The electronic structure of cobalt(II) phthalocyanine adsorbed on Ag(111)

The electronic states of submonolayers and multilayers of cobalt(II) phthalocyanine (CoPc) adsorbed on Ag(111) were examined with photoelectron spectroscopy to obtain insight into the details of the substrate–adsorbate interaction. UV photoelectron spectroscopy (UPS) reveals the presence of two interaction-related valence states in the direct vicinity of the Fermi edge, in agreement with previous DFT calculations. X-ray photoelectron spectra indicate that the substrate–adsorbate interaction results in transfer of electron density from the substrate to the Co(II) ion. Substantial changes in the Co 2p multiplet structure, a spectral pattern induced by the open-shell character of the central Co(II) ion, indicate a complete quenching of the molecular spin. While pristine CoPc molecules are paramagnetic with S = 1/2, molecules in direct contact to the Ag(111) substrate appear to be in a diamagnetic state.     

A new study on the thick disk population component of the Galaxy

The newly-raised problem as to whether our Galaxy may contain a thick disk population component has aroused great interest. But up until now no conclusion has been reached unanimously for lack of observed data. Here this problem is discussed based on seven Basel field data calibrated recently and strong evidence is provided. New results on the values of structural parameters, luminosity functions and metal structure of the thick disk are also presented.     

On-Surface Metathesis of an Ionic Liquid on Ag(111)

We investigated the adsorption, surface enrichment, ion exchange, and on-surface metathesis of ultrathin mixed IL films on Ag(111). We stepwise deposited 0.5 ML of the protic IL diethylmethylammonium trifluoromethanesulfonate ([dema][TfO]) and 1.0 ML of the aprotic IL 1-methyl-3-octylimidazolium hexafluorophosphate ([C₈C₁Im][PF₆]) at around 90 K. Thereafter, the resulting layered frozen film was heated to 550 K, and the thermally induced phenomena were monitored in situ by angle-resolved X-ray photoelectron spectroscopy. Between 135 and 200 K, [TfO]⁻ anions at the Ag(111) surface are exchanged by [PF₆]⁻ anions and enriched together with [C₈C₁Im]⁺ cations at the IL/vacuum interface. Upon further heating, [dema][PF₆] and [OMIm][PF₆] desorb selectively at ∼235 and ∼380 K, respectively. Hereby, a wetting layer of pure [C₈C₁Im][TfO] is formed by on-surface metathesis at the IL/metal interface, which completely desorbs at ∼480 K. For comparison, ion enrichment at the vacuum/IL interface was also studied in macroscopic IL mixtures, where no influence of the solid support is expected.     

Coupled Continuous Time Random Maxima

Continuous Time Random Maxima (CTRM) are a generalization of classical extreme value theory: Instead of observing random events at regular intervals in time, the waiting times between the events are also random variables which have arbitrary distributions. In case that the waiting times between the events have infinite mean, the limit process that appears differs from the limit process that appears in the classical case. With a continuous mapping approach, we derive a limit theorem for the case that the waiting times and the subsequent events are dependent as well as for the case that the waiting times depend on the preceding events (in this case we speak of an Overshooting Continuous Time Random Maxima, abbr. OCTRM). We get the distribution functions of the limit processes and a formula for the Laplace transform in time of the CTRM and the OCTRM limit. With this formula we have another way to calculate the distribution functions of the limit processes, namely by inversion of the Laplace transform. Moreover, we present governing equations which in our case are time fractional differential equations whose solutions are the distribution functions of our limit processes.     

Erd s–Turán Type Theorems on Quasiconformal Curves and Arcs

The theorems of Erd s and Turán mentioned in the title are concerned with the distribution of zeros of a monic polynomial with known uniform norm along the unit interval or the unit disk. Recently, Blatt and Grothmann (Const. Approx.7(1991), 19–47), Grothmann (“Interpolation Points and Zeros of Polynomials in Approximation Theory,” Habilitationsschrift, Katholische Universität Eichstätt, 1992), and Andrievskii and Blatt (J. Approx. Theory88(1977), 109–134) established corresponding results for polynomials, considered on a system of sufficiently smooth Jordan curves and arcs or piecewise smooth curves and arcs. We extend some of these results to polynomials with known uniform norm along an arbitrary quasiconformal curve or arc. As applications, estimates for the distribution of the zeros of best uniform approximants, values of orthogonal polynomials, and zeros of Bieberbach polynomials and their derivatives are obtained. We also give a negative answer to one conjecture of Eiermann and Stahl (“Zeros of orthogonal polynomials on regularN-gons,” in Lecture Notes in Math.1574(1994), 187–189).     

On σ-discrete borel mappings via quasi-metrics

Let X and Y be metrizable spaces. We show that, for a mapping f : X Y, there exists a quasi-metric X inducing the topology of X such that f regarded as a mapping from (X, max{, ^–1}) to Y is continuous if and only if f in the original topology of X is a -discrete map of Borel class 1. Further, we prove that, for every -discrete mapping f: X Y of Borel class + 1, there exists a compatible quasi-metric on X such that f : (X, max{, ^–1}) Y is of Borel class . We also investigate a more general situation when the range of the mapping under consideration is not necessarily metrizable. In passing, we obtain some results related to the behaviour of absolutely Borel sets and absolutely analytic spaces with respect to compatible quasi-metrics.     

On the period matrix of a Riemann surface of large genus (with an Appendix by J.H. Conway and N.J.A. Sloane)

Summary Riemann showed that a period matrix of a compact Riemann surface of genusg1 satisfies certain relations. We give a further simple combinatorial property, related to the length of the shortest non-zero lattice vector, satisfied by such a period matrix, see (1.13). In particular, it is shown that for large genus the entire locus of Jacobians lies in a very small neighborhood of the boundary of the space of principally polarized abelian varieties.We apply this to the problem of congruence subgroups of arithmetic lattices in SL₂(). We show that, with the exception of a finite number of arithmetic lattices in SL₂(), every such lattice has a subgroup of index at most 2 which is noncongruence. A notable exception is the modular groupSL ₂().     

D-Domains of attraction of stable measures on stratified Lie groupsof attraction of stable measures on stratified Lie groups

LetG be a stratified Lie group and (_t)_{t 0} be a continuous convolution semigroup of probability measures onG. A probability measurev is said to belong to the -domain of attraction of ₁, if there exists a sequence (a _n ) of positive real numbers such that weakly, where ₁ denotes the natural dilation onG. We prove convergence criteria for discrete convolution semigroups. These are used to obtain a simple necessary and sufficient condition for the existence of sucha _n if (_t)_{t 0} has no Gaussian component. For the proof we introduce the notion of regularly varying measures onG and develop the necessary theory of regular variation.