Crystallographic report: Crystal structure of tetra(4‐methyl‐5‐imidazole‐carboxyaldehyde)zinc(II) diperchlorate

The central zinc(II) atom in the title complex is tetrahedrally coordinated by four nitrogen atoms derived from 4‐methyl‐5‐imidazolecarboxyaldehyde ligands with Zn? N in the range 2.007(3) to 2.026(4) Å. Copyright © 2003 John Wiley & Sons, Ltd.     

Crystallographic report: Crystal structure of a one‐dimensional zinc(II) coordination polymer containing 4,4′‐biphenyldicarboxylate hemihydrate

A one‐dimensional zinc(II) coordination polymer has been constructed from zinc(II), 4,4′‐biphenyldicarboxylate and pyridine in which each zinc(II) atom is coordinated by two pyridine ligands and two monodentate 4,4′‐biphenyldicarboxylate ligands that define a distorted tetrahedral geometry. Copyright © 2003 John Wiley & Sons, Ltd.     

Preparation,thermal properties,and flame retardance of epoxy–silica hybrid resins

A novel epoxy system was developed through the in situ curing of bisphenol A type epoxy and 4,4′‐diaminodiphenylmethane with the sol–gel reaction of a phosphorus‐containing trimethoxysilane (DOPO–GPTMS), which was prepared from the reaction of 9,10‐dihydro‐9‐oxa‐10‐phosphaphenanthrene‐10‐oxide (DOPO) with 3‐glycidoxypropyltrimethoxysilane (GPTMS). The preparation of DOPO–GPTMS was confirmed with Fourier transform infrared, ¹H and ³¹P NMR, and elemental analysis. The resulting organic–inorganic hybrid epoxy resins exhibited a high glass‐transition temperature (167 °C), good thermal stability over 320 °C, and a high limited oxygen index of 28.5. The synergism of phosphorus and silicon on flame retardance was observed. Moreover, the kinetics of the thermal oxidative degradation of the hybrid epoxy resins were studied. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 2354–2367, 2003     

Synthesis and characterization of wholly aromatic poly(azomethine)s containing donor–acceptor triphenylamine moieties

N‐(4‐nitrophenyl)‐4′,4″‐bisformyl‐diphenylamine was synthesized from N‐(4‐nitrophenyl)‐diphenylamine by the Vilsmeier‐Haack reaction. Soluble aromatic poly(azomethine)s (PAMs) were prepared by the solution polycondensation of N‐(4‐nitrophenyl)‐4′,4″‐bisformyl‐diphenylamine and aromatic diamine in N‐methyl‐2‐pyrrolidone (NMP) at room temperature under reduced pressure. All the PAMs are highly soluble in various organic solvents, such as N,N‐dimethylacetamide (DMAc), chloroform (CHCl₃), and tetrahydrofuran (THF). Differential scanning calorimetry (DSC) indicated that these PAMs had glass‐transition temperatures (T_gs) in the range of 170–230 °C, and a 10% weight‐loss temperatures in excess of 490 °C with char yield at 800 °C in nitrogen higher than 60%. These PAMs in NMP solution showed UV‐Vis charge‐transfer (CT) absorption at 405–421 nm and photoluminescence peaks around 462–466 nm with fluorescence quantum efficiency (Φ_F) 0.10–0.99%. The highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) energy levels of these PAMs can be determined from cyclic voltammograms as 4.86–5.43 and 3.31–3.34 eV, respectively. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 4921–4932, 2007     

Metallo‐supramolecular micelles: Studies by analytical ultracentrifugation and electron microscopy

