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Consider a scalar O.D.E. of the form _ x = f (t; x), where f is possibly discontinuous w.r.t. both variables t; x. Under suitable assumptions , we prove that the corresponding Cauchy problem admits a unique solution, which depends HH older continuously on the initial data. Our result applies in particular to the case where f can be written in the form f (t;(More)
The paper is concerned with a non-cooperative differential game for two players. We first consider Nash equilibrium solutions in feedback form. In this case, we show that the Cauchy problem for the value functions is generically ill-posed. Looking at vanishing viscosity approximations, one can construct special solutions in the form of chattering controls,(More)
Current bacterial detection methods require the collection of samples followed by preparation and analysis in the laboratory, both time and labour consuming steps. More importantly, because of cost, only a limited number of samples can be taken and analyzed. This paper presents the results of an investigation to directly detect Salmonella typhimurium on(More)
In this paper we study a dimensionless model of granular matter. The model can be rewritten into a system of balance laws. We prove that, every sufficiently small, compactly supported perturbation of a Lipschitz continuous de-coupled initial data gives decoupled solution in finite time. Moreover, no gradient catastrophe occurs, i.e., the solution does not(More)
In this work, we try to solve the problem of day-ahead prediction of electricity demand using an ensemble forecasting model. Based on the Pattern Sequence Similarity (PSF) algorithm, we implemented five forecasting models using different clustering techniques: K-means model (as in original PSF), Self-Organizing Map model, Hierarchical Clustering model,(More)