Equidistribution of Zeros of Holomorphic Sections in the Non-compact Setting

We consider tensor powers L ^N of a positive Hermitian line bundle (L,h ^L ) over a non-compact complex manifold X. In the compact case, B. Shiffman and S. Zelditch proved that the zeros of random sections become asymptotically uniformly distributed as N→∞ with respect to the natural measure coming from the curvature of L. Under certain boundedness assumptions on the curvature of the canonical line bundle of X and on the Chern form of L we prove a non-compact version of this result. We give various applications, including the limiting distribution of zeros of cusp forms with respect to the principal congruence subgroups of SL ₂(?) and to the hyperbolic measure, the higher dimensional case of arithmetic quotients and the case of orthogonal polynomials with weights at infinity. We also give estimates for the speed of convergence of the currents of integration on the zero-divisors.     

Metric betweenness,Ptolemaic spaces,and isometric embeddings of pretangent spaces in ℝ

We study some properties of pretangent spaces describing the infinitesimal geometry of general metric spaces. The necessary and sufficient conditions characterizing Ptolemaic pretangent spaces and pretangent spaces, where every three points are situated “on a single straight line,” are found. As a corollary, we obtain a criterion of embeddability of pretangent spaces into the set ℝ of real numbers endowed by the natural metric.     

Characterization and functionalization of cellulose microbeads for extracorporeal blood purification

In the frame of this work, cellulose microbeads with an average particle size of 2.3 μm were characterized with respect to porosity using a batch solute exclusion method and two groups of model substances, namely proteins and polystyrene sulfonates. The pores of the microbeads were almost completely accessible to proteins with Stokes radii below 2.5 nm. More than 60% of the pores were accessible to albumin, which is relevant for the application in blood purification, since many target substances are albumin bound. Activation of the microbeads with increasing amounts of sodium metaperiodate yielded matrices with dialdehyde contents between 100 and 1,000 μmol/g. The activated beads were well suited for the covalent attachment of functional ligands, such as antibodies. Immobilization of antibodies against the pro-inflammatory cytokine TNF-α resulted in efficient TNF-α adsorbents which possess application potential in extracorporeal blood purification, e.g. for the modulation of cytokine levels as supportive therapy for sepsis and other inflammatory disorders.     

Ylide‐Functionalized Phosphines: Strong Donor Ligands for Homogeneous Catalysis

Phosphines are important ligands in homogenous catalysis and have been crucial for many advances, such as in cross‐coupling, hydrofunctionalization, or hydrogenation reactions. Herein we report the synthesis and application of a novel class of phosphines bearing ylide substituents. These phosphines are easily accessible via different synthetic routes from commercially available starting materials. Owing to the extra donation from the ylide group to the phosphorus center the ligands are unusually electron‐rich and can thus function as strong electron donors. The donor capacity surpasses that of commonly used phosphines and carbenes and can easily be tuned by changing the substitution pattern at the ylidic carbon atom. The huge potential of ylide‐functionalized phosphines in catalysis is demonstrated by their use in gold catalysis. Excellent performance at low catalyst loadings under mild reaction conditions is thus seen in different types of transformations.     

Octahedral Rhenium Cluster Complexes with 1,2-Bis(4-pyridyl)ethylene and 1,3-Bis(4-pyridyl)propane as Apical Ligands

A series of eight new octahedral rhenium cluster complexes with the general formula trans-[{Re₆Q₈}L₄X₂] (Q = S or Se; L = 1,2-Bis(4-pyridyl)ethylene (bpe) or 1,3-Bis(4-pyridyl)propane (bpp); X = Cl or Br) was synthesized and investigated. While bpe is a ligand with a conjugated aromatic system, bpp represents a molecule of opposite type and has independent aromatic systems of the two pyridine rings. It was shown that this difference in the electronic structure of the ligands has a fundamental effect on the electronic structure, electrochemical and luminescent properties of the corresponding cluster complexes. Specifically, the [{Re₆Q₈}(bpe)₄X₂] complexes in solutions show multiple quasi-reversible electrochemical transitions associated with reduction of the organic ligands. At the same time, the trans-[{Re₆Q₈}(bpp)₄X₂] complexes show multielectron quasi-irreversible reduction processes, which correlate with the mixed character of the lowest unoccupied molecular orbitals of these complexes. All the obtained new compounds exhibit red photoluminescence. The photophysical parameters (emission lifetimes and quantum yields) measured for the bpp complexes exceed those revealed for bpe complexes by more than an order of magnitude.     

