Amorphe Potenzen kompakter Räume

A set is amorphous, if it is not a union of two disjoint infinite subsets. The following variants of the Tychonoff product theorem are investigated in the hierarchy of weak choice principles. TA1: An amorphous power of a compactT ₂ space is compact. TA2: An amorphous power of a compactT ₂ space which as a set is wellorderable is compact. In ZF⁰TA1 is equivalent to the assertion, that amorphous sets are finite. RT is Ramsey's theorem, that every finite colouring of the set ofn-element subsets of an infinite set has an infinite homogeneous subset and PW is Rubin's axiom, that the power set of an ordinal is wellorderable. In ZF⁰RT+PW implies TA2. Since RT+PW is compatible with the existence of infinite amorphous sets, TA2 does not imply TA1 in ZF⁰. But TA2 cannot be proved in ZF⁰ alone. As an application, we prove a theorem of Stone, using a weak wellordering axiomD ₃ (a set is wellorderable, if each of its infinite subsets is structured) together with RT.

Diese Arbeit ist Teil der Habilitationsschrift des Verfassers im Fachgebiet Mathematische Analysis an der Technischen Universität Wien.     

Synthese de derives mono- ou disilicies au niveau d'un carbone fonctionnel

Aliphatic saturated amides treated with Me₃SiCl/Li/THF were found to react in two ways. Either alkoxysilanes, mono- or di-silylated at the functional carbon, or C-silylated amines were obtained dependent of the original amide structure and the experimental conditions. (Me₃Si)₂CHN(SiMe₃)₂ exhibited Physicochemical properties that are particular for hindered rotation about the CN bond. A general mechanism is proposed to explain these results.     

Strong intramolecular secondary si.N bonds in trifluorosilylhydrazines

The simple silylhydrazines F(3)SiN(Me)NMe(2) (1), F(2)Si(N(Me)NMe(2))(2) (2), and F(3)SiN(SiMe(3))NMe(2) (3) have been prepared by reaction of SiF(4) with LiN(Me)NMe(2) and LiN(SiMe(3))NMe(2), while F(3)SiN(SnMe(3))NMe(2) (4) was prepared from SiF(4) and (Me(3)Sn)(2)NNMe(2) (5). The compounds were characterized by gas-phase IR and multinuclear NMR spectroscopy ((1)H, (13)C, (14/15)N, (19)F, (29)Si, (119)Sn), as well as by mass spectrometry. The crystal structures of compounds 1-5 were determined by X-ray crystallography. The structures of free molecules 1 and 3 were determined by gas-phase electron diffraction. The structures of 1, 2, and 4 were also determined by ab initio calculations at the MP2/6-311+G** level of theory. These structural studies constitute the first experimental proof for the presence of strong Si.N beta-donor-acceptor bonds between the SiF(3) and geminal NMe(2) groups in silylhydrazines. The strength of these non-classical Si.N interactions is strongly dependent on the nature of the substituent at the alpha-nitrogen atom of the SiNN unit, and has the order 3>4>1. The valence angles at these extremely deformed alpha-nitrogen atoms, and the Si.N distances are (crystal/gas): 1 104.2(1)/106.5(4) degrees, 2.438(1)/2.510(6) A; 3 83.6(1)/84.9(4) degrees, 2.102(1)/2.135(9) A; 4 89.6(1) degrees, 2.204(2) A.     

Synthesis and structural revision of naturally occurring ayapin derivatives

The synthesis of three highly oxygenated naturally occurring coumarins, 8-methoxy-6,7-methylenedioxycoumarin, 5-methoxy-6,7-methylenedioxycoumarin and 5,8-dimethoxy-6,7-methylenedioxycoumarin is described for the first time, together with a new method for the preparation of ayapin (6,7-methylenedioxycoumarin). Comparison of the spectroscopic data of the synthetic tetraoxygenated coumarin 5,8-dimethoxy-6,7-methylenedioxycoumarin with literature reports resulted in the structural revision of several natural coumarins. Two coumarins, both identified as 5,8-dimethoxy-6,7-methylenedioxycoumarin must have other structures, while the structure of another coumarin, described as the isomeric 7,8-dimethoxy-5,6-methylenedioxycoumarin has to be revised to 5,8-dimethoxy-6,7-methylenedioxycoumarin.     

