Proper actions on cohomology manifolds

Essential results about actions of compact Lie groups on connected manifolds are generalized to proper actions of arbitrary groups on connected cohomology manifolds. Slices are replaced by certain fiber bundle structures on orbit neighborhoods. The group dimension is shown to be effectively finite. The orbits of maximal dimension form a dense open connected subset. If some orbit has codimension at most , then the group is effectively a Lie group.

     

Algebraic composition operators

The focus of this paper is on the following problem. Given a linear space F of complex-valued functions on a set X and a polynomial p(z), is there an algebraic composition operator on F whose characteristic polynomial equals p(z)? We show that the supply of all the polynomials p(z) for which the answer to this question is affirmative depends heavily on the structure of the space F.     

Comparison of location models for stochastic processes

Summary Let (Q) be the statistical experiment based on the observation of an unknown function in the presence of an additive noise process with distributionQ. The (possible) loss of information whenQ is replaced by some other noise distributionP is measured by the deficiency of (P) relative to (Q). This deficiency and its relation to the variational distance ofP andQ are studied mainly for Gaussian noise processes. Gaussian diffusion processes and special set-indexed processes are treated in detail.Research supported by a Heisenberg grant of the Deutsche Forschungsgemeinschaft     

On the separation of initial and final state effects in photoelectron spectroscopy using an extension of the auger-parameter concept

First, we show that the quantity Δβ(i) = ΔE_A(kii) + 2ΔE_B(i) — ΔE_B(k) is directly related to the final state relaxation contribution ΔE_R(i) of the binding energy shift ΔE_B(i). ΔE_A(kii) is the kinetic energy shift of the Auger transition which corresponds to the decay of a hole state with a hole in level k into a final state with two holes in level i. The shift parameter Δβ(i), which is based on information on two binding energies, is conceptually similar to Wagner's Auger parameter. To establish the relation between Δβ(i) and ΔR(i) one needs, however, less drastic approximations than in the case of Auger parameter shifts. The only approximation necessary is the assumption that ΔR(i) is determined by coulomb contributions.Secondly, we use Δβ (i) to analyse the experimental data of eighteen gaseous phosphorus-containing compounds obtained by Sodhi and Cavell¹. It is shown that ΔR(P_2p) is strongly related to changes in the polarizability of the ligands. The initial state effects derived from our study deviate from those expected on the basis of simple electronegativity considerations.     

Experimental observation of four-photon entanglement from parametric down-conversion

We observe polarization entanglement between four photons produced from a single down-conversion source. The nonclassical correlations between the measurement results violate a generalized Bell inequality for four qubits. The characteristic properties and its easy generation with high interferometric contrast make the observed four-photon state well suited for implementing advanced quantum communication schemes such as multiparty quantum key distribution, secret sharing, and telecloning.     

Growth and decay of the Pd(1 1 1)-Pd5O4 surface oxide: Pressure-dependent kinetics and structural aspects

Growth and decomposition of the Pd₅O₄ surface oxide on Pd(1 1 1) were studied at sample temperatures between 573 and 683 K and O₂ gas pressures between 10⁻⁷ and 6 × 10⁻⁵ mbar, by means of an effusive O₂ beam from a capillary array doser, scanning tunnelling microscopy (STM) and thermal desorption spectrometry (TDS). Exposures beyond the p(2 × 2)O adlayer (saturation coverage 0.25) at 683 K (near thermodynamic equilibrium with respect to Pd₅O₄ surface oxide formation) lead to incorporation of additional oxygen into the surface. To initiate the incorporation, a critical pressure beyond the thermodynamic stability limit of the surface oxide is required. This thermodynamic stability limit is near 8.9 × 10⁻⁶ mbar at 683 K, in good agreement with calculations by density functional theory. A controlled kinetic study was feasible by generating nuclei by only a short O₂ pressure pulse and then following further growth kinetics in the lower (10⁻⁶ mbar) pressure range.Growth of the surface oxide layer at a lower temperature (573 K) studied by STM is characterized by a high degree of heterogeneity. Among various metastable local structures, a seam of disordered oxide formed at the step edges is a common structural feature characteristic of initial oxide growth. Further oxide nucleation appears to be favoured along the interface between the p(2 × 2)O structure and these disordered seams. Among the intermediate phases one specifically stable phase was detected both during growth and decomposition of the Pd₅O₄ layer. It is hexagonal with a distance of about 0.62 nm between the protrusions. Its well-ordered form is a superstructure.Isothermal decay of the Pd₅O₄ oxide layer at 693 K involves at first a rearrangement into the structure, indicating its high-temperature stability. This structure can break up into small clusters of uniform size and leaves a free metal surface area covered by a p(2 × 2)O adlayer. The rate of desorption increases autocatalytically with increasing phase boundary metal-oxide. We propose that at close-to-equilibrium conditions (693 K) surface oxide growth and decay occur via this intermediate structure.     

Surface termination of BaTiO3 (001) single crystals: A combined electron spectroscopic and theoretical study

The surface termination of oxide surfaces is of crucial importance for the growth of a second material like metals or other oxides. In this study we have investigated the surface of a BaTiO₃ (001) single crystal during sample preparation by various electron spectroscopic methods. It is shown by X-ray photoelectron spectroscopy (XPS), ultraviolet photoelectron spectroscopy (UPS) and metastable induced electron spectroscopy (MIES) that during sputtering a Ba rich overlayer is formed, in which the Ba²⁺ ions are under coordinated. Below this layer, an oxygen deficient BaTiO₃ layer is found. During annealing, we observe the reformation of the crystalline structure. UP and MIE spectra provide clear evidence of a BaO terminated surface. X-ray photoelectron diffraction studies support this result, comparing recorded polar angle scans with calculated intensity modulations using multiple scattering cluster models.     

Relaxation of hyperpolarized 129Xe in a deflating polymer bag

In magnetic resonance imaging with hyperpolarized (HP) noble gases, data is often acquired during prolonged gas delivery from a storage reservoir. However, little is known about the extent to which relaxation within the reservoir will limit the useful acquisition time. For quantitative characterization, 129Xe relaxation was studied in a bag made of polyvinyl fluoride (Tedlar). Particular emphasis was on wall relaxation, as this mechanism is expected to dominate. The HP 129Xe magnetization dynamics in the deflating bag were accurately described by a model assuming dissolution of Xe in the polymer matrix and dipolar relaxation with neighboring nuclear spins. In particular, the wall relaxation rate changed linearly with the surface-to-volume ratio and exhibited a relaxivity of κ=0.392±0.008 cm/h, which is in reasonable agreement with κ=0.331±0.051 cm/h measured in a static Tedlar bag. Estimates for the bulk gas-phase 129Xe relaxation yielded T1bulk=2.55±0.22 h, which is dominated by intrinsic Xe-Xe relaxation, with small additional contributions from magnetic field inhomogeneities and oxygen-induced relaxation. Calculations based on these findings indicate that relaxation may limit HP 129Xe experiments when slow gas delivery rates are employed as, for example, in mouse imaging or vascular infusion experiments.