Global Laurent expansions on Riemann surfaces

We discuss global Laurent expansions for meromorphich-forms on a compact Riemann surface of genusg2. Our approach is motivated by Krichever and Novikov's work on string theory.Supported in part by the Department of Energy under Grant DE-FG02-88ER25065     

Preparation of tissue samples for X-ray fluorescence microscopy

As is well-known, trace elements, especially metals, play an important role in the pathogenesis of many disorders. The topographic and quantitative elemental analysis of pathologically changed tissues may shed some new light on processes leading to the degeneration of cells in the case of selected diseases. An ideal and powerful tool for such purpose is the Synchrotron Microbeam X-ray Fluorescence technique. It enables the carrying out of investigations of the elemental composition of tissues even at the single cell level.

The tissue samples for histopathological investigations are routinely fixed and embedded in paraffin. The authors try to verify the usefulness of such prepared tissue sections for elemental analysis with the use of X-ray fluorescence microscopy. Studies were performed on rat brain samples. Changes in elemental composition caused by fixation in formalin or paraformaldehyde and embedding in paraffin were examined.

Measurements were carried out at the bending magnet beamline L of the Hamburger Synchrotronstrahlungslabor HASYLAB in Hamburg.

The decrease in mass per unit area of K, Br and the increase in P, S, Fe, Cu and Zn in the tissue were observed as a result of the fixation. For the samples embedded in paraffin, a lower level of most elements was observed. Additionally, for these samples, changes in the composition of some elements were not uniform for different analyzed areas of rat brain.     

Local rings of singularities andN=2 supersymmetric quantum mechanics

We investigate the Kähler structure arising inn-component,N=2 supersymmetric quantum mechanics. We defineL ²-cohomology groups of a modified and relate them to the corresponding spaces of harmonic forms. We prove that the cohomology is concentrated in the middle dimension, and is isomorphic to the direct sum of the local rings of the singularities of the superpotential. In the physics language, this means that the number of ground states is equal to the absolute value of the index of the supercharge, and each ground state contains exactlyn fermions.Supported in part by the Department of Energy under Grant DE-F602-88ER25065     

Spectroscopic properties of neodymium(III)-containing polyoxometalates in aqueous solution

The spectroscopic properties of the neodymium(III)-containing polyoxometalates (POMs) [Nd(PW(11)O(39))(2)](11-), [Nd(PMo(2)W(9)O(39))(2)](11-), [Nd(PMo(4)W(7)O(39))(2)](11-), [Nd(PMo(6)W(5)O(39))(2)](11-), [Nd(SiMo(2)W(9)O(39))(2)](13-), [Nd(P(2)W(17)O(61))(2)](17-), [NdW(10)O(36)](9-), [NdP(5)W(30)O(110)](12-) and [NdAs(4)W(40)O(140)](25-) are described. Absorption spectra of aqueous solutions of the complexes have been recorded and the transition intensities are parameterised in terms of the Judd-Ofelt intensity parameters Omega(lambda) (lambda=2, 4, 6). Marked differences were found between the luminescence lifetimes of the complexes of the type Nd(POM) and those of the type Nd(POM)(2), due to a better shielding of the neodymium(III) ions from the bulk water molecules in the latter type of complexes.     

Convenient processes for the synthesis of aromatic ketones from aryl bromides and carboxylic anhydrides using a cobalt catalysis

The cross-coupling of various para- and meta-substituted aromatic bromides, mostly bearing sensitive moieties, with several carboxylic acid anhydrides is reported. This reaction can be carried out in two steps, by forming an aromatic organozinc reagent via cobalt catalysis in the first step, or even more interestingly in a single step, also by using a cobalt-based catalyst. The aromatic ketones are obtained by these new, mild, and convenient methods in 30-79% yields versus starting aryl bromide. Results are also disclosed that suggest the role played by cobalt species in the coupling of organozinc reagents with electrophiles could be similar to those of more commonplace transition metal complexes.     

Quantitative strain mapping applied to aberration--corrected HAADF images.