New peak broadening parameter for the characterization of separation capability in capillary electrophoresis

The influence of separation conditions on peak broadening is usually estimated by the number of theoretical plates. Using the data available in literature and experimental data, it is shown that in pressure‐assisted capillary electrophoresis the plate number is not directly related to the separation capability of conditions used. The experiments at different electrolyte flow velocities demonstrate that a higher plate number (the best separation efficiency) can be obtained with a lower peak resolution. Since ions are separated by electrophoresis due to the difference in electrophoretic mobilities, the peak width in terms of electrophoretic mobility is suggested as a new peak broadening parameter describing the separation capability of the conditions used. The parameter can be calculated using the tailing factor and the temporal peak width at 5% of the peak height. A simple equation for the resolution calculation is derived using the parameter. The advantage of the peak width in terms of mobility over other parameters is shown. The new parameter is recommended to be used not only in pressure‐assisted capillary electrophoresis but also in general capillary electrophoresis when in a number of runs the virtual separative migration distance and separation capability of the conditions used change widely.     

Preparation and Isolation of a Chiral Methandiide and Its Application as Cooperative Ligand in Bond Activation

The activation of element–hydrogen bonds by means of metal–ligand cooperation has received increasing attention as alternative to classical activation processes, which exclusively occur at the metal center. Carbene complexes derived from methandiide precursors have been applied in this chemistry enabling the activation of a series of E?H bonds by addition reactions across the M?C bond. However, no chiral carbene complexes have been applied to realize stereoselective transformations to date. Herein, we report the isolation and structure elucidation of an enantiomerically pure dilithiomethane, which could be prepared by direct double deprotonation. The obtained dilithium salt was used for the preparation of the first chiral methandiide‐derived carbene complex, which was applied in stereoselective cooperative S?H bond activation.     

Liquid and gas chromatographic studies of the anaerobic degradation of baker’s yeast wastewater

The digestion of baker’s yeast wastewater was monitored by gas production intensity and composition of gaseous and liquid phases. Favorable coexistence of sulfate reducing bacteria and methanogens was explained by the presence and metabolism of trimethylamine, a degradation product of betaine. Concentration of sulfides decreased at the expense of betaine degradation with final products S₀ and N₂. Since biological wastewater treatment was complicated by both high content of SO₄^2-, eventually becoming reduced to toxic H₂S, and high total nitrogen content, a technological solution that links sulfate reduction to elemental sulfur coupled with reactions producing gaseous nitrogen may have great practical value.     

A Quick and Reproducible Silanization Method by Using Plasma Activation for Hydrophobicity-Based Kinesin Single Molecule Fluorescence–Microscopy Assays

Single-molecule assays often require functionalized surfaces. One approach for microtubule assays renders surfaces hydrophobic and uses amphiphilic blocking agents. However, the optimal hydrophobicity is unclear, protocols take long, produce toxic waste, and are susceptible to failure. Our method uses plasma activation with hydrocarbons for hexamethyldisilazane (HMDS) silanization in the gas phase. We measured the surface hydrophobicity, its effect on how well microtubule filaments were bound to the surface, and the number of nonspecific interactions with kinesin motor proteins. Additionally, we tested and discuss the use of different silanes and activation methods. We found that even weakly hydrophobic surfaces were optimal. Our environmentally friendly method significanty reduced the overall preparation effort and resulted in reproducible, high-quality surfaces with low variability. We expect the method to be applicable to a wide range of other single-molecule assays.     

Über eine neue Synthese von Desmethylambraoxid

A new synthesis of the title compound starting from abietic acid is described. Regioselective osmylation of the ^{13, 14}-double bond of abietic acid methyl ester (6) and subsequent hydrogenation furnishes dihydrodihydroxyabietic acid methyl ester (12) with anall-trans-connection of the three rings. Periodate cleavage of12 leads to13 which can be transformed into the triester14 byBaeyer-Villiger oxidation. The configuration of the aldehyde group in13 as well of the formyloxy group in14 has been ensured to be equatorial.LAH-reduction of14 leads to the triol16 which after cyclisation and reductive dehydroxylation furnishes the fragrance compound4.

Auszugsweise vorgetragen auf der 5. wissenschaftlichen Tagung der Österreichischen Pharmazeutischen Gesellschaft am 16. April 1985 in Graz.