arXiv subjects
Publications and source records attributed to Nadja Kutz.
The following is an outline of possible strategies in using semantic web techniques and math with regard to environmental issues. The article uses concrete examples and applications and provides partially a rather basic treatment of semantic web techniques and math in order to adress a broader audience.
A proposal to store unsteady energy in potential energy via lifting masses with a rough quantitative overview. Some applications and methods to harvest the potential energy are also given. A focus is put on photovoltaically generated energy.
The article collects arguments for the necessity of a global academic internet platform, which is organized as a kind of ``global scientific parliament''. With such a constitution educational and research institutions will have direct means for communicating scientific results, as well as a platform for representing academia and scientific life in the public.
Flows on (or variations of) discrete curves in $\R^2$ give rise to flows on a subalgebra of functions on that curve. For a special choice of flows and a certain subalgebra this is described by the Toda lattice hierachy. In the paper it is shown that the canonical symplectic structure on $\R^{2N}$, which can be interpreted as the phase space of closed discrete curves in $\R^2$ with length $N,$ induces Poisson commutation relations on the above mentioned subalgebra which yield the tri-hamiltonian poisson structure of the Toda lattice hierachy.
In this paper we investigate flows on discrete curves in $\C^2$, $\CP^1$, and $\C$. A novel interpretation of the one dimensional Toda lattice hierarchy and reductions thereof as flows on discrete curves will be given.
It is shown that the factorization relation on simple Lie groups with standard Poisson Lie structure restricted to Coxeter symplectic leaves gives an integrable dynamical system. This system can be regarded as a discretization of the Toda flow. In case of $SL_n$ the integrals of the factorization dynamics are integrals of the relativistic Toda system. A substantial part of the paper is devoted to the study of symplectic leaves in simple complex Lie groups, its Borel subgroups and their doubles.
We extend the notion of space shifts introduced by L. D. Faddeev and A. Yu. Volkov (Phys. Lett. B 315 (1993)) for certain quantum light cone lattice equations of sine-Gordon type at root of unity. As a result we obtain a compatibility equation for the roots of central elements within the algebra of observables (also called current algebra). The equation which is obtained by exponentiating these roots is exactly the evolution equation for the "classical background" as described in V. Bazhanov, A. Bobenko, N. Reshetikhin (Comm. Math. Phys. 175 (1996)). As an application for the introduced constructions, a one to one correspondence between a special case of the quantum light cone lattice equations of sine-Gordon type and free massive fermions on a lattice as constructed in Destri and de Vega (Nucl. Phys. B 290 (1987)) is derived.