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.     

Analysis of human brain tissue, brain tumors and tumor cells by infrared spectroscopic mapping

This study uses infrared (IR) spectroscopic, point detection, mapping procedures to examine tissue samples from normal brain specimens and from astrocytic gliomas, the most frequent human brain tumors. Model systems were derived from cultured glioma cell lines. IR spectra of normal tissue sections distinguished white matter from gray matter by increased spectral contributions from lipids and cholesterol. Qualitatively the same differences were found in IR spectra of low and high grade glioma tissue sections pointing to a significant reduction of brain lipids with increasing malignancy. Whereas spectral contributions of proteins and lipids were similar in IR spectra of glioma cells and tissues, nucleic acid bands were more intense for cells suggesting higher proliferative activities. For statistical analyses of IR spectroscopic maps from 71 samples, a parameter for the lipid to protein ratio was introduced involving the CH(2) symmetric stretch band with lipids as main contributors and the amide I band of proteins. As this parameter correlated with the grade of gliomas obtained from standard histopathological examination, it was applied to classify brain tissue sections based on IR spectroscopic mapping.     

Near infrared Raman spectroscopic mapping of native brain tissue and intracranial tumors

This study assessed the diagnostic potential of Raman spectroscopic mapping by evaluating its ability to distinguish between normal brain tissue and the human intracranial tumors gliomas and meningeomas. Seven Raman maps of native specimens were collected ex vivo by a Raman spectrometer with 785 nm excitation coupled to a microscope with a motorized stage. Variations within each Raman map were analyzed by cluster analysis. The dependence of tissue composition on the tissue type in cluster averaged Raman spectra was shown by linear combinations of reference spectra. Normal brain tissue was found to contain higher levels of lipids, intracranial tumors have more hemoglobin and lower lipid to protein ratios, meningeomas contain more collagen with maximum collagen content in normal meninges. One sample was studied without freezing. Whereas tumor regions did not change significantly, spectral changes were observed in the hemoglobin component after snap freezing and thawing to room temperature. The results constitute a basis for subsequent Raman studies to develop classification models for diagnosis of brain tissue.     

Unusual peak defocusing in capillary GC on hexakis(2,6-diO-pentyl-3-O-acetyl)-α-cyclodextrin stationary phase

An unusual peak defocusing effect influencing chromatographic performance over a limited range of elution temperatures is described for hexakis(2,6-di-O-pentyl-3-O-acetyl)-α-cyclodextrin stationary phase. Since this phenomenon is likely to be dependent on minor details of the cyclodextrin molecule, full assignment of the ¹H- and ¹³C-NMR-spectra are given.