, the more variable its actions will be. Actions are planned with a stochastic "model of the future," and relevance is established through blind mathematical search. In the 1950 neoPavlovian affair, he came under strong attack and had to stop experimenting. It is argued that the consistency of his work derived both from both dialectical materialism and the relentless attacks of the neoPavlovians. Copyright © Taylor & Francis Group, LLC

Diagonal spherical means

We introduce a mean for functions and distributions of two vector variables, (Formula presented.) , the diagonal spherical mean K, defined as (Formula presented.) We study several properties of these means as well as identities satisfied by them. We show that the Dirac delta function in the diagonal of the unit ball (Formula presented.) in (Formula presented.) admits a representation as the diagonal spherical mean of certain kernels κ, (Formula presented.) distributionally for (Formula presented.). These representations of the delta function solve the problem of reconstruction of a distribution with compact support inside (Formula presented.) if its standard spherical Radon transform is known in the boundary (Formula presented.)