The multislope ski-rental problem [LPSR08a] is an extension of the classical ski-rental problem [KMRS88], where the player has several lease options in addition to the pure rent and buy options. In this problem an instance, which is the setting of the options, significantly affects the player’s performance. There is an algorithm that for a given instance, computes the best possible strategy [AI...

The integrating factor technique is widely used to solve numerically (in particular) the Schrödinger equation in context of spectral methods. Here, we present an improvement this method exploiting freedom provided by gauge condition potential. Optimal conditions are derived considering and temporal numerical resolution with adaptive embedded scheme arbitrary order. We illustrate approach nonlin...

This work is concerned with planar real analytic differential systems with an analytic inverse integrating factor defined in a neighborhood of a regular orbit. We show that the inverse integrating factor defines an ordinary differential equation for the transition map along the orbit. When the regular orbit is a limit cycle, we can determine its associated Poincaré return map in terms of the in...

This work is concerned with planar real analytic differential systems with an analytic inverse integrating factor defined in a neighborhood of a regular orbit. We show that the inverse integrating factor defines an ordinary differential equation for the transition map along the orbit. When the regular orbit is a limit cycle, we can determine its associated Poincaré return map in terms of the in...