A p Interpolation in the Unit Ball

We study interpolating sequences in the unit ball for A^–pwith p > 0, the Banach space of holomorphic functions f with(1 – |z|²)^p |f(z)| bounded. The finite unions of A^–p-interpolatingsequences are characterized by a Carleson type condition.     

Hybrid dynamics of two coupled oscillators that can impact a fixed stop

We consider two linearly coupled masses, where one mass can have inelastic impacts with a fixed, rigid stop. This leads to the study of a two degree of freedom, piecewise linear, frictionless, unforced, constrained mechanical system. The system is governed by three types of dynamics: coupled harmonic oscillation, simple harmonic motion and discrete rebounds. Energy is dissipated discontinuously in discrete amounts, through impacts with the stop. We prove the existence of a non-zero measure set of orbits that lead to infinite impacts with the stop in a finite time. We show how to modify the mathematical model so that forward existence and uniqueness of solutions for all time is guaranteed. Existence of hybrid periodic orbits is shown. A geometrical interpretation of the dynamics based on action coordinates is used to visualize numerical simulation results for the asymptotic dynamics.     

Zero sets of holomorphic functions in the unit ball with slow growth

We study the zero-varieties of holomorphic functions in the unit ball satisfying the growth condition log |f(z)|≤c _fλ(|z|), where λ:(0,1)→ℝ⁺ is a positive increasing function. We obtain some sufficient conditions on an analytic variety to be defined by such a function. Some results for the particular case λ(r)=log(e/(1−r)), corresponding to the classA ^−∞, generalize those of B. Korenblum in one variable. Both authors supported by DGICYT grant PB92-0804-C02-02.     

A quantum-mechanical normal-mode approach to collinear collisions of identical diatomics. Perturbed stationary state formulation

A quantum mechanical perturbed stationary state study of the collinear collision of two identical diatomic molecules within the normal mode decomposition technique is presented. Various collision systems are investigated and are classified in three different groups according to their dynamical behaviour.     

On the use of high-Tc superconductors for Perot-Fabry mirrors coatings

In a very rough experiment using two MgO plates, coated with a 200 Å thick YBaCuO film to increase their reflectivity, and facing each other their YBaCuO films to make a Perot-Fabry (PF) interferometer, we have observed a 43% maximum transmission and a finesse around 33 at v=29 cm^–1, in good accordance with a new phenomenological model for YBaCuO. Much higher performances can be expected by optimizing the YBaCuO film thickness.