Abstract
We present the construction of new pseudo-smooth structures, near the singularities, such that the pseudo-Anosov maps are diffeomorphisms, in this pseudo-smooth structures, and have the property that the stable and unstable foliations are uniformly contracted and expanded by the pseudo-Anosov dynamics. We construct the C(1+) orthogonal charts of such pseudo-Anosov diffeomoprhisms.

Abstract
The theory of planned behaviour studies the decision-making mechanisms of individuals. We propose the Bayesian-Nash equilibria as one, of many, possible mechanisms of transforming human intentions in behaviour. This process corresponds to the best strategic individual decision taking in account the collective response. We show that saturation, boredom and frustration can lead to splitted strategies, in opposition to no saturation that leads to a constant strategy.

Abstract
We study the problem of determination of asset prices in an incomplete market proposing three different but related scenarios. One scenario uses a market game approach whereas the other two are based on risk sharing or regret minimizing considerations. Dynamical schemes modelling the convergence of the buyer's and of the seller's prices to a unique price are proposed.

Abstract
The consequences of regulatory T cell (Treg) inhibition of interleukine 2 secretion are examined by mathematical modelling. We determine the analytic formula that describes the fine balance between Regulatory T cells and T cells at controlled and immune response equilibrium states. We demonstrate that cytokine dependent growth exhibits a quorum T cell population threshold that determines if immune responses develop on activation. We determine the analytic formulas of T cell proliferation thresholds that allow us to study the sensibility of the quorum growth thresholds controlling immune responses.

Abstract
We study a mathematical model of immune response by T cells where the regulatory T cells (Treg) inhibit interleukin 2 secretion. The bystander proliferation to an immune response is modelled. We consider an asymmetry reflecting that the difference between the growth and death rates can be higher for the active T cells and Tregs than for the inactive. This asymmetry leads to a better understanding of the bystander proliferation. An exposure to a pathogen results in an increased proliferation rate of the bystander T cells. If the population of the bystander T cells becomes large enough, autoimmunity can arise, eventually after a long transient period.

Abstract
We introduce a resort pricing model, where different types of tourists choose between different resorts. We study the influence of the resort prices on the choices of the different types of tourists. We characterize the coherent strategies of the tourists that are Nash equilibria. We find the prices that lead to the bankruptcy of the resorts and, in particular, their dependence on the characteristics of the tourists.