L p-discrepancy and statistical independence of sequences

We characterize statistical independence of sequences by the L ^p-discrepancy and the Wiener L ^p-discrepancy. Furthermore, we find asymptotic information on the distribution of the L ²-discrepancy of sequences     

Nitrate degradation without 15N enrichment: a hydrochemical and isotopic study of a fractured rock aquifer including embedded lakes

Water samples from three quarry lakes and the surrounding fractured rock aquifer were investigated for delta18O and delta2H (H2O), delta15N and delta18O (NO3-), as well as anions and cations. Lake water and groundwater can be distinguished by their different chemical and isotopic composition. Because of evaporation processes, 18O and 2H are enriched in the lake water and can be used as natural tracers for the water dynamic of the lakes. The groundwater is characterised by high nitrate concentrations (up to 120 mg/l). Lake internal processes reduce the nitrate concentration in the quarry lakes. However, no enrichment of delta15N and delta18O in nitrate, typical for microbial nitrate degradation, is observed in the lake water. Because of the complex flow paths in the fractured rock aquifer and the intense chemical transformations at the interface between groundwater and lake water, isotopic and hydrochemical data of lake water and groundwater alone do not conclusively explain hydrological and hydrochemical processes of the investigated lake-groundwater system.     

Self-chemical ionization of diethylzinc

The self-chemical ionization of diethylzinc is examined by Fourier transform ion cyclotron resonance (FT-ICR) mass spectrometry and semiempirical molecular orbital calculations. Electron impact of diethylzinc neutral produces the radical cation, C(4)H(15)Zn(+) (m/z x 122), which reacts further with the neutral (C(2)H(5))(2)Zn to give the following product ions: Zn(+) (m/z x 64), C(2)H(5)Zn(+) (m/z x 93), C(4)H(9)Zn(+) (m/z x 121), C(4)H(11)Zn(2)(+) (m/z x 187), and C(6)H(15)Zn(2)(+) (m/z x 215). To determine the structure and pathways for production of these ions, monoisotopic (12)C(4)H(15)(64)Zn(+), (64)Zn(+) and (12)C(2)H(5)(64)Zn(+) were individually isolated and reacted with the neutral background. We also performed semiempirical molecular orbital calculations (ZINDO/1). The molecular orbital calculations and experimental data are consistent in predicting that the ethyl group on the diethylzinc cation carries the positive charge. Copyright 1999 John Wiley & Sons, Ltd.     

Josephson-junction qubits: entanglement and coherence

We review briefly the problems that are driving the search for a quantum computer. These include, primarily, methods for encryption and decryption based on Shor’s algorithm for factoring large integers and the use of Pell’s equation for encryption. We also outline some of the approaches that have been suggested for implementing a quantum computer and then focus on Josephson-junction systems as qubits. We have been investigating the current-biased Josephson junction for this application, a suggestion we made about 2 years ago. We have studied macroscopic quantum tunneling and energy level spectroscopy, using microwaves, in single junctions and recently we have begun measurements of the two-quantum bit (qubit) system, i.e. two capacitively coupled junctions. Theoretical studies of energy levels and their dynamic evolution are also in progress. In the present report we discuss the basics of single Josephson junctions and compare their potential as qubits with the potentials of other systems. We also discuss our future plans to obtain greater isolation of the junctions from sources of decoherence and to develop realistic qubits. An important first step must be to exhibit quantum entanglement and measure coherence times. Then it must be shown that the states of the qubits can be initialized, that gate operations can be performed, and that the results can be read out.     

Dynamics of argon in confined geometry

The role of geometrical confinement on the dynamics of argon is studied. We have investigated ³⁶Argon adsorbed in nanoporous Gelsil glass by inelastic neutron scattering. By fractional filling the `dimensionality' of the system is tuned from a two-dimensional towards the bulk state. Ab-initio calculations of plane sheets of Ar atoms and of bulk Ar are compared to the experimental results. A shift of various phonon modes to lower energies with decreasing dimensionality is observed in the results of both methods.     

Methyl-perthiooxalate und deren Reaktion mit Ph3P

Methyl-perthiooxalates and their Reaction with Ph₃ O-Methyl-1,1-dithiooxalate reacts with d⁸ transition metal ions with the spontaneous formation of mononuclear perthio/dithiooxalate complexes [(i-dtoMe)M(ptoMe)] (M = Ni, Pd, Pt). The mass spectrometric fragmentation of this complexes is discussed. The spontaneous sulfur insertion can be reversed by reaction with Ph₃P. Following up reactions with different Ph₃P equivalents are investigated for the Ni^II compound. Beside the synthesis of the square planar mixed ligand complex [(Ph₃P)Ni(i-dtoMe)₂] a Ni^I complex was detected by EPR spectroscopy.     

Deformation spaces of one-dimensional formal modules and their cohomology

Let Mm be the formal scheme which represents the functor of deformations of a one-dimensional formal module over equipped with a level-m-structure. By work of Boyer (in equal characteristic) and Harris and Taylor, the ?-adic étale cohomology of the generic fibre Mm of Mm realizes simultaneously the local Langlands and Jacquet-Langlands correspondences. The proofs given so far use Drinfeld modular varieties or Shimura varieties to derive this local result. In this paper we show without the use of global moduli spaces that the Jacquet-Langlands correspondence is realized by the Euler-Poincaré characteristic of the cohomology. Under a certain finiteness assumption on the cohomology groups, it is shown that the correspondence is realized in only one degree. One main ingredient of the proof consists in analyzing the boundary of the deformation spaces and in studying larger spaces which can be considered as compactifications of the spaces Mm.