Interpolation by positive definite functions on locally compact groups with application to SO (3)

In this research a method for interpolation on arbitrary locally compact groups is developed. The method is based on positive definite functions definable on spaces with group multiplication. To be able to use these functions two steps are necessary. First, positive semidefinite functions are determined using Bochners theorem on commutative groups respectively representation theory in the non commutative case. Then transformations are given to get positive definite out of positive semidefinite functions. For the compact group 50(3) the result is explicitly calculated and implemented in the case of three and five dimensional representations, and is applied to the approximation of energy functions of molecule interactions in 3-space.     

Littlewood–Paley Theory for Triangle Buildings

For the natural two-parameter filtration \(\left( {\mathcal {F}_\lambda }: {\lambda \in P}\right) \) on the boundary of a triangle building, we define a maximal function and a square function and show their boundedness on \(L^p(\Omega _0)\) for \(p \in (1, \infty )\). At the end, we consider \(L^p(\Omega _0)\) boundedness of martingale transforms. If the building is of \({\text {GL}}(3, \mathbb {Q}_p)\), then \(\Omega _0\) can be identified with p-adic Heisenberg group.     

Exploring the phase diagram of strongly interacting matter; news from SPS and RHIC

Two experimental programs are aiming to study nuclear collisions in the energy regime in order to explore an essential part of the phase diagram of strongly interacting matter. The programs are motivated by observations that indicate a phase transition to take place in this energy domain: the onset of deconfinement. The STAR collaboration proposes an energy scan in the Relativistic Heavy Ion Collider (RHIC) at BNL. The ongoing program of the NA61/SHINE experiment consists of a two-dimensional energy-system size scan in nuclear and elementary collisions. The goal of both programs is to study the properties of the onset of deconfinement and to eventually discover the conjectured critical point of strongly interacting matter. A comparison of the strengths and limitations reveals the complementarity of the two programs.     

Physico-Chemical Properties of Magnetic Dicationic Ionic Liquids with Tetrahaloferrate Anions

A series of imidazolium-based symmetrical and asymmetrical dicationic ionic liquids (DcILs) with alkyl spacers of different length and with [FeCl₃Br]⁻ as counter ion have been synthesized. The synthesized DcILs are characterized by using FTIR and Raman spectroscopy as well as mass spectrometry, along with single-crystal XRD analysis. Physicochemical properties such as solubility, thermal stability and magnetic susceptibility are also measured. These compounds show low melting points, good solubility in water and organic solvents, thermal stability, and paramagnetism. The products of molar susceptibility and temperature (χ_mol⋅T) for the synthesized DcILs have been found between 4.05 to 4.79 emu mol⁻¹ K Oe⁻¹ and effective magnetic moment values have also been determined to be compared to that expected from the spin-only approximation.     

Mechanistic insights into NO3* induced self-terminating radical oxygenations, part 1: a computational study on NO3* and its addition to alkynes

The geometry of the nitrate radical, NO3*, for which unrestricted Hartree-Fock (HF) breaks spatial symmetry of the wave function, was optimized using hybrid density functionals that include varying fractions of Hartree-Fock exchange. Although symmetry breaking was not observed even when the functional with the highest HF exchange (BHandHLYP) was used, only B3LYP correctly describes the D(3h) symmetry of NO3* as ground-state structure with the lowest energy. Further, geometries and energies of the stationary points in the addition of NO3* to ethyne, propyne, and 2-butyne were calculated using ab initio and density functional methods. The reactions proceed through Z-configurated transition states leading to Z-configurated vinyl radicals with the activation barrier decreasing with increasing methyl substitution at the C[triple bond]C by ca. 11 kJ mol(-1) per methyl group. It was found that the results obtained at the BHandHLYP/cc-pVDZ level of theory are in good agreement with the data from single-point QCISD and CCSD(T) calculations.     

On the origin of the unique properties of supported Au nanoparticles

The unique catalytic activity of supported Au nanoparticles has been ascribed to various effects including thickness/shape, the metal oxidation state, and support effects. Previously, we reported the synthesis of ordered Au monolayers and bilayers on TiO(x), with the latter being significantly more active for CO oxidation than the former. In the present study, the electronic and chemical properties of ordered monolayer and bilayer Au films have been characterized by infrared reflection adsorption spectroscopy using CO as a probe and ultraviolet photoemission spectroscopy. The Au overlayers are found to be electron-rich and to have significantly different electronic properties compared with bulk Au. The common structural features of ordered Au bilayers and Au bilayer nanoparticles on TiO2(110) are described, and the exceptionally high catalytic activity of the Au bilayer structure related to its unique electronic properties.     

