White-light imaging with fractal zone plates

We report the achievement of the first images to our knowledge obtained with a fractal zone plates (FraZPs). FraZPs are diffractive lenses characterized by the fractal structure of their foci. This property predicts an improved performance of FraZPs as image forming devices with an extended depth of field and predicts a reduced chromatic aberration under white-light illumination. These theoretical predictions are confirmed experimentally in this work. We show that the polychromatic modulation transfer function of a FraZP affected by defocus is about two times better than one corresponding to a Fresnel zone plate.     

Threshold strangeness production in pp interactions

During the actual lectures, features of the COSY-Jülich accelerator were presented, followed by a short summary of ongoing experiments at the COoler SYnchrotron COSY using internal as well as external beams in the range of 45 MeV to 2.5 GeV. Here the research of the COSY-11 collaboration is presented. This °⁰ facility studies the hidden and open strangeness production observing the ν and η′ as well the K⁺Y and K⁺K^? production in the proton—proton interactions at the respective thresholds.     

Geometric Analysis and Symbol Calculus: Fourier Transform Magnetic Resonance Imaging and Wavelets

Due to its unequalled advantages, the magnetic resonance imaging (MRI) modality has truly revolutionized the diagnosis and evaluation of pathology. Because many morphological anatomic details that may not be visualized by other high tech imaging methods can now be readily shown by diagnostic MRI, it has already become the standard modality by which all other clinical imaging techniques are measured. The unique quantum physical basis of the MRI modality combined with the imaging capabilities of current computer technology has made this imaging modality a target of interdisciplinary interest for clinicians, physicists, biologists, engineers, and mathematicians. Due to the fact that MRI scanners perform corticomorphic processing, this modality is by far more complex than all the other high tech clinical imaging techniques. The purpose of this paper is to outline a phase coherent wavelet approach to Fourier transform MRI. It is based on distributional harmonic analysis on the Heisenberg nilpotent Lie group G and the associated symplectically invariant symbol calculus of pseudodifferential operators. The contour and contrast resolution of MRI scans which is controlled by symplectic filter bank processing gives the noninvasive MRI modality superiority over X-ray computed tomography (CT) in soft tissue differentiation.     

Actinide Organometallic Complexes with π-Ligands

Recent developments and results from the organometallic chemistry of the actinides are reviewed. In the last one and a half years the structural data of about 15 organometallic complexes of transuranium actinides (Np or Pu) have been published, all involving π-ligands in the coordination sphere of the metal ion. On the basis of these data, a comparison of these molecules is presented. Depending on the steric demands of the ligands, effects like the actinide contraction seem to be stronger or weaker in the structural features. This indicates that the interplay between the actinide ion and the π-ligand is rather flexible, enabling the formation of stable bonds over a broad range of actinide ion oxidation states.     

Electrical analogy of transient heat flow in laser rods

An analog circuit is presented for the determination of the transient thermal profile in optically pumped laser rods. The model can be used to simulate the behavior of solid and hollow cylindrical rods under single shot and repetition rate conditions. The design of a particular circuit is given as well as experimental results.     

Impact of the sublinear photoconductivity law on the interpretation of holographic results in BaTiO3

Thick holographic refractive index gratings are written in nominally pure and in iron doped BaTiO₃ crystals. The phase shift between refractive index grating and light pattern is studied as a function of an externally applied electric field by a direct phase shift measuring technique. The choice of the method is suggested by a theoretical analysis which allows for the effect of a nonlinear relation between photoconductivity and light intensity on the holographic writing process.     

Frobenius-Perron operators and approximation of invariant measures for set-valued dynamical systems

A set-valued dynamical systemF on a Borel spaceX induces a set-valued operatorF onM(X) — the set of probability measures onX. We define arepresentation ofF, each of which induces an explicitly defined selection ofF; and use this to extend the notions of invariant measure and Frobenius-Perron operators to set-valued maps. We also extend a method ofS. Ulam to Markov finite approximations of invariant measures to the set-valued case and show how this leads to the approximation ofT-invariant measures for transformations , whereT corresponds to the closure of the graph of .