Two measure preserving dynamical systems are weakly disjoint if some pointwise convergence property is satisfied by ergodic averages on their direct product (a precise definition is given below). Disjointness implies weak disjointness. We start studying this new concept, both by stating some general properties and by giving various examples. The content of the article is summarized in the intro...

In this article we obtain a Pohozaev-type inequality for Sobolev spaces with variable exponents. This inequality is used for proving the nonexistence of nontrivial weak solutions for the Dirichlet problem −∆p(x)u = |u|q(x)−2u, x ∈ Ω u(x) = 0, x ∈ ∂Ω, with non-standard growth. Our results extend those obtained by Ôtani [16].

We prove that a countable simple unidimensional theory that eliminates hyperimaginaries is supersimple. This solves a problem of Shelah in the more general context of simple theories under weak assumptions.

`̀ The worst thing one can do with words,'' wrote George Orwell a half a century ago, ``is to surrender to them.'' If language is to be `̀ an instrument for expressing and not for concealing or preventing thought,'' he continued, one must `̀ let the meaning choose the word, and not the other way about.'' The argument of this article is that the social sciences and humanities have surrendered to th...

When does a small drift increase the hitting probability of a boundary point / the expected hitting time of the boundary, compared to the driftless case? We analyze this for diffusion processes on [0,1] by expanding the Green function. In this way, in the appropriate diffusion approximation setting, we rederive and extend the one-third rule of evolutionary game theory (Nowak et al., 2004) and e...

`̀ The worst thing one can do with words,'' wrote George Orwell a half a century ago, ``is to surrender to them.'' If language is to be `̀ an instrument for expressing and not for concealing or preventing thought,'' he continued, one must `̀ let the meaning choose the word, and not the other way about.'' The argument of this article is that the social sciences and humanities have surrendered to th...

We prove that a homogeneous and isotropic universe containing a scalar field with a power-law potential, V (φ) = Aφn, with 0 < n < 1 and A > 0 always develops a finite-time singularity at which the Hubble rate and its first derivative are finite, but its second derivative diverges. These are the first examples of cosmological models with realistic matter sources that possess weak singularities ...

Spatial correlations of the observed sizes and luminosities of galaxies can be used to estimate the magnification that arises through weak gravitational lensing. However, the intrinsic properties of galaxies can be similarly correlated through local physical effects, and these present a possible contamination to the weak lensing estimation. In an earlier paper we modelled the intrinsic size cor...

In this paper we present a brief review of some important results on weak compactness in the space of vector valued measures. We also review some recent results of the author on weak compactness of any set of operator valued measures. These results are then applied to optimal structural feedback control for deterministic systems on infinite dimensional spaces.