Positon and positon-like solutions of the Korteweg-de Vries and Sine-Gordon equations

It is shown that the positon solution, reported recently for the Korteweg-de Vries and other completely integrable equations, can be regarded as a limiting case of the well-known 2-soliton formula. The existence of integrals of motion related to singular positon solutions is also discussed.     

Analysis of powder mixtures with the help of abrasive stripping voltammetry and coulometry

Summary Abrasive stripping voltammetry was applied to the quantitative analysis of the following powder mixtures: MnO₂-FeOOH, HgS-HgO, HgO-PbO. Therefore, g-amounts of the powder mixture were transferred onto a solid electrode and the electrochemical response of the solid sample is recorded. The calibration was made by measuring the percentage peak height of each component taking the sum of peak currents of both components as 100%. The relative standard deviation ranges from 3 to 15%. A calibration-free method based on microcoulometric measurements can be used in the case of powder mixtures of AgCl-AgI. The integration of staircase voltammograms directly yields the charges required to reduce AgCl and AgI and thus also gives the ratio of both components. The relative standard deviation was 10%. Microcoulometric measurements gave evidence that, in abrasive stripping voltammetry, the amount of electroactive substance ranges between 10^–12 and 10^–9 mole.On leave from University of Warsaw, Poland     

On the asymptotic and invariantσ-algebras of random walks on locally compact groups

Summary Consider a random walk of law on a locally compact second countable groupG. Let the starting measure be equivalent to the Haar measure and denote byQ the corresponding Markov measure on the space of pathsG . We study the relation between the spacesL (G , ^a ,Q) andL (G , ⁱ ,Q) where ^a and ⁱ stand for the asymptotic and invariant -algebras, respectively. We obtain a factorizationL (G , ^a ,Q) L (G , ⁱ ,Q)L (C) whereC is a cyclic group whose order (finite or infinite) coincides with the period of the Markov shift and is determined by the asymptotic behaviour of the convolution powers ⁿ.     

Diastereoselective synthesis of the polyol-containing side chain of the ent-bengamides

The synthesis of the non-natural antipode of the bengamide polyol-containing side chain has been achieved utilizing a diastereoselective oxygenated-enolate aldol reaction as the key step. A substrate-controlled reduction was used to complete the stereochemical array.     

Master equation — The information gain minimum approximation

Approximate time-dependent solutions of a master equation having unique stationary solution can be obtained by minimizing the information gain functional subject to constraints for mean values of a number of chosen observables. We study mathematical properties of such an approximation. We find the region of applicability, prove that the approximate solutions are globally asymptotically stable, and show how the approximation is related to some exact integrodifferential equation governing the time evolution of the mean values of the chosen observables.     

Prediction of liquid-liquid flow in an SMX static mixer using large eddy simulations

The main purpose of the paper is to apply the large eddy simulations (LES) technique and to verify its use as a predicting tool for turbulent liquid-liquid flow in an SMX static mixer. LES modeling was carried out using the Smagorinsky-Lilly model of the turbulent subgrid viscosity for the Reynolds number of 5000 and 10000. The continuous phase was water and the dispersed phase was silicon oil. The investigation covers the effects of the density ratio between the phases. Three different cases of liquid densities were considered. The dispersed phase concentration distribution in the mixer cross-sections was compared with the corresponding time averaged results obtained formerly for the same configuration in a steady-state simulation using the standard RANS approach with the k-ɛ model. The dependency of the standard deviation of the dispersed phase concentration on the distance from the mixer inlet and the impact of the centrifugal force on the phase concentration distribution were investigated. The presented results for the SMX static mixer confirm conclusions of previous studies by Jaworski et al. (2006) obtained for a Kenics static mixer and show less a pronounced influence of the centrifugal force on the phase concentration distribution of the LES results in comparison to the RANS case.     

Zinspy sensors with enhanced dynamic range for imaging neuronal cell zinc uptake and mobilization

Thiophene moieties were incorporated into previously described Zinspy (ZS) fluorescent Zn(II) sensor motifs (Nolan, E. M.; Lippard, S. J. Inorg. Chem. 2004, 43, 8310-8317) to provide enhanced fluorescence properties, low-micromolar dissociation constants for Zn(II), and improved Zn(II) selectivity. Halogenation of the xanthenone and benzoate moieties of the fluorescein platform systematically modulates the excitation and emission profiles, pH-dependent fluorescence, Zn(II) affinity, and Zn(II) complexation rates, offering a general strategy for tuning multiple properties of xanthenone-based metal ion sensors. Extensive biological studies in cultured cells and primary neuronal cultures demonstrate 2-{6-hydroxy-3-oxo-4,5-bis[(pyridin-2-ylmethylthiophen-2-ylmethylamino)methyl]-3H-xanthen-9-yl}benzoic acid (ZS5) to be a versatile imaging tool for detecting Zn(II) in vivo. ZS5 localizes to the mitochondria of HeLa cells and allows visualization of glutamate-mediated Zn(II) uptake in dendrites and Zn(II) release resulting from nitrosative stress in neurons.