SU(2) Chern-Simons theory at genus zero

We present a detailed study of the Schrödinger picture space of states in theSU(2) Chern-Simons topological gauge theory in the simplest geometry. The space coincides with that of the solutions of the chiral Ward identities for the WZW model. We prove that its dimension is given by E. Verlinde's formulae.     

Feasibility of a liquid-phase microextraction sample clean-up and liquid chromatographic/mass spectrometric screening method for selected anabolic steroid glucuronides in biological samples

Anabolic androgenic steroids (AAS) are metabolized extensively in the human body, resulting mainly in the formation of glucuronide conjugates. Current detection methods for AAS are based on gas chromatographic/mass spectrometric (GC/MS) analysis of the hydrolyzed steroid aglycones. These analyses require laborious sample preparation steps and are therefore time consuming. Our interest was to develop a rapid and straightforward method for intact steroid glucuronides in biological samples, using liquid-phase microextraction (LPME) sample clean-up and concentration method combined with liquid chromatographic/tandem mass spectrometric (LC/MS/MS) analysis. The applicability of LPME was optimized for 13 steroid glucuronides, and compared with conventional liquid-liquid extraction (LLE) and solid-phase extraction (SPE) procedures. An LC/MS/MS method was developed for the quantitative detection of AAS glucuronides, using a deuterium-labeled steroid glucuronide as the internal standard. LPME, owing to its high specificity, was shown to be better suited than conventional LLE and SPE for the clean-up of urinary AAS glucuronides. The LPME/LC/MS/MS method was fast and reliable, offering acceptable reproducibility and linearity with detection limits in the range 2-20 ng ml(-1) for most of the selected AAS glucuronides. The method was successfully applied to in vitro metabolic studies, and also tested with an authentic forensic urine sample. For a urine matrix the method still has some unsolved problems with specificity, which should be overcome before the method can be reliably used for doping analysis, but still offering additional and complementary data for current GC/MS analyses.     

Simultaneous determination of DTPA,EDTA, and NTA by capillary electrophoresis after complexation with copper

We present a method for simultaneous determination of the aminopolycarboxylic acids DTPA, EDTA and NTA in dishwashing detergents, paper mill waters, and natural waters by capillary electrophoresis (CE). The complexing agents were examined as their copper(II) complexes and separated by conventional CE with reversed polarity of the applied voltage. The optimum separation conditions were established by varying the pH and phosphate and tetradecyltrimethylammonium bromide (TTAB) concentrations in the run buffer. The separations were carried out in a fused-silica capillary (61 cm×75 m i.d.) filled with phosphate buffer (80 mmol L^–1, TTAB concentration 0.5 mmol L^–1, pH 7.1, voltage –20 kV) using direct UV detection at 191 and 254 nm. With this CE method all the peaks in the electropherograms were properly separated, the calibration plots gave good correlation coefficients and all three complexing agents could be detected in less than 4 min. Linear calibration plots were obtained for CuDTPA, CuEDTA and CuNTA; limits of detection were 0.03 mmol L^–1 for all complexing agents and recoveries for all tested samples were within the range 104±7%. Results obtained from dishwashing detergent samples were found to be reliable and comparable with those from HPLC (R²=0.989) and UV–Vis (R²=0.985) methods.     

On the 1/n expansion

The 1/n expansion is considered for then-component non-linear -model (classical Heisenberg model) on a lattice of arbitrary dimensions. We show that the expansion for correlation functions and free energy is asymptotic, for all temperatures above the spherical model critical temperature. Furthermore, the existence of a mass gap is established for these temperatures andn sufficiently large.Supported in part by the National Science Foundation under Grant PHY 79-16812     

In situ reaction mechanism studies on the atomic layer deposition of Al2O3 from (CH3)2AlCl and water

Reaction mechanisms between dimethylaluminum chloride and deuterated water in the atomic layer deposition (ALD) of Al2O3 were studied at 150-400 degrees C using a quartz crystal microbalance (QCM) and a quadrupole mass spectrometer (QMS). The observed reaction byproducts were DCl and CH3D. QMS showed that about one-third of the chlorine, and half of the methyl ligands were released during the (CH3)2AlCl pulse. The growth rate deduced from the QMS and QCM data was in qualitative agreement with the previously published growth rate from ALD film growth experiments.     

