Eine geometrische Deutung der eingliedrigen Untergruppen der allgemeinen Ebenen isotropen Ähnlichkeitsgruppe

In this paper the one-parameter subgroups of the several conformal transformation groups of the isotropic plane I ₂ are investigated. In the first part we develop invariants of the groups such as differential of arc and curvature and in the second part we give a geometrical interpretation of these invariants.     

Iterationsverfahren für monotone,nicht notwendig Lipschitz-beschränkte Operatoren im Hilbert-Raum

Summary We state three theorems concerning iterative methods for solving equations containing monotone, but not necessarily uniformly monotone operators in Hilbert space, which may be not Lipschitz bounded, thus extending results obtained by Sibony [9, 10]. We apply the method to a nonlinear elliptic Dirichlet problem of laminar flow theory of non Newtonian fluids, thus improving the rather experimental treatment given in Ames [1] and removing the condition of nonzero difference quotients assumed by Cryer [3].     

Estimation of nonlinear autoregressive models using design-adapted wavelets

We estimate nonlinear autoregressive models using a design-adapted wavelet estimator. We show two properties of the wavelet transform adapted to an autoregressive design. First, in an asymptotic setup, we derive the order of the threshold that removes all the noise with a probability tending to one asymptotically. Second, with this threshold, we estimate the detail coefficients by soft-thresholding the empirical detail coefficients. We show an upper bound on thel ₂-risk of these soft-thresholded detail coefficients. Finally, we illustrate the behavior of this design-adapted wavelet estimator on simulated and real data sets. Financial support from the contract ‘Projet d'Actions de Recherche Concertées’ nr. 98/03-217 from the Belgian government, and from the IAP research network nr. P5/24 of the Belgian State (Federal Office for Scientific, Technical and Cultural Affairs) is gratefully acknowledged.     

Structural characterization of U(VI) surface complexes on kaolinite in the presence of humic acid using EXAFS spectroscopy

To determine the influence of humic acid (HA), pH, and presence of atmospheric CO2 on the sorption of U(VI) onto kaolinite, the structure of the surface complexes was studied by U L III-edge extended X-ray absorption fine structure (EXAFS) spectroscopy. The best fits to the experimental EXAFS data were obtained by including two uranium coordination shells with two axial (O ax) and five equatorial (O eq) oxygen atoms at 1.77+/-0.02 and 2.34+/-0.02 A, respectively, and two coordination shells with one Al/Si atom each at 3.1 and 3.3 A. As in the case of the binary system U(VI)-kaolinite, uranium forms inner-sphere surface complexes by edge sharing with aluminum octahedra and/or silicon tetrahedra. HA and atmospheric CO2 as well as pH had no influence on the EXAFS structural parameters in the pH range of 5-8. Despite the presence of HA, U(VI) prefers to sorb directly onto kaolinite and not to HA that is bound to the clay surface. X-ray photoelectron spectroscopy (XPS) measurements of kaolinite particles that had been exposed to HA suspensions showed that significant parts of the kaolinite surface are not covered by HA.     

Binary and ternary uranium(VI) humate complexes studied by attenuated total reflection Fourier-transform infrared spectroscopy

The complexation of U(VI) with humic acid (HA) in aqueous solution has been investigated at an ionic strength of 0.1 M (NaCl) in the pH range between pH 2 and 10 at different carbonate concentrations by attenuated total reflection Fourier-transform infrared (ATR FT-IR) spectroscopy. For the first time, the formation of binary and ternary U(VI) humate complexes was directly verified by in situ spectroscopic measurements. The complex formation constants for the binary U(VI) humate complex (UO(2)HA(II)) and for the ternary U(VI) mono hydroxo humate complex (UO(2)(OH)HA(I)) as well as the ternary U(VI) dicarbonato humate complex (UO(2)(CO(3))(2)HA(II)(4-)) determined from the spectroscopic data amount to log β(0.1 M) = 6.70 ± 0.25, log β(0.1 M) = 15.14 ± 0.25 and log β(0.1 M) = 24.47 ± 0.70, respectively, and verify literature data.     

Electron lifetime in a Shockley-type metal-organic interface state

The lifetimes of electrons at the interface between 3,4,9,10-perylene-tetracarboxylic acid dianhydride (PTCDA) and Ag(111) have been studied by means of time- and angle-resolved two-photon photoemission. We observe a dispersing unoccupied state 0.6 eV above the Fermi level with an effective electron mass of 0.39m{e} at the Gamma[over ] point. The short lifetime of 54 fs is indicative of a large penetration of the wave function into the metal. Supported by model calculations this interface state is interpreted as predominantly arising from an upshift of the occupied Shockley surface state of the clean metal due to the interaction with the PTCDA overlayer.     

On the worst-case evaluation complexity of non-monotone line search algorithms

A general class of non-monotone line search algorithms has been proposed by Sachs and Sachs (Control Cybern 40:1059–1075, 2011) for smooth unconstrained optimization, generalizing various non-monotone step size rules such as the modified Armijo rule of Zhang and Hager (SIAM J Optim 14:1043–1056, 2004). In this paper, the worst-case complexity of this class of non-monotone algorithms is studied. The analysis is carried out in the context of non-convex, convex and strongly convex objectives with Lipschitz continuous gradients. Despite de nonmonotonicity in the decrease of function values, the complexity bounds obtained agree in order with the bounds already established for monotone algorithms.