Unitary rotation of square-pixellated images

The unitary rotation of square-pixellated images is based on the finite su(2)-oscillator model, which describes systems whose values for position, momentum and energy, are discrete and finite. In a two-dimensional position space, this allows the construction of angular momentum states, orthonormal and complete, for which rotations are defined as multiplication by phases that carry the rotation angle. The decomposition of a digital square images in terms of these angular momentum states determines a unitary (hence invertible) rotation of the image, whose kernel can be computed as a four-dimensional array of real numbers.     

Preparation,characterization, crystal and molecular structure of Na2[N(CH2COO)3 99Tc(IV) (μ-O)2 99Tc(IV)N(CH2COO)3] · 6H2O

The title compound and its potassium analog have been prepared from corresponding aqueous solutions of ⁹⁹TcO at pH ≈? 2 with SO₂ as a reducing agent. An X-ray structure determination of the Na-salt showed Tc coordinated to the tetradentate N(CH₂COO) ligand (NTA). Two Tc-NTA moieties are joined via two bridging O-atoms into a four-membered Tc₂O₂ ring. The observed diamagnetism, a strong absorption band at 19 950 cm^?1, and a short Tc-Tc distance of 2.363 Å are typical for the Tc₂O₂-fragment with its strong metal-metal interaction. The structural trans-influence at Tc and the network of H-bonds are consistent with Tc in oxidation state IV.     

Eine Charakterisierung der Schwartzschen Distributionen

Ohne ZusammenfassungHerrn ProfessorGottfried Köthe zum 60. Geburtstag gewidmet     

Adsorbed surfactants as templates for the synthesis of morphologically controlled polyaniline and polypyrrole nanostructures on flat surfaces: from spheres to wires to flat films

Nanostructures of polyaniline (PAni) and polypyrrole (PPy) with controlled morphologies have been synthesized on atomically flat surfaces using adsorbed surfactant molecules as templates. Atomic force microscopy (AFM) has been used to investigate polymer film formation on highly oriented pyrolytic graphite (HOPG) and chemically modified HOPG. Morphological control over the resulting polymer film is possible by the addition of coadsorbing molecules, manipulation of the length of the surfactant hydrophobe, or by changing the surface chemistry of the adsorbing substrate. Phase transitions between spheres, cylinders/wires, and featureless films have been observed which exactly parallel transitions between spheres, cylinders, and flat layers in the adsorbed surfactant. Parallel arrays of PAni nanowires can be synthesized with alignment evident over large areas in a simple self-assembly technique in which fabrication and arrangement take place simultaneously. Such a technique in which one can engineer sub-100-nm-ordered nanoscale pi-conjugated polymer structures of a desired shape by a simple self-assembly process presents potential as templates, sensors, and microelectronic devices.