A Note on Exponential Stability for Evolutionary Equations.

An abstract notion of exponential stability within the framework of evolutionary equations is provided. Sufficient conditions for the exponential stability are given in terms of the so-called material-law operator, which is defined via an operator-valued analytic function. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Investigation of potential flow using the soap film analogy – a historical review

The soap film analogy is a tool for analysing potential flow in complex geometries. It has been used around 1960 in Dresden to investigate the flow in high-pressure turbine cascades. The present paper briefly reviews the technique and reports on the comparison between historical results, achieved with the soap film analogy, and numerical simulations. It illustrates the capabilities of the method and the historical progress made since then. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Preparation of planar‐chiral multidonor phosphanylferrocene carboxamides and their application as ligands for palladium‐catalysed asymmetric allylic alkylation

Amide coupling of (S_p)‐2‐(diphenylphosphanyl)ferrocene‐1‐carboxylic acid with appropriate terminal amines mediated by 1‐hydroxybenzotriazole and a carbodiimide affords multi‐donor amides terminally functionalized with planar‐chiral (S_p)‐2‐(diphenylphosphanyl)ferrocen‐1‐yl moieties in good to excellent yields. Palladium catalysts based on these ligands efficiently promote asymmetric allylic alkylation of 1,3‐diphenylallyl acetate with in situ generated dimethyl malonate anion to give the C‐alkylated product with ees up to 93% at room temperature. Copyright © 2010 John Wiley & Sons, Ltd.     

Dynamic uncapacitated lot sizing with random demand under a fillrate constraint

This paper deals with the single-item dynamic uncapacitated lot sizing problem with random demand. We propose a model based on the “static uncertainty” strategy of Bookbinder and Tan (1988). In contrast to these authors, we use exact expressions for the inventory costs and we apply a fillrate constraint. We present an exact solution method and modify several well-known dynamic lot sizing heuristics such that they can be applied for the case of dynamic stochastic demands. A numerical experiment shows that there are significant differences in the performance of the heuristics whereat the ranking of the heuristics is different from that reported for the case of deterministic demand.     

A Highly K+‐Selective Two‐Photon Fluorescent Probe

A highly K⁺‐selective two‐photon fluorescent probe for the in vitro monitoring of physiological K⁺ levels in the range of 1–100 mM is reported. The two‐photon excited fluorescence (TPEF) probe shows a fluorescence enhancement (FE) by a factor of about three in the presence of 160 mM K⁺, independently of one‐photon (OP, 430 nm) or two‐photon (TP, 860 nm) excitation and comparable K⁺‐induced FEs in the presence of competitive Na⁺ ions. The estimated dissociation constant (K_d) values in Na⁺‐free solutions (K_d^OP=(28±5) mM and K_d^TP=(36±6) mM ) and in combined K⁺/Na⁺ solutions (K_d^OP=(38±8) mM and K_d^TP=(46±25) mM ) reflecting the high K⁺/Na⁺ selectivity of the fluorescent probe. The TP absorption cross‐section (σ_2PA) of the TPEF probe+160 mM K⁺ is 26 GM at 860 nm. Therefore, the TPEF probe is a suitable tool for the in vitro determination of K⁺.