J-aggregation of a water-soluble tetracationic porphyrin in mixed LB films with a calix[8]arene carboxylic acid derivative

The molecular organization of a mixed film, containing a water-soluble tetracationic porphyrin (TMPyP) and a p-tert-butyl calix[8]arene octacarboxylic acid derivative (C8A), at the air-water interface and on a solid support (LB film), has been investigated. Although the TMPyP aggregation was not detected at the air-water interface, TMPyP J-aggregates have been found in the LB films (Y-type). Unlike tetraanionic porphyrins, for example TSPP, the TMPyP J-aggregates are not induced by a zwitterion formation. The TMPyP J-aggregation is a result of a "double comb" configuration, where porphyrins from opposite layers are interwoven in a linear infinite J-aggregate. Our results confirm that TMPyP molecules tend to self-aggregate strongly, provided the electrostatic repulsions of their peripheral groups are cancelled by the anionic groups of the C8A matrix.     

Stable cellulose nanospheres for cellular uptake

Pure, perfectly spherical cellulose nanoparticles with sizes of ≈80-260 nm can be prepared by dialysis starting from trimethylsilylcellulose (TMSC). The aqueous suspensions obtained are storable for several months. Subsequent covalent labeling of the cellulose nanoparticles with FITC has no influence on particle size, shape, and stability. The particles can be sterilized and suspended in biological media without structural changes. Incorporation of FITC-labeled cellulose nanoparticles into living human fibroblasts is studied using confocal LSM. In contrast to cellulose nanocrystals, fast cellular uptake is found for the nanospheres without transfection reagents or attachment of a receptor molecule. This suggests an influence of the geometry of biocompatible nanomaterials on endocytosis.     

Syntheses, structures and intermolecular interactions of tetraorganoammonium, -phosphonium and -stibonium dimethyl- and diphenyltetrahaloantimonates

The syntheses and spectroscopic (NMR, MS) investigations of the antimonates [Ph₄P]⁺[Me₂SbCl₄]⁻ (1), [Me₄Sb]⁺[Me₂SbCl₄]⁻ (2), [Et₄N]⁺[Ph₂SbCl₄]⁻ (3), [Bu₄N]⁺[Ph₂SbCl₄]⁻ (4), [Me₄Sb]⁺[Ph₂SbCl₄]⁻ (5), [Et₃MeSb]⁺[Ph₂SbCl₄]⁻ (6), [Et₄N]⁺[Ph₂SbF₄]⁻ (7) and [Et₄N]⁺[Ph₂SbBr₄]⁻ (8) are reported. Halogen scrambling reactions of Et₄NBr or Ph₄EBr (E = P, Sb) with R₂SbCl₃ (R = Me, Ph) produce mixtures of compounds from which crystals of [Et₄N]⁺[Ph₂SbBr_1.24Cl_2.76]⁻ (9), [Et₄N]⁺[Ph₂SbBr_2.92Cl_1.08]⁻ (10) or [Ph₄Sb]⁺[Me₂SbCl₄]⁻ (11) were isolated. The crystal and molecular structures of 1 and 3-11 are reported.     

161Dy Time‐Domain Synchrotron Mössbauer Spectroscopy for Investigating Single‐Molecule Magnets Incorporating Dy Ions

Time‐domain synchrotron Mössbauer spectroscopy (SMS) based on the Mössbauer effect of ¹⁶¹Dy has been used to investigate the magnetic properties of a Dy^III‐based single‐molecule magnet (SMM). The magnetic hyperfine field of [Dy(Cy₃PO)₂(H₂O)₅]Br₃?2 (Cy₃PO)?2 H₂O?2 EtOH is with B₀=582.3(5) T significantly larger than that of the free‐ion Dy^III with a ⁶H_15/2 ground state. This difference is attributed to the influence of the coordinating ligands on the Fermi contact interaction between the s and 4f electrons of the Dy^III ion. This study demonstrates that ¹⁶¹Dy SMS is an effective local probe of the influence of the coordinating ligands on the magnetic structure of Dy‐containing compounds.