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.     

N-1 Substituted ethyl 4-pyrazolecarboxylates: Synthesis and spectroscopic investigations

The synthesis of various N-1 substituted ethyl 4-pyrazolecarboxylates via reaction of ethyl 2-formyl-3-oxo-propionate (= ethoxycarbonylmalondialdehyde) with appropriately substituted hydrazines is described. Moreover, detailed nmr-spectroscopic investigations with the title compounds are presented.     

Polyethylene compounds with antimicrobial surface properties

The present study aims at antimicrobial polyethylene surfaces. To achieve this, LLDPE was compounded with the polymeric biocide poly(2-tert-butylaminoethyl) methacrylate TBAM (bulk modification with 1.5-5.0 wt.% of TBAM). Surfaces of these polymer compounds were then subjected to microbial assays. Using standard methods the colony forming units (CFU) for Escherichia coli and Staphylococcus aureus were determined on these surfaces. In all cases, polyethylene surfaces with highly antimicrobial properties were achieved. An average reduction of 10⁴ CFU ml⁻¹ compared to neat LLDPE was achieved. The surfaces of these LLDPE/TBAM compounds were assessed by electrokinetic (zeta potential) measurements. The results indicate a relation between the antimicrobial activity and the zeta-potential of the polymer compounds. Moreover, the antimicrobial compounds were investigated towards biofilm formation. Compared to pristine LLDPE, the surfaces of the polymer compounds showed less adhering biofilm after a testing period of 16 weeks.     

On the convergence of generalized Padé approximants

Letf be an analytic function with all its singularities in a compact set \(E_f \subset \bar C\) of (logarithmic) capacity zero. The function may have branch points. The convergence of generalized (multipoint) Padé approximants to this type of function is investigated. For appropriately selected schemes of interpolation points, it is shown that close-to-diagonal sequences of generalized Padé approximants converge in capacity tof in a certain domain that can be characterized by the property of the minimal condenser capacity. Using a pole elimination procedure, another set of rational approximants tof is derived from the considered generalized Padé approximants. These new approximants converge uniformly on a given continuum \(V \subset \bar C\backslash E_f\) with a rate of convergence that has been conjectured to be best possible. The continuumV is assumed not to divide the complex plane.