Entrée-sortie dans un tourbillon
On étudie un champ de vecteurs lent-rapide de nommé tourbillon pour lequel on démontre l’existence d’une fonction entrée-sortie.
On étudie un champ de vecteurs lent-rapide de nommé tourbillon pour lequel on démontre l’existence d’une fonction entrée-sortie.
In many markets, especially in energy markets, electricity markets for instance, the detention of the physical asset is quite difficult. This is also the case for crude oil as treated by Davis (2000). So one can identify a good proxy which is an asset (financial or physical) (one)whose the spot price is significantly correlated with the spot price of the underlying (e.g. electicity or crude oil). Generally, the market could become incomplete. We explicit exact hedging strategies for exponential...
We give a survey of results on global stability for deterministic compartmental epidemiological models. Using Lyapunov techniques we revisit a classical result, and give a simple proof. By the same methods we also give a new result on differential susceptibility and infectivity models with mass action and an arbitrary number of compartments. These models encompass the so-called differential infectivity and staged progression models. In the two cases we prove that if the basic reproduction ratio...
We present a unified mathematical approach to epidemiological models with parametric heterogeneity, i.e., to the models that describe individuals in the population as having specific parameter (trait) values that vary from one individuals to another. This is a natural framework to model, e.g., heterogeneity in susceptibility or infectivity of individuals. We review, along with the necessary theory, the results obtained using the discussed approach....
A fixed point theorem in ordered spaces and a recently proved monotone convergence theorem are applied to derive existence and comparison results for solutions of a functional integral equation of Volterra type and a functional impulsive Cauchy problem in an ordered Banach space. A novel feature is that equations contain locally Henstock-Kurzweil integrable functions.
Nous démontrons l’unicité des solutions faibles pour une classe d’équations de transport dont les vitesses sont partiellement à variations bornées. Nous nous intéressons à des champs de vecteurs du typeavec une borne sur la divergence de chacun des champs . Ce modèle a été étudié récemment dans [LL] par C. Le Bris et P.-L. Lions avec une régularité ; nous montrons ici également que, dans le cas , le contrôle de la divergence totale du champ est suffisant. Notre méthode consiste à démontrer...