We study p-harmonic functions on metric measure spaces, which are formulated as minimizers to certain energy functionals. For spaces supporting a p-Poincaré inequality, we show that such functions satisfy an infinitesmal Lipschitz condition almost everywhere. This result is essentially sharp, since there are examples of metric spaces and p-harmonic functions that fail to be locally Lipschitz co...

In this paper we present new results for differentiability of delay systems with respect to initial conditions and delays. After motivating our results with a wide range of delay examples arising in biology applications, we further note the need for sensitivity functions (both traditional and generalized sensitivity functions), especially in control and estimation problems. We summarize general...

The global exponential stability is investigated for a class of generalized Cohen–Grossberg neural networks with discrete delays. By means of the combination of the nonlinear measure approach and constructing a novel Lyapunov functional together with some nonlinear functional analysis and inequality techniques, general sufficient conditions are obtained for the existence, uniqueness and global ...

Let us now come to our first attempts to define fractals in an intrinsic way and to deal with infinities and with their non-differentiability. We first consider the case of fractal curves drawn in a plane. The von Koch construction may be generalized in the complex plane by first giving ourselves a base (or “generator”) F1 made of p segments of length 1/q. The coordinates of the p points Pj of ...

There are multiple reasons why anisotropic basis functions may be needed or be more appropriate. The most obvious is that if the basis function is to be defined on Rn × T then there is no natural norm on this space that would reflect the unique properties of time. A second reason is that function being interpolated or approximated may incorporate a directional dependence. Thirdly, differentiabi...

presented here is a generalization of the implicit enumeration algorithm that can be applied when the objec-tive function is being maximized and can be rewritten as the difference of two non-decreasing functions. also developed is a computational algorithm, named linear speedup, to use whatever explicit linear constraints are present to speedup the search for a solution. the method is easy to u...