Supersymmetry, homology with twisted coefficients and n-dimensional knots

Let $n$ be any natural number. Let $K$ be any $n$-dimensional knot in $S^{n+2}$. We define a supersymmetric quantum system for $K$ with the following properties. We firstly construct a set of functional spaces (spaces of fermionic \{resp. bosonic\} states) and a set of operators (supersymmetric infinitesimal transformations) in an explicit way. Thus we obtain a set of the Witten indexes for $K$. Our Witten indexes are topological invariants for $n$-dimensional knots. Our Witten indexes are not zero in general. If $K$ is equivalent to the trivial knot, all of our Witten indexes are zero. Our Witten indexes restrict the Alexander polynomials of $n$-knots. If one of our Witten indexes for an $n$-knot $K$ is nonzero, then one of the Alexander polynomials of $K$ is nontrivial. Our Witten indexes are connected with homology with twisted coefficients. Roughly speaking, our Witten indexes have path integral representation by using a usual manner of supersymmetric theory.Comment: 10pages, no figure

Reducing DMU fuel consumption by means of hybrid energy storage

Purpose: This paper discusses a hybrid energy storage concept and its control strategy for hydro-mechanical DMUs. The hybrid energy storage consists of double layer capacitors and batteries. The new concept aims on reducing fuel consumption and avoiding unhealthy emissions during idling in station area. Methods: Development of a hybrid propulsion concept and control strategy requires adequate methods for modeling system behavior. The simulation environment Dymola is used to develop and evaluate the control strategy and for dimensioning the system components. Results: Simulations indicated fuel savings of up to 13% depending on track characteristics. Measurements of a scaled storage system in a HiL-environment showed good accordance of the simulated and measured behavior of battery and double layer capacitor. Conclusions: The newly developed storage system and its control strategy enable reduction of fuel consumption and unhealthy emissions in station areas