We prove that for a subring R⊆Q and free group F of rank at least 2 the length Bousfield's HR-localization tower is ω+ω. The key ingredient proof theory polynomial functors over Q.

In this paper we study the problem of learning context-free grammar from a corpus. We investigate a technique that is based on the notion of minimum description length of the corpus. A cost as a function of grammar is defined as the sum of the number of bits required for the representation of a grammar and the number of bits required for the derivation of the corpus using that grammar. On the A...

The paper deals with a special problem concerning the transport of electrically charged species via di usion, drift, and reaction mechanisms. We prove for a variety of models that without knowing any a priori estimate for the chemical potentials one can estimate the free energy from above by the corresponding dissipation rate. The inequality presented here can be interpreted as a nonlinear anal...