We perform a Inönü–Wigner contraction on Gaudin models, showing how the integra-bility property is preserved by this algebraic procedure. Starting from Gaudin models we obtain new integrable chains, that we call Lagrange chains, associated to the same linear r-matrix structure. We give a general construction involving rational, trigonometric and elliptic… (More)
A constructive procedure to obtain superintegrable deformations of the classical Smorodinsky–Winternitz Hamiltonian by using quantum deformations of its underlying Poisson sl(2) coalgebra symmetry is introduced. Through this example, the general connection between coalgebra symmetry and quasi-maximal superintegrability is analysed. The notion of comodule… (More)
We exhibit a stochastic discrete time model that produces the Eigen model (Naturwissenschaften 58:465-523, 1971) in the deterministic and continuous time limits. The model is based on the competition among individuals differing in terms of fecundity but with the same viability. We explicitly write down the Markov matrix of the discrete time stochastic model… (More)
—Fabry–Pérot interferometry (FPI), which was originally invented for spectroscopy, is now evolving as a basic technology for ultrafine dimensional stabilization and measurement. To this end, the light path length of an optical cavity and the wavelength of a laser source injected into the cavity have to be tuned to each other through a set of frequency… (More)
In this paper we discuss the bihamiltonian formulation of the (rational XXX) Gaudin models of spin–spin interaction, generalized to the case of sl(r)–valued " spins ". In particular, we focus on the homogeneous models. We find a pencil of Poisson brackets that recursively define a complete set of integrals of the motion, alternative to the set of integrals… (More)
The development of a large noncoding fraction in eukaryotic DNA and the phenomenon of the code bloat in the field of evolutionary computations show a striking similarity. This seems to suggest that (in the presence of mechanisms of code growth) the evolution of a complex code cannot be attained without maintaining a large inactive fraction. To test this… (More)
By means of a recently introduced bihamiltonian structure for the homogeneous Gaudin models, we find a new set of Separation Coordinates for the sl(r) case.
We address the study of the classical Gaudin spin model from the bi-Hamil-tonian point of view. We describe in details the sl(2) three particle case