Local Nash Realizations

In this paper we investigate realization theory of a class of non-linear systems, called Nash systems. Nash systems are non-linear systems whose vector fields and readout maps are analytic semi-algebraic functions. In this paper we will present a characterization of minimality in terms of observability and reachability and show that minimal Nash systems are isomorphic. The results are local in nature, i.e. they hold only for small time intervals. The hope is that the presented results can be extended to hold globally.Comment: 8 pages, extended conference pape

Realizations of Thermal Supersymmetry

We investigate realizations of supersymmetry at finite temperature in terms of thermal superfields, in a thermally constrained superspace: the Grassmann coordinates are promoted to be time-dependent and antiperiodic, with a period given by the inverse temperature. This approach allows to formulate a Kubo-Martin-Schwinger (KMS) condition at the level of thermal superfield propagators. The latter is proven directly in thermal superspace, and is shown to imply the correct (bosonic and fermionic) KMS conditions for the component fields. In thermal superspace, we formulate thermal covariant derivatives and supercharges and derive the thermal super-Poincar\'e algebra. Finally, we briefly investigate field realizations of this thermal supersymmetry algebra, focussing on the Wess-Zumino model. The thermal superspace formalism is used to characterize the breaking of global supersymmetry at finite temperature.Comment: 27 pages, no figures, LaTeX. Typos corrected and references added. To appear in Nucl. Phys.

On one-multiplier implementations of FIR lattice structures

One-multiplier realizations for certain recently reported FIR lossless lattice structures are investigated. The multiplier extraction approach is used to show that there does not exist a real one-multiplier realization whereas it is possible to get complex one-multiplier realizations. This is unlike the situation in conventional linear-prediction FIR lattice structures, where real one-multiplier realizations are possible

Complex analytic realizations for quantum algebras

A method for obtaining complex analytic realizations for a class of deformed algebras based on their respective deformation mappings and their ordinary coherent states is introduced. Explicit results of such realizations are provided for the cases of the $q$-oscillators ($q$-Weyl-Heisenberg algebra) and for the $su_{q}(2)$ and $su_{q}(1,1)$ algebras and their co-products. They are given in terms of a series in powers of ordinary derivative operators which act on the Bargmann-Hilbert space of functions endowed with the usual integration measure. In the $q\rightarrow 1$ limit these realizations reduce to the usual analytic Bargmann realizations for the three algebras.Comment: 18 page