One of the remarkable things about this theorem is the way in which it suggests that geometry informs arithmetic. The geometric genus g is a manifestly geometric condition, yet it is controlling what seems to be an arithmetic property. Why should the number of integral solutions to xn + yn = zn have anything to do with the shape of the complex solutions? You might argue that that the genus is e...

• Banach-Alaoglu: compactness of polars • Variant Banach-Steinhaus/uniform boundedness • Second polars • Weak boundedness implies boundedness • Weak-to-strong differentiability The comparison of weak and strong differentiability is due to Grothendieck, although the original sources are not widely available.

Recently it has been shown that the conventional notions of stability in the sense of Lyapunov and asymptotic stability can be used to characterize the stability properties of a class of “logical” discrete event systems (DES). Moreover, it has been shown that stability analysis via the choice of appropriate Lyapunov functions can be used for DES and can be applied to several DES applications in...

In this paper, a novel adaptive sliding mode control for rigid robot manipulators is proposed. In the proposed system, since there may exist explicit unknown parameters and perturbations, a Lyapunov based approach is presented to increase system robustness, even in presence of arbitrarily large (but not infinite) discontinuous perturbations. To control and track the robot, a continuous controll...