On a New Formulation of the Real-Time Propagator

The development of theoretical tools for the study of dynamical phenomena of many-particle systems on the quantum level is a fundamental challenge since many decades. A lot of efforts have been invested on Feynman's path integral approach, however, no computationally tractable method for investigating realistic systems could be developed up to now. In this paper we propose an alternative representation of the real-time many-body evolution operator formulated within the framework of the auxiliary field formalism. Our goal is to derive a new auxiliary field functional integral representation, in which the large oscillations of the functional integrand are reduced, in order to render the auxiliary field approach more attractive for real-time computation. This objective is attained using a generalized version of the method of Gaussian equivalent representation of Efimov and Ganbold [Phys. Stat. Sol. 168 (1991) 165], which eliminates the low-order fluctuations of the auxiliary field from the interaction functional.     

Effect of Groundwater Composition on Arsenic Detection by Bacterial Biosensors

A luminescent bacterial biosensor was used to quantify bioavailable arsenic in artificial groundwater. Its light production above the background emission was proportional to the arsenite concentration in the toxicologically relevant range of 0 to 0.5 μM. Effects of the inorganic solutes phosphate, Fe(II) and silicate on the biosensor signal were studied. Phosphate at a concentration of 0.25 g L⁻¹ phosphate slightly stimulated the light emission, but much less than toxicologically relevant concentrations of the much stronger inducer arsenite. No effect of phosphate was oberved in the presence of arsenite. Freshly prepared sodium silicate solution at a concentration of 10 mg L⁻¹ Si reduced the arsenite-induced light production by roughly 37%, which can be explained by transient polymerization leading to sequestration of some arsenic. After three days of incubation, silicate did not have this effect anymore, probably because depolymerization occurred. In the presence of 0.4 mg L⁻¹ Fe(II), the arsenite-induced light emission was reduced by up to 90%, probably due to iron oxidation followed by arsenite adsorption on the less soluble Fe(III) possibly along with some oxidation to the stronger adsorbing As(V). Addition of 100 μM EDTA was capable of releasing all arsenic from the precipitate and to transform it into the biologically measurable, dissolved state. The biosensor also proved valuable for monitoring the effectiveness of an arsenic removal procedure based on water filtration through a mixture of sand and iron granules.     

A theory of pseudo-differential boundary value problems with discontinuous conditions I

Summary The paper deals with mixed boundary value problems and transmission problems for elliptic differential and pseudo-differential operators. These problems are considered as elements of an algebra (where is the considered domain, x=, YX a submanifold of codimension 1, where the conditions have a jump, and x is a certain compactification of X/Y), the elements of which are described on a symbolic level. By means of additional conditions (of trace and potential type, with respect to Y) a given mixed problem is extended to an operator, and the Fredholm property of is established under an ellipticity condition, the parametrix is constructed on symbolic level and ind is expressed. In the second part the authors also study classes of special cases, namely differential operators of second and higher order with mixed boundary conditions for dim 2, where explicit index expressions are derived.     

Cooperative effects in binuclear zirconocenes: Their synthesis and use as catalyst in propene polymerization

The mono- and bis-cyclopentadienyl compounds 1-(Cp″)-4-(CH₃)C₆H₄ (1) and 1, 4-(Cp″)₂C₆H₄ (2) (Cp″ = 3,4-dimethylcyclopenta-1,3-diene-1-yl) have been synthesized. The reactions of the lithium salts of 1 and 2 with CpZrCl₃ · dme (dme = dimethoxyethane) and Cp*ZrCl₃(CP* = C₅(CH₃)₅) yielded the mono- and bi-nuclear bridged zirconocenes 1-(Cp″ZrCpCl₂)-4-(CH₃)C₆H₄ (3), 1,4-(Cp″ZrCpCl₂)₂C₆H₄ (4) and 1,4-(Cp″ZrCp*Cl₂)₂C₆H₄ (5). When activated with methylaluminoxane (MAO), the mono- and bi-nuclear zirconocenes 3 and 4 catalyse the polymerization of propene. The influence of the catalyst composition on the polymerization kinetics and molecular weight is discussed.     

Propene polymerization using homogeneous MAO-activated metallocene catalysts: Me2Si(Benz[e]Indenyl)2ZrCl2/MAO vs. Me2Si(2-Me-Benz[e]Indenyl)2ZrCl2/MAO

Propene was polymerized at 40°C and 2-bar propene in toluene using methylalumoxane (MAO) activated rac-Me₂Si(Benz[e]Indenyl)₂ZrCl₂ ( BI ) and rac-Me₂Si(2-Me-Benz[e]Indenyl)₂ZrCl₂ ( MBI ). Catalyst BI /MAO polymerizes propene with high activity to afford low molecular weight polypropylene, whereas MBI /MAO is less active and produces high molecular weight polypropylene. Variation of reaction conditions such as propene concentration, temperature, concentration of catalyst components, and addition of hydrogen reveals that the lower molecular weight polypropylene produced with BI /MAO results from chain transfer to propene monomer following a 2,1-insertion. A large fraction of both metallocene catalyst systems is deactivated upon 2,1-insertion. Such dormant sites can be reactivated by H₂-addition, which affords active metallocene hydrides. This effect of H₂-addition is reflected by a decreasing content of head-to-head enchainment and the formation of polypropylene with n-butyl end groups. Both catalysts show a strong dependence of activity on propene concentration that indicates a formal reaction order of 1.7 with respect to propene. MBI /MAO shows a much higher dependence of the activity on temperature than BI /MAO. At elevated temperatures, MBI /MAO polymerizes propene faster than BI /MAO. © 1995 John Wiley & Sons, Inc.     

Organocatalytic asymmetric alpha-bromination of aldehydes and ketones

The first organocatalytic enantioselective alpha-bromination of aldehydes and ketones is presented; a C2-symmetric diphenylpyrrolidine catalyst afforded the alpha-brominated aldehydes in good yields and up to 96% ee, while ketones were alpha-brominated by a C2-symmetric imidazolidine in up to 94% ee; furthermore, the organocatalytic enantioselective alpha-iodination of aldehydes is also demonstrated to proceed with up to 89% ee.     

Quantitative analysis of small pharmaceutical drugs using a high repetition rate laser matrix-assisted laser/desorption ionization source

In this work, a high repetition rate laser matrix-assisted laser desorption/ionization (MALDI) source is studied on a quadrupole-time-of-flight (QqTOF) and a triple quadrupole (QqQ) mass spectrometer for rapid quantification of small pharmaceutical drugs. The high repetition rate laser allows an up to 100-fold higher pulse frequency as compared with regular MALDI lasers, resulting in much larger sample throughput and number of accumulated spectra. This increases the reproducibility of signal intensities considerably, with average values being around 5% relative standard deviation after taking into account the area ratio of the analyte to an internal standard. Experiments were conducted in MS/MS mode to circumvent the large chemical background due to MALDI matrix ions in the low mass range. The dynamic range of calibration curves on the QqTOF mass spectrometer extended over at least two orders of magnitude, whereas on the QqQ it extended over at least three orders of magnitude. Detection limits ranged from 60-400 pg/microL on the QqTOF and from 6-70 pg/microL on the QqQ for a series of benzodiazepines. The benzodiazepine content of commercial pill formulations was quantified, and less than 5% error was obtained between the present method and the manufacturer's certified values. Furthermore, a high sample throughput was achieved with this method, so that a single MALDI spot could be quantitatively scanned in as little as 15 s, and an entire 96-well MALDI plate in 24 min.