Almost periodic evolution systems with impulse action at state-dependent moments

We study the existence of almost periodic solutions for semi-linear abstract parabolic evolution equations with impulse action at state-dependent moments. In particular, we present conditions excluding the beating phenomenon in these systems. The main result is illustrated with an example of impulsive diffusive logistic equation.Comment: 16 pages, minor changes from the previous versio

Existence results for a fourth order partial differential equation arising in condensed matter physics

We study a higher order parabolic partial differential equation that arises in the context of condensed matter physics. It is a fourth order semilinear equation whose nonlinearity is the determinant of the Hessian matrix of the solution. We consider this model in a bounded domain of the real plane and study its stationary solutions both when the geometry of this domain is arbitrary and when it is the unit ball and the solution is radially symmetric. We also consider the initial-boundary value problem for the full parabolic equation. We summarize our results on existence of solutions in these cases and propose an open problem related to the existence of self-similar solutions.Comment: To appear in Mathematica Bohemic

A Hardware Implementation of Artificial Neural Network Using Field Programmable Gate Arrays

An artificial neural network algorithm is implemented using a field programmable gate array hardware. One hidden layer is used in the feed-forward neural network structure in order to discriminate one class of patterns from the other class in real time. With five 8-bit input patterns, six hidden nodes, and one 8-bit output, the implemented hardware neural network makes decision on a set of input patterns in 11 clocks and the result is identical to what to expect from off-line computation. This implementation may be used in level 1 hardware triggers in high energy physics experimentsComment: 13 pages, 4 figures, submitted to Nucl. Instr. Meth.