A systematic distortion in high-angle annular dark-field scanning transmission electron microscope (HAADF-STEM) images, which may be caused by residual electrical interference, has been evaluated. Strain mapping, using the geometric phase methodology, has been applied to images acquired in an aberration-corrected STEM. This allows this distortion to be removed and so quantitative analysis of HAADF-STEM images was enabled. The distortion is quantified by applying this technique to structurally perfect and strain-free material. As an example, the correction is used to analyse an InAs/GaAs dot-in-quantum well heterostructure grown by molecular beam epitaxy. The result is a quantitative measure of internal strain on an atomic scale. The measured internal strain field of the heterostructure can be interpreted as being due to variations of indium concentration in the quantum dot.     

On the nature of interactions in the F2OXe…NCCH3 complex: Is there the Xe(IV)?N bond?

Nature of the bonding in isolated XeOF₂ molecule and F₂OXe^…NCCH₃ complexes have been studied in the gas phase (0 K) using Quantum Chemical Topology methods. The wave functions have been approximated at the MP2 and DFT levels of calculations, using the APFD, B3LYP, M062X, and B2PLYP functionals with the GD3 dispersion correction. The nature of the formal Xe?O bond in the XeOF₂ monomer depends on the basis set used (all‐electron vs. the ecp‐28 approximation for Xe). Within the all‐electron basis set approach the bond is represented by two bonding attractors, V_{i = 1,2}(Xe,O), with total population of about 1.06e and highly delocalized electron density in both bonding basins. No bonding basins are observed using the ecp‐28 approximation. These results shows that the nature of xenon–oxygen is complicated and may be described with mesomeric equilibrium of the Lewis representations: Xe⁽⁺⁾O^(?) and Xe^(–)O⁽⁺⁾. For both the xenon–oxygen and xenon–fluorine interactions the charge‐shift model can be applied. The F₂OXe^…NCCH₃ complex exists in two structures: “parallel,” stabilized by non‐covalent C^…O and Xe^…N interactions and “linear” stabilized by the Xe^…N interaction. Topological analysis of ELF shows that the F₂OXe^…NCCH₃ molecule appears as a weakly bound intermolecular complex. Intermolecular interaction energy components have also been studied using Symmetry Adapted Perturbation Theory. © 2016 Wiley Periodicals, Inc.     

The protocovalent NO bond: Quantum chemical topology (QCT of ELF and ELI-D) study on the bonding in the nitrous acid HONO and its relevancy to the experiment

Topologically challenging, the protocovalent NO bond, which belongs to a distinct class called charge-shift bonds, has been identified in the HONO (cis, trans) molecules on the basis of topological analysis of the ELF and ELI-D functions obtained from the B3LYP and CASSCF(12,10) calculations. The presence of the protocovalent NO bond is associated with energetically possible dissociation channel: HONO(¹A′) → OH(²π) + NO(²π).     

Synthesis and reactivity of new heterodinuclear iron/rhenium Cx complexes of the formula (η-C5Me5)Re(NO)(PPh3)(CC)n(η-dppe)Fe(η-C5Me5) (n = 3, 4): Redox properties and a dicobalt hexacarbonyl adduct

We report in this communication the synthesis and characterization of two Fe/Re heterodinuclear complexes 3_n of formula (η⁵-C₅Me₅)Re(NO)(PPh₃)(CC)_n(η²-dppe)Fe(η⁵-C₅Me₅) (n = 3, 4) as well as the hexacarbonyl dicobalt adduct (4) of the hexatriynediyl complex 3₃. We show by cyclic voltammetry that the “electronic communication” between the organometallic endgroups and thereby the thermodynamic stability of the corresponding mixed-valent (MV) parent 3_n⁺ is strongly influenced by bridge extension or by complexation of the [Co₂(CO)₆] fragment. In the case of the hexatriynediyl complex, the MV complex 3₃⁺ or 4 can be isolated by performing the chemical oxidation of 3₃ at low temperature. Spectroscopic studies of this compound and of other stable oxidized redox congeners should now help us to unravel how bridge extension modifies the electronic communication between the different redox-active endgroups in this family of unsymmetrically-substituted polyynediyl compounds.