A finiteness result for Heegaard splittings

In this paper we show that for a given 3-manifold and a given Heegaard splitting there are finitely many preferred decomposing systems of 3g−3 disjoint essential disks. These are characterized by a combinatorial criterion which is a slight strengthening of Casson-Gordon's rectangle condition. This is in contrast to fact that in general there can exist infinitely many such systems of disks which satisfy just the Casson-Gordon rectangle condition.     

Radiation copolymerization of vinyl acetate with the diethyl esters of maleic and fumaric acids

The radiation-induced copolymerization of vinyl acetate with diethyl maleate and with diethyl fumarate was investigated in the temperature range from ?40 to 90°C over a wide range of comonomer compositions. Both the rates of copolymerization and the molecular weights of the resulting copolymers were found to depend strongly on the initial comonomer compositions. The apparent activation energy was found to change at 13°C with an increase in temperature from a value of 1.76 kcal/mole to a value of 4.31 kcal/mole in the copolymerization with diethyl maleate, while in the case of the copolymerization with diethyl fumarate the apparent activation energy changed at 21°C from a value of 1.76 kcal/mole to a value of 5.98 kcal/mole. Scavenger studies indicate that a free-radical mechanism prevails over the entire temperature range investigated in the case of both copolymerizations.     

Different modes of aggregation in organoaluminium and -gallium hydroxylamides

The organoaluminium and -gallium hydroxylamides (Me2GaONMe2)2, (tBu2AlONMe2)2, (tBu2GaONMe2)2 and (Me2AlONiPr2)2 have been prepared by the reaction of the hydroxylamines Me2NOH and iPr2NOH with the trialkylmetal compounds trimethylgallium, tri-tbutylaluminium and tri-tbutylgallium, respectively. All compounds have been characterised by NMR spectroscopy (1H, 13C, 15N, 17O and 27Al), by mass spectrometry and elemental analyses. The crystal structures of the four compounds have been determined, showing that they all form dimers but with different modes of aggregation: (Me2GaONMe2)2 has a Ga2O2N2 six-membered ring, (tBu2AlONMe2)2 and (Me2AlONiPr2)2 have Al2O2 four-membered rings, (tBu2GaONMe2)2 forms a Ga2O2N five-membered ring.     

13 C Saturation-Transfer Difference (STD)-NMR Experiments Using INEPT Polarization Transfer

Saturation-transfer difference (STD)-NMR spectroscopy has been widely used to screen potential ligands for binding to large receptor molecules. The STD-NMR experiment is typically based on a proton NMR spectrum, which can suffer from spectral overlap, leading to missing information in STD-based epitope mapping. Two-dimensional STD-NMR experiments can alleviate spectral overlap, but are time consuming. Here, we examine the feasibility of saturating protons in a receptor molecule and observing the STD effect on nearby carbon nuclei after transferring polarization from protons to carbons using the insensitive nuclei enhanced by polarization transfer (INEPT) pulse sequence. We show that under favorable conditions, a 1H→13C STD-INEPT experiment can give information similar to that obtained from a two-dimensional heteronuclear experiment, but in significantly less time. The STD-INEPT experiment could be especially useful when studying mixtures of ligands in which the peak positions in the proton and HSQC spectrum change significantly, and in particular, when using high-throughput, automated methods to analyze the data.     

Indications about the shape of the universe from the Wilkinson microwave anisotropy probe data

It is shown that the recent observations of NASA's Explorer mission, "Wilkinson Microwave Anisotropy Probe," hint that our Universe may possess a nontrivial topology. As an example we discuss the Picard space which is stretched out into an infinitely long horn but with finite volume.     

Untersuchung von Fetten

Analytical and Bioanalytical Chemistry -