Positive mass theorem for the Yamabe problem on spin manifolds

Let (M, g) be a compact connected spin manifold of dimension n ≥ 3 whose Yamabe invariant is positive. We assume that (M, g) is locally conformally flat or that n ∈ {3, 4, 5}. According to a positive mass theorem by Schoen and Yau the constant term in the asymptotic development of the Green’s function of the conformal Laplacian is positive if (M, g) is not conformally equivalent to the sphere. The proof was simplified by Witten with the help of spinors. In our article we will give a proof which is even considerably shorter. Our proof is a modification of Witten’s argument, but no analysis on asymptotically flat spaces is needed.Received: March 2004 Revised: June 2004 Accepted: June 2004     

Nucleophilic Additions to Unactivated Carbon-Carbon Double Bonds. Base-Catalysed Ether Formation. Preliminary Communication

Several examples (3 → 5, 4 → 7, 6 → 7, 9 → 10) of base-catalysed intramolecular ether formation involving nucleophilic attack on an unactivated carbon-carbon double bond are described.     

1H bridging and terminal hydride T1 values. Comments on classical vs non-classical hydride identification using T1 criteria

Hydride ¹H T₁ values are reported for a selected series of ruthenium, iridium and platinum complexes. These T₁ values range from 6.9 to 0.05 s with the shortest value, 0.05 s, assigned to a complex containing both hydride and coordinated molecular hydrogen, i.e. “M(H₂)”. There are nuclear Overhauser enhancements arising both from protons on coordinated ligands and other hydride ligands. It is suggested that the molecular weight of the complex and the measurement conditions can be important factors for T₁.     

Lipophilic salts as membrane additives and their influence on the properties of macro- and micro-electrodes based on neutral carriers

The influence of salts containing lipophilic cations and anions on the electrical resistance of the membranes of calcium ion-selective macro- and micro-electrodes based on a neutral carrier is described. The resistance of macroelectrodes was decreased by a factor of about 50 or of about 3 compared to membranes without and with potassium tetrakis- (p-chlorophenyl)borate, respectively. No significant reduction of the membrane resistance was achieved for microelectrodes. The lower detection limit and the Ca²⁺/K⁺ selectivity factor were improved for both types of electrode.     

Exciton-like energy collection in an oligothiophene wire end-capped by Ru- and Os-polypyridine chromophores

Ru(II)- and Os(II)-polypyridine termini are linked by a quinquethiophene bridge (the inter-metal separation is ca. 1.9 nm) wherein excitation energy flows into the luminescent Os-based unit by way of a conductive level.     

Bromine enrichment in the near-surface region of Br-doped NaCl single crystals diagnosed by Rutherford backscattering spectrometry

Bromine released from sea-salt aerosols and seawater ice is known for its high chemical reactivity. Previous studies have suggested that its availability to the gas-phase could be enhanced by segregation processes increasing Br concentration on the aerosol surface as compared to the bulk. However, little is known about the composition within the near-surface region, that is, the outermost approximately 100 monolayers. We used Rutherford backscattering spectrometry (RBS) to measure Br concentration profiles to a depth of about 750 nm of Br-doped NaCl single crystals to characterize the thermodynamics and kinetics of Br segregation to the near-surface region in moist air. These experiments were carried out on cleavage planes of melt-grown and of annealed solution-grown crystals at room temperature and relative humidities (RH) too low for formation of a stable liquid phase. Segregation of Br was below the detection limit on melt-grown crystals with Br/Cl = 0.01. In the case of annealed solution-grown crystals with Br/Cl = 0.002, average segregations of (0.24 +/- 0.11) x 10(15) and (0.42 +/- 0.12) x 10(15) Br atoms cm-2 were observed at 50% and 65% RH, respectively. No segregation was found at 20% RH. The observed Br segregation can be explained by the formation of an adsorbed liquid layer (depending on crystal surface properties and relative humidity) and preferential, diffusion-limited dissolution of Br into this layer according to the partition coefficient of Br between aqueous and solid NaCl. The thickness of the adsorbed liquid layer, which depends on crystal surface geometry and on relative humidity, can be estimated to range from 4 to at most 59 nm on the basis of measured Br concentrations and partition coefficients. Applying this concept of partitioning to natural sea salt suggests a Br/Cl molar ratio of up to 0.2 in adsorbed surface water of crystallized natural aerosol particles compared to about 0.0015 in seawater. This would have a major impact on heterogeneous reactions on sea-salt particles under dry conditions such as in the freeze-dried Arctic boundary layer.     

Anion Selectivity of Metalloporphyrins in Membranes

Lipophilic Co(III) and Mn(III) complexes of 5,10,15,20-tetrakis[4-(hexyloxycarbonyl)phenyl]porphyrin act as positively charged carriers for anions and induce anion selectivities in membranes clearly deviating from the sequence of classical anion exchangers. Different anion selectivities are observed for the Co(III) and Mn(III) porphyrins.     

LC-MS/MS determination of potential endocrine disruptors of cortico signalling in rivers and wastewaters

A targeted analytical method was established to determine a large number of chemicals known to interfere with the gluco- and mineralocorticoid signalling pathway. The analytes comprise 30 glucocorticoids and 9 mineralocorticoids. Ten out of these corticosteroids were primary metabolites. Additionally, 14 nonsteroids were included. These analytes represent a broader range of possible adverse modes of action than previously reported. For the simultaneous determination of these structurally diverse compounds, a single-step multimode solid-phase extraction and pre-concentration was applied. Extracts were separated by a short linear HPLC gradient (20 min) on a core shell RP column (2.7 μm particle size) and compounds identified and quantified by LC-MS/MS. The method provided excellent retention time reproducibility and detection limits in the low nanograms per litre range. Untreated hospital wastewater, wastewater treatment plant influent, treated effluent and river waters were analysed to demonstrate the applicability of the method. The results show that not all compounds were sufficiently eliminated by the wastewater treatment, resulting in the presence of several steroids (～20 ng/L) and nonsteroids in the final effluent, some of them at high concentrations up to 200 ng/L. Most of the detected mono-hydroxylated steroidal transformation products were found at significantly higher concentrations than their parent compounds. We therefore recommend to include these potentially bioactive metabolites in environmental toxicity assessment.