We prove two relative local variational principles of topological pressure functions P (T,F ,U , y) and P (T,F ,U|Y ) for a given factor map π, an open cover U and a subadditive sequence of real-valued continuous functions F . By proving the upper semi-continuity and affinity of the entropy maps h{·}(T,U | Y ) and h+{·}(T,U | Y ) on the space of all invariant Borel probability measures, we show...

An ultrafilter U on a countable base set B has continuous Tukey reductions if whenever an ultrafilter V is Tukey reducible to U , then every monotone cofinal map f : U → V is continuous with respect to the Cantor topology, when restricted to some cofinal subset of U . We show that the slightly stronger property of having basic Tukey reductions is inherited under Tukey reducibility. It follows t...

Here we prove an o-minimal fixed point theorem for definable continuous maps on definably compact definable sets, generalizing Brumfiel’s version of the Hopf fixed point theorem for semi-algebraic maps. Résumé Dans cet article nous montrons un théorème de point fixe o-minimal pour les applications définissables continues sur les ensembles définissables et définissablement compacts, qui générali...

Recently, quantile regression (QR) models are often applied for longitudinal data analysis. When the distribution of responses seems to be skew and asymmetric due to outliers and heavy-tails, QR models may work suitably. In this paper, a semi-parametric quantile regression model is developed for analysing continuous longitudinal responses. The error term's distribution is assumed to be Asymmetr...

I am very honoured and pleased to participate in the commemoration of the 50 th anniversary of the founding of the CWI of the Dutch Foundation Mathematical Centre. The subject of my talk is concerned not with diierential equations but with something that is used all the time in various nonlinear analytic problems , namely degree theory. It seems particularly appropriate to speak on this subject...

Heterogeneity is one of the distinguishing features in spatial econometric models. It is a frequent problem in applied work and can be very damaging for statistical inference. In this paper, we focus on the problems implied by the existence of instabilities in the mechanism of spatial dependence in a spatial lag model, assuming that the other terms of the specification remain stable. We begin t...