Fractional Hamiltonian Monodromy

We introduce fractional monodromy in order to characterize certain non-isolated critical values of the energy–momentum map of integrable Hamiltonian dynamical systems represented by nonlinear resonant two-dimensional oscillators. We give the formal mathematical definition of fractional monodromy, which is a generalization of the definition of monodromy used by other authors before. We prove that the 1:( − 2) resonant oscillator system has monodromy matrix with half-integer coefficients and discuss manifestations of this monodromy in quantum systems. Communicated by Eduard Zehnder Submitted: February 25, 2005; Accepted: November 17, 2005     

On variable stepsize Runge-Kutta approximations of a Cauchy problem for the evolution equation

We consider a Cauchy problem for the sectorial evolution equation with generally variable operator in a Banach space. Variable stepsize discretizations of this problem by means of a strongly A(φ)-stable Runge-Kutta method are studied. The stability and error estimates of the discrete solutions are derived for wider families of nonuniform grids than quasiuniform ones (in particular, if the operator in question is constant or Lipschitz-continuous, for arbitrary grids).     

A catalyst-free one-step synthesis of N-pyrimidinyl amidines from endocyclic enamines and 4-azidopyrimidines

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Formation of spanning water networks on protein surfaces via 2D percolation transition

The formation of spanning hydrogen-bonded water networks on protein surfaces by a percolation transition is closely connected with the onset of their biological activity. To analyze the structure of the hydration water at this important threshold, we performed the first computer simulation study of the percolation transition of water in a model protein powder and on the surface of a single protein molecule. The formation of an infinite water network in the protein powder occurs as a 2D percolation transition at a critical hydration level, which is close to the values observed experimentally. The formation of a spanning 2D water network on a single rigid protein molecule can be described by adapting the cluster analysis of conventional percolation studies to the characterization of the connectivity of the hydration water on the surface of finite objects. Strong fluctuations of the surface water network are observed close to the percolation threshold. Our simulations also furnish a microscopic picture for understanding the specific values of the experimentally observed hydration levels, where different steps of increasing mobility in the hydrated powder are observed.     

Structure and properties of nonclassical polymers

Utilizing an extended Hubbard-type Hamiltonian which incorporates both nearest-neighbour Coulomb repulsion and exchange interactions, we have studied the energy dispersion of the lowest elementary excitation from the ferromagnetically aligned state of quasi one-dimensional alternant hydrocarbon networks. It was found that the main effect of the long range Coulomb interaction may be thought of as a renormalization (screening) of the on-site Hubbard integral. This implies an enhancement of the kinetic exchange term and impairs the stability of the ferromagnetic state towards single spin inversions. However, for physically relevant values of the parameters entering the model Hamiltonian, the collective spin excitation represents a magnon, whose energy band lies above the reference value pertaining to the magnetically saturated configuration.Dedicated to Prof. Dr. Adolf Neckel on the occasion of his 60th birthday     

Synthesis and capsule formation of upper rim substituted tetra-acrylamido calix[4]arenes

Upper rim substituted tetraiodo calix[4]arenes are coupled to a variety of acrylamides using the palladium catalysed Heck reaction. Tetra-acrylamido upper rim substituted calix[4]arenes are obtained in good yields with exceptionally high stereoselectivity, to produce the all-trans isomers. Tetra-acrylamido calix[4]arenes derived from secondary acrylamides are shown to dimerise via eight hydrogen bonds to form dimeric capsules, which are able to include small organic molecules.     

光同时诱导水中Cr(Ⅵ)的还原与橙黄Ⅱ的氧化

光同时诱导水中Cr(Ⅵ)的还原与橙黄Ⅱ的氧化;染料;橙黄Ⅱ;Cr(Ⅵ);光还原;光降解     

Detection of trace amounts of Ni by laser-induced fluorescence in graphite furnace with intensified charge coupled device

A laser-induced fluorescence in graphite furnace (LIF-GF) set-up has been equipped with an intensified CCD detector (ICCD) that enables simultaneous multichannel detection of large wavelength regions. The main advantages of such a system in comparison with conventional photomultiplier detection are: simultaneous detection of several fluorescence wavelengths for easy characterization of excitation and fluorescence spectra and for an increase of the absolute sensitivity and spectral selectivity; simultaneous monitoring of background signals, such as those due to matrix interferences, blackbody radiation and scattered laser light; decrease of the susceptibility to radio-frequency pick-ups emitted from the pump laser due to the delayed read-out procedure; time-resolved studies of fluorescence spectra for improved elemental selectivity or for studies of atomization processes, and a possibility to perform two-dimensional imaging of height distributions of atomization and, in combination with an imaging spectrometer, diffusion processes in the furnace. The first work on LIF-GF with ICCD detection has been performed on Ni. The most sensitive and versatile excitation and detection wavelengths have been identified. Detection limits in water solutions by the LIF-GF technique have been improved by two orders of magnitude and are found to be 0.015 pg with ICCD and 0.01 pg using a photomultiplier at the most sensitive excitation and detection wavelengths. Nickel in concentrations has been detected in aqueous standard reference samples with sodium concentrations ranging from to % (riverine water and estuarine water) with good accuracy and precision. The Ni contents of standard riverine and estuarine water were determined to 1.00 ± 0.11 and 0.75 ± 0.07 ng/ml, respectively. The certified concentrations are 1.03 ± 0.10 and 0.743 ± 0.078 .