In aqueous solutions, amphiphilic block copolymers in which a polystyrene (PS) segment is connected to a poly(ethylene oxide) (PEO) block via a bis(2,2′:6′,2″‐ terpyridine ruthenium) complex can form micelles. Such micelles of the protomer type PS₂₀‐[Ru]‐PEO₇₀, according to the preparation procedure representing frozen micelles, were studied by sedimentation velocity and sedimentation equilibrium analysis in an analytical ultracentrifuge and by transmission electron microscopy, with different techniques applied for the sample preparation. The particles obtained were surprisingly multifarious in size. In ultracentrifugation experiments performed at relatively low salt concentrations, the distributions of the sedimentation coefficient s_20,w showed a pronounced peak at 9.6 S and a broad, only partly separated second peak around 14 S. The molar mass of the particles at the peak was around 430,000 g/mol, corresponding to an aggregation number of approximately 85. The average hydrodynamic diameter of the particles in the peak fraction was approximately 13 nm. In electron micrographs of negatively stained samples, spheres of diameters between 10 and 25 nm were the most abundant particles, but larger ones with a wide size range were also visible. The latter particles apparently were composed of smaller ones. The data from both sedimentation analysis and electron microscopy showed that (1) the studied compound formed primary micelles of diameters around 20 nm and (2) the primary micelles had a tendency toward aggregation. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 3159–3168, 2003     

Homology equivalences inducing an epimorphism on the fundamental group and Quillen's plus construction

Quillen's plus construction is a topological construction that kills the maximal perfect subgroup of the fundamental group of a space without changing the integral homology of the space. In this paper we show that there is a topological construction that, while leaving the integral homology of a space unaltered, kills even the intersection of the transfinite lower central series of its fundamental group. Moreover, we show that this is the maximal subgroup that can be factored out of the fundamental group without changing the integral homology of a space.

     

Hopf Algebras, Renormalization and Noncommutative Geometry

We explore the relation between the Hopf algebra associated to the renormalization of QFT and the Hopf algebra associated to the NCG computations of tranverse index theory for foliations. Received: 14 August 1998/ Accepted: 5 October 1998     

Single-server queues with spatially distributed arrivals

Consider a queueing system where customers arrive at a circle according to a homogeneous Poisson process. After choosing their positions on the circle, according to a uniform distribution, they wait for a single server who travels on the circle. The server's movement is modelled by a Brownian motion with drift. Whenever the server encounters a customer, he stops and serves this customer. The service times are independent, but arbitrarily distributed. The model generalizes the continuous cyclic polling system (the diffusion coefficient of the Brownian motion is zero in this case) and can be interpreted as a continuous version of a Markov polling system. Using Tweedie's lemma for positive recurrence of Markov chains with general state space, we show that the system is stable if and only if the traffic intensity is less than one. Moreover, we derive a stochastic decomposition result which leads to equilibrium equations for the stationary configuration of customers on the circle. Steady-state performance characteristics are determined, in particular the expected number of customers in the system as seen by a travelling server and at an arbitrary point in time.     

Intramolecular motion and isotope effects in muonium‐substituted chloroalkyl radicals

Muon irradiation of pure liquid 3‐chloropropene, CH₂=CH-CH₂Cl, yields a primary radical, \dot\mboxCH₂-CHMu-CH₂Cl, and a secondary radical, MuCH₂-\rm\dot\mboxCH-CH₂Cl. 2‐methyl‐3‐chloropropene yields only the tertiary radical, MuCH₂-\rm\dot\mboxC(CH₃)-CH₂Cl. These three chloroalkyl radicals have been characterized by μSR and μLCR, and the hyperfine coupling constants (hfcs) have been determined over a range of temperatures, either in the pure liquid precursor or in concentrated solution. The temperature variation of the hfcs has been analyzed to obtain estimates of the barrier to internal rotation about the C_\alpha-C_\beta axis for various alkyl groups, and also their minimum energy conformations, i.e. their orientations with respect to the axis of the 2p_z orbital of the unpaired electron. The tertiary radical is particularly interesting because all three methyl‐like groups, -CH₃,-CH₂Cl and -CH₂Mu, are represented. The results can be compared to electron spin resonance data for analogous radicals, to provide information on the effects of Mu substitution for H. This revised version was published online in August 2006 with corrections to the Cover Date.