Algebraic properties of discrete box splines

The central objective of this paper is to discuss linear independence of translates of discrete box splines which we introduced earlier as a device for the fast computation of multivariate splines. The results obtained here allow us to draw conclusions about the structure of such discrete splines which have, in particular, applications to counting the number of nonnegative integer solutions of linear diophantine equations.     

A characterization of the \Sigma_1-definable functions of KP\omega + (uniform\; AC)

The subject of this paper is a characterization of the -definable set functions of Kripke-Platek set theory with infinity and a uniform version of axiom of choice: . This class of functions is shown to coincide with the collection of set functionals of type 1 primitive recursive in a given choice functional and . This goal is achieved by a G?del Dialectica-style functional interpretation of and a computability proof for the involved functionals. Received October 9, 1996     

Two Ergodic Sample-Path Properties of the Poisson Process

For increasing sequences of real numbers we consider two types of asymptotic behavior that remind of the defining property of a (homogeneous) Poisson process according to which the numbers of points in disjoint intervals are independent and follow Poisson distributions with specified parameters. We prove that almost all paths of a Poisson process show this asymptotic behavior, and characterize the Poisson process by these properties. Further we discuss the connection to equidistribution notions.     

AUTOMATED MECHANICAL STIMULATION AND MEASUREMENT OF BIOLUMINESCENCE IN MARINE DINOFLAGELLATES

A new integrated system for reproducible, automated mechanical stimulation and measurement of bioluminescence (BL) in multiple samples of marine dinoflagellate cell suspensions is described. The system was designed to allow the application of standardized experimental routines to parallel test vials for the purpose of toxicity testing. A sample tray delivered test vials to the position of mechanical stimulation and BL measurement. Mechanical stimulation of BL was applied as sharp rotation-onset of the test vial about its vertical axis. Thus, any direct chemical or physical perturbation of the cell suspension was avoided. A silicon photovoltaic cell measured the emitted light. Stimulation, measurement and recording of BL were integrated and controlled by specially developed software, which runs on a personal computer in the graphic environment of MS-Windows. Precise scheduling, flexible programming and identical repetition of experimental routines are possible in practice. For Gonyaulax polyedra, details of BL, as stimulated and measured with the new system, are presented and discussed. We conclude that the system exhibits specific features that offer wide potential of application in several fields of research on dinoflagellate BL, particularly for toxicity testing.