New aspects of the luminescence of magnesiumtitanate part I: Activation with chromium

Mg₂TiO₄:Cr³⁺ annealed at 560°C shows luminescence properties which differ considerably from those of the unannealed phosphor used so far. In both cases the regular Cr³⁺ ions only absorb the irradiated energy transferring it radiationless to the real luminescence centres, but the annealed phosphor reveals a new spectrum consisting of a few sharp lines. The radiance of the single lines can be influenced by powdering, which in connection with the annealing effect shows that the centres of both types of phosphors consist of clusters of lattice defects and octahedrally coordinated Cr³⁺ ions. These clusters or associates form themselves by thermal diffusion during the annealing process. Furthermore criteria have been found showing that the R lines do not come from only one but from two Cr³⁺ ions situated in non-equivalent lattice sites.     

Radiative and nonradiative lifetimes in excited states of Ar,Kr and Xe atoms in a neon matrix

Synchrotron radiation with its intense continuum and its excellent time structure has been exploited for time resolved luminescence spectroscopy in the solid state. By selective excitation of n = 1, n′ = 2 exciton states of Xe, Kr and Ar atoms in a neon matrix we were able to identify the emitting states involved. Lifetimes within the cascade of radiative and radiationless relaxation between excited states as well as the radiative lifetimes for transitions to the ground state have been derived from the decay curves. Energy positions and radiative lifetimes of the emitting states correspond quite well with those of the free atoms. Radiative and radiationless relaxation processes take place within the manifold of excited states of the guest atoms. The rate constants for radiationless decay confirm an energy gap law. The order of the radiationless processes reaches in some cases extremely high values. Selection rules for spin and angular momentum are essential to understand the observed radiationless transition rates.     

A mathematical model of an anthrax epizoötic in the Kruger National Park

An outbreak of anthrax in a single homogeneous geographical region is modelled. The spread of the disease to neigbouring regions is also simulated and the model is compared with data from the 1970 epizoötic in the Kruger National Park.Two possible driving mechanisms for the epizoötic are proposed and examined, viz. environmental contamination or direct contact between vulnerable animals and fresh carcases. In the latter case, it is shown that the model exhibits a threshold effect, in that an epizoötic will only arise if the vulnerable population exceeds a threshold value which is determined in terms of one of the parameters of the model.     

Layered Ising model: Spontaneous magnetization under influence of grain boundaries and surfaces

The extrema of the position dependent spontaneous magnetization in a periodically layered two-dimensional Ising model are calculated exactly. Theor asymptotic behaviour for large width of a homogeneous sublayer is given, the magnetization increase far from a free surface discussed.     

The Lévy-Hinčin representation for random compact convex subsets which are infinitely divisible under Minkowski addition

Summary This paper establishes the Lévy-Hinčin representation for all random compact convex subsets of ℝ which are infinitely divisible for Minkowski addition. Research partially supported by NSF grants No. MCS 8100728 and DMS-8318610 Research partially supported by NSF grant No. MCS 8301326     

Central limit theorem and weak law of large numbers with rates for martingales in Banach spaces

This paper is concerned with large-$\text{O}$ error estimates concerning convergence in distribution as well as norm convergence for Banach space-valued martingale difference sequences. Indeed, two general limit theorems equipped with rates of convergence for such difference sequences are established. Applications of these lead to the central limit theorem and the weak law of large numbers with rates for Banach space-valued martingales.     

Nucleic acid based biosensors: the desires of the user

The need for nucleic acid based diagnostic tests has increased enormously in the last few years. On the one hand, this has been stimulated by the discovery of new hereditary genetic disease loci following the completion of the Human Genome Project, but also by the presence of new rapidly spreading viral threats, such as that of the SARS epidemic, or even micro-organisms released for the purpose of biological warfare. As in many instances rapid diagnoses of specific target genetic loci is required, new strategies have to be developed, which will allow this to be achieved directly at the point-of-care setting. One of these avenues being explored is that of biosensors. In this review, we provide an overview of the current state of the art concerning the high-throughput analysis of nucleic acids, and address future requirements, which will hopefully be met by new biosensor-based developments.