Expanding the Scope of the Cleavable N-(Methoxy)oxazolidine Linker for the Synthesis of Oligonucleotide Conjugates

Oligonucleotides modified by a 2′-deoxy-2′-(N-methoxyamino) ribonucleotide react readily with aldehydes in slightly acidic conditions to yield the corresponding N-(methoxy)oxazolidine-linked oligonucleotide-conjugates. The reaction is reversible and dynamic in slightly acidic conditions, while the products are virtually stable above pH 7, where the reaction is in a ‘‘switched off-state’’. Small molecular examinations have demonstrated that aldehyde constituents affect the cleavage rate of the N-(methoxy)oxazolidine-linkage. This can be utilized to adjust the stability of this pH-responsive cleavable linker for drug delivery applications. In the present study, Fmoc-β-Ala-H was immobilized to a serine-modified ChemMatrix resin and used for the automated assembly of two peptidealdehydes and one aldehyde-modified peptide nucleic acid (PNA). In addition, a triantennary N-acetyl-d-galactosamine-cluster with a β-Ala-H unit has been synthesized. These aldehydes were conjugated via N-(methoxy)oxazolidine-linkage to therapeutically relevant oligonucleotide phosphorothioates and one DNA-aptamer in 19–47% isolated yields. The cleavage rates of the conjugates were studied in slightly acidic conditions. In addition to the diverse set of conjugates synthesized, these experiments and a comparison to published data demonstrate that the simple conversion of Gly-H to β-Ala-H residue resulted in a faster cleavage of the N-(methoxy)oxazolidine-linker at pH 5, being comparable (T_0.5 ca 7 h) to hydrazone-based structures.     

Improved Bohr’s inequality for locally univalent harmonic mappings

We prove several improved versions of Bohr’s inequality for the harmonic mappings of the form $f=h+\overline{g}$, where $h$ is bounded by 1 and $\left|g^{\prime }\left(z\right)\right|\le \left|h^{\prime }\left(z\right)\right|$. The improvements are obtained along the lines of an earlier work of Kayumov and Ponnusamy, i.e. (Kayumov and Ponnusamy, 2018) for example a term related to the area of the image of the disk $D(0,r)$ under the mapping $f$ is considered. Our results are sharp. In addition, further improvements of the main results for certain special classes of harmonic mappings are provided.     

Coexistence of Two Different Distorted Octahedral [MnF6]3− Sites in K3[MnF6]: Manifestation in Spectroscopy and Magnetism

As a consequence of the static Jahn-Teller effect of the ⁵E ground state of Mn^III in cubic structures with octahedral parent geometries, their octahedral coordination spheres become distorted. In the case of six fluorido ligands, [MnF₆]³⁻ anions with two longer and four shorter Mn−F bonds making elongated octahedra are usually observed. Herein, we report the synthesis of the compound K₃[MnF₆] through a high-temperature approach and its crystallization by a high-pressure/high-temperature route. The main structural motifs are two quasi-isolated, octahedron-like [MnF₆]³⁻ anions of quite different nature compared to that met in ideal octahedral Mn^III Jahn-Teller systems. Owing to the internal electric field of C_i symmetry dominated by the next-neighbour K⁺ ions acting on the Mn^III sites, both sites, the pseudo-rhombic (site 1) and the pseudo-tetragonally elongated (site 2) [MnF₆]³⁻ anions are present in K₃[MnF₆]. The compound was characterized by single-crystal and powder X-ray diffraction, and magnetometry as well as by FTIR, Raman, and ligand field spectroscopy. A theoretical interpretation of the electronic structure and molecular geometry of the two Mn sites in the lattice is given by using a vibronic coupling model with parameters adjusted from multireference ab-initio cluster calculations.     

The vane method and kinetic modeling: shear rheology of nanofibrillated cellulose suspensions

We conduct rheological characterization of nanofibrillated cellulose (NFC) suspensions, a highly non-Newtonian complex fluid, at several concentrations. Special care is taken to cope with the prevalent problems of time scale issues, wall depletion and confinement effects. We do this by combining the wide-gap vane geometry, extremely long measurement times, and modeling. We take into account the wide-gap related stress heterogeneity by extending upon mainstream methods and apply a gap correction. Furthermore, we rationalize the experimental data through a simple viscous structural model. With these tools we find that, owing to the small size of the particles subjected to Brownian motion, the NFC suspensions exhibit a critical shear rate, where the flow curve experiences a turning point. This makes the steady state of these suspensions at low shear rates non-unique. To optimize various mixing and pumping applications, such history dependent tendency of NFC suspensions to shear band needs to be taken into account.