Circle actions on 4-manifolds I

Using cohomological methods it is proved that the intersection form of a closed (cohomology-) 4-manifoldM withH ₁(M)=0 which admits a non-trivial circle action is the sum of one- and two-dimensional forms provided every fixed point has a neighbourhood containing at most 4 orbit types.     

Polymer brushes via surface-initiated polymerizations

Polymer brushes produced by controlled surface-initiated polymerization provide a route to surfaces coated with well-defined thin polymer films that are covalently bound to the substrate. All of the major controlled polymerization techniques have been applied to the synthesis of polymer brushes and examples of each are presented here. Many examples of brush synthesis in the literature have used the living atom transfer radical polymerization (ATRP) system, and in this tutorial review a particular focus is given to examples of this technique.     

Recent developments in polymer-based sorbents for solid-phase extraction

A review with 136 references on the principles and recent developments in the solid-phase extraction based on polymer sorbents is presented. New polymer-based materials, chromatographic modes, experimental configurations are described and their advantages for a rapid sample preparation of certain classes of compounds with different functional groups are discussed and compared to silica-based sorbents.     

Analysis of carbohydrates using different quaternized polystyrene-divinylbenzene particles and pulsed amperometric detection

Summary This paper reports on the use of a polymer-based, strong anion-exchange stationary phase for rapid, selective and sensitive analysis of physiological important mono-, di- and oligosaccharides by high-performance anion-exchange chromatography (HPAEC) with pulsed amperometric detection (PAD) under alkaline conditions. The adsorbent was obtained by direct nitration of 3 and 5 μm, spherical non-porous highly cross-linked, styrene-divinylbenzene copolymer (PS-DVB) beads, followed by reduction of superficially introduced nitro groups with nascent hydrogen and quaternization of the resultant amino groups with iodomethane. Extended exposure to high pressure and strong alkaline conditions did not have any untoward effect on mechanical stability and chromatographic performance. A comparison of the 3 and 5 μm beads showed, that the synthesized 3 μm highly cross-linked PS-DVB particles are the preferred phases for the separation of monosaccharides and the 5 μm particles are preferable for the separation of oligosaccharides. To demonstrate the suitability for the analysis of complex samples, the optimized and validated system was used for the determination of glucose, fructose and sucrose in apple juice and other soft drinks such as Coca Cola. Finally, analysis within a few minutes without sample pretreatment down to a lower limit of detection of 0.174–0.504 μg mL⁻¹ at a linearity with R²>0.994 and a repooducibility higher than 98% further confirmed the efficiency of these polymeric sorbents.     

Photochemical deuterium exchange of the m-methyl group of 3-methylbenzophenone and 3-methylacetophenone in acidic D2O

Photolysis of the title compounds in acidic aqueous solution results in "activation" of the distal m-methyl group, resulting in deuterium exchange (Phi approximately 0.1) when D(2)O is used. The reaction is not observed in neutral aqueous solution or in deuterated organic solvents such as CD(3)CN. The reaction is best rationalized by a mechanism involving initial protonation at the carbonyl oxygen of the triplet excited state. [reaction: see text]     

On percolation and ‐hardness

The edge‐percolation and vertex‐percolation random graph models start with an arbitrary graph G, and randomly delete edges or vertices of G with some fixed probability. We study the computational complexity of problems whose inputs are obtained by applying percolation to worst‐case instances. Specifically, we show that a number of classical ‐hard problems on graphs remain essentially as hard on percolated instances as they are in the worst‐case (assuming ). We also prove hardness results for other ‐hard problems such as Constraint Satisfaction Problems and Subset‐Sum, with suitable definitions of random deletions. Along the way, we establish that for any given graph G the independence number and the chromatic number are robust to percolation in the following sense. Given a graph G, let be the graph obtained by randomly deleting edges of G with some probability . We show that if is small, then remains small with probability at least 0.99. Similarly, we show that if is large, then remains large with probability at least 0.99. We believe these results are of independent interest.