Adapting ideas of Daubechies and Klauder we derive a continuum path-integral formula for the time evolution generated by a spin Hamiltonian. For this purpose we identify the finite-dimensional spin Hilbert space with the ground-state eigenspace of a suitable Schödinger operator on L(R), the Hilbert space of square-integrable functions on the Euclidean plane R, and employ the Feynman-Kac-Itô for...

This paper introduces a novel Markov process formulation of stochastic fault growth modeling, in order to facilitate the development and analysis of prognostics-based control adaptation. A metric representing the relative deviation between the nominal output of a system and the net output that is actually enacted by an implemented prognostics-based control routine, will be used to define the ac...

Diierential equations which explicitly but discontinuously depend on time are rarely studied objects even though they promise important applications e.g. in control theory or in the theory of random dynamical systems. In this paper we continue a previous study of qualitative properties of so-called Carath eodory type diierential equations whose feature is measurable dependence of the right-hand...

‎In this paper we consider the minimization of a positive semidefinite quadratic form‎, ‎having a singular corresponding matrix $H$‎. ‎We state the dual formulation of the original problem and treat both problems only using the vectors $x in mathcal{N}(H)^perp$ instead of the classical approach of convex optimization techniques such as the null space method‎. ‎Given this approach and based on t...

The unsmooth boundary will greatly affect motion morphology of a shallow water wave, and a fractal space is introduced to establish a generalized KdV-Burgers equation with fractal derivatives. The semi-inverse method is used to establish a fractal variational formulation of the problem, which provides conservation laws in an energy form in the fractal space and possible solution structures of t...

The contribution of this paper is the formulation of the wind farm power maximization problem as a multi-stage dynamic programming problem. This formulation is made possible by introducing a state-space model to describe the evolution of the wind velocity profile as a function of the free-stream wind velocity and the wind turbine control variables. This state-space model is coupled with a multi...