An isometry theorem for quadratic differentials on Riemann surfaces of finite genus

Assume both and are Riemann surfaces which are subsets of compact Riemann surfaces and respectively, and that the set has infinitely many points. We show that the only surjective complex linear isometries between the spaces of integrable holomorphic quadratic differentials on and are the ones induced by conformal homeomorphisms and complex constants of modulus 1. It follows that every biholomorphic map from the Teichmüller space of onto the Teichmüller space of is induced by some quasiconformal map of onto . Consequently we can find an uncountable set of Riemann surfaces whose Teichmüller spaces are not biholomorphically equivalent.

     

On summability of pairs of convolution sequences of probability measures on locally compact semigroups

In this paper we study the problem of convergence in the weak and the vague topology of the sequence

On the Spectrum of the Surface Maryland Model

We study spectral properties of the discrete Laplacian H on the half space Z₊ ^d+1 = Z^d× Z₊ with a boundary condition (n,-1) = tan( ... n + )(n,0), where [0,1]^d. We denote by H₀ the Dirichlet Laplacian on Z₊ ^d+1. Whenever is independent over rationals (H) = R. Khoruzenko and Pastur have shown for a set of 's of Lebesgue measure 1, the spectrum of H on R\ (H₀) is pure point and that corresponding eigenfunctions decay exponentially. In this Letter we show that if is independent over rationals, then the spectrum of H on the set (H₀) is purely absolutely continuous.     

Nanoscale degradation of polypyrrole films under oxidative stress: An atomic force microscopy study and review

Atomic force microscopy (AFM) is employed to monitor the surface morphology of polypyrrole (PPy) films grown on vitreous carbon substrates during the catalytic reduction of Cr(VI) to Cr(III). The morphology of freshly-prepared films depends on substrate characteristics. Upon reaction, uniform nodules of aggregated PPy clusters appear. No significant differences in surface morphology are found between its oxidized and reduced forms. Loss of catalytic activity after 8-9 oxidation/reduction cycles of exposure to the chromate solution (oxidation) and electrochemical recharging of the film at negative potentials (reduction) correlates well with the observed polymer film dissolution/detachment from the carbon substrate. Formation of well-defined circular features (PPy rings) at different stages leads to a model for the film degradation process that includes formation of Cl₂ gas inside the polymer matrix. In the final stages, the bulk of the film typically fractures and detaches from the electrode. A catalytically inactive, ultrathin PPy layer remains on the substrate even after prolonged exposure to the target solution. A review of techniques for the study of PPy aging/degradation is given.     

Photo-induced electron emission from 17beta-estradiol and progesterone and possible biological consequences

It was established for the first time, that the sexual hormones 17beta-estradiol (17betaE2) and progesterone (PRG) are able to emit electrons from their excited single state in water-ethanol mixtures. The yield of the "solvated electrons" (e(s)(-)) depends on the substrate concentration, the ratio of water-alcohol-mixtures and the temperature. The e(s)(-) yield obtained from 17betaE2 is by two orders of magnitude higher than this of PRG. The possible relationship of the resulting hormone transients from 17betaE2 leading via specific metabolites to breast cancer is discussed.     

A linearized path integral description of the collision process between a water molecule and a graphite surface

Quantum effects in the scattering and desorption process of a water molecule from a graphite surface are investigated using the linearized path integral model. The graphite surface is quantized rigorously using the fully quantum many-body Wigner transform of the surface Boltzmann operator, while the water molecule is treated as rigid. Classical dynamics with these quantized initial conditions show that quantizing the surface at 100 and 300 K results in markedly different results, compared to a fully classical analysis. The trapping probability (defined as the probability of multiple encounters with the surface) is not sensitive to the choice of dynamical treatment, but the residence time on the surface is much shorter in the quantum case. At 300 K the transiently trapped molecules desorb from the surface with a rate constant which is 60-70% larger than the corresponding classical value. Lowering the surface temperature to 100 K decreases the quantum rate constant by approximately a factor of 3 while all trapped molecules stick to the surface in the classical case. The stability of the quantum initial state for the highly anisotropic graphite crystal is discussed in detail as well as the dynamical consequences of energy redistribution during the scattering process. The graphite surface application demonstrates that the Boltzmann operator Wigner transform for a system with 900 degrees of freedom can be obtained by the so-called gradient implementation [Poulsen et al. J. Chem. Theory Comput. 2006, 2, 1482] of the underlying Feynman-Kleinert effective frequency theory, an implementation that only requires a force and potential routine for the system at hand, and hence is applicable to any molecule-surface collision problem.     

Mean‐Field Evolution of Fermionic Mixed States

In this paper we study the dynamics of fermionic mixed states in the mean‐field regime. We consider initial states that are close to quasi‐free states and prove that, under suitable assumptions on the initial data and on the many‐body interaction, the quantum evolution of such initial data is well approximated by a suitable quasi‐free state. In particular, we prove that the evolution of the reduced one‐particle density matrix converges, as the number of particles goes to infinity, to the solution of the time‐dependent Hartree‐Fock equation. Our result holds for all times and gives effective estimates on the rate of convergence of the many‐body dynamics towards the Hartree‐Fock evolution.© 2015 Wiley Periodicals, Inc.     

Localization of Surface Spectra

We study spectral properties of the discrete Laplacian H on the half-space with random boundary condition ; the V(n) are independent random variables on a probability space and λ is the coupling constant. It is known that if the V(n) have densities, then on the interval [-2(d+1), 2(d+1)] (=σ(H ₀), the spectrum of the Dirichlet Laplacian) the spectrum of H is P-a.s. absolutely continuous for all λ [JL1]. Here we show that if the random potential P satisfies the assumption of Aizenman–Molchanov [AM], then there are constants λ _d and Λ _d such that for |λ|<lambda; _d and |λ|> Λ _d the spectrum of H outside σ(H ₀) is P-a.s. pure point with exponentially decaying eigenfunctions. Received: 3 December 1998 / Accepted: 27 May 1999