Sets of sampling and interpolation in Bergman spaces

Properties of the unions of sampling and interpolation sets for Bergman spaces are discussed in conjunction with the examples given by Seip (1993). Their relationship to the classical interpolation sequences is explored. In addition, the role played by canonical divisors in the study of these sets is examined and an example of a sampling set is constructed in the disk.

     

Common luminescence intensity fluctuations of single particle and single molecules in non-conducing matrices

Optical spectroscopy in combination with wide field or confocal optical microscopy enables the investigation of single quantum objects such as organic molecules, II/VI semiconductor quantum dots and silicon nanocrystals. They all have fluctuations of luminescence intensities on time scales longer than μs in common. A comparison reveals that despite the large differences of the nature of the respective quantum objects, the intensity fluctuations are related to a slow ionisation process followed by a trapping of the photoejected charge in the non-conducing environment. Detailed aspects of the dynamics are controlled by the dielectric properties of the matrix.     

Amorphous Fe–Mg alloy thin films: magnetic properties and atomic vibrational dynamics

Amorphous (a-) Fe _x Mg_1?x alloys are interesting materials for the investigation of non-Debye-like low-energy vibrational excitations. We have prepared a-Fe _x Mg_1?x alloy thin films (0.3 ≤ × ≤0.7) by vapour quenching. The amorphous state was confirmed by conversion electron Mössbauer spectroscopy between 4.2–300 K, and the x- and temperature-dependence of the isomer shift and hyperfine magnetic field was measured. For x= 0.6 and 0.7, magnetic ordering occurs below ~150 K. The atomic vibrational density of states, g(E), was determined by nuclear resonant inelastic scattering, providing clear evidence for the non-Debye-like low-energy vibrational excitations.     

Of Dogs and Fleas: The Dynamics of N Uncoupled Two-State Systems

The historical Ehrenfest model dating back to 1907 describes the process of equilibration together with fluctuations around the thermal equilibrium. This approach represents a special case in the dynamics of N uncoupled two-state systems. In this article we present a generalization of the original model by introducing an additional parameter p which denotes the probability of a single state change. Analytical solutions for the probability distribution of the system's state as well as the fluctuation distribution are derived. Interestingly, close inspection of the fluctuation distribution reveals an intrinsic time scale. Sampling the system's state at much slower rates yields the familiar macroscopic exponential distribution for equilibrium processes. For faster measurements a power law extends roughly over log₁₀ N orders of magnitude followed by an exponential tail. At some point, further increases of the sampling rate merely result in a shift of the fluctuation distribution towards higher values leaving plateau at small fluctuation sizes behind. Since the generic solution is rather unwieldy, we derive and discuss simple and intuitive analytical solutions in the limit of small p and large N. Furthermore, we relax the quantization of time by considering a complementary approach in continuous time. Finally we demonstrate that the fluctuation distributions resulting from the two different approaches bear identical characteristic features.     

Estimating the strength of chaos from the power spectrum

It is rigorously proved that for nonlinear dynamical systems whose time dependence is described by one dimensional, everywhere expanding maps, the width of broadband noise in the power spectrum is bounded by the generalized entropiesK ₂ andK ₃, which measure the strength of chaos in this system asK ₂2K ₃.Dedicated to Professor Harry Thomas on the occasion of his 60th birthday     

A graph-theoretic approach to quantitative structure—activity/reactivity studies

Characterization of molecular species based on the use of suitable graph invariants (graph paths, in particular) can provide a quantitative means of encoding structure; the technique is complementary to commoner approaches to studies of quantitative structure— activity relationships. Graph path encoding is here applied to quantitative studies of relationships between molecular structures and biological activity; the examples are the rates of various substrate reactions with hexoldnase, and the potential opiate-like activity of enkephalin analogs.