Convergent sequences of composition operators

Composition operators Cφ on the Hilbert Hardy space H² over the unit disk are considered. We investigate when convergence of sequences {φn} of symbols, (i.e., of analytic selfmaps of the unit disk) towards a given symbol φ, implies the convergence of the induced composition operators, Cφn→Cφ. If the composition operators Cφn are Hilbert-Schmidt operators, we prove that convergence in the Hilbert-Schmidt norm, ‖Cφn−CφHS_‖→0 takes place if and only if the following conditions are satisfied: ‖φn−φ_‖2→0, ∫1/(1−²|φ|)<∞, and ∫1/(1−²|φn|)→∫1/(1−²|φ|). The convergence of the sequence of powers of a composition operator is studied.     

Temporary attachment of carbohydrates to cyclopeptide templates: a new strategy for single-bead analysis of multivalent neoglycopeptides

Employing a cleavable carbohydrate–peptide linker, a new strategy for single-bead analysis of multivalent cyclic neoglycopeptides based on Edman degradation is described. Edman degradation of glycopeptides is hampered by the acid lability of the glycosidic bond and potential incompatibilities of phenylthiohydantoin (PTH) derivatives of glycosylated amino acids with PTH derivatives of the proteinogenic amino acids. To overcome this problem, carbohydrates are detached from the cyclopeptide templates before single-bead analysis, allowing for micro sequencing under routine conditions. With this strategy, application of multivalent cyclic neoglycopeptides in split-mix libraries with a subsequent screening process becomes possible for the first time.     

On extremally disconnected topological groups

We introduce the notion of a partially selective ultrafilter and prove that (a) if G is an extremally disconnected topological group and p is a converging nonprincipal ultrafilter on G containing a countable discrete subset, then p is partially selective, and (b) the existence of a nonprincipal partially selective ultrafilter on a countable set implies the existence of a P-point in ω^∗. Thus it is consistent with ZFC that there is no extremally disconnected topological group containing a countable discrete nonclosed subset.     

Kirwan-Novikov inequalities on a manifold with boundary

We extend the Novikov Morse-type inequalities for closed 1-forms in 2 directions. First, we consider manifolds with boundary. Second, we allow a very degenerate structure of the critical set of the form, assuming only that the form is non-degenerated in the sense of Kirwan. In particular, we obtain a generalization of a result of Floer about the usual Morse inequalities on a manifold with boundary. We also obtain an equivariant version of our inequalities.

Our proof is based on an application of the Witten deformation technique. The main novelty here is that we consider the neighborhood of the critical set as a manifold with a cylindrical end. This leads to a considerable simplification of the local analysis. In particular, we obtain a new analytic proof of the Morse-Bott inequalities on a closed manifold.

     

Half-width temperature dependence of nitrogen broadened lines in the ν2 band of H2O

Forty-seven N₂ broadened water vapor line-widths have been measured in the 1845-2140 cm⁻¹ spectral range with a Fourier Transform spectrometer in the 258-330 K temperature range at a spectral resolution of 0.005 cm⁻¹ for the lines with upper state rotational quantum number up to 16. The measured exponents of the temperature dependence of the width exhibit a large range of values from 1.60 to −0.86. Theoretical calculations were made using a semi-empirical technique based on the Anderson theory. The calculated broadening coefficients as well as the temperature exponents for the half-width agree satisfactory with measured values.     

The Ideal Ionic Liquid Salt Bridge for the Direct Determination of Gibbs Energies of Transfer of Single Ions,Part I: The Concept

Described is a procedure for the thermodynamically rigorous, experimental determination of the Gibbs energy of transfer of single ions between solvents. The method is based on potential difference measurements between two electrochemical half cells with different solvents connected by an ideal ionic liquid salt bridge (ILSB). Discussed are the specific requirements for the IL with regard to the procedure, thus ensuring that the liquid junction potentials (LJP) at both ends of the ILSB are mostly canceled. The remaining parts of the LJPs can be determined by separate electromotive force measurements. No extra‐thermodynamic assumptions are necessary for this procedure. The accuracy of the measurements depends, amongst others, on the ideality of the IL used, as shown in our companion paper Part II.     

New selective cyclizations of alk-4-ynals with primary amines and azoles:one-pot synthesis of 2-azolylpyrrolidines and 3-iminocyclopentenes

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Towards a Sustainable Synthesis of Oxymethylene Dimethyl Ether by Homogeneous Catalysis and Uptake of Molecular Formaldehyde

Oxymethylene dimethyl ethers (OME_n; CH₃(‐OCH₂‐)_nO‐CH₃, n=3–5) are a novel class of sustainable synthetic fuels, which are of increasing interest due to their soot‐free combustion. Herein a novel anhydrous OME_n synthesis route is presented. Catalyzed by trimethyloxonium salts, dimethoxymethane takes up monomeric gaseous formaldehyde instantaneously and forms high purity OME_n at temperatures of 25–30 °C. This new anhydrous approach using molecular formaldehyde and catalytic amounts of highly active trimethyloxonium salts represents a promising new step towards a sustainable formation of OME_n emanating from CO₂ and H₂.     

Li atoms deposited on single crystalline MgO(0 0 1) surface. A combined experimental and theoretical study

In this Letter the interaction of Li atoms with terrace sites of MgO(0 0 1) surfaces is characterized by combining EPR spectroscopy with theoretical calculations. The Li atoms adsorbed to MgO terrace sites show a reduction of the isotropic hyperfine coupling constant by approximately 50% with respect to Li atoms in the gas phase. In combination with theoretical calculations it can be shown that this reduction of the hyperfine coupling constant is not due to a charge transfer between Li and MgO but can be understood by a polarization of the Li atoms which are essentially neutral.     

Visualization of Protein‐Specific Glycosylation inside Living Cells

Protein glycosylation is a ubiquitous post‐translational modification that is involved in the regulation of many aspects of protein function. In order to uncover the biological roles of this modification, imaging the glycosylation state of specific proteins within living cells would be of fundamental importance. To date, however, this has not been achieved. Herein, we demonstrate protein‐specific detection of the glycosylation of the intracellular proteins OGT, Foxo1, p53, and Akt1 in living cells. Our generally applicable approach relies on Diels–Alder chemistry to fluorescently label intracellular carbohydrates through metabolic engineering. The target proteins are tagged with enhanced green fluorescent protein (EGFP). Förster resonance energy transfer (FRET) between the EGFP and the glycan‐anchored fluorophore is detected with high contrast even in presence of a large excess of acceptor fluorophores by fluorescence lifetime imaging microscopy (FLIM).