Development of a sensitive enzyme immunoassay for the detection of phenyl-β-d-thioglucuronide in human urine

Immunoassays for the measurement of glucuronides in human urine can be a helpful tool for the assessment of human exposure to toxic chemicals. Therefore an enzyme immunoassay (EIA) for the specific detection of phenyl-β-d-thioglucuronide was developed. The immunoconjugate was formed by coupling p-aminophenyl-β-d-thioglucuronide to the carrier protein thyroglobulin leaving an exposed glucuronic acid. The hapten-protein conjugate was adsorbed to gold colloids in order to enhance the immunogenic effect. Rabbits were injected with the immunogold conjugates to raise polyclonal antibodies. The resulting competitive assay showed an inhibition by phenyl-β-d-thioglucuronide at sample concentrations of 23.0 ± 1.3 ng/mL (50% B/B₀) and a high cross-reactivity to p-aminophenyl-β-D-thioglucuronide (120%). Little cross-reactivities (< 2%) were observed for potential urinary cross reactants. In addition human urine samples were incubated with β-glucuronidase in order to investigate the EIA for specific matrix effects. An integration of high-performance liquid chromatography (HPLC) and EIA was developed in an attempt to decrease the matrix effects and increase the sensitivity of the overall method. The hyphenated technique HPLC-EIA may be used to monitor human exposure to toxic thiophenol which is excreted by mammals as urinary phenyl thioglucuronide.     

Regularisierte Faltung von Distributionen. Teil 1: Zur Berechnung von Fundamentallösungen

Zusammenfassung Für 2 Distributionen, deren Faltung nicht existiert, wird—mehrdeutig—eine bezüglich eines Differentialoperators regularisierte Faltung definiert.An 4 Beispielen wird die Anwendbarkeit der regularisierten Faltung bei der Berechnung von Fundamentallösungen faktorisierbarer Differentialoperatoren gezeigt. Dabei wurde die Fundamentallösung in Beispiel 3.2. erstmalig ohne Überlegungen physikalischer Art hergeleitet. Beispiel 3.3. verallgemeinert bekannte Ergebnisse, wobei diese als Spezialfälle erscheinen (Bemerkung 3) oder als fehlerhaft nachgewiesen werden (Bemerkung 4). Die Fundamentallösungen der Beispiele 3.1 und 3.4 scheinen in dieser Form neu zu sein.Schließlich folgen einige einfache Sätze, mittels derer Fundamentallösungen von iterierten Differentialoperatoren angegeben werden können. Sie werden im 2. Teil der Arbeit (Eine Tabelle von Fundamentallösungen) angewendet. Literaturhinweise finden sich am Ende von Teil 2.

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Summary For two distributions (whose convolution does not necessarily exist) we define a (manyvalued) convolution regularized with respect to a differential operator.We illustrate by four examples the usefulness of the concept of a regularized convolution for computing fundamental solutions of factorisable differential operators. The fundamental solution of example 3.2 is derived for the first time without considerations from physics. Example 3.3 generalizes well-known results, which either appear as special cases (remark 3) or are proved to contain errors (remark 4). The fundamental solutions of examples 3.1 and 3.4 seem to be new in this form.Finally we give some simple propositions concerning fundamental solutions of iterated differential operators. They will be used in part 2 of this paper (a table of fundamental solutions)The references are given at the end of part 2.

     

Optimization of an electrolytic conductivity detector for determination of toxic nitrogen-containing food contaminants separated by open tubular column gas chromatography

The combination of open tubular column gas chromatography with electrolytic conductivity detection has been evaluated for the determination of nitrogen-containing pesticide residues in food extracts. Optimization of the column position at the column-detector interface was crucial to the successful operation of the detector. The signal-to-noise ratio and response stability of the detector are greatly influenced by the composition of the electrolyte solvent. Large volume splitless injections using retention gaps and optimized detector operating conditions enabled pesticide residues in food extracts to be determined at sub parts-per-million levels. Although the electrolytic conductivity detector is less sensitive than the thermionic ionization detector, its greater nitrogen selectivity can he crucial to the determination of nitrogen-containing contaminants in food extracts, particularly in complex mixtures where phosphorus-containing contaminants or matrix compounds are also present.     

Hydrogen‐bonding patterns in rac‐1‐acetyl‐5‐methyl‐2‐thioxoimidazolidin‐4‐one

In the title compound, C₆H₈N₂O₂S, also known as N‐acetyl‐2‐thiohydantoin–alanine, the molecules are joined by N—H...O hydrogen bonds, forming centrosymmetric R₂²(8) dimers; these dimers are linked by C—H...O interactions to form R₂²(10) rings, thus forming C₂²(10) chains that run along the [